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Dense Gas Dispersion in the Atmosphere

Morten Nielsen

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Ris0 National Laboratory, Roskiide, Denmark September 1998 DISCLAIMER

Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. Ris0-R-1O3O(EN)

Dense Gas Dispersion in the Atmosphere

Morten Nielsen

Ris0 National Laboratory, Roskilde, Denmark September 1998 8 Abstract Dense gas dispersion is characterized by buoyancy induced gravity currents and reduction of the vertical mixing. Liquified gas releases from industrial accidents are cold because of the heat of evaporation which determines the den­ sity for a given concentration and physical properties. The temperature deficit is moderated by the heat flux from the ground, and this convection is an additional source of turbulence which affects the mixing. A simple model as the soil heat flux is used to estimate the ability of the ground to sustain the heat flux during release. The initial enthalpy, release rate, initial entrainment and momentum are discussed for generic source types and the interaction with obstacles is considered. In the MTH project BA experiments sourcee with and without momentum were applied. The continuously released propane gas passed a two-dimensional remov­ able obstacle perpendicular to the wind direction. Ground-level gas concentrations and vertical profiles of concentration, temperature, wind speed and turbulence were measured in front of and behind the obstacle. Ultrasonic anemometers pro­ viding fast velocity and concentration signals were mounted at three levels on the masts. The observed turbulence was influenced by the stability and the ini­ tial momentum of the jet releases. Additional information were taken from the ‘Dessert Tortoise ’ ammonia jet releases, from the ‘Fladis’ experiment with transi­ tion from dense to passive dispersion, and from the ‘Thorney Island’ continuous releases of isothermal freon mixtures. The heat flux was found to moderate the negative buoyancy in both the propane and ammonia experiments. The heat flux measurements are compared to an estimate by analogy with surface layer theory.

The present report is a slightly revised version of a Ph.D. thesis originally sub­ mitted to the Technical University of Denmark (DTU) on December 31, 1997. Prof. Dr. FI. Bo Pedersen from the Department of Hydrodynamics and Water Re­ sources (ISVA) acted as supervisor together with Dr. N.O. Jensen from the Wind Energy and Atmospheric Physics Department (VEA), Ris0 National Laboratory. Dr. N.E. Ottesen Hansen and Prof. Dr. T. Fannelpp acted as external examiners.

ISBN 87-550-2362-2 ISSN 0106-2840

Information Service Department • Risp • 1998 Contents

1 Introduction 5

2 Box models 6

3 Dense gas fronts 11

4 Mixing and entrainment 18

5 Obstacles 30

6 Concentration fluctuations 37

7 Surface temperature ^0

8 Dense gas sources 45

9 Cloud density 58

10 More on box models 71

11 Propane experiments with obstacles 82

12 Large-scale ammonia experiments 125

13 More ammonia experiments 135

14 Isothermal freon experiments 154

15 Conclusions 168

Acknowledgement 171

References 171

Summary 183

Sammendrag — summary in Danish 186

A The MTH Project BA propane experiments 191

B The FLADIS ammonia experiments 198

C Gas concentrations from sonic anemometers 219

D Anemometer coordinate transformations 226

E Thermo dynamic background 227

F Fluid mechanical background 236

Ris0-R-1O3O(EN) 3 G Micrometeorological background 246

H Literature guide 257

I Substance properties 234

Notation 260

Index 273

4 Ris0-R-1O3O(EN) 1 Introduction

In recent decades it has been realized that gas clouds of negative buoyancy disperse in a way quite different from that of a passive tracer. The gravity force influences a dense gas cloud in two ways - it generates internal currents, and the stratification between the dense cloud and the lighter air above reduces the turbulent mixing. In this situation the theory of ordinary atmospheric dispersion is insufficient. A practical definition of the problem is: problem definition atmospheric dispersion affected by buoyancy forces acting on the cloud volume as a whole. This includes dispersion of substances with low molecular weight provided that the temperature is low enough to create a sufficient density surplus. On the other hand dispersion of dilute mixtures of gases with high molar weight - for instance a tracer gas like SFg - is considered to be an ordinary dispersion problem. Clouds, which are dense because of small particles, are not considered directly, but they should behave similarly if the deposition time is long compared to the time scale of the dispersion, see eg Bettis, Makhvildze & Nolan (1987) and Bonnecaze, Hallworth, Huppert & Lister (1995). The duration of a typical dense gas dispersion phase is only a few minutes - depending on the release size and the wind conditions. Dense gas clouds of concern emerge from accidental releases in industrial process applications units or during transport. This is not an every day event, but a risk of handling toxic or inflammable gases. Toxic gases is a hazard to the staff and in some cases even to a nearby population. Fire and explosions may cause severe physical damage and injuries, but the hazardous concentrations of flammable gases are usually much higher than those of toxic gases, so the endangered area is smaller. In practice, risk management considers a lot of topics which have no accurate answers. These matters could be: - recognition of relevant scenaria and probability estimates - the toxic effects on human beings and environment - the size of the endangered population - the risk of ignition and the physical damages after fire or explosion - possible mitigation methods - the benefits of improved training, regular inspection, and alarm systems. Dispersion modelling plays an important role in risk analysis, but it is not the only issue. The risk engineer and his client do usually not ask for fine details on the process. Most people are familiar with the theatrical effect, when a mist of smoke covers related phenomena the stage. This artificial cloud is often dense and flows along the floor, so it is a relevant picture for visualisation. Gravity currents are also important in geophys ­ ical phenomena like avalanches, volcanic emission, katabatic winds and maritime dense bottom currents. It is possible to draw parallels between these research areas and the fluid mechanical part of the dense gas problem.

Organization of the present report

As hinted by the title the objective is to learn from dense gas field experiments. This point-of-view has led to particular interest in the thermodynamics of cold gas clouds, source dynamics, turbulence characteristics and the effects of variable wind directions. The report is organized in the following main parts:

Ris0-R-1O3O(EN) 5 Chapter 2—10: The physics of dense gas dispersion. Chapter 11-14: Studies of selected field data.

Appendices: Material for selective reading. Acknowledgement , references and summaries in English and Danish are inserted before the appendices. List of notation and topic index are found at the end of the report. Dense gas experts will probably take most interest in the chapters which discuss experimental data. Chapter 2 gives a brief introduction to the widely used dense gas box models. dense gas physics This is followed by two chapters on dense gas dynamics, ie chapter 3 on dense gas fronts, chapter 4 on the mixing with ambient air. Chapters 5 and 6 discuss the effects of obstacles and the concentration fluctuations of a spreading gas cloud. Heat transfer from the ground to a cold gas cloud gives internal convection which affects the turbulence, and in chapter 7 the time development of this process is examined. Boundary conditions like source strength, initial momentum, liquid fraction and temperature are important for the dispersion, and chapter 8 gives an introduction to the physics of typical gas sources. Chapter 9 describes how to calculate the cloud density including the effect of a non-isothermal release. The box models introduced in chapter 2 are further discussed in chapter 10. In chapter 11 continuous release experiments with liquified propane are analysed. experiments The effects of initial momentum and an obstacle perpendicular to the wind direc­ tion are discussed with emphasis on the internal cloud turbulence. Chapter 12 contain a description of some large-scale ammonia dispersion experiments with focus on details complementary to the information from the propane experiments, in particular measurements of the heat flux from the ground. In chapter 13 an­ other set of ammonia experiments is used to demonstrate the effects of plume meandering. In chapter 14 turbulence data from an isothermal freon experiments without heat convection is discussed. Appendices A and B present details on the experiments analysed in chapters 11 appendices and 13. Appendix C describes a method for estimates of fast gas concentration time series based on sound virtual temperature measurements from sonic anemometers with attached thermocouples. Appendix D explains the geometrical transforma­ tion used for the alignment of three dimensional wind speed time series after the mean wind direction. Thermodynamic, fluid mechanical, and micro-meteorological concepts are presented in appendices E, F and G. Appendix H is a short introduc­ tion to experimental work, sources of literature and available data bases. Finally appendix I contains a collection of physical and toxicological gas properties.

2 Box models

The interest in dense gas dispersion is stated by the potential hazards of inflam­ introduction mable or toxic chemicals. Risk assessment is usually based on complex informa­ tion from many disciplines, and it is often argued that a crude description of the dispersion problem is sufficient. Therefore dispersion models with fast solutions to ordinary differential equations and just a few model parameters have become popular, eg HEGADAS (Witlox 1994), DEG ADIS (Spicer & Havens 1986), SLAM (Ermak 1990), and DRIFT (Webber, Jones, Tickle & Wren 1992). The present chapter introduces this model concept. My intention is to illustrate chapter summary only how the physical processes to be described in the following chapters interact with each other, not to develop a complete model. Four box models with different geometries simulating different release scenarios are presented. Each of these is

6 Ris0-R-1O3O(EN) formulated as a system of main variables (mass, enthalpy, ...) which are inte­ grated in time. The time integration applies a set of auxiliary variables (density, entrainment rate, ...) which is deduced from the main variables. Many of these variables are independent of model geometry. The presentation in this chapter will be brief, but chapter 10 contains more details on box models.

Figure 1. Box model for an instantaneous release. All properties are uniformly distributed in a cylinder with height h and radius r at position x.

Generic box model for instantaneous releases The dense gas cloud from an instantaneous release is approximated by a cylinder with radius r and height h as shown in figure 1. In the classic box model all properties (concentration c, density p, absolute temperature T, enthalpy difference AH, et cetera) are assumed to be uniformly distributed within this volume. The radius grows with a front velocity u/, and the centre of mass x moves with the advection velocity u. The gradual increase of the cloud mass is modelled by an entrainment velocity ue through the top cloud interface, and the enhanced mixing at the front is modelled by the front entrainment velocity u{. The generic boxmodel for instantaneous releases is described by the differential main variables equations

dx Position: = u dt dr Radius: = Uf dt dm Mass: = Pair • (vrr2 • ue + 2nrh • u{) ~dt dAH Enthalpy: = irr2(p dt Many alternative formulations have been presented in literature. When thermo­ dynamic effects are included it is however simpler to write correct balances for the mass m and enthalpy AH, than for volume V and temperature T. In the present report the cloud enthalpy is defined by AH = 0 at the temperature of the ambient air. The advantage of this choice is that the enthalpy of the entrained air will be zero by definition, and the integral cloud enthalpy will depend only on additional heat inputs ip such as heat convection from the ground. M and Ma;r are the molar weights of the gas and air and c is the gas concentration by volume. For simplic­ ity, the cloud advection u is sometimes set to the wind speed at a typical height,

Ris0-R-1O3O(EN) 7 eg at the top of the cloud. Alternatively the cloud advection is determined by a momentum budget, see chapter 10. Auxiliary variables like concentration c, temperature T, density p and volume auxiliary variables V are derived from the main variables above:

mo/M concentration: c mo/M+(m-roo)/M ai,

specific enthalpy: AH = [(1 -c)Mair + cM]^

temperature: T = h(AH,c)

density: P = h (c,T,p) volume: = m V P V height: h = ITT2

9' B=£™-g reduced gravity: = Pair y

front velocity: Uf = Frfy/gH

edge entrainment: Ufe = a ■ Uf

top entrainment: Ue = f3(g'h,u,ip)

heat flux: H> = fi(T ~ Tsur, pep,u ,g h)

In the present report the molar gas concentration c is preferred to the concentra­ tion by mass mo/m, ie the ratio between the mass of the contaminant gas mo and the cloud mass m. We therefore need the specific molar enthalpy difference AH [kJ/mole] rather than the total cloud enthalpy difference A~H [kJ]. Determination of the temperature T and density p will be described in chapter 9, and at present they are just written as the unspecified functions fi(AH,c) and f2(c, T,p). In a two-phase mixture the liquid fraction a affects the thermodynamic state of the cloud, and in case of chemical reactions the degree of reaction e plays a similar role. It is a great computational advantage if the cloud mixture is assumed to be in homogeneous equilibrium, since in this case a and e are internal parameters in the fi sub-model. The front velocity uj and edge entrainment u{ will be de­ scribed in chapter 3. The top entrainment velocity ue = f3(g'h,u,ip) is a process which has been parametrized in many ways in literature, see eg the comparisons by Webber (1983). Normally the top entrainment depends on a bulk Richardson number like g'h/u\, where is the ambient friction velocity. In chapter 4 we shall see that internal convection driven by the surface heat flux enhances the mixing process. The heat flux from the ground

Generic box model for continuous releases

Continuous gas release may be described by a similar box model with the down­ wind development as sketched in figure 2. The increasing plume width b is modelled by the front velocity at the two edges, and the cloud mass and enthalpy are now

8 Ris0-R-1O3O(EN) Figure 2. Box model for a continuous release. All properties are uniformly distrib­ uted in rectangular cross sections of height h and width b. substituted by their corresponding fluxes m and AW.. dx position: = u dt db width: = 2 Uf dt (3) dm mass flux: = Pair (bu e + 2hu{) |u| dt dAW enthalpy flux: = (pb\u\ dt The auxiliary variables are determined just as in the instantaneous release model, except the plume dimensions which are found from

area of cross section: A = (4) height: h = i If the release duration is comparable to the time scale of heat transfer, the heat flux ip will gradually decrease as explained in chapter 7.

Drag force orientation

(i, j, k) are orthogonal

Figure 3. Box model for an elevated dense gas plume.

Generic box model for elevated plumes

A continuous dense gas release from an elevated source or from a source with an upward momentum follows a ‘ballistic’ path before it reaching the ground.

Ris0-R-1O3O(EN) 9 Figure 3 shows a simple box model for such a release inspired by Ooms & Duijm (1983) and the GReAT model (Ott 1990). With an axisymmetric local geometry the system is described by the differential equations

dx position: = u m dm mass flux: = Pair27rrue|lt dt d&H (5) enthalpy flux: = 0 dt d(mu) momentum: + {P~ Pa\r)Ag\u\ + Fd|tt| dt

The plume dimension is not needed as a main variable in this model and the enthalpy flux is constant. The entrainment depends on the ambient turbulence and the velocity shear between the plume and air, both along the axis and in the perpendicular direction. Therefore the entrainment rate ue will differ from that of the grounded box models as explained at the end of chapter 4. The momentum equation is needed in order to describe the curved plume trajectory. The three terms on the right hand side of this equation are the momentum of the entrained air, the gravity force minus buoyancy and a drag force. The drag force is the integral of the pressure forces around the plume similar to the drag on a solid body. The following auxiliary variables are different from those of the grounded- plume model.

radius: r (6) drag: Ci’KT Pairuair± |tTair± | where Ooms & Duijm (1983) suggest a drag coefficient of Cd — 0.3. The drag force is perpendicular to the plume trajectory and lies in a plane defined by the plume and wind velocities u and u&jr. The strength of the drag force is proportional to the square of the perpendicular component of the wind velocity With reference to the local coordinate system (i,j,k) defined in figure 3 u . _ u&\t x u M 3 Kiri • M k = ix j (7) The wind components parallel and perpendicular to the plume trajectory may be calculated by:

|uair ‘ u\ • «a X U\ uair|| — Uairl = (8 ) M M

It is noted that the drag force Fd has a downward component in case of a rising plume and an upward component when it is diving.

10 Ris0-R-1O3O(EN) Apyg

Figure 4■ Box model for an elevated dense gas volume.

Generic box model for an elevated instantaneous release

Following the usual approach we describe an elevated instantaneous release by the spheric box model sketched in figure 4:

dx position: = u dt dm mass flux: -Tr = pair47rr2ite dt dm (9 ) enthalpy flux: = 0 dt d(mu) momentum: = + {P~ Pair)Vg + -Fd dt

The auxiliary variables specific for this model are

radius: r = (10) drag: Fd = cdp a\rirr2(uair - u)\uair - u\

3 Dense gas fronts

In the early stages of a dense gas dispersion the cloud boundary is a sharp propa­ introduction gating front. The driving potential of the front propagation is the excess pressure resulting from the density difference between the cloud and the ambient air. In order to predict dense gas dispersion it will be necesary to determine the front velocity uj and edge entrainment u{ in the turbulent wake behind the front. This chapter starts with the simple model of Kranenburg (1978) and continues chapter summary with a review of experimental studies found in literature. The gas distribution of most large-scale field experiments is detected by a fixed array of concentration sensors with limited spatial resolution and slow response time. These limitations and unsteady wind conditions makes it difficult to obtain accurate information on front velocity and edge entrainment. Therefore most of the available information originate from small-scale laboratory experiments - in particular the moving-belt experiments of Simpson & Britter (1979). The effects of ambient wind and tur­ bulence, sloping terrain and a vanishing driving potential caused by heating of a cold gravity current are discussed.

Ris0-R-1O3O(EN) 11 Po+Ap

Figure 5. Kranenburg ’s (1978) flow problem: A dense bottom current intrudes a light fluid with a free upper surface. The frame-of-reference is moving with the velocity of the front.

A first estimate of the front velocity

Benjamin (1968) analysed the problem of air intrusion into a horizontal pipe filled with water. A moving frame-of-reference following the front of the air was applied in the analysis. With this approach the flow around the front was treated as quasi-stationary. Kranenburg (1978) made a similar analysis of the intrusion of a dense bottom current into a light fluid with a free upper surface, see figure 5. The upstream ambient fluid has a density po and height hi and flows toward the front with velocity ui- The dense bottom current has a density po+Ap and height /14 and is assumed to be stagnant. The downstream light fluid has depth hg and velocity U2- Downstream and upstream of the front the streamlines are assumed to be parallel and the pressure is determined by a hydrostatic balance. The height of the free surface is not necessarily constant hi /12 + hi, since the light fluid must accelerate and instabilities just behind the front may dissipate energy. The flow is described by a continuity and energy equation for the upper layer and a Bernoulli equation along the floor.

uihi — U2/12 (11) /ii+5=/i4+/i2+5+fcB (12)

hi + —- = hi 4- /12 H---- —hi (13) 2 g po where the latter term in equation 12 accounts for the energy loss which is taken proportional to the front velocity, ie velocity ui using an energy loss coefficient k. Equation 13 is derived from a streamline following the lower boundary to the foremost point of the front, which in the chosen frame-of-reference is a stagnation point. The pressure at this point is equal to the hydrostatic pressure in the lower layer. When combining the three equations it is seen that

(14) 2 g

A cubic equation for /12 is obtained by insertion of equation 14 into equation 13. The cubic equation is solved numerically with a given combination of hi, hi and Ap, and the front velocity Ui is then found by insertion of /12//14 into equation 14. In case of a dense gas release in the open atmosphere, the depth of the ambient fluid is much larger than that of the gas layer hi » hi, and in this limit

lim ui (15) h i-»oo

12 Ris0-R-1O3O(EN) where g' = Ap/po is called the reduced gravity. The front velocity is occasionally set to y/2g'hi in literature corresponding to the energy conservation. Benjamin (1968) did however show that part of the energy must dissipate except in the very special case, where the front height is equal to half of the height of the ambient fluid hi = hi/2.

Empirical front velocity

The front velocity in equation 15 may be written as ui = Frj\fgrhl, where Frj is the Froude number of the front. In dense gas models this is often set to an empirical value Frj ~ 1.1 corresponding to an energy loss coefficient of k = 0.6. Kranenburg (1978) found a similar value of k by analysis of Wilkinson & Wood ’s (1972) laboratory experiments. Brighton, Prince & Webber (1985) studied aerial photographs from the Thorney Island dense gas experiments and found that the visible cloud advavanced in accordance with u/ = Frfy/g'h after an initial acceleration phase. Based on ten successful Thorney Island trials the front Froude number was found to be Fr/ = 1.05 ± 0.12 equivalent to an energy loss coefficient of k — 0.8.

Front anatomy in a calm environment

Simpson & Britter (1979) describe a laboratory experiment on the dynamics of the head of a dense bottom current. As in the theoretical analysis it was found convenient to study the flow pattern in a moving frame-of-reference following the front. Figure 6 illustrates how this was obtained by an opposing flow and a moving belt on the floor. When the velocity of the moving belt was equal to the opposing stream, the situation became equivalent to a front in a calm environment. The main difference from Kranenburg ’s (1978) model was the existence of a mixing layer in the wake of the front with height hz, see figure 7. Because of the inertia of the light fluid, the mixing layer was moving backwards relative to the front. This transport of dense material was compensated by an inflow of dense material with the excess velocity Ui. The relative strength of the inflow and front velocity was measured to Ui/ui = 0.16±0.04 and found to be almost independent on the depth ratio hi/h\. This is a measure of the mixing at the front called ‘edge entrainment’, and it is proportional 1 to height hi and front velocity ui. edge entrainment The observation that the gravity current has an excess velocity and transports dense material to the front explains why the front remains sharp. The energy loss previously modelled by ku\/2g is related to this mixing process. Simpson & Britter (1979) measured the velocity and concentration distributions in the mixing layer and found the approximations c(z) u(z) c4 and = i-C4 (16) Co «2 where £ = 1 — h/hz with h is measured from the lower boundary of the mixing layer, see figure 7. A mass balance of the dense material feeds into the front by the gravity current, and the flux in the mixing layer gives rh3 4 UihiCo = / u(z)c(z)dz => Uihi = — • u%hz (17) Jo 45 The wake is affected by stratification and velocity shear and it was suggested that the wake turbulence was initiated by Kelvin-Helmholtz instability. This hy-

*The description of simple box models may give the false impression that the cloud actually entrains air through its vertical boundary.

Ris0-R-1O3O(EN) 13 Saline1 tank Working section 1 m

Moving floor Bench

400 1.

Floor

Figure 6. Set-up of the experiment in Simpson & Britter (1979). The original figure text is ‘Apparatus for maintaining the head of a gravity current in a steady state. A metered flow of water runs from the top reservoir on the left through a flow straightener into the working section. The floor can be moved in the same direction, and the gravity current brought to rest. The input of saline flow corresponding to the rate of mixing at the gravity current head is also metered. The flow over the weir can be either drained or recycled. ’

Figure 7. Notation of the analysis in Simpson & Britter (1979). The original figure text is ‘A two-dimensional model of the flow near a gravity current head in the axes which hold the gravity current head stationary. At AB and FC the velocities are horizontal and the pressure hydrostatic. 0 is a stagnation point, U(h), C(h) are the profiles of velocity and concentration of dense fluid in the flow close behind the head. U, h, p, refer to velocity, height and density respectively. ’ pothesis was supported by visual observations and an almost constant bulk layer Richardson number Ri

Ri = ~ 0.55 (18) (Au)2 where the relevant velocity scale is the velocity shear across the mixing layer A U = U2+ U4. In contrast to Kranenburg ’s (1978) model the foremost point of the front was elevated nose observed to be elevated. This is because the approaching flow has a truly uniform velocity profile with equal kinetic energy for all the streamlines while the velocity

14 Ris0-R-1O3O(EN) distribution inside the gravity current has the profile indicated in figure 7. The streamline matching the ambient energy level is therefore not the one at the wall. Simpson & Britter (1979) used this information in their momentum balance as a measure of the pressure difference over the front. Simpson (1972) had previ­ ously correlated the relative height of the stagnation point h$/(hz + /i<) with the Reynolds number, but the relative nose height of large-scale fronts is more likely to depend on surface roughness, and Simpson & Britter (1980) used the value /is/(/i3 + h) = 1/8 to describe atmospheric meso-scale fronts. The fine structure of the front is three-dimensional. The light fluid, which is front vortices squeezed under the stagnation point in figure 7, does not mix directly into the gravity current, but penetrates the front in vertical clefts and splits the nose of the front into several billows (Simpson 1972). Grobelbauer, Fannelpp & Britter (1993) performed a series of experiments using non-Boussinesq fronts a variety of gases in a chamber that could be divided into two by a lock gate. By choosing pairs of gases with very different molar weights, eg helium and Freon, it was possible to stage cases where the Boussinesq approximation clearly is wrong. Because of the different inertia the light-gas front at the ceiling was clearly faster than the dense-gas front at the floor. The shape of the light-gas fronts was less blunt and more stable than the heavy-gas fronts.

Ambient wind velocity

The moving-belt experiment was later on extended with a series of tests with variable moving belt velocities (Simpson & Britter 1980). The excess velocity of the moving belt uq—ui was interpreted as an ambient wind velocity ua;r toward the front. Observations of a range of ambient wind velocities —Uf

Uf = 0.91 • U/o + 0.62 • Uair (19) where u/o is the front velocity in calm conditions uajr = 0. Most box models as­ sume that these velocities are additive u/ = u/o + uair- Factor 0.62 in equation 19 was significantly different from unity whereas factor 0.91 reflects the experi­ mental uncertainty. The observed dependence on the ambient wind velocity ua;r was explained by changes in the front structure. The velocity profile of the grav­ ity current became more uniform with decreasing moving belt velocity simulating head wind conditions. As a result the stagnation point moved closer to the wall until the front became an arrested wedge. The nose height was proportional to the velocity ratio of the moving belt and the opposing flow uq/ui. The shape of the mixing-layer profiles and the bulk Richardson number of the mixing layer remained unchanged. Rottman, Hunt & Mercer (1985) observed that the initial front velocity in the field observations Thorney Island dense-gas field experiments was in accordance with the correlation in equation 19. The height of the nose of the upstream front was gradually de­ pressed to ground level until the front approached the shape of an arrested wedge. The attachment point of the arrested wedge remained stationary for quite some time, presumably because the ambient wind velocity was zero at the surface.

Ambient turbulence

Sometimes the gravitational spreading is insignificant compared to turbulent dis­ persion. Britter & McQuaid (1988) reviewed transition criteria from various lab­ oratory and field experiments and suggest that the dispersion may be regarded as effectively passive when transition to passive dispersion

Ris0-R-1O3O(EN) 15 u, > 0.35 (20) where g'0 is the initial reduced gravity, V q is release rate by volume and b is the plume width at the place of interest2. According to this transition criterion, a modest 10% change of the turbulent velocity scale u* requires a 33% change of the plume width at transition corresponding to a substantial downwind distance. Atmospheric wind speeds are unsteady and most likely a region with intermittent dense-gas and passive-tracer behaviour will exist.

Figure 8. Definition sketch of a gravity current on an incline used in Britter & Linden (1980).

Terrain effects Britter & Linden (1980) made laboratory experiments on the motion of fronts on inclines of variable slope angles. Based on dimensional analysis they argued that the front velocity u/, height h and length l of the head of the front followed the scaling laws

= 0W/Vi(9,ae)

£ = Me, Be) (21)

i = where x is the distance along the incline and fi, /a, and fz are functions of the slope angle 9 and Reynolds number Re, see figure 8. The authors identified a linear relationship between u/ and the scaling velocity {q^Vq)1^ and they showed that the Reynolds number dependence was insignificant in their experiments. For a wide range of slope angles 5° <6 < 90° the function fi(0) was almost constant with a value of 1.5, not much higher than the fi(0) % 1 value for a horizontal surface. The reason why the front velocity u/ did not depend more on the slope angle 6 was an increasing entrainment u{. The head of the front kept growing as it moved down the incline, and the mixed layer behind the front (see figure 7) did not exist for large slope angles in contrast to a front on a horizontal surface. The

2The third root dependence in the Britter & McQuaid velocity scale is consistent with the previous square root dependence of the front velocity, since uf oc (g'V/bl1/3 oc (g'uh)1/3 => u

16 Ris0-R-1O3O(EN) growth of the front head correlated with the slope angle angle by

(22) and its geometrical aspect ratio was

(23)

The direct entrainment into the head of the front was similar to the development of an instantaneously released volume in a similar experiment by Beghin, Hopfin- ger k Britter (1981). The fluid in the head did however not dilute as fast as in an instantaneous release because of the supply of dense material from the gravity cur­ rent. This difference is similar to the difference between buoyant vertical releases from maintained and instantaneous sources (Morton, Taylor & Turner 1956). Muller (1997) made two types of experiments with fronts on slopes. Lock- exchange experiments confirmed the above findings that because of enhanced entrainment the down-slope front velocity increased only a little. Additional three- dimensional instantaneous releases on a slope were found to produce clouds of the slice-of-orange wedge-shape predicted by the model of Webber, Jones & Martin (1993), see page 76.

Front Arrival Time

- 0- 0.4 kg (waim surface) Supply of —#— 0.4 kg (cold surface) cooling gas - E> 0.2 kg (warm surface) —|— 0.2 kg (cold surface)

Front position [m]

Evaporation chamber Cold gravity .current

. \ \ \ \ ^ \ \ \ \ \ "X

Rotating tray False floor Gas detection by thermocouples Chanels for cooling gas

Figure 9. Double-floor channel used by Grobelbauer (1995) (not to scale). When the floor is not cooled, the front velocity decreases because of decreasing layer buoyancy.

Effect of heat convection

Grobelbauer (1995) made laboratory experiments with the set-up shown in figure 9 and demonstrated an interesting effect of heat convection from the ground. A known amount of liquified nitrogen was released upon a water basin at ambient temperature. This nitrogen quickly evaporated in the source chamber. Then the gate to the flow channel was opened and released a cold gravity current. An array of thermocouples measured several vertical temperature profiles and detected the

Ris0-R-1O3O(EN) 17 arrival of the gas front. The test channel was optionally cooled by a similar nitrogen flow through cooling channels underneath the floor. Vigorous heat convection was observed without cooling. As explained in chapter 9 there is an almost linear relationship between concentration and density in case of adiabatic mixing. The driving potential f Apgdz is therefore nearly unaffected by adiabatic entrainment, since the density reduction is compensated by the increased layer thickness. The two solid lines in the plot inserted in figure 9 show that the front velocity remains constant throughout the experiments with adiabatic mixing. The cases with heat supply had the same initial velocities as the corresponding adiabatic caces, but these gravity currents gradually slowed down as the heat supply through the floor caused a decrease of the driving potiential. This is of practical concern, since most laboratory experiments are conducted with isothermal gases of high molar weight, whereas the sources of similar industrial dense gas accidents and most field experiments are liquified gases with low molar weight, like in the experiment of Grobelbauer (1995).

4 Mixing and entrainment

Detailed numerical modeling of dense gas mixing is difficult because turbulent introduction diffusion depends on the stratification which in turn depends on the developing concentration field. If the density and flow fields are represented by a discrete com­ putational grid, this should be fine or flexible enough to resolve the steep gradients near the cloud boundary. FEM3 (Ermak Sc Chan 1988), MERCURE (Riou 1988), ADREA-HF (Andronopoulos, Bartzis, Wiirtz Sc Asimakopoulos 1994) , the mod­ els of Sutton, Brandt &; White (1986) and Pereira Sc Chen (1996) are examples of three-dimensional k—e models. These models parametrize the turbulent mixing by concentration gradients and anisotropic diffusion coefficients which are predicted by the local turbulent kinetic energy, local stratification and distances to solid surfaces, eg the ground. A typical grid is a mesh of 30 x 30 x 30 cells and often arranged with an irregular spacing which enhances the resolution near the source and the ground. An alternative and computationally cheaper method is to parametrize the mix­ ing process by an entrainment function. Following this approach, the dense fluid and ambient are considered to be two distinct volumes and the mixing zone is idealized to an interface. The concept of entrainment is an important aspect of box models and two-dimensional layer-integrated models such as SLAM (Ott Sc Nielsen 1996) or the model of Wiirtz (1993). This chapter is initiated by clasic examples of entrainment mechanisms and chapter summary some slightly different mixing processes relevant to dense gas dispersion. Follow­ ing Jensen Sc Mikkelsen (1984) I assemble a list of empirical mixing rates deter­ mined by idealized reference experiments found in literature. This list is used to discuss selected entrainment functions. A new entrainment function is developed by scale analysis of the turbulent kinetic energy budget of a dense gas layer includ­ ing an explicit term for buoyancy production by the heat flux from the warmer ground. Practical application of this entrainment function requires estimates of the mechanical and convective turbulence production inside the gas layer. This is provided by in-plume Monin-Obukhov scaling as suggested by Jensen (1981b). The chapter is concluded by a review of entrainment functions for jets and elevated negatively buoyant volumes.

18 Ris0-R-1O3O(EN) Definitions

Hunt, Rottman & Britter (1983) complained that there is much confusion as to entrainment how researchers define entrainment. I therefore state that entrainment is the mass flux across an interface surrounding the control volume.

Interface movements caused by horizontal divergence typical of a spreading gas cloud do not contribute to the entrainment, and the term ‘entrainment velocity ’ ue is simply the mass flux across the interface divided by local density. My definition is not as precise as it may appear at first sight since it does not define the interface. An interface near a steep gradient in the concentration field is preferable, but the interface concentration field of a dense gas cloud is usually smeared in a broad mixing zone without steep gradients as in figure 10a. In this report I define the interface by a typical vertical length scale, eg two times the centre of mass for the contaminant 2h as suggested by van Ulden (1983). The advantage of this choice is the direct relation between the interface height and potential energy of the gas layer, ie not depending on the gradually changing vertical density distribution.

\\\\\\\\\\\\\\\\\\\\\\Y

Figure 10. Three classic examples _ of entrainment: a) Dense bottom current on a slope, b) free convection, c) a jet. The dashed lines indicate the interfaces and white arrows illustrate the entrainment.

Entrainment processes in the environment

Entrainment processes occur in many natural flows. Simpson (1982) describes a examples variety of gravity current near a rigid boundary as in figure 10a, eg katabatic winds, avalanches, oceanic dense bottom currents, and pyroclastic surges from vulcanic emissions. The velocity of the dense layer is determined by a balance between the gravity force, the Reynolds stress near the wall and the inertia of the entrained fluid. The dense layer in figure 10b has no mean flow but the buoyancy flux from the ground drives large turbulent eddies. The fluid in the lower layer is well mixed and buoyant plumes rise to the interface where they provide energy for turbulent mixing. This process is called free penetrative convection and it may also be driven by a negative buoyancy flux from an upper surface, eg salt brine production in the sea by evaporation or ice formation (Mpller 1984). Figure 10c shows a jet in a calm environment. The velocity shear creates turbulence which causes the jet to entrain the ambient fluid. In these classic examples the entrainment is directed

Ris0-R-1O3O(EN) 19 toward the turbulent active fluid where the diffusion is much more efficient than in the quiescent surroundings.

Mean kinetic energy Recovery of turbulent Work done Work done kinetic energy because by gravity by Motion of entrainment f Turbulent convection Potential Turbulent energy kinetic energy \%=------^ Dissipation

Recovery of potential i— energy because Heat of entrainment

Figure 11. Energy transformations related to entrainment.

It is instructive to consider the energy conversion of a turbulent flow as in the energy conu diagram of figure 11. The four boxes represent the relevant energy forms and the shaded arrows represent the main energy conversion. In this process the potential energy is converted into mean kinetic energy, which transforms itself into turbulent kinetic energy, which finally dissipates into heat caused by the work of viscous forces. In a state of equilibrium the energy conversion is measured by the rate of dissipation. The dashed arrow from potential energy to turbulent kinetic energy in figure 11 illustrates that in case of convection the gravity force produces turbulent kinetic energy directly, since the convection cells are usually not considered to be a mean flow3. The white arrows represent two feed-back mechanisms which are particular for entraining flows. In the stratified flows of figure 10a and 10b the entrainment elevates the interface. This work is done against gravity and thus the entrainment recovers part of the potential energy. If the turbulent kinetic energy level is quasi-stationary and higher than that of the surroundings, the entrained fluid must adjust to the energy level of the active fluid. This implies that the total turbulent kinetic energy of the layer increases, and thus the entrainment recovers part of the turbulent kinetic energy. The recovery of potential energy is larger than the recovery of turbulent kinetic energy for sub-critical flows (Fr&. < 1) and vice versa for super-critical flows (Fr& > 1). Bo Pedersen (1980) defined the bulk flux Richardson number Rj as the ratio of energy recovered (both potential Rj number and kinetic) relative to the energy production. This may be regarded as the over­ all efficiency of the entrainment mechanism, and it appeared that the value was Rj % 0.045 for sub-critical flows and Rj ~ 0.18 for super-critical flows.

Dense gas entrainment

Dense gas dispersion resembles all of the flows shown in figure 10; it involves gravitational spreading, heat convection from the warmer ground and excess mo­ mentum. These processes are likely to dominate the dilution near the source. Figure 12a shows a typical situation further downstream where the gas layer is advected on horizontal ground by the ambient wind. In this case the main source of turbulence is velocity shear and the ambient air is at least as turbulent as the gas layer. This implies that the classic definition of entrainment into a cloud is misleading. Nonetheless it is a tradition in dense gas modeling to parametrize also * &

3This is perhaps just a matter of definition, and large-eddy-simulation models (Nieuwstadt & de Valk 1987) discriminate between these motions and small-scale turbulence.

20 Ris0-R-1O3O(EN) b)

Figure 12. Two additional ‘entrainment’ cases relevant for dense gas dispersion: a) a dense plume submerged in a shear low and b) removal of dense material from a cavity by crosswind. the mixing of a slightly dense gas cloud by an entrainment velocity. Figure 12b shows dense gas removal from a valley by crosswind. This problem was studied in the 2D wind-tunnel experiments of Briggs, Thompson & Snyder (1990) and Castro, Kumar, Snyder, Pal & Arya (1993). The authors focus on the typical concentration in a valley and the overall flush rate. Billeter & Fannelpp (1995) conducted a series of experiments with gravity- currents in still air using a two-dimensional set up similar to the one shown in figure 9, although with isothermal argon instead of cold LNG. Fast responding concentration sensors were arranged in a mesh sufficiently fine to provide accurate mass balances and entrainment estimates. Most of the entrainment was generated by turbulence in the wake of the front.

Figure 13. Similarity profiles in which the shape is universal but the amplitude and vertical length scale are changing.

The sketch in figure 13, shows self-similar concentration profiles. The shape is self-similarity uniform whereas the scales vary. It is impossible to identify a distinct interface in such profiles, and the definition of the interface height hi will inevitably be arbitrary. If the advection velocity u is approximately constant, the entrainment function ue/u is proportional to the interface slope dhi/dx. The dotted lines in figure 13 correspond to two interface definitions and their different slopes demon­ strate the influence on the entrainment rate. Table 1 gives an overview of empirical entrainment velocities ue normalized by reference cases

Ris0-R-1O3O(EN) 21 Table 1. Empirical mixing rates in special reference cases.

Situation Mixing Rate Conditions Passive dispersion of a surface plume® Riu. —> 0 and tv* = 0

Stratified shear flow6 u. — Riu. Riu. 3> 0 and w* = 0 Weak free convection® Riw. -> 0 and u, = 0 ttf ~ X) Strong free penetrative convection* 1 tv* Riw* Riw. 0 and u»= 0

“The analysis in appendix G leads to Ai = 0.75 6Kato & Phillips (1969) measured A2 = 2.5 “Bo Pedersen (1980) interpreted Farmer’s (1975) measurements as A3 = 0.37 jDeardorff, Willis & Stockton (1980) measured A4 = 0.25 the turbulence velocity scales u* — (—u'w1 o)-1^2 and w* = (ghiw'T'o/21))-1/3. The two Richardson numbers are defined by Riu. = Apghi/pu^ and Riw. = A pghi/pwl- - The spreading of a plume of neutral buoyancy from a surface-line source is nearly proportional to the friction velocity u*. In appendix G the coefficient is estimated to Ai % 0.75 using van Ulden’s (1983) interface definition of twice the centre of gravity hi = 2h and Sutton’s (1953, p. 281) analytical solution based on eddy diffusion. The alternative definition of hi = h corresponds to Ai % 0.4.

- The entrainment rate in the limit of strongly stratified shear flow was deter­ mined in a laboratory experiment by Kato & Phillips (1969). The set-up was an annular tank with stratified water and constant shear stress induced by a moving screen at the surface. This produced a turbulent well-mixed upper layer which gradually entrained the quiescent stratified fluid below. - The entrainment rate in the limit of weak free convection is Bo Pedersen’s (1980) interpretation4 of Farmer’s (1975) measurements of the developing thermal profile in an ice-covered lake in the spring season. The solar heating near the surface produced a well-mixed convective layer 5 and the ice sheet prevented additional turbulence production by wind shear. The mixing rate in the limit of weak convection was deduced from the phase angles of the diurnal component of the temperature signals at various levels of the mixed layer.

- The entrainment rate in the limit of strong free penetrative convection was measured in the laboratory experiment of Deardorff et al. (1980) in which initially stratified water was heated from the bottom. The turbulence devel­ oped a well-mixed lower layer which gradually entrained the quiescent fluid above. The uniform density distributions of the turbulent active layers in the latter three cases are consistent with the hi = 2h interface definition. Table 2 presents a selection of entrainment functions. The asymptotes in the literature review rightmost columns are included for comparison with the entrainment rates of table 1. The first two functions0,6 (indices refer to table footnotes) describe wind- driven entrainment of a stratified water body and free penetrative convection. Unlike the remaining functions of the table these are not specific for dense gas dispersion. They are included for comparison since they were calibrated against a

4This involved an estimate of the average heating over night and day. 5The thermal expansion coefficient of water is negative at low temperatures.

22 Ris0-R-1O3O(EN) Table 2. Selected entrainment functions. The turbulent velocity scales u* and tv» are evaluated in-plume. Note that the definitions of the combined turbulence scale e and thus the Richardson number Rie differ.______Entrainment function Definitions Asymptotes for reference cases ------TO* = 0___ u* = 0

Riu, RiO Riw,x 0 Riw.»0

2.3 Riu.=^r 0.38 M: — — Bs " 6+%.

0.18 0.36 0.18 Qs- 0.54*-Rtttf e Riu,.

Ri«.=^r 2.85 0.41 2.85 — 6.95+%. Riu. BS h=^

%=art 2.5 0.39 7.7 0.21 1.2 0% - 8.7+% e=(1.3u.)2+(0.7tu.)2 Riu.

0.56i^ ^+0.25^ Risu=j£ 0.25 BS i+RUu tfm=(l-h/L)-1'3 Hiw+

2.2s(^|)3+0.25 %=^ 2.5 0.25 U171 %v? 1 0.1 ~ 2.5+% e=u2+w2 Riu. Riu,.

%=^ e=u2+0.25w2 0.35(1+0:) 3.7 0.46 “=Ui(m)“ 0.46 0.23 B* 0.88+0.099-%- o4 +1.4-10-25-.Ri‘-7 Riu. Riu,. 0.4(1+0:) c=co exp [-(^.)1+“] ~ 1+0.125%

%=^ 0.4 0.4 1.4 0.21 0.2 0* — 1+0.28% e=u2+0.02<$u2+0.27tu2 Riu. ■ftt'iu*

13-9 (^?)3+1-39 (^t)3 11-4 Us. %=2r1 2.5 0.25 □[71 V? 0.75 0.34 — 3.33+% e=(u2+0.1tv2)2/3 Riu. Riu,.

“Wind-driven stratified flow in lakes (Bo Pedersen 1980). ‘Free penetrative convection (Bo Pedersen 1980) with the new notation Riu,. = Rr~^w ‘Isothermal dense plume in shear flow (Britter 1988). ^Eidsvik’s (1980) dense gas dispersion model. ‘Zeman’s (1982) dense gas dispersion model. /HEAVYPUFF dense gas dispersion model (Jensen & Mikkelsen 1984). 9DEGADIS dense gas dispersion model (Spicer & Havens 1986). ‘SLAB dense gas dispersion model (Morgan, Kansa & Morris 1983). ‘This report page 26.

wide range of field and laboratory data. The third function0 by Britter (1988) is a fit to wind-tunnel experiments with isothermal dense gas plumes in ambient shear flow as sketched in figure 12a. Britter’s (1988) function0 is almost equal to the first function" of Bo Pedersen (1980) even though the flow and density profiles were very different. Furthermore Bo Pedersen’s (1980) function" was optimized for large values of Riu, whereas the wind-tunnel experiments were conducted un­ der the relatively small Richardson number conditions typical for atmospheric dense gas dispersion. Eidsvik (1980) realized the need for an entrainment function with combined mechanical and convective turbulence production and proposed an

Ris0-R-1O3O(EN) 23 entrainment function* 7 in which the Richardson number Rie is based on the turbu­ lent kinetic energy e. This was evaluated by a weighted sum of the squares of the mechanical and convective turbulence velocity scales u* and w, which was based on empirical knowledge of the convective atmospheric boundary layer (Zeman & Tennekes 1977). At that time turbulence had not been measured in a dense gas cloud. The asymptotic limits of Eidsvik’s (1980) function* 7 are not in good agreement with the reference case of table 1, probably because it was calibrated with sparse data from the pioneering dense gas experiments of Picknett (1981). The function6 7of Zeman (1982) was developed from an entrainment model of the convective atmospheric boundary layer with a velocity shear Su across the top interface. Zeman (1982) argued that this is a relevant case for strong gravity cur­ rents in the initial stage of large-scale dense gas clouds, but his function6 seems inappropriate for the later stages of the dispersion process. Jensen & Mikkelsen (1984) developed a function^ by scale analysis of the turbulent kinetic energy bud­ get which will be described below. Unlike Eidsvik (1980) the velocity scales were assumed to contribute with equal weights to turbulent kinetic energy e = u% +w^. The overall scale may be chosen freely and compensated by other coefficients in the entrainment function, whereas the relative emphasis on u* or w* could be sig ­ nificant. The analysis of in-plume dense gas turbulence measurements on page 100 suggests a correlation e = 3.5%, + 2.4w* - with substantial uncertainty. The next functions5’71 in the table are part of two popular dense-gas dispersion models. DE- GADIS is designed with a smooth transition to passive diffusion under variable atmospheric stability and this complicates the notation. However the cloud height h is just the centre of gravity calculated by the assumed concentration profile6 and the entrainment function may be simplified (Britter 1988) to a form very similar to Eidsvik’s (1980) entrainment function'7. The entrainment function7* of SLAB is also of this type with inclusion of velocity shear 5u at the top of the cloud similar to Zeman’s (1982) function6. A later version of SLAB (Ermak 1990) includes a smooth transition to a passive plume (and complex notation) similar to the DE- GADIS parametrization. The last function1 of the table is an extension of Jensen & Mikkelsen’s (1984) function-^ to be developed below.

The turbulent kinetic energy budget

The theoretical basis for entrainment functions is the turbulent kinetic energy balance, see equation F.17. t\ *2 *3 -t6 &pe dpuje dpu'jU'jU^ dp ’u'j dui P>ui9i ~ pu\u' pe (24) dt + dxj dxj dxi 1 dxj where p is density, t is time, u, is velocity in direction a%, y, is gravitational acceleration, p is pressure, e = is turbulent kinetic energy 7 and e is the energy dissipation rate. Repeated indices indicate summation, a bar indicates time averaging and a prime indicates the deviation from this, see appendix F. The physical interpretations of the individual terms tn are: interpretations oft n

ti temporal changes of the turbulent kinetic energy level; t2 changes associated with transport of turbulent kinetic energy by the mean flow. If quiescent fluid is entrained into a turbulent volume, this term reduces

6The exponent a « 0.1-0.25 is evaluated from the velocity profile which is fitted to a log- linear Monin-Obukhov profile. The implicit relation between the exponents in the velocity and concentration profiles corresponds to a linear height dependence of the eddy diffusivity, see appendix G. 7In micrometeorologic tradition the turbulent kinetic ‘energy ’ has the dimension m2/s2

24 Ris0-R.-1O3O(EN) the turbulent kinetic energy level, ie this term accounts for the recovery of turbulent kinetic energy; tg divergence in diffusive transport of turbulent kinetic energy. This process may transmit energy away from a rigid surface or a strongly stratified region; t\ work of gravity associated with the buoyancy flux. Entrainment in a strati­ fied flow consumes turbulent kinetic energy whereas free convection produces energy; fg gradients in the pressure-velocity correlations, eg downward movements which tend to increase the pressure. This term is called pressure transport. It is very difficult to measure pressure transport directly, and in practice it is estimated as the residual of the remaining terms. In the atmospheric boundary layer the tg and fg terms tend to balance each other (Jensen & Busch 1982, p. 195). The combined effects of fg and fg may however transmit turbulent kinetic energy by internal gravity waves in strongly stratified regions; fg mechanical turbulence production by velocity shear and Reynold stress; tf viscous dissipation.

Development of an entrainment function

Two different approaches are applied to develop entrainment functions; the terms in equation 24 are either evaluated by scale analysis or estimated by depth in­ tegrals. Dense gas dispersion models need quite a versatile entrainment function applicable in a range of situations where the flow, turbulence and density pro­ files may change considerably. Therefore the simple approach is preferred to layer integration. It is advisable to design the entrainment function with a smooth transition to the typical dilution rate in the limit of passive dispersion. In this limit equation 24 is of little use since the energy conversions which are associated with the energy recovery by entrainment and illustrated by the white arrows in figure 11, vanish8 . Jensen (1981a) simplified the turbulent kinetic energy budget in equation 24 to

t2 te <3+t 5 t7 a p'u'i (25) and made the scale analysis:

ti+t2 t6 <3+^5 *7

e-eo Wi,3 wl (P - Pa) • Ueg =3/2 g3/2 Cg T~ + Cg —------+ Cg- ■ — C4- (26) Ci—Ue hi hi Pa ~hi hi e = ul + (C5W,)2 where c,- are calibration constants and eo are the turbulent kinetic energy outside the cloud. The pressure perturbations p' are assumed to be proportional to the turbulent kinetic energy level e, and the dissipation is proportional to the cube of a turbulence velocity scale divided by a suitable length scale, ie oc e3/2//t£. The change of energy level ti +12 is approximated by de de dhi e — eo dt ~ dz dt ~ hi Ue

8 The 'passive ’ state does not include the jet case where the turbulent kinetic energy level is very different from the ambient.

Ris0-R-1O3O(EN) 25 where e — eo is the difference between the turbulent kinetic energy inside and outside the cloud. Jensen (1981a) disregarded the turbulence production by heat convection 9 (eg = 0) and deduced the entrainment function

Ue_ _ <»(%) + c3 — c4

Vi C!(l -f) + Rie K }

This has almost the same form as the majority of the entrainment functions in table 2, but unfortunately the denominator approaches zero for the important limit of passive diffusion where eg = e and Rie = 0. In order to avoid this singularity Jensen & Mikkelsen (1984) changed the denominator to the usual form c\ + Re. At first sight this seems equivalent to an implicit assumption of an ever quiescent ambient fluid - in general an invalid assumption, but the motivation is simply that the function must approach the passive limit shown in table 1. Such pragmatism is permitted since in the limit of passive dispersion the energy budget reduces to a balance between production and dissipation with insignificant energy feedback by entrainment. The similarity between the entrainment function6 of Britter (1988) and function0 of Bo Pedersen (1980), ie two calibrated entrainment functions for situations with and without ambient turbulence, justifies the neglect of eg in the denominator. Jensen & Mikkelsen (1984) used the first (with Ai = 1), second, and fourth limit of table 1, set eg = 1, and derived the function-^ shown in table 2. The model was later implemented in the user friendly MS-DOS program (Nielsen & Ott 1988). The partial derivative a paradox

dUe 0.625 + 0.75% - 11.25 3

= (2.5 + Rie)2 (28)

is negative for some conditions, eg the combination u* = 0.5, w* = 0.25 and Rie = 1. This is puzzling since one might expect a positive response to increased turbulence in all conditions. The explanation of the paradox is that given a con­ stant buoyancy g'h and average cloud velocity u, the addional heat flux also in­ creases the friction velocity u« and the net result is the expected increase of the entrainment rate. In the following I reintroduce the term of turbulent kinetic energy production by new parametrization heat convection (eg ^ 0). This is justified if we regard equation 27 as representative for the layer as a whole rather than at the top of the cloud. The entrainment function is now assumed to be of the form

ue_ = c°- fe) +Cg te) ~c4 with e = (ul -t- c\w\)2/z (29) yfe Cl + Rie where the denominator is not in strict accordance with the turbulent kinetic energy budget - as in Jensen & Mikkelsen (1984) and for the same reason. It is most likely that the pressure transport and diffusion of turbulence are insignificant (eg = 0) leaving us with five unknown calibration constants and four reference cases in table 1. The constant-#^ assumption (Bo Pedersen 1980) is an obvious candidate for the missing boundary conditions which will close the system, and this gives a relation between turbulence production and dissipation.

{c2u\ + cgtu2) • (1 - Rj) = Ci{u\ + wz) (30)

This condition motivates the re-parametrization of the turbulent kinetic energy e in equation 29. The limits for u* ui* are the same as e = u2+c%w2

®The heat convection term should vanish at the top of the gas cloud

26 Ris0-R-1O3O(EN) with a maximum relative difference of 26% for u./w, = C5. The following system is obtained by comparison of equation 29 with the four reference cases in table 1 and the two independent conditions which may be derived from equation 30. C2-C4 Ai \ Cl Cl

C2 — C4 A2 C2 C6-C4c;j As ClC% ^#Ai Ag C4 A (31) c6 - cAc\ A4 A4 C5 (1 — Rj)C2 c4 Cg d

This solution specifies a relation between the four constants A%, A2, A3 and A4. This conditions is fulfilled if the limit of free weak convection is changed from As = 0.37 (Farmer’s (1975) temperature measurements in an ice-covered lake) to As = 0.34. The bulk flux Richardson number is set to RiJ = 0.18 since the flow in dense gas dispersion usually is supercritical (FYa > 0), and insertion of the coefficients in equation 29 leads to the last function1 in table 2.

Estimates of in-plume turbulence

The heat transfer in dense gas dispersion varies from free to forced convection depending on the velocity and temperature difference between cloud and surface. Jensen (1981b) proposed an analogy with the atmospheric surface layer in which the Monin-Obukhov scaling is applied. These velocity and temperature profiles are “w = if{ln (£)""*" (1)}

(32) where the velocity and temperature scales u, and T, are related to the tur­ bulent heat flux by u'T' — u»T». The heat exchange coefficient defined by ip = pc 9p chu(T0 - T{z)) is

(33) [ln (t) “ (f)] [ln (^) “ ^ (f)] where k is the von Karman constant, zq is the surface roughness, and the two correction functions ip m and iph depend on the stability parameter z/L, see ap­ pendix G. Elimination of u* and T* from the definition of Monin-Obukhov length L yields an equation for the stability parameter z/L

[ln(t)-Mr)f

— = RIat (34) ln (#) where the convection Richardson number Riat is defined from T(z)-T0 gz Riat = (35) T u{zY

Jensen’s (1981b) method was to evaluate the heat convection Richardson number RIat , to find the internal cloud stability z/L by iteration and then calculate c/,,

Ris0-R-1O3O(EN) 27 Influence of instability with fixed In z/zn = 4 Influence of z/zn with fixed Ri,\T = -1

'= -1.0

T—i—r f—;—i—i—i

z/L z/L

Figure 14. The function Mat [in - V’m (f)] [in - iph (f)] (right- hand side of equation 34) plotted as function of z/L for different combinations of z/zQ and Mat (thick lines). The solutions are the intersections with the thin 1:1 line. u„, w, and

10 K • 9.8 m/s2 • 1 m | = -0.40 Rat 280 K • (2 m/s)2 °'°88

Ch = 0.012

V = pc 9p Chu(To — T(z)) = 310 W/m2

u« = liifL = 0.21 m/s (37)

-11/3 gzchu(z)(T0-T(z)) w. = T = 0.20 m/s

e = u2 + 0.216iu2 = 0.045 m2/s2

28 Ris0-R-1O3O(EN) Note that the cloud is unstable seen from the surface z/L < 0 and that the dia- batic correction intensifies the friction velocity it*. Setting the cloud buoyancy to g'h=l m2/s2 the last function i of table 2 predicts ue = 0.020 m/s. An isothermal calculation with similar flow and buoyancy results in u*=0.17 m/s, iu»=0 m/s, e=0.030 m2/s2 and ue = 0.012 m/s, ie a significant reduction of the entrainment velocity.

Entrainment in elevated dense gas plumes and jets

Ricou & Spalding (1961) measured entrainment into axisymmetrical jets of hy ­ drogen, air, carbon dioxide and propane, ie jets with initial density ratios p/Pair in the range between ^ and ||. Independent of this variation the mass flow rate rh was found to correlate with distance x by

771 = 0.283 (38) x y/ Ajet/lair where Fjet is the jet momentum and pair is the ambient density. Part of the experi­ ments were repeated with the apparatus turned upside down in order to show that the work of the buoyancy force had an insignificant effect on the jet momentum. It is of interest to interprete the result in terms of a box model with ‘top-hat’ velocity u and density p distributions within the radius r leading to the flow rate rh and momentum Fjet

77i = nr2pu and Pjet = nr2pu 2 (39)

Insertion of these expressions into equation 38 gives

-j- = 0.283 \Znr2 pu 2 pah (40) ax and a comparison with the entrainment relation from chapter 2 leads to dm — = 2 (41)

Of course this result is valid only when the model parameters (u, p, and r) are defined in accordance with equation 39. Ooms & Duijm (1983) reviewed models for buoyant stack plumes and concluded that many of these including Ooms’ (1972) own model were applicable also for dense gas plumes. The excess velocity profile was approximated by an axisymmet- ric Gaussian distribution MO = Ay o exp j-^ j (42)

where £ is the radial distance from the plume centre line and uq is the centre-line excess velocity (with a slightly modified notation). The flow rate and momentum found by integration are in accordance with equation 39 when the plume radius and velocity scale are chosen to r = %/2crr Au = O.SAuq. In Ooms’ (1972) model the entrainment rate is split into three contributions from longitudinal jet shear, shear by the wind component normal to the plume axis and passive diffusion:

Ue = ailU- uair||| + a2|uairx| + a3(er)1/3 (43) where uair|| and uair± are the wind components parallel and perpendicular to the plume axis and e is the dissipation rate of ambient flow. Ooms (1972) chose a model radius in accordance with equation 39, a centre-line excess velocity which is twice the velocity of equation 39 and coefficients ai = 0.057, ct2 = 0.5 and a3 = 1.0. The normal velocity shear initiates a vortex pair which is a much more efficient

Ris0-R-1O3O(EN) 29 entrainment mechanism than that of the longitudinal shear, and this is the reason for the large difference between the first two coefficints (a# > Qi). The latter term accounts for passive dispersion by ambient turbulence. Muralidhar, Jersey, Krambeck & Sundaresan (1995) corrected the first term in accordance with the measurements of Ricou & Spalding (1961) and suggested the formula:

ue = O.O81 l-^—\u — ua;r|| | + 0.5|uairx| + l.O(er)1/3 (44) V Pair The latter term will remain insignificant in a typical dense gas emission.

Entrainment into elevated volumes

Turner (1964) discussed the dynamics of a buoyant volume moving through quies­ cent ambient fluid. The internal motion was described as an expanding vortex ring similar to the two-dimensional vortex pattern of a plume with significant velocity shear in its normal direction. The internal mixing by this vortex ring created a much sharper boundary than in a similar volume of neutral buoyancy subject to passive dispersion. The volume growth with height was known to be linear and this was found to be in agreement with the entrainment expression of equation 9 in chapter 2 d(§«r3) = 47r r2ue dt The motions outside the volume were described by potential flow theory with insignificant friction, and by a similarity argument the vorticity of the vortex ring was assumed to remain constant. Turner (1964) developed a linear relation between the entrainment rate ue and vertical velocity w of the centre of the volume.

ue ~ 0.23w (45)

This formula is valid as long as the volume has significant buoyancy relative to the surroundings, ie as long as the internal vorticity is sustained. Obtaining a correct model of the empirical vertical velocity w Turner (1964) had to account for the flatness of the volume10. Use of a spherical model volume will however only distort the travelling time not the dilution at a given height. For the box model introduced at the end of chapter 2 we need to consider a negative buoyant volume with or without initial momentum and ambient wind. As a simple estimate we may use an equivalent to Turner’s (1964) theory and assume

ue = 0.23|u — uair| + l.O(er)1/3 (46)

Jensen (1981a) expected the horizontal acceleration of an instantaneous release to be insignificant in practice, since large amounts of ambient air are entrained by the typical blow-out process.

5 Obstacles

A situation with a dense gas release as a major hazard may occur inside chemical introduction process plants or urban environments, where the flow is affected by obstacles. An introduction to this topic is needed also for discussion of the field experiments in

10The shape was considered an oblate spheroid with a ratio of the major to minor axis equal to 1.4.

30 Ris0-R-1O3O(EN) chapter 11. Dispersion in a complex topography may either be calculated by three- dimensional numerical models, studied in wind-tunnel simulations, estimated by semi-empirical rules or one may ignore the obstacle effect. To simply ignore the obstacle effect may seem careless, but in practice this is a normal choice. It is argued that the interaction between obstacle and ambient wind induces more turbulence, which enhances the mixing and dilutes the gas cloud. In this way a dispersion calculation without obstacles is often regarded as a safe upper limit for the expected concentration - provided that there is an ambient wind. The three-dimensional numerical approach is a feasible but time-consuming alternative, and with the present state-of-the-art it must be regarded as a research area rather than an engineering tool. It is not easy to make a versatile model which adapts to the variety of obstacle configurations in the real world. In fact this is difficult, even for dispersion of a gas with neutral buoyancy. The wake circulation and obstacle-induced vortices are quite strong and ex­ chapter summary pected to exist also in dense gas dispersions. This chapter is therefore initiated by a review of unstratified flow around buildings and a presentation of Vincent’s (1977) idea of wake resistance time. The other extreme is dense gas dispersion among obstacles in still air where the obstacles may block and canalize the gas flow completely. Konig (1987) made a systematic study of a range of obstacles with and without ambient wind. He found that many obstacles have a mitigating effect because the enhanced dilution by obstacle-induced turbulence more than compensates the restricted horizontal spreading. An exception from this rule is dispersion within a canyon oriented in parallel to the wind direction.

Shear Shear Uniform Boundary flow profile layer profile

Wake Circulation Wake Circulation

Front Eddy

Figure 15. Two-dimensional flow over a long fence: a) with uniform upstream flow profile, b) with an upstream boundary layer profile.

Flow around obstacles

A two-dimensional flow over a fence is the simplest obstacle configuration possible. two-dimensional flow Figure 15a illustrates the flow separation from the edge of the fence and the circulation in the wake. The flow accelerates just above the fence and the boundary between this jet and the wake becomes a region with a strong velocity shear and enhanced turbulence production. Further downstream the separated streamline will reattach to the ground, and to some extent the wake is decoupled from the main flow. When the upstream velocity profile is a boundary layer as in figure 15b, the stagnation pressure of the streamlines increases with height, and so do the pressure on the upstream side of the fence. This vertical pressure difference generates an upstream vortex as shown in figure 15b. Two-dimensional flow over a building, which is not too long in the flow direction, is similar to the flow over a fence, but the separated streamline may reattach to the roof of a long building as in figure 16. In this case the flow will separate

Ris0-R-1O3O(EN) 31 from both the upwind and downwind edge of the obstacle. The streamline which separates from the downwind edge of the obstacle will initially be horizontal, and the volume of this wake is smaller than that of a wake behind a fence of equal height.

Velocity Profile

Front Eddy Wake Circulation

Figure 16. Two-dimensional flow over a obstacle with a rectangular cross section.

Vortex in a street canyon

Vortex axis

Figure 17. Circulation in a street canyon when the ambient flow has a skew wind direction.

The rough sketch in figure 17 illustrates how three-dimensional obstacles create three-dimensional flow three-dimensional flow pattern. In this case the combined effect of the wake vortex and the wind component along the street canyon makes the fluid elements spiral. Therefore it is difficult to estimate the ambient wind direction from local wind directions near obstacles.

Figure 18. Some flow patterns behind a three-dimensional obstacle, a) edge vor­ tices, b) trailing vortices.

The axes of the dominating vortices behind a slender obstacle will be vertical, as sketched in figure 18a. For obstacles with moderate height-to-width ratios the ambient flow may go around as well as over the obstacle, and the extent of the downstream circulation zone is short compared to that of a two-dimensional flow. The flow behind a three-dimensional obstacle will often have two counter-rotating vortices as indicated in figure 18b. This may be explained partly as a reminiscence

32 Ris0-R-1O3O(EN) of the upstream front eddy and partly as a flow pattern generated by the low pressure at the roof of the building.

Figure 19. An example of interaction between two obstacles: A jet is generated between regions of high and low pressure.

Two obstacles close to each other will interact. In the example in figure 19 a secondary flow is initiated between the region of excess pressure in front of the building at the right-hand side and the region of low pressure in the wake of the building to the left-hand side in the figure. To summarize this section the flow around an obstacle depends on

- height, width and depth of the obstacle

- the angle of edges from which the flow will separate

- the orientation relative to the ambient flow - the velocity profile of the upstream flow

- the pressure disturbance from nearby obstacles.

The information have been found in the comprehensive review article by Hosker (1984).

Ordinary dispersion near obstacles

A simple dispersion model for emissions in the wake of an obstacle is to assume that the volume Kvake is well mixed and that the fluid elements have the aver­ age residence time Twake in the wake. According to this model the average wake concentration c^ake is described by the differential equation

dc wake , C'vvake V • Co ------1------~ ------(47) dt Twake Vvake where volume V is the release rate and cq is the release concentration. Vincent (1977) released smoke in the wake of cubic obstacles and estimated the average concentration from the extinction of a laser beam across the wake. When the source was suddenly turned off, the wake concentration was observed to decay ex­ ponentially in accordance with equation 47. The wake volume K,ake and residence time 7wake was correlated with the size and orientation of the cubic obstacle and the eddy diffusivity of the free air stream. Hosker (1984) lists correlations between obstacle geometry (height, width, length) and the geometry of the wake for a wide range of obstacle geometries. The flow fields around obstacles affect the nearby concentration field. For in­ stance, if a tracer is released inside a street canyon with a flow pattern as in figure 17, fresh air is supplied near the wall of the downstream building and the maximum concentrations are therefor found under cover of the upstream building. In case of a pair of trailing vortices as shown in figure 18b the outward flow at ground level has a tendency to bifurcate a plume in the wake of an obstacle.

Ris0-R-1O3O(EN) 33 Dense gas dispersion in still air

Heidorn, Murphy, Irwin, Sahota, Misra & Bloxam (1992) observed some peculiar obstacle arrays gas cloud shapes for dense gas dispersion in obstacle arrays without ambient wind. The gas cloud was instantaneously released in the middle of the array, and the front advanced between the obstacle elements as indicated in figure 20. For the staggered obstacle array, shown on the left-hand side of figure 20, the shape of the cloud became hexagonal whereas the cloud in the regular array of obstacles, shown on the right-hand side of figure 20 became diamond shaped. At first sight

Staggered array of cubic obstacles Regular array of cubic obstacles

...... »S A O...... •□•□3D-D-D-D-D-D°D D°0-0-0-0-D-DiD-Q-Cl-0-0-D°D G0n-D:D:n:D:qin :D:D:n;D0n □ □ □=D:D;D;Din-D;D;D<) □ □ □ □ □°D:D:a:D:a:[p|n:[i)°D □ □ □ □ n0D-D;D;DiD;D-D°D □ □ □ □ □ n°D;n:n";D;D";Hin □ □ □ □ □ □ □ □°D°ajpD°n □ □ □ □ □ □ □ □ □ □ □ □ □□□□□□ □ □ □ □ □ □ □ □ □ □ □ □°D;D°D □ □ □ □ □ □□□□□□□□□□□□□□ □ □□□□□ 6=6 □□□□□□

Hexagonal cloud boundary Diamond shaped cloud boundary

Release point Release point

Figure 20. Dense gas spreading in an array of obstacles with no ambient wind velocity as observed by Heidorn et al. (1992). The cloud boundary was found to be hexagonal with a staggered array of obstacles and diamond shaped with a regular array of obstacles. these cloud shapes are surprising, since the shape of an instantaneously released cloud in unobstructed terrain is circular. Consider however the paths from release point S to points A and B at the top of figure 20. When the length of these paths is measured in the centre of the gaps, routes S — A and S — B are of equal length, ie the observed cloud shapes indicate that the front velocity is equal for each section of the cloud boundary and independent of the orientation. Similar cloud shapes were observed with obstacle elements of other sizes as long as they were higher than the cloud. With ambient wind the effect of the obstacle arrays on cloud spreading was less clear. The obstacles sketched in figure 20 were sufficiently large to prevent the gas blocking from flowing over them. Estimates of the necessary obstacle height are provided by blocking theory, see Baines (1984) and appendix F. This theory is based on energy conservation. The basic assumption is that flow over the crest of an obstacle is critical (Fr = 1) in the blocking situation, because this corresponds to the maximum flow rate for the available energy head. From this condition a set of blocking criteria may be derived, eg as in equation F.50:

1 + ^Frl - h0 ~

34 Ris0-R-1O3O(EN) which is a criterion for partial blocking in a one-dimensional single-layer flow of initial height ho and initial Fronde number Fro when passing an obstacle with height H. Blocking criteria have been experimentally verified by laboratory ex­ periments where the obstacle is towed through a water tank. This experimental set-up is particularly convenient for studies of blocking in stratified flows since the initial density distribution is easier to control in a calm environment. In general blocking criteria for two-layer flows involve the dynamics of both layers, but if the undulations of the interface are not too steep and the depth of the outer layer is large, the blocking criteria for single layer flows translate to similar criteria for two-layer flows with the Froude numbers Fr = u/y/gh substituted by the den- simetric Froude numbers F>a = u/y/g'h, using the reduced gravity g' = p ^° g- Criteria for complete blocking and for porous lines of obstacles are included in appendix F. They are derived on the simplifying assumptions that all flow pro­ files are uniform and that the obstacle topography is sufficiently smooth to leave the vertical pressure distribution hydrostatic. With boundary layer flows and real buildings these assumptions are of course not strictly valid.

Source

High wall parallel to the wind Low wall parallel tothe wind Two walls parallel to the wind

Source

Source Source-

Low walls parallel to the wind Semi-circular wall Crossroad between high walls

\ a t v Source

Crosswind canyon Two walls 45° to the wind

Figure 21. Obstacle configurations examined by Konig (1987).

Dense gas dispersion with ambient air flow

Konig (1987) performed wind tunnel studies of dense gas dispersion with generic obstacles. Ground-level concentrations were measured for each of the obstacle configurations shown in figure 21. Both instantaneous and continuous releases were examined with and without ambient wind. The release conditions were quantified the scaling parameters in table 5. The ambient wind was usually set to u = 0 or u = 1.0 Uc, and the height of the obstacles were either H = 0.1 Lc or H = 1.0 Lc. With the high wall parallel to the wind direction in figure 21a the gas cloud wall parallel to the wind remained on one side of the obstacle. Compared to similar unobstructed releases the average concentrations increased, ie in this case it was not safe to ignore the obstacle effect on the dispersion. The mixing in the local boundary layer of the

Ris0-R-1O3O(EN) 35 Table 3. Characteristic length Lc, time Tc and velocity Uc defined in Konig (1987). The source is defined by the initially reduced gravity g'0 and by the released volume V$ or the release rate Vq for instantaneous and continuous releases respectively.

Length scale Time scale Velocity scale Lc, = v;!'3 T„- = (i^)1'2 uci = (£,«;,)1/2 Instantaneous ^=(¥)"5 r-ter "--OUT Continuous wall was insignificant. With the low wall parallel to the wind in figure 21b the observed concentration fields were almost the same as with the high wall in the absence of ambient wind. With ambient wind, part of the gas cloud spilled over the wall. With a release between two high walls parallel to the wind direction, as shown two walls parallel to the in figure 21c, all of the gas remained inside the street canyon, and there was little wind difference between the concentration at the centre of the street and near the walls. The gas concentration at a given distance from the source increased considerably compared to an unobstructed reference case. For the instantaneous release it was found that at a given position downwind of the release point the concentration was lower with ambient wind than without. This effect was not observed with the continuous release. With the two low walls shown in figure 21d part of the gas cloud escaped beyond the walls leading to lower concentrations within the street canyon. The semi-circular wall shown in figure 21e, was a model of a large-scale field trial semi-circular wall (Thorney Island no 20). The ambient wind and wall height were set to it = 0.5 Uc and H = 6.0 Lc (rather high) in accordance with the full-scale experiment. The agreement with the field trial observations was fair, and not surprisingly this large obstacle had a significant effect on the downstream concentration. The obstacle shown in figure 21f was a crossing of two street canyons with crossroad dimensions similar to those of the single street canyon in figure 21c. In case of ambient wind the concentrations were much reduced in the street perpendicular to the wind direction. This was probably caused by a wind induced vortex similar to the one sketched in figure 17. The obstacle shown in figure 21g was a trench of depth 0.29 Lc situated down­ trench stream of the source and perpendicular to the wind direction. At all locations the concentrations were lower than in an unobstructed flat terrain case - in particular downstream of the trench. The obstacle configuration shown in figure 21h was a street canyon orientated two walls 45° to the wind with an 45°oblique angle relative to the ambient wind. The concentrations inside the canyon were low compared to a street canyon parallel to the wind with a significant difference between the upstream and downstream side of the street, suggesting the existence of a street vortex as in figure 17. The obstacle configurations examined by Konig (1987) were constructed by long walls, where the orientation relative to the wind direction was very important. The obstacles had a tendency to confine the spreading of the gas layer leading to higher gas concentration. In case of ambient wind at oblique angles relative to the obstacles the wake vorticity did, on the other hand, enhance the local mixing. The high concentrations observed with strictly parallel walls may overpredict the concentrations in the atmosphere since the natural wind direction is variable with a standard deviation rsIO0.

36 Ris0-R-1O3O(EN) 6 Concentration fluctuations

In the previous chapters the spreading gas was considered to have a continuous introduction quasi-steady spatial distribution. In a turbulent atmosphere this is however only true for the ensemble averaged concentration field - instantaneous gas distribu­ tions have significant fluctuations, as will be shown in chapter 13. Concentration fluctuations are of practical interest in risk analysis because they intensify the risk of ignition of inflammable gases and the human response to toxic gases. This chapter is initiated by a description of concentration fluctuations observed chapter summary in plumes of neutral byoyancy, and the concepts of signal average, variance, inten­ sity and intermittency are introduced. It is explained that a significant amount of the variability is caused by plume meandering which intermittently sweeps the plume towards and away from a local observation point. Some relevant statistical models are presented.

Average Variance Intensity Intermittency

Moving c frame

Figure 22. Crosswind distributions of average concentration c, variance of the local concentration ac, signal intensity I and intermittency 7. The distributions are shown for a fixed frame of reference and a moving frame of reference relative to the instantaneous plume centre line yc. Sketch after real data by J0rgensen & Mikkelsen (1993).

The spatial variation in a plume of neutral buoyancy

Jprgensen & Mikkelsen (1993) applied a remote-sensing lidar system to detect the concentration distribution in a continuous surface plume of neutral buoyancy. The measuring path of the lidar was aimed horizontally across the plume 160 m downwind of the source and 2 m above terrain. Figure 22 outlines some statistics of these measurements. The statistical properties in the top row of the figure are plotted as a func­ fixed-frame statistics tion of distance along the measuring path y. The time averaged concentration c had the Gaussian distribution which is consistent with Fickian dispersion from a point source in a flow field with uniform advection and diffusivity. The spatial distribution of the variance of the concentration fluctuations was approximately Gaussian as usual in field experiments. One of the theories in Hanna’s (1988) re­ view on concentration fluctuations in plumes predicts the spatial distribution of the fluctuations by a conservation equation with eddy diffusivities very similar to

Ris0-R-1O3O(EN) 37 the equation for the average concentration field. This theory is able to reproduce the observed Gaussian distribution in a state where the fluctuation production term is negligible compared to dispersion and viscous dissipation, ie not too close to the source11. It also predicts a wider variance distribution than the average dis­ tribution and this explains the 'U-shape of the intensity distribution defined as the ratio of variance and average I = trc/c. The minimum intensity at the plume centre line depends on factors such as source characteristics, advection time, tur­ bulence level and possible velocity shear. The rightmost profile in the top row of the figure shows the intermittency defined as the probability of non-zero concen­ trations 7 = P{C > 0}. The turbulence length scale of the atmosphere is often large compared to the plume dimension, and large eddies occasionally move the instantaneous plume away from local measuring positions. This plume meander is the main reason why the intermittency is smaller than unity even on the plume centre line. The intermittency approaches zero far from the centre line where non­ zero concentrations are rare. The intermittency is sensitive to measuring problems like noise and base-line drift and in practice data are filtered by a threshold level before this analysis. Gifford (1959) proposed a meandering-plume model describing the concentra­ moving-frame statistics tion field by a fixed spatial distribution relative to a random instantaneous centre­ line position yc. Jorgensen & Mikkelsen (1993) calculated yc as the centroid of the instantaneous lidar profile and repeated their analysis in a frame of reference relative to the moving centre line y — yc, as sketched in the bottom row of fig­ ure 22. The average distribution was still Gaussian with a narrow width and high centre-line concentration relative to the fixed-frame average distribution. The in­ stantaneous distributions were not of a fixed shape in disagreement with Gifford’s (1959) simplistic model. The observed spatial distribution of the variance of these in-plume fluctuations was nearly Gaussian with a maximum comparable to that of the fixed-frame variance distribution and a smaller width consistent with an overall variance reduction. The width of the moving-frame intensity distribution was significantly narrower with a smaller minimum than in the fixed frame. The moving-frame intermittency distribution was narrow with a larger maximum than the fixed-frame intermittency distribution. It did however still have a smooth de­ crease at the plume edges in conflict with Gifford’s (1959) model. The observed moving-frame profiles were smoother and more symmetric than the corresponding fixed-frame distributions. The statistical accuracy depends on the duration of the sample period relative to the time scale of the stochastic process. The moving-frame analysis removes variance from the low frequency range of the turbulent spectra and thus the integral time scale of the stochastic process will decrease. This improves the accuracy of moving-frame estimates. Ensemble averages of fixed-frame profiles for finite average periods will grad­ average time ually approach moving-frame profiles for a decreasing observation period. Fi­ nite average-time statistics are of practical interest to dense gas dispersion since most field experiments have relatively short release durations in the order of a few minutes. Most dense gas models ignore the influence on the average pro­ files although the SLAB model (Ermak 1990) corrects the plume width by ay re ay o • (T/T0)0'2 where T is the average time of interest and To is a 10-min refer­ ence period with the corresponding plume width gv q. Wilson (1995) noted that Gy

11 Variance distributions with two local maxima at the plume edges have been observed in laboratory experiments, eg the data sets used by Chatwin & Sullivan (1990).

38 Ris0-R-lO3O (EN) Probability distributions

The probability of ignition or the human response to a toxic gas are not linearly proportional to the gas concentration, see appendix I, and the average concentra­ tion usually underestimates the hazard. The local probability distribution would provide a better input to models for gas ignition or physiological response. The turbulent eddies convolute and stretch the tracer gas into fine strands. the a-(3 model Chatwin & Sullivan (1990) considered the limit of negligible molecular diffusion where the local concentration is either zero or equal to a strand concentration Cmax- If the probability of being in the contaminant fluid12 is set to 7, the moments of the two-state binomial distribution become:

} 7<-max E{(C-c)2} (T-f)cLx E{C2} 7^max E{{C-cf} (7 “ 372 + 273) C^ax (48) E{C3} 7^max E{{C- c)4} (7 - 472 + 67s - 374)4ax E{C*} I't'max The intensity 7, skewness S and kurtosis K of this distribution are

' = vf 5 = E{iC°^ } = ^5^7) (49)

tv - _ gfCC-c) 4} _ 1—37+372 A “ f - 7(1-7) and it is noted that the skewness and kurtosis follow the relation K = S2 + 1 (50)

The moments are related to the average value by E{{C-C)2} = C(cmax-C) E{(C-c)3} = c(cmax-c)(cmax-2c) (51) S{(C-c)4} = c(cmax-c)(4ax-3cmaxc + 3c2) and Chatwin & Sullivan (1990) suggested that the effect of molecular diffusion might be modelled by the expression E{(C — c)2} = fic(aco — c) (52) where a and /3 are parameters which develop during the disperesion process. The strand concentration cmax is almost impossible to measure and therefore it was substituted by a more convenient local concentration scale cq, eg the average concentration at the plume centre line. The /? coefficient accounts for variance reduction by diffusion or the inevitable instrumental averaging. With similar ap­ proximations for the higher order moments E{(C - c)3} = p 2c{occo - c)(aco - 2c) . . E{(C — c)4} = Pzc(aco - c)(a2co2 - 3acoc + 3c2) 1 the K-S relation in equation 50 becomes a lower bound for continuous probability density functions (Mole 1995). Zimmerman & Chatwin (1995) presented a model in which the molecular diffusion gradually smeared the concentration field of the fine strands to a Gaussian spatial distribution of increasing thickness and decreasing maximum concentration. The model predicted decaying intensity I, skewness S and kurtosis I< and the skewness-kurtosis relationship was K ~ 1.06S2 +1.32 for short molecular diffusion times. Similar parabolic skewness-kurtosis relations have been observed in field and laboratory data (Chatwin, Lewis, Robinson, Sweatman & Zimmerman 1994). Another approach is to fit empirical probability distributions to experimental empirical distributions

^Instrumental averaging usually prevents direct comparison of measured intermittency 7 and fine-scale intermittency of the a-@ model.

Ris0-R-1O3O(EN) 39 data. A relatively simple model, which will be applied in chapter 13, is a combi­ nation of a finite probability of zero concentration and a gamma distribution for the non-zero concentrations. This is written r(fc,c/A) P{C < c} = (1 - 7) + 7 • (54) rw where C is the stochastic signal and c is an arbitrary concentration level and T (k, c/A) and F (k) are the incomplete and ordinary gamma functions as defined by Davis (1964). The shape and scale parameters (k and A) relate to the basic statistics by

7<72 + (7 — l)c: k = A A = (55) 7<72 + (7 — 1 )c-2 7c where c and a are the measured average and standard deviation including zero- concentration measurements. Deardorff & Willis (1988) applied the distribution in equation 54 for concentration fluctuations in a convective mixed layer. Wilson (1995) considered it to be a reasonable approximation also for ground level plumes although he recommends the almost equally simple log-normal distribution.

Spatial structure In some risk-assessment problems the probability distribution of the concentra­ tion fluctuations needs a complementary description of the spatial or temporal structure, eg very fast fluctuations will be averaged during inhalation and will be irrelevant for toxic effects inside the humans lungs. The spatial structure of the concentration fluctuations and the temporal structure of a time series are related to the mixing process. The high frequency part of the spectrum of an at­ mospheric concentration time series follows the S(/) oc /~5/3 power law which is a characteristic of turbulence with an inertial subrange (Panofsky & Dutton 1984). Richardson (1926) described the spatial structure of the concentration fluctuations by a distance-neighbour function:

J c(y)c(y + Sy) dy and deduced that this should be oc c2 exp {—<5y 2/3}. This function has a rapid decay for small separations which are difficult to observe in practice. Jorgensen (1994) did however prove that an apparent disagreement with lidar observations could be explained by instrumental averaging.

7 Surface temperature

The dispersion of a cold dense gas cloud is affected by convective heat transfer introduction from the warm ground. This gradually increases the cloud enthalpy and thereby moderates the cloud density. It also gives an extra contribution to the turbulence and in this way it intensifies the entrainment rate. These effects are sometimes neglected in numerical and wind-tunnel models, but an analysis of non-isothermal field experiments (chapters 11 to 12) shows that they are significant. One may wonder whether the heat flux will be sustained by a constant ground surface temperature or whether a time development must be anticipate. Obviously the surface temperature must eventually decrease, but it is not certain how fast the temperature drops compared to the time scale of the cloud development. This problem is analysed by a model of the heat flux from the ground when chapter summary

40 Ris0-R-1O3O(EN) suddenly exposed to a cold gas cloud. Heat conduction in the soil is described by linear diffusion and this allows superposition of a class of solutions from Carslaw & Jaeger (1959). The surface heat flux is matched with a simplistic forced con­ vection model for the heat flux in the gas layer. Analytical expressions for the time development of the surface temperature are derived for the idealized cases of constant gas temperature and linearly decreasing temperature. Based on these solutions it is concluded that the temperature may be considered constant in an instantaneous gas release but not necessarily in a continuous gas plume. In chap­ ter 12 the model will be further developed and compared with field observations of temperatures at a finite distance from the surface.

Heat conduction in a semi-infinite solid

The temperature development in a homogeneous semi-infinite solid is described by an ordinary heat conduction equation 8T . d2T PsoilCsoil — ^soil (56) where Psoil = soil density Csoil heat capacity of soil T = temperature t = time Xsoil : soil conductivity Z = depth into soil We are interested in solutions where a sudden thermal forcing is imposed on the surface z = 0 and the semi-solid is in initial thermal equilibrium. A wide range of diffusion problems are examined by Carslaw & Jaeger (1959) - one of them with the following boundary conditions:

%o\\{z,t) = Tq for t < 0 TsoU(0,t) = T0 + AT • in/2 for t > 0 (57) where T is any time scale and n is any positive integer including zero. The solution Tsoii(z,f) for t > 0 is

t) = T„ + AT • r (f +1) («) 1 . ,-erfc (58) where the latter function is shorthand for n integrations 13 over the complementary error function. 2 rc a for n = 0 i" “*<*> = { Fr-Um (59) for n > 1

In practice the integrals are found using the recursive formula

in erfc(ar) = [in~2 erfc(a:) — 2a: • in_1 erfc(x)] (60) When the argument is zero, this reduces to

inerfc(0) = [2nr Q + l)]”1 (61) since erfc(O) = 1 and i-1 erfc(O) = 2/VtF. Equation 56 is linear, and superposition of solutions is therefore allowed. Thus a surface temperature of the type “ / t\nl2 Tsoi. (0, t) = To - AT an ( == ) (62) n=0 / 13the symbol ‘i’ refers to the integral operator not the imaginary number i = V—1

Ris0-R-1O3O(EN) 41 results in the ground temperature

^ / PsoilCsolT Tsoil(z, t) = To - AT ^ an • 2n • T (? + 1)(T)'i,erfc (63) 2 y ASoil^ n=0 The heat flux y is equal to the temperature gradient multiplied by the conductivity ASoii. By differentiation and insertion of in erfc(O) we get the time dependence of the surface heat flux. The sign is reversed because the semi-solid depth z was defined in the downward direction, but actually we want to study the heat flux from the solid to the gas cloud, i.e in the opposite upward direction. (p(z,t) = As0ii • ^

■ -A-'fVW (64)

• o„ • 2" • r (| + l) • in 1 erfc % jPsoilCsoil 2 n=0 ' ' V Asoil£ This depth dependent heat flux will be used in chapter 12, but the remaining part of this chapter will focus on the heat flux to the gas cloud, ie the flux at the surface. Inserting z = 0 and the values in equation 61, the surface heat flux becomes: n —1 ' AsoilPsoilCsoil , r(j + i) (t 2 ip( 0, t) = AT (65) T £”r« + t) \T The idea is now to match this heat flux with the heat flux in the gas cloud, and the simplest model for this is

V^sur — PCpC/ltt(T’sur Tm ix) (66)

where Cp is the heat capacity of the gas, % is a heat transfer coefficient, u is the gas velocity and Tsur — Tm-,x is the temperature difference between the surface and gas mixture. The heat exchange coefficient may be estimated by the internal cloud surface layer method described in chapter 4.

Constant gas temperature

In a continuous dense gas release the plume temperature Tm\x remain approxi­ mately constant at a given downwind position will f To for t < 0 \ T0-AT for t > 0 (67)

but the surface temperature will be time dependent Tsur(f) = TSoii(0,t) and the surface heat flux will therefore decrease. The local gas arrival time is the starting time. The time development is found by combination of equations 65 and 66 with insertion of the surface temperature from equation 63. ^AsoilPsoilCsoil CO r(f + i) 53 On (68 ) r(§ + !) n/2' = pCpChuAT < 1

This equation can be transformed to a recurrence formula for the constants on, but first we introduce the heat transfer time scale Theat AsoilPsoilCsoil Theat — (69) {pcpc hu)2

42 Ris0-R-1O3O(EN) which is inserted into equation 69 and after some re-arranging we have:

-1/2 oo + (70) CO (f)t W2 _ En=0

This is solved for o„

0 for n = 0 n/2 (71) dn — H)"« (t£t) r(f+i) for n > 1 and the time development of the surface temperature becomes

(72)

The sum is identified as an analytic function

(73)

df 0--1/2 3-----/ = —7=— 1 # /($) = 1 - exp(a:) erfc(V$) uX y 7T The temperature difference between the surface and the gas is then

TSur(t) - T0 = AT [l - exp (t/%eat) erfc \A/7heat] (74)

The development of the surface temperature is plotted in figure 7. For release durations comparable to the heat transfer time scale Theat, the assumption of time independent surface temperature leads to an 0(2) over-prediction of the surface heat flux.

Surface temperature deficit in a plume

Relative time t/7heat

Figure 23, Temperature difference between surface and a gas cloud of constant temperature.

Ris0-R-1O3O(EN) 43 Variable gas temperature The cloud temperature of an instantaneous release increases because of the en­ trainment of ambient air. In order to evaluate the effect on the surface temperature this is modelled by a linear variation. T0 for t < 0 To — AT • ^1 — ^ for 0 < t < 7t (75) where 7r is a time scale for the cloud temperature development. Similar to equa­ tion 69 we equate the heat transfer in the soil surface and in the gas cloud. The only difference is the decreasing gas temperature described by equation 75. n — 1 •^soilPsoilCsoil 2 AT v, £($±31/1 T £ r(f + |) It n/2' t — pCpChgatt/AT \ 1' (76) Tt

This is again transformed to a recurrence formula for the an coefficients describing the surface temperature development

(77)

The o„ coefficients now becomes for n = 0 n/2 H)n+1 (t£t) Cln — 4 r(f+i) for n = 1,2 (78) . (i- V)■ H>n+1 (thS* ittW f™”23 and the time development of the surface temperature is .n/2 Theat A (”1)n+1 (t6t) Tsur(i)=r0-AT- (79) Tt "4 r(f+ i)

+ rPT which is simplified to Theat TSUr(t)—To = —AT- ./ 2 fJZ_ JL\ (80) Tt 1 VV Theat Theat J

fl - -jl-exp (t/Theat) erfc VVThUt} +

The curves in figure 24 are calculated from this formula but plotted relative to the gas temperature time scale Tt- The figure shows the temperature difference between cloud and surface for different ratios of the time scales for cloud temper­ ature change and heat conduction Tr/Theat- The dotted line is the limit where the surface temperature does not change and the decreasing temperature difference is caused by changing gas temperature alone, ie the limit of maximum heat flux. Another important time scale is the cloud passage time T^ass which typically will be less than Tt-

44 Ris0-R-1O3O(EN) Surface temperature deficit in a puff

* Insignificant cooling o'

Jr = 7h,

Relative time t/Tr

Figure 24■ Temperature difference between surface and a gas cloud with linearly decreasing temperature. The time is normalized with the time scale for cloud tem­ perature development Tt, and shown for different heat transfer time scales Theat-

Time scale for heat transfer Theat 0.1 “•••.. 1 ' • • ..10 sec ' • . . . ‘ . -... ' • • . .1 min

1 • • . ’ ' •.. 10 min <5 0.01

-.1 hour ' • • .

. • . .10 hours

0.001 ______i______10 U

Figure 25. Heat transfer time scale Theat dependence on heat transfer coeffi­ cient Ch and velocity u. The physical properties for solid and air are taken as Asoil =0.5 W/(mI<), Csoii —1.8 kJ/(kgK), p soi\=2000 kg/m 3, p^ —l.S kg/m 3 and c™ =1.0 kJ/(kgK).

The heat transfer time scale Theat

The heat transfer time scale Theat defined in equation 69 is plotted in figure 25 as a function of the wind speed u and heat exchange coefficient c& using typical properties for soil and gas. A wide range of heat transfer time scales are possible, but an example with u=4 m/s and c& = 5 -10-3 gives Theat = 50 min. This is long compared to the typical temperature development of an instantaneous release

Ris0-R-1O3O(EN) 45 Tt < Theati and the temperature difference between gas cloud and surface will be close to the linear line in figure 24. The duration of a continuous release depends on the storage volume, but a duration 0(10) min seems plausible, and this is sufficient to reduce the temperature deficit significantly. The simplifying ‘constant surface temperature’ approach is justified for instantaneous releases, but for continuous releases it may lead to over-predictions of heat flux and convection with a factor 0(2). Kunsch & Fannelgp (1995) performed a laboratory experiment with a gravity current of very cold LNG advancing over an initially warm surface and comple­ mented it by analytical and numerical models. It should be said that they reached a slightly different conclusion predicting significant effects also for the case of in­ stantaneous gas releases. The reason for is that if the dispersing gas is very cold (initial stages of LNG dispersion) and the surface heat conductivity is relatively low (light snow or dry grass) the heat transfer time scale could be comparable to the temperature development by dilution (large gas cloud), ie 7r — Theat-

8 Dense gas sources

Prior to analysis of any dense gas dispersion problem the release conditions must introduction be defined. The parameters of interest for the dispersion calculations are - source strength

- release duration - initial density - initial momentum - initial temperature - initial aerosol fraction Three generic types of release are identified: 1. A continuous leak through a narrow exit, 2. an evaporating pool and 3. a seriously damaged storage where all of the material escapes instantaneously. A combination of these cases may also occur, eg if the aerosols in a plume rain out and form a pool as a secondary gas source after the main release. The initial enthalpy is higher for an evaporating pool than for a flashing jet and this leads to a lower plume density. In addition the typical pool evaporation rate is weaker than the preceding liquid spill rate, so refrigerated containers are intrinsically safer than pressurized ones. Much effort is made to avoid total container failures and such accidents are much less frequent than broken pipes and hoses, valve malfunction or operational errors. Large installations have security valves with the purpose of releasing material from the gaseous phase in case of when alarming pressure. A total container failure is therefore more likely to result from a traffic accident than from normal operation. Estimation of source parameters might have been considered as a separate prob­ chapter summary lem, but in practice this is closely related to the description of the dispersion process, and it is appropriate to include its main principles. The three generic types of release defined above are considered one by one with emphasis on para­ meters of interest. The physics of the source can be complex and this presentation should not be considered as more than an introduction. In chapter 9 it will be demonstrated how initial temperature and liquid fraction affect the cloud density.

46 Ris0-R-1O3O(EN) Liquid phase outflow

Calculation of the outflow from a leaking storage depends on the source geometry and the phase of material. This is of course not known in advance, but a practical method is to work with a range of possible release scenarios. Modeling of these release scenarios often includes determination of liquid flow through pipes, which is a standard problem described in many fluid mechanical textbooks, eg Engelund & Bo Pedersen (1978, pp. 93-136). The pressure loss in the pipe because of friction is related to the square of the velocity u2 = m2/A2 using friction coefficients and single loss resistance factors. AT Tjlj £n Aa P=^7 (81) v [k * A? k where the liquid density p' and flow rate mmay are taken constant. The pipe is divided into I uniform parts parts described by their cross section A;, friction factor n, length Z, and hydraulic radius of d;14. Pressure loss at the inlet, outlet, pipe bendings et cetera is described as N single losses with the resistance factor £n. The resistance factors t* and £n may be found in literature, eg Engelund & Bo Pedersen (1978, p. 300). If the material remained in liquid phase, the relevant pressure drop Ap is the difference between the tank and environment - including hydrostatic pressure because of the weight of liquid. The source strength m is then derived to

2p'Ap m = (82) N 23j=i + £n=i % However if the pressure approaches the vapour pressure, a phase transition will take place leading to a two-phase flow with variable density. Two-phase flow is examined below after the description of pure gas flow.

Gas phase outflow

The velocity in a compressible gas flow also depends on the specific volume 1/p and increases with decreasing pressure, so the flow must accelerate to keep the mass flow rate constant. This type of flow is also a standard problem - see Schmidt (1949). In order to demonstrate the critical or choked flow phenomenon we consider an adiabatic frictionless flow of an ideal gas with initial tank pressure p 0, density p 0, temperature T0 but negligible initial velocity u0 ~ 0. For an adiabatic expansion of ideal gas the relationship between pressure and density is:

Pip) = Po ■ (83) where 7 = cp /cv. This equation is applied in a very simple flow equation relating acceleration to the pressure gradient.

, . du dp 2j po I

— 1- <§. (84) 1 dx \ 1 \P°)

Now the mass flux m/A0 = up can be related to the pressure.

(85)

l4The hydraulic radius is the area of a cross section divided by the wall perimeter, ie 1 of the diameter in a circular pipe.

Ris0-R-1O3O(EN) 47 Sometimes a maximum mass flow rate exists as seen by differentiation of m/A0 critical flow with respect to p/p0.

Further pressure reduction will not increase the flow rate and the flow is said to be critical or choked. In this state the velocity reaches the speed of sound, and pressure disturbances or information of the downstream conditions can not travel upstream. If the atmospheric pressure is higher than pcr the flow does not reach the critical state and the release rate is just determined by insertion of the atmospheric pressure in equation 85. If the pressure at outlet p Q is higher than the ambient pressure p a\T, the pressure flow force difference p 0 — Pair gives an extra contribution to the flow force Fjet of the jet outflow. m2 Fjet — p0U0 -Ao 4" (Po Pair) * Aq "vv - Fjet — ~Z h (Po Pair) * Aq (87) PqAo The flow expands just outside the outlet where the pressure reduces to the am­ bient level and this accelerates the flow and increases the jet momentum. From a momentum balance it can be shown that the flow force remains constant if the jet is clear of boundaries, so the flow force of the release F}et is equal to the jet momentum after expansion. The expansion of the gas affects the temperature and density. For an adiabatic exit temperature expansion the temperature is found from the relationship

but if a flow of limited duration passes through a long pipe heat transfer from the pipe may moderate this temperature depression. For an accurate analysis the friction forces and sometimes also the heat exchange should be included in the equations.

Psat(^l)

Figure 26. Sketch of the pressure reduction in an outflow from a pressurized storage containing liquified gas.

Two-phase outflow

Figure 26 is a sketch of an outflow from a storage of liquified gas through a horizontal pipe. In the first section the flow is in the liquid phase, but because of friction forces the pressure gradually decreases until it reaches the vapour pressure

48 Ris0-R-1O3O(EN) Psatpi) where the liquid starts boiling. The formation of a gas phase expands the fluid, and with a constant mass flow rate m the flow must accelerate. This relationship between pressure and density implies that the flow may reach a critical or choked state just as in the case of homogeneous gas flow. The problem is greatly simplified by the following assumptions:

- no velocity slip between the phases

- no heat exchange with the flow boundaries

- flow in steady state

- homogeneous equilibrium between phases

The velocity slip can be ignored as long as most of the material is in the liquid phase and the vapour bubbles are fine. The heat exchange becomes important for long pipes or large temperature differences, but if the flow is allowed to continue for some time, the pipe temperature will approach the temperature of the fluid. If the pipe is non-horizontal or if the geometry encourages resonance, there is a change that the flow becomes unsteady. Nyren & Winter (1987) measured pressure and temperature in a release of liquified ammonia through a pipe and concluded that the homogeneous equilibrium did develop in the field experiment, but not in a small-scale laboratory test. When the pipe in the field test was exchanged with an aperture, the flow rate increased significantly because the boiling was delayed until the flow had passed the narrow exit, ie the flow was not in thermodynamic equilibrium at the exit. If a liquified gas container is punctured directly on its side, the mass flow should be calculated from equation 81 using the full pressure head between the storage and atmosphere. A simple model was presented by Nielsen (1991). In this model the developing a two-phase flow model two phase flow is described by the one-dimensional flow equation:

du dp rpu 2 dp , , pu • — = pdp + (89) dx dx 2d where r is a friction factor and d is the hydraulic radius. This is integrated from location xi to location (*y —-’g* (90) W -21n(«f)+/.B5a where pressures pi and P2 and densities pi and p 2 correspond to the locations xi and X2 respectively. The two phases are assumed to be in homogeneous equilib­ rium, and the pressure is related to temperature T by Clapeyron ’s equation dp (91) 8T where p' and p" are the liquid and gas-phase densities, M is the molar number and L is the latent heat. In chapter 9 the mixture density will be found to be 1 1 — a V M (92) P RT Here R is the universal gas constant and the liquid mass fraction a is found from an enthalpy budget

Lda = — (c" - a • Acp) dT (93)

Ris0-R-1O3O(EN) 49 in which Acp is the difference between the heat capacity in the two phases c" — c'p . The two-phase flow equation may then be written as a function of temperature T. -2S%p{T)$dT (94) r-(x2-aQ

The integration starts at temperature T\ and ends at temperature T2, which is either the ambient pressure or the temperature of the choking point. The mass flux raj A is calculated for a range of temperatures T2, and if a maximum mass flux exists with a saturation pressure Psatpa) > Pair, this is identified as the choked flow solution. The pressure difference in the initial liquid flow is described by equation 81 which may be written

(m\- 2p'(p 0 — Psat(Ti)) W T+& where £n is the resistance factors related to pressure drop at the pipe inlet. The final equation in Nielsen (1991) is derived from a combination of equations 81 and 95 and with the assumptions that T\ — To, the friction factor r is approx­ imately equal for the two flow regimes and that the distance 3% is equal to the total length of pipe L. 2p' (Po - PsatCTo)) ~ 2 jg p(T)$dT (96) -2l-ti9) + T + i. It is noted that only the flow conditions upstream of the choking point determine the flow rate and that the pressure drop at the pipe outlet is not included in the formula. The model has been validated with data from experiments with superheated water and the accuracy was found to be within 10%. Normally the pressure in the gas-phase of a tank will be the saturation pressure, tank pressure and the pressure at the inlet to the pipe in figure 26 is therefore po = Psat (T0) + p'hg. However Nyren & Winter (1987) noted that the pressure in the 1400 kg release tank exceeded the saturation pressure for quite some time after each tank fill. Apart from being an experimental complication, this piece of information is also relevant for risk assessment, ie one might consider the possibility that the security valve is out of order during filling and that for some reason the operator fails to respond to the high pressure. The jet flow force is calculated as in equation 87,

l*jet — "k (PsatfTa) Pair) ‘ A (97) where p 0 and p 0 refer to the exit conditions, ie the choking point.

Flashing jet

The boiling is completed outside the pipe, where the jet is allowed to expand and the pressure soon reaches the atmospheric level in a so-called flash boiling. At this stage the equilibrium temperature is equal to the atmospheric boiling point, but it may be realized that it will drop even further as the air is entrained. For simplicity we shall only consider pure aerosols without condensed water from the air. If these liquid aerosols are in homogeneous equilibrium with the surrounding gas, the temperature matches the saturation pressure psat(T). The

50 Ris0-R-1O3O(EN) partial pressure is therefore linked to the concentration c and the degree of con­ densation a by Psat(r) _ c • (1 - a) (gg) p 1 - c-a When the last aerosol evaporates (a = 0) and some air is entrained (c < 1), the equilibrium saturation pressure will be lower than 1 atm, ie Tm\n is less than the atmospheric boiling point. Figure 27 shows a numerical simulation of a flashing jet using the GReAT model (Ott 1990). The calculation is started after flash boiling and the temperature is seen to decrease from the boiling point until the last aerosol is evaporated. It is possible to write an expression for the minimum temperature Tm-m from an enthalpy balance in a flashing jet (Tair-Tmi„)-[Ma!rcf + c-(Mcp-Ma;rcf)]+c-ffo = 0 => (99)

PsatC^min) ______(^air ~ Tmin) ' Ma\TCp'r______

P —Hq — (Tajr — Tm;n) • (MCp — MairC®lr) where Hq is the difference between the contaminant enthalpy in the storage and the enthalpy at atmospheric conditions. The concentration is equal to the pressure ratio pSat(T)/p. In chapter 9 the release enthalpy for a flashing material will be estimated by Ho « M ■ [-L + c'p (T0 - Tboii) - c"(Tair - Tboi,)] (100) which is very close to the heat of evaporation —ML. Table 4 is calculated from equation 99 using the thermodynamic properties from appendix I with the condi­ tions T0 = Tair=15°C and pair=l atm. The calculated minimum temperatures in table 4 are seen to be considerably lower than the boiling point temperature and this is important, eg if personnel approach the jet in an attempt to mitigate the release. Some of the aerosols in a two-phase jet may deposit on nearby surfaces, eg when rain out the jet hits an obstacle or in case the aerosols are so large that fall velocity is significant. The liquid rain out affects the subsequent dispersion because it mod­ erates the effective release rate and changes the enthalpy of the released material. Suppose that the mass fraction which leaves the jet is /ra;n and that the typical temperature of these aerosols is Trajn. The separated aerosols will then provide a heat input Mc'p (T0 — Tra*„), and the enthalpy change AUrain of the remaining part of the release is

Atfrain = 1 Mc'p (T0 - Train) (101) 1 /rain where c'p is the heat capacity of the contaminant in the liquid phase.

Pool evaporation

If the temperature of a liquid spill is below the atmospheric boiling point, the released material will form a pool on the ground. The mass balance for the sub­ sequent evaporation can be written in terms of fluxes per surface area %.

^source — (/sink — (/evap "h (/storage (102) where

(/source = liquid supply from the leakage (/evap = evaporation to the atmosphere %ink = loss by processes other than evaporation (/storage = accumulation in pool

Ris0-R-lO3O (EN) 51 Table 4■ Boiling point and minimum temperature in a two-phase flashing jet as­ suming adiabatic mixing and homogeneous equilibrium. The atmospheric condi­ tions are set to 6atr=15°C and p=l atm. Substance gboil ymin Ethylene C2H4 169 K 160 K Ethane c2h6 184 K 167 K Propylene c3h6 225 K 195 K Propane C3Hg 231 K 199 K Butadiene c4h6 269 K 220 K i-Butane iC4H10 263 K 218 K n-Butane nC4Hio 272 K 222 K Ammonia nh3 240 K 203 K Hydrogen Sulfide h2s 211 K 183 K Hydrogen Chloride HC1 189 K 167 K Sulphur Dioxide S02 263 K 217 K Chlorine Cl2 239 K 200 K

Flashing NH3 jet temperature

772=108 kg/s

<$> u=5 m/s

Axial position x [m]

Figure 27. Temperatures in a flashing jet calculated by the GReAT model. The release conditions are equal to those of the Desert Tortoise experiments, release number four (see chapter 12).

The liquid supply g source is the outflow from the liquified gas containment and the loss term q Sink accounts for possible soil infiltration or surface run-off. The evaporation qevaP is the source term for the gas dispersion. The model of Mikesell, Buckland, Diaz & Kives (1991) generalized the problem to evaporation of a multi-component liquid with a mass balance for the individual components. In multi-component mixtures the most volatile liquid will evaporate first and if the liquid is well mixed, the composition will change during evaporation. The condensation of air humidity on the cold pool surface is also considered and this gives an extra heat contribution for the evaporation. The saturation pressure for the individual components depends on the liquid composition, so the source

52 Ris0-R-1O3O(EN) strength will change during the process. The evaporation mass flux g evap requires the heat input

yevap — I* ' 9evap (103) where L is the heat of evaporation. The available heat tpevap is determined from an enthalpy budget including the following terms tpi

V^short H" yiong "h ^sensible H" conduct d* ^source %ink = Pevap d* (^storage (104) where y>short = net short-wave radiation received V’long = net long-wave radiation received ^sensible = heat contribution from the air above the pool ^conduct = conduction from the surface below the pool ^source = heat contribution from the source y?sink = heat loss because of removal by other processes than evaporation tfievap = heat consumed by evaporation ^storage = accumulation because of changing temperature

Quite a lot of parameters are involved in these processes and in practice it is advisable to select a model which has been developed for conditions similar to that of the application, and which has been validated by experimental data. Concerning the individual heat contributions:

- the short-wave radiation ^hort depends on the solar angle, cloud cover, re­ flection from the pool surface and shelter from nearby obstacles;

- the long-wave radiation terms y>i ong depend on the temperature of the emit­ ting objects, ie atmosphere, clouds and pool surface. The long-wave radia­ tions may be modelled by Stefan-Boltzmann radiation law cp oc 0T4 with suitable coefficients for emission, absorption, transmission and reflection. If the long-wave radiation from the sky is unknown, it can be parametrized by air temperature, air humidity and cloud cover;

- the sensible heat flux Sensible is the turbulent transport of heat from the air to the pool. The low pool temperatures resulting from liquified gases may be quite low so this boundary layer can be strongly stratified. This term will be discussed below; - the terms Source and v’sink depend on the temperature of mass fluxes ^source and <7si„k, which may differ; - as a first estimate, the conduction from the underlying surface Conduct can be considered as the ordinary heat conduction problem from a semi-solid similar to the calculations in chapter 7. However Drake & Reid (1975) discussed experiments with cryogenic pools on soils and emphasized the importance of liquid percolation into the soil. When the cryogenic liquid penetrates the soil and boils below the surface, the heat transfer become more efficient than estimated by the semi-solid theory, but the time development still followed the £~2 dependence. If the soil is moist, an additional heat input is obtained from freezing, but on the other hand the ice might stop percolation. Pools spilled on water is a special problem. Because of turbulent and heat convective motions in the water volume the heat supply from below becomes much more efficient. In literature there has been some speculation as to whether a cryogenic pool could freeze the water to an isolating ice layer. Waite, Whitehouse, Winn & Wakeham (1983) explain that an isolating vapour film could form under the cryogenic liquid during very vigorous evaporation. It is convenient to use

Ris0-R-1O3O(EN) 53 the pool surface temperature to characterize the evaporation, but this may be slightly different from the bulk of the liquid. MacKay & Matsugu (1973) introduced a bulk resistance factor for heat flux from the soil to the liquid surface (where the heat is consumed by evaporation) including the internal heat transfer in the pool;

- it is convenient to neglect pool enthalpy changes Storage j ie to regard the problem as quasi-stationary. Which term is then the dominating one? Well, if a cryogenic liquid such as liquified natural gas is poured on the ground, the temperature will be at the boiling point or lower and the conduction from the soil ^conduct will dominate all the other heat fluxes. For releases on land the time dependence of heat conduction Conduct will be t~i, and the other heat contributions will gradually become significant. At a later stage the heat available for evaporation y> evap is reduced and the pool is no longer boiling. With a weaker source strength the concentration in the boundary layer above the pool is reduced, and with similar arguments as in the discussion of the flash boiling jet, the temperature of the pool is expected to be beyond the boiling point. The incoming radiation terms and the source enthalpy are external conditions, whereas the radiation away from the pool, the conduction from below and the enthalpy of the removed material y> s,nk are functions of the pool temperature fpsur)- The two remaining fluxes in the enthalpy budget Sensible and yWp (equal to qevap/L ) are related to the turbulent mixing in the boundary layer above the pool, and the mixing efficiencies in the boundary layer mainly depend on the wind speed. The sensible heat flux Sensible and (p svap can be parametrized in terms of the surface temperature and surface concentration, and the surface concentration is related to temperature through the vapour pressure xPsur) = Psat (Tsur)/p. The method of most evaporation models is therefore to solve equation 104 for the pool surface temperature Tsur. The mixing of momentum, heat and contaminant in the boundary layer above pool boundary layer the pool are turbulent processes which may be described by:

T —pu'w'

(105)

where Sensible is positive in the downward direction from the air to the pool, not following the usual meteorological convention. It is tempting to assume that the pool boundary layer can be described by surface-layer theory and in this way develop exchange coefficients similar to those inside a dense gas cloud discussed by Jensen (1981a) and in chapter 4.

^sensible — pCp ' Ch * W • (T 2"sur) (106) tfevap — -Pjfc; ' Ce • U ■ (c — x(T sur))

The Monin-Obukhov profiles in the boundary above the pool are:

= IT • [ln t ~ ^ (f)] T(z) — Tsur (107) cp) - xPsur) = IT ' [in ^7 - V’c (f)] where the exchange processes are modelled by suitable roughness lengths zq, Zok and zqc as discussed in appendix G. The buoyancy flux depends on both heat flux

54 Ris0-R-1O3O(EN) and evaporation and the stability parameter z/L becomes

z _ nzgp'w 1 _ Kzg / AMdw' T'w'\ L ~ pu% u% V Mnix T ) (108) leading to

£ AM(c-x(T.Yr))gz fln^-^m(f)]2 L Mmix -u2 ln 75r~v,c(t) (109) (T-T.ar)gz [ln ^-^m(r)]2 T-u This is solved for the stability parameter z/L, and the two transfer coefficients c* and ce are found from ______Ch = [ln^-^m(t)j [ln^_^h(t)j ^11Qj

Ce — [in )j [in ^-^c(t)]

The parametrization in equation 110 is convenient for the determination of the pool surface temperature Tsur, but there are a few remaining problems. First, the pool boundary layer is growing and the steepness of concentration and temperature gradients decreases in the downwind direction. Secondly, the roughness parameters zo, zoh and zqc must be determined in some way. In the case of a very weak wind the surface could be smooth with a viscous sub-layer, but in most cases ripples on the pool surface would make it rough. Brutsaert (1982) reviewed z^/zq and Zcq /zq results for both smooth and rough surfaces. When the liquid is boiling, the surface ejects aerosols into the air, and this enhances the surface exchange process and affects zq/, and zqc. Both Kawamura & Mackay (1987) and Mikesell et al. (1991) use the semi- empirical mixing empirical parametrization of the turbulent fluxes averaged over the pool area found in MacKay & Matsugu (1973)

^sensible = 0.029 u^^r 0'^Pr °-67 •/9Cp(T air - To) (111) <7evap = 0.029 ufJ*r-0-uSc-0-67 ■ p-$rx(Tsur) where uiom is the wind velocity at the 10 m level (in [m/hr]), r is the pool diameter or downwind length of the pool (in [m]), Pr is Prandtl number in air and Sc is the contaminant Schmidt number. The exponents for the wind speed and pool diameter account for the effect of the growing boundary layer. The values were originally deducted by Sutton (1934) who made an analytical solution to the diffusion equation dc u (112) dx for the concentration c(x, z) in an ordinary boundary layer above the pool using power law approximations for profiles of velocity u{z) and mixing diffusivity K(z), with the fixed surface concentration c(x, 0) = x(Tsur) as the boundary condition - see appendix G. The total flux is equal to the transport g evapr = f£°ucdz at the downstream edge of the evaporating surface. Use of this solution implies that - the surface roughness change from the upstream surface to the smooth pool is neglected;

the inertia of the evaporated material is neglected, i.e only modest concen­ trations are considered;

Ris0-R-1O3O(EN) 55 - the buoyancy of the evaporating material is considered not to affect the sta­ bility of the pool boundary layer. These assumptions will probably not be valid over a large cold pool so equation 111 could be a crude estimate. Brighton (1985) used a more refined approach fitting a suitable power-law to the actual logarithmic wind profile rather than using a fixed 1/7 exponent and chosed the mixing diffusivity to be linear. Brighton (1985) also derived a correction for inertia of the evaporated material important for high vapour pressures and discuss the effect of turbulence reduction by density stratification. The maximum pool temperature is the boiling point = Tboii and the min­ pool temperature range imum pool surface temperature T™‘n is obtained when the sensible heat Sensible is the only contribution. In this situation the enthalpy budget for the boundary layer above the pool is simplified to c • M ■ L = (1 - c) • /Ta'r Mair • cfdt » (1 - c). Maircf • (Tair - 2%") (113)

The molar concentration c is equal to the vapour pressure divided by the total pressure so the surface temperature is p sat(TZn) ML (114) p - Psat(Ts™n) MairCair which can be solved for inserting the vapour pressure curve pSat(T) from appendix E. This is seen to be a little lower than the minimum temperature of the flashing jet in equation 99, which also had a contribution from cooling of the liquid material equivalent to ^source- With a pool colder than the surroundings the net radiation yshort+^iong and the conduction from the lower surface ^conduct are positive, so the pool temperature will normally be in the range T%" < Tsur < T* max ^sur * If the heat contribution from the soil is of the form (^conduct = y>o -t~5, the source spreading cryogenic pool strength would be infinite just after pool formation. However Jensen (1983) points out that the pool needs some time to cover the surface, and this limits the overall source strength. The area integrated evaporation is

when the heat supply from the soil is the dominating contribution and the local local exposure times are taken into account. If the heat supply tp(t) and the growing pool area A(t) are written as power laws tp(t) - -

A(t) = A0-tn (116) the integral in equation 115 can be written m{t) = ^2 . tm+n • f1 sm(l - s)n—1ds

■b JO

_ <£oAo m+„ r(m + l)r(n) L r(m + n + l) { >

In conclusion the power of the integral source strength is the sum of powers for the local source strength and pool spreading m + n. Heat conduction in a semi-solid was considered in chapter 7. For constant surface temperature the heat flux at the top of the semi-solid in equation 65 is simplified to

^soilPsoilCsoil

56 Ris0-R-1O3O(EN) Using the typical values of soil properties Ason, Psoil and Cs0ii chosen in chapter 7 and a temperature difference of AT =50 K, the constant surface tension. In the initial phase the dominating retarding force is inertia, and Britter (1979) provides simple power laws for different release geometries.

1.5 (g'V/by/H 2/3 Instantaneous 2-D 1.1 {g'V/bflH Continuous 2-D A(f) to < (119) 7.5 {g'Vf/H Instantaneous axisymmetric 2.2g'V)1lH3l2 Continuous axisymmetric

The constant for the continuous 2-D case is not experimentally verified, but estimated from the formula in Britter (1979) using the front Froude number F tj = 1.1. Effects of evaporation, percolation, sloping surface or roughness are not taken into account, and the formulae are only valid when the contaminant is in initial phase. From equation 117 the approximate source strengths are found to:

3.9 ipo/Ug'V/by/H 1/6 Instantaneous 2-D 2.2y>o/Z(0 ,y/6)W/2 Continuous 2-D rh(t) to < (120) lSpo/Lfo'IOW/ 2 Instantaneous axisymmetric 3.5¥>0/£(9'U)1/2* Continuous axisymmetric

The main point is that the overall source strength does not follow the t~i power law of local heat conduction but continues to increase as long as the pool is spreading. When the pool has reached its full size, it decreases with m oc t". The methods to mitigate the emission from an evaporating pool are to cover mitigation methods the pool, to reduce the surface area and to reduce the heat input. The ideal con­ tainment basin placed under a liquid storage should be constructed by a material which has a low thermal diffusivity and which is not porous. An isolating con­ crete could reduce y>o and m to | of the value for ordinary concrete (Drake & Reid 1975), and a foam could be sprayed over the pool in order to reduce the sensible heat flux (McRae, Cederwall, Ermak, H. C. Goldwire, Hippie, Johnson, Koopman, McClure & Morris 1987). However in the initial phases of pool evapo­ ration most of the heat contribution comes from the ground below and the foam cover has little effect in case of a boiling pool. Since contains a lot of heat, it should in no circumstances be added to a cryogenic pool.

Instantaneous release of superheated liquid

When a liquified gas container is seriously damaged, the pressure drop is felt almost instantaneously everywhere in the liquid. The material will then start to boil in the entire volume, and the two-phase mixture will expand in an almost explosive manner. The model of Hardee & Lee (1975) assumes that the expansion is isentropic and without energy transfer from the surroundings, and two conservation equations for entropy and energy are applied:

a • S'(p sat(T),T) + (a - 1) • 5"(psat(T),T) = S0 (121) a . H'(p Szt(T),T) + (a - 1) • H"(p s&i{T),T) + ±Mu2 = H0 (122)

Ris0-R-1O3O(EN) 57 where a is the liquid mass fraction, M is the molar weight, u is a typical velocity for the expanding cloud, 50 and H0 are the initial entropy and enthalpy in the container, S' and H' are entropy and enthalpy for the aerosol part of the mixture and S" and H" are entropy and enthalpy for the gas phase. For common substances tables of S', S", H', H" are found in literature, eg in Vargaftik (1975). With an assumption of homogeneous equilibrium, the pressure is considered to be the vapor pressure psat(T). This system is then applied to find the bulk expansion velocity u. The flash boiling continues until the pressure has reached ambient pressure, and the authors use the velocity at the end of the expansion to model the subsequent entrainment. Webber, Tickle, Wren & Kukkonen (1992) discuss a recent laboratory experi­ ment with instantaneous releases of pressurized freon from glass spheres performed by the UK Health and Safety Executive. It seems that models of the type above overestimate the expansion velocity. The dispersion just after the flash expansion is complex, but it only takes a few seconds. In the Heavypuff model for instantaneous dense gas releases (Nielsen & Ott 1988) the default initial condition is the stage where all aerosols have evapo­ rated and the air entrainment is sufficient to raise the temperature to the boiling point. A user may choose to adjust either the initial temperature or the initial concentration, but the enthalpy of the mixture will be conserved. Actually this enthalpy conservation is in conflict with equation 122, but it should be sufficiently accurate for a calculation of the release temperature and density.

9 Cloud density

The density difference between cloud and ambient air is the key parameter in dense introduction gas dynamics. This difference drives the gravitational spreading and reduces the vertical mixing. The relation between gas concentration and density is affected by the source type, and the temperature depression caused by initial evaporation is often more important than the molar weight of the contaminant. A good example is a release of liquefied ammonia: if the ammonia aerosols evaporate before de­ positing, the heat required for the phase transition will reduce the temperature so much that the cloud mixture becomes denser than the ambient air, even though the molar weight of ammonia is lower than that of air. Gases used in industry are often stored and transported in liquid form at high pressure and/or low temperature. The advantage of this design is a smaller con­ tainer volume, but the density of an accidental release will be amplified and this increases the hazard. The density calculation is first considered for isothermal homogeneous gas-phase chapter summary mixtures and then for more complex cases with phase transitions and chemical reactions. The purpose is both to show how density calculations are incorporated in numerical models, such as the box models in chapter 2, and to provide a theory for analysis of field data. The effective molar weight Mer is suggested as the appropriate molar weight for isothermal wind-tunnel simulations of non-isothermal adiabatic gas releases - although it provides an inaccurate density model for the two-phase flow near the source. This is not always a problem since initial source momentum often dominates near-source dispersion and in a not too humid atmosphere the liquid aerosols often evaporate within a short distance. Comparisons with an advanced phase transition model does on the other hand lead to a severe warning against isothermal wind-tunnel modelling of field experiments in humid conditions. The reference model is a binary ammonia/water phase-transition model capable of sim­

58 Ris0-R-1O3O(EN) ulating the extra aerosol formation caused by the hygroscopic effect of ammonia. It is concluded that in most practical applications the hygroscopic water/ammonia model could be substituted by a more general and computationally simpler pure water vapour condensation model. Heat flux from the ground to a cold gas cloud increases the total cloud enthalpy and thereby reduces the density difference. The heat-flux effect on density cannot be described independent of the dispersion process and it is therefore illustrated by a simplistic box model. The model predicts the heat-flux effect on density to be most significant in case of weak ambient wind. Initial dilution close to the source decreases the cloud temperature deficit before ground contact and tends to reduce subsequent heat transfer. Similar enthalpy budgets will be applied in chapters 11 to 12 where selected field experiments are shown to have been non-adiabatic. The possible effects of chemical reactions are two-fold: they may release heat and alter the total number of molecules and average molar weight. This is illustrated by an example taken from Raj & Morris (1987). The last section illustrates how generic release scenarios defined in the previous chapter influence Meg through their variable initial enthalpy deficit for a range of compounds. The largest density effect is produced by a flashing jet with no aerosol rainout.

Gas-phase mixtures

The ideal gas law is a good approximation at the moderate pressures in the at­ mosphere and the mixture density is therefore / (123) where

p is the pressure R is the universal gas constant = 8.314 K.^ol - T is absolute temperature of the mixture Mi is the molar weight of component i The concentration (ie the mole fraction xi) of each component i is defined by

Xi = (124) in which m is the number of moles of component i. Dry air is considered as a uniform compound with density

Pair — (125) ETai The pressures inside and outside the gas cloud are almost identical, and with use of equations 123 and 125 the relative density deficit becomes

Ap _ Tair • )Ct=l xiMj (126) Pair T " -Mair where Ap = p — pair.

Dry isothermal mixing

The density of an isothermal gas release is simply A p A M ----- = C • —— (isothermal mixing) (127) Pair Man

Ris0-R-1O3O(EN) 59 where AM = M — Mair is the molar weight difference and c is the gas concentra­ tion. The case of isothermal mixing is relevant to many wind-tunnel simulations of dense gas dispersion. In an ideal gas molar concentration is identical to the concentration by volume, so

jt {cV) = 0 (128) and therefore the cloud bouancy ApV is a conserved property for isothermal gas buoyancy conservation releases. Dry isothermal releases of high molar weight gases are often applied in wind tunnel experiments. This is a convenient choice because it is virtually impossible simultaneously to obtain correct scaling of heavy gas effects and con­ vective ground heat flux (Britter 1987). Furthermore the often used aspirated hot wire probes (eg Hall, Waters, Marsland, Upton & Emmott 1991, Oort & Builtjes 1991, Konig 1987, Billeter 1995) respond to temperature differences.

Dry adiabatic mixing The density calculation of a homogeneous gas mixture with no heat input other than mixing, no chemical reactions and no aerosol formation is relatively simple. In general the heat capacities Cp will be functions of temperature, but as a first ap­ proximation they may be taken as constant. With these assumptions the enthalpy budget of the mixture becomes

AH (T - Ta!r) • [(1 - c) • Maircf + c • Mcp] = c ■ AH0 (129) where the molar gas concentration c and the air concentration (1 — c) are used instead of the mole fractions and AHq enthalpy difference between the release material at source and ambient conditions. The advantage of using enthalphy differences instead of absolute values is that the contribution from the entrained air is zero by definition. The enthalpy budget is used to derive the cloud temperature T

C • AHq T Tair + (1 - c) • MairC^ir + C • MCp

C • AHq 1 + (130) ((1 - c) • Maircj“r + c • Mcp) ■ Tai The relative density deficit given in equation 126 is then

A M Ap 1 + c • M»ir c-AHo -1 (131) Pair 1 + ((1 —c)-MairC"ir+C-MCp)-Tair

As noted by Webber (1983), the unlinear relationship between density and con­ centration implies that the cloud buoyancy ApV is not a conserved property for non-isothermal releases. However in most cases the gas will dilute c«l already within a short distance from the source, and we linearize the expression to Ap r am AJJp \ (dry adiabatic mixing) (132) Pair lMair Maircg irTair / In this linearized version the effect of enthalpy is equivalent to excess molar weight, effective molar weight M» and we may define an effective molar weight M, = M- AHo/c™T &iT (133) where AHq usually is negative. In the case of dry adiabatic mixing, M* would be the relevant molar weight of a model gas in isothermal wind-tunnel simulations of a non-isothermal release. The effective molar weight M* will be used as a simple diagnostic tool throughout this report.

60 Ris0-R-1O3O(EN) Two-phase mixtures

Entrainment of moist air and cloud temperature below the dew point will produce liquid aerosols. The density of a two-phase mixture is calculated by the specific volume which then is the sum of specific volume of the two phases. 1 a 1 — a p~7 + ~ where

a is the liquid mass fraction p' is the density of the liquid phase p" is the density of the gas phase

In search of the main effect of condensation we insert the ideal gas law and obtain a crude estimate

1 V ELi XjMj 1 V ZL XjMj (135) 1 - a • (1 - p"/p') RT 1 — a RT where A'; are vapour phase concentrations. In atmospheric conditions the liquid phase is much denser than the gas phase, so we may neglect factor 1 — p"/p', except when the liquid fraction a is close to unity. An increase of the liquid mass fraction tends to increase the density, but this is counteracted by the temperature increase because of heat of condensation. The density change dp by condensation is approximately

da dT' dp ~ + lwdT ~ p ' (136) 1 — a T

The temperature change is related to evaporation so Mm\x c™tx dT to MLda where L is heat of evaporation (either for the contaminant or water depending on aerosol composition) and Mmixe™lx is the average heat capacity of the mixture. For diluted mixtures in humid air the vapour phase consists mainly of air and the liquid phase consists mainly of water. This leads to

Mn2oLn 2o to —3.8 p (137) M^dpT Thus aerosol formation results in a density reduction.

Table 5. Cloud composition before and after aerosol formation. aH2o and agas are the degrees of condensation for water vapour and contaminant.

Before condensation At equilibrium

Vapour Gas c (1 - Qfgas) • c H20 q • (i - c) (1 - <* h2o) • q • (1 - c) Dry air (1 - q)1 (1 - c) (1 - q) • (1 - c) Total 1 1 — ctgas • c — aH2o • q • (1 — c) Aerosol Gas 0 ttgas " c H20 0 c* h2o • q ■ (l - c) Total 0 Qigas • C + aH2o • q • (1 — c)

Wet adiabatic mixing

An accurate density calculation must be based on the exact composition of the two phases, eg on the mole budget shown in table 5. The released gas is mixed

Ris0-R-1O3O(EN) 61 with humid air, and the liquid phase consists of both water and contaminant, c is the gas concentration before aerosol formation, q is the absolute humidity of the entrained air, and aH2o and agas are the degrees of condensation of water and contaminant. With this notation the total liquid fraction is

a = agasc + aH20g(l - c) (138) and the vapour concentrations are A'gas = 1 agase and XH 0 = 1 aH2°g(l - c) (139) 1 — a I — a These concentrations determine the average molar weight of the gas phase which has the density

P [«TgasM + X h20MH2o 4~ (1 —

Psat (T) X h2o — for aH2o > o (141) Pair for water vapour as well as for the contaminant. For pure aerosols, eg in case of immiscible liquids, the saturation vapour pressure curves psat will be functions of temperature only. Vapour pressures over binary aerosols depend on the liquid com­ position as discussed in appendix E. The validity of the homogeneous equilibrium assumption between the two phases has been debated (Kukkonen & Vesala 1991) homogeneous equilibrium because the aerosols are not in equillibrium during the mixing process. The dif­ assumption ference in temperature and vapour pressure could be substantial across the lami- nary boundary layer surrounding each aerosol. Lately Kukkonen, Kulmala, Nikmo, Vesala, Webber & Wren (1994) compared predictions of the AERCLOUD model for binary NH3/H2O aerosols ventilated by their fall velocities to homogeneous equilibrium predictions of the DRIFT model. The conclusion was that the ho­ mogeneous equilibrium assumption gives reasonably accurate results for aerosol diameteres less than 100 pm. This condition is usually met in two-phase jets from pressure liquefied containers, whereas emissions from semi-refrigerated storages may produce aerosol which are too large for the assumption. The enthalpy budget for wet adiabatic mixing includes a contribution AHcon from the heat of condensation. A H ,------A------\ (adiabatic mixing) (T — Ta-,r) • [(1 — c) • MairCpir + c- MCp] + A-ffcon = c ■ AH0 (142)

It may be argued that the kinetic energy of a flash boiling jet release should be included in this but estimating the maximum velocity to 100 m/s, the maximum kinetic energy is only 5 kJ/kg, ie small compared to the O (500) kJ/kg heat of evap­ oration for the chemical substances listed in appendix I. The heat of condensation Alien amounts to

Aficon — Olgas cAii'gas 4* (%H2og(l c)A4h2qZ/h2q 4" OtAHm\x (143) where Lgas and LH2o are latent heats and AHm-IX accounts for heat released after mixing in the liquid phase. The degree(s) of condensation and the mixture temper­ atures is/are found from the saturation vapour pressure curve(s) in combination with the enthalpy budget. In practice the iteration will apply a linearization of these equations. Webber, Tickle, Wren & Kukkonen (1992) formulated a range of phase-transition models which were later implemented as interchangable modules in the DRIFT

62 Ris0-R-1O3O(EN) M* approximation H20 aerosols Immiscible aerosols Hygroscopic aerosols

Fladis 9 (Ammonia) T . =16 °C and R.H.=86%

i i i i m

Mixture Concentration, c [mole%]

Figure 28. Density difference of a two-phase mixture of ammonia and humid air as a function of concentration. The four models are simply the M* approxima­ tion, pure water aerosols, immiscible aerosols and Wheatley’s (1987) hygroscopic ammonia phase-transition model. dense gas dispersion model (Webber, Jones, Tickle & Wren 1992), see also ap­ pendix E. Figure 28 is a comparison of the M* approximation and some phase transition models for ammonia. The mixing is assumed to be adiabatic and the release parameters are taken from the most humid case of the ammonia field exper­ iments described in appendix B. Wheatley ’s (1987) model (solid line) is believed to be the most accurate one, since it includes the hygroscopic effect of ammonia. This solution may be divided into three domains: dry mixing, nearly pure wa­ ter aerosols and nearly pure ammonia aerosols. Experimentation with the model input shows that the moisture affects the aerosol formation in'two ways: the rela­ tive humidity determines the limit of transition between the dry and wet mixing, while the absolute humidity (depending on air temperature) determines the mag­ nitude of deviation from dry mixing. The immiscible aerosol model (dashed line) is doing surprisingly well with just a slight overprediction of the density in the domain of almost pure water aerosols. Most dense gas sources are associated with some initial dilution, and the initial domain of almost pure ammonium aerosols is unimportant for dense gas dispersion. Therefore the relatively simple pure wa­ ter condensation model (thin line) will probably be adequate for most heavy-gas dispersion models. The M» approximation (dotted line) describes the domain of dry mixing quite well, but with a deviation of up to 78% in the domain of almost pure water aerosols. The test scenario is however a demanding one, partly because of the high relative humidity and partly because of the large heat of evaporation and low molar weigh of ammonia. The simple M* approximation will be more succesful in other release conditions.

Cloud visibility

Severe accidents are often followed by a consequence report, and for this purpose it would be useful to correlate the outline of the visible cloud from photographs or

Ris0-R-1O3O(EN) 63 eyewitness reports to approximate concentrations. The visible cloud corresponds to the limit of condensation, which is quite sensitive to air humidity. If the main aerosol component is water, the visible concentration level CviS may be estimated by dew point temperature Tdew (see appendix E).

AH0 MiirCplr • (Tair — Tdew) Tair — Tde —c • Cyjs ^5 (144) Mairc2!r A~H0

The difference between dew point and actual temperature varies with more than a decade, so knowledge of the air humidity is essential for the interpretation of visual information. This illustrates the dense-gas - fair light and blue sky for contrast are usually correlated with unimpressive gas clouds. Table 6 shows examples of visible concentration limits for two source types and variable humidity.

Table 6. Visible concentration limits [%] as a function of dew point temperature. Examples are calculated for an evaporating pool at boiling temperature and a flash­ ing jet. Substance Tair “" ^dew Pool evaporation Flashing Jet 1°C 3°C 10°C 1°C 3°C 10°C Ethylene c2h4 0.8 2.3 7.8 0.17 0.50 1.66 Ethane c2h6 0.6 1.9 6.5 0.16 0.48 1.61 Propane c3h8 0.8 2.4 8.2 0.13 0.40 1.33

Reference Propane in dry air rh = 3 kg/s uio = 2 m/s zq = 0.01 m Ta;r = 288 K Pair = I Bar

Initial dilution 1: No heat transfer. by 2: Extra source dilution- flash evaporation Increased wind speed IE-2 — at boiling point. 'M: Enhanced entrainment

Reference case Comparisons 1: ip = 0 2: 3x dilution 3: uio = 4 m/s M m T I I I I II 4: ue doubled

Mixture Concentration, c [mole%]

Figure 29. Predicted heat-flux effect on the density difference of a propane plume as a function of concentration. The test cases are explained and discussed in the text.

64 Ris0-R-1O3O(EN) Surface heat flux

The accumulated effect of ground heat flux to a cold heavy-gas cloud modifies the cloud temperature and accordingly the density difference. The cloud temperature is determined by

(T - Tair) • [(1 - c) • MajrCpir + c • Mcp] + AiTcon = AH > c ■ AH0 (145) ie similar to the calculations in the previous sections, with the exception that the enthalpy is no longer conserved. The development of the enthalpy deficit AH de­ pends on the time history of the temperature deficit and the size of contact area between cloud and ground. Therefore the heat flux effect on cloud density cannot be parametrized independent of the disperion process. Figure 29 shows some ex­ amples calculated by the box model in chapter 2 with the following sub-models for cloud temperature, density, heat flux and entrainment rate:

71. j______a h______Temperature: T J-&M -r (i-c)Mairc£'r+cMcp

Density: p

Top entrainment: ~ 6.95 2+iiu<, with Riu. = Apgh/pul

Heat flux: = p [(1 -c) • Cp,r + c-Cp] Ch.u(T — Tsur) The purpose of this simplistic parametrization is to focus on the principal ef­ fect of the surface heat flux. The temperature and density calculations are based on dry gas-phase mixing, and the entrainment function (Britter 1988) neglects the turbulence enhancement by heat convection. The plume velocity u, previously taken as constant, is here calculated by a simple momentum budget dm fi\dm 3, = Uair(h)— - pCDU°b (146) dt Both the drag- and heat-transfer coefficients are calculated by

K 2 CD = C/i = (147) In h/zo ie in a simpler way than suggested in chapter 4. The release is chosen to be flash boiling liquefied propane, and the dispersion calculation is initiated at a state where the evaporation is complete and the temperature is at boiling point. The initial concentration cq is calculated by a balance between the heat of evaporation and heat from the temperature depression:

CqML = (Tair — Tboii)' [(1 — Co) • Ma\rCp T + Co • Mcp] (148)

The release conditions of the reference case are listed in figure 29. The density of the reference case (thick solid line) is significantly different from the case of no heat transfer (thin solid line), and the effect is seen to accumulate. This development is strongest in the beginning of the dispersion process where the temperature difference is large. Comparison with test cases shows that the heat-transfer effect depends on the release conditions. If the initial source dilution is more efficient than in the reference case, eg for an elevated release point, the cloud will be warmer when touching the ground and this moderates the heat transfer effect.

Other moderating factors are enhanced wind speed u 10 and entrainment rate ue which increase the dilution process15. The surface roughness zq has a similar effect on the mixing and also on the heat transfer coefficient, see equation 147. Its net

15Turbulence production by heat convection enhances the entrainment rate and thus counter ­ acts the primary heat flux effect on cloud density.

Ris0-R-1O3O(EN) 65 result (not shown in the figure) is to increase the heat transfer effect. The release rate m and the initial plume width appeared to have little effect on the calculation. The effect of surface heat flux is significant for low wind velocities. Unfortunately it is seems to be sensitive to near-source mixing which however is difficult to predict in an acurate way.

Chemical reactions

The density effect of a chemical reaction is two-fold: the released heat of reaction changes the temperature, and in some cases it also changes the total number of molecules. This density change may not always be significant for the dispersion process, but the exact composition is also of interest from a toxicological point- of-view. Consider a system where compounds A\ and Ai react and form A3 and A4 according to the stoichiometric equation:

iq.Ai + Z/2A2 ^—- Z/3A3 + Z/4A4 A H® (149)

A change toward the products on the right hand side of the stoichiometric equation releases the reaction heat AH° (positive or negative) and the mole number of each components n* is changed by

dni = —v\ de dn2 — —v2 de dnz = 1>2de dn4 — v4de (150)

where de is the degree of reaction. If v\ + 1/2 7^ z/3 + z/4 this will affect the total number of molecules by / dni = Az/ - de (151) t=i where Az/ = z/3+Z/4—v\—v2. The usual convention is to assign a positive coefficient for products on the right-hand side of the stoichiometric equation and negative coefficients for consumed components on the left-hand side. The enthalpy change associated with the reaction is

dAH = AH°(T)-de (152)

where AH°(T) is found either directly in literature or from the enthalpy of for­ mation Hf of each compound in the reaction.

AH0 = vzHl + - z/iid? - v2H% (153)

The equilibrium ideal gas-phase chemical balance is determined by the law of mass action derived in equation E.27 of appendix E

V3 x 3 P_ Vl -1/2 = K(T) (154) x 1 ,Po where po is a reference pressure of 1 atm, and K(T) is a function of temperature. The components on the left-hand side of the stoichiometric equation are placed in the denominator and contribute to a positive power of the pressure. A more refined theory for non-ideal systems may be found in literature. The average molar weight is the total mass divided by the total number of moles 1 £i=i niMj y, xiMi = (155) EL", i=i

The chemical reaction changes £i=1 n,, but the mass of mixture ]£i=i ni^i is conservation of mass effectively constant (neglecting small relativistic changes). In the mixture density

66 Ris0-R-1O3O(EN) calculation we need therefore only to consider the weight of components before reaction and just correct for the change in the number of molecules: p Mair + cAM P~ RT 1 + (156) where AM is the excess molar weight before reaction. Az/ is the net change of the number of moles for a complete shift to the right-hand side of the stoichiometric equation 149, and the stoichiometric coefficient vc corresponds to the contaminant before reaction. The temperature is affected by the heat of reaction and in case of enthalpy conservation we obtain

(T - fair) • ((1 - c) • Maircf + c • MCp) = c • (AH0 + AH0 • e) (157)

By insertion the relative density deficit becomes

Ap ______1______l + cfl£ (158) p i , c-(AHo+AH°-e)______^ -t- ((1 -c).Mairc-ir+C.Mcp)T.ir "<= which is linearized to A p (AM AH0 + AH°-e Au-e\ (159) p \Ma ir MairC^Tair Vc )

It is important to consider the kinetic of the reaction. The time scale of a feasi­ reaction kinetic ble chemical reaction may well be slow compared to the time scale of the mixing process (the Damkohler number Da 1), and in this case we simply ignore the chemical process. If the reaction kinetic is fast compared to the mixing process (Da

Example: nitrogen tetroxide in humid air

The release of nitrogen tetroxide N2O4 was investigated by Raj & Morris (1987), and it is an illustrative example of density calculations for mixtures with chemical reactions. A wide range of nitrogen oxides exists in the atmosphere, but it was concluded that the only ones, which could change the composition within the duration of dense gas dispersion 0(1 min), were decomposition to NO2 followed by reaction with air moisture. The stoichiometric equations for these reactions are

N2O4 2N02 AH a = -57 kJ/mole (160) 3N02 + H20 NO + 2HN03 AHb = -116 kJ/mole with the equilibria [N02]2 [N2O4]

[N0][HN03]2 W'*a(T) (161) [N02]3[H20]

Ris0-R-1O3O(EN) 67 and the temperature dependencies are

Ka « exp ^21.161 — —|

Kb « exp (-51.40+ 139 ^— according to Raj & Morris (1987). Consider a mixture of c moles of N2H4 and (1 — c) moles of humid air with the humidity q. The two chemical reactions alter the composition as shown in table 7, where ca and eg are the two degrees of reaction. By insertion of the equilibrium concentrations we obtain two relations

Table 7. Number of moles before mixing N2O4 with humid air and at equilibrium.

Before mixing At equilibrium n204 c (1 - ca) • c no2 0 (2ca — 3eg) • c NO 0 eg -c HNO3 0 2 eg - c H20 q ■ (1 - c) q ■ (1 — c) — eg • c Dry air (1 - q) ■ (1 - c) (1 - q) ■ (1 - c) Total l 1 + c • (ca — eg)

between the degrees of reaction ca and eg, the [N2O4] equivalent concentration c, temperature T and pressure p.

(2eA — 3eg) 2 Po ^(T) (162) l-eA P c -1 ( -V__ t__ ~ (») ■Kb (T) (163) \2ca — 3 eg/ g(l — c) — egc The temperature is determined by the enthalpy budget T T c • (AH + ca ^Ha + egAJfg) (164) air M&irc*' r + c • A(Mcp) where

ambient temperature AH enthalpy because of other processes A(Mcp)

The system of equations 163 to 164 must be solved simultaneously for ca, eg and T. Solutions to the present example are shown by Raj & Morris (1987). Table 7 shows that the total number of moles is changed by reaction and the density is therefore

P Mair + c ■ AM (165) RT1 + c • (ca — eg) Factors +1 and -1 for the degrees of reactions ca and eg are the net change of the number of molecules Ai/ by each reaction, ie Ava = +1 because the first reaction produces one and Az/g = — 1 because the second reaction consumes one mole. The calculations by Raj & Morris (1987) illustrate how to incorporate chemical reactions in density calculations of a homogeneous gas phase. Koopman, McRae, Goldwire, Ermak & Kansa (1986) does however report on formation of HNO3 aerosols in the ‘Eagle ’ experiments with liquified N2O4 in conflict with the above assumption of dry mixing.

68 Ris0-R-1O3O(EN) Source effects

The topic of this last section of the chapter is the source effect on cloud density, or more specifically the initial enthalpy difference AH0. Tables of enthalpy H(T,p) are found in literature for common gases (Vargaftik 1975) and the most accurate procedure is to look up the enthalpy at the storage pressure and temperature and to compare it with the enthalpy in atmospheric conditions. If detailed data are unavailable, the following formulae may be used to determine the release enthalpy. Isothermal gas releases. In this case there is no enthalpy difference from the surroundings AH0 = 0, and the density is determined solely by the molar weight.

Blow-down from the gas phase. The outlet temperature Tout after adiabatic expansion of an ideal gas is

where T0 and p 0 are container temperature and pressure and 7 = Cp/cy. In general the container pressure is lower than the saturation pressure p 0 < Psatpo)) but an accidental overpressure may prevail for some time as discussed in chapter 8. The initial enthalpy is

fTout AH0 = / Mcpdt => Ai?o « —Mcp • (Tair — Tout) (167)

The heat capacity is here assumed to be approximately constant. In some cases the adiabatic expansion results in partial condensation. Evaporation from a pool. The material from an evaporating pool has the ini­ tial enthalpy

Atf0 = Mc'^dt AH0 st -Me" • (Ta-,r - Tsur) (168)

where Tsur is the pool surface temperature. In chapter 8 this was estimated to be in the range of T™‘n < Tsur < T™?x , where the upper limit = Tboii corresponds to a boiling pool and the lower limit T™‘n corresponds to a volatile liquid where the heat from air entrained in the boundary layer above the pool is the only heat supply. This is found from the implicit equation 114

Psat(T%") M ■ L p-p Sat(T™n)Mair-cf

which must be solved for Ts™n inserting an expression for the vapour pressure curve Psat(T).

Flash boiling liquid. The enthalpy deficit of a flash boiling liquid is estimated by an equivalent thermo dynamic process, where we first cool the liquid from the container temperature T0 to its atmospheric boiling point Tboii, evaporate it at the atmospheric pressure and then heat the gas phase to air temperature Tair. This calculation is convenient because as a rule latent heat data are presented at atmospheric pressure in literature.

Z*-Z"boil P*!air AHq = / Mc'dt — MLrbon + / Mcpdt => JTo •'Tboii AH0 « -MLrboil + MCp • (T0 — Tboii) — Mcp • (Tair— Tboii) (169) If part of the liquid material deposits on we must evaluate the rain out fraction aerosol rain out /rain and the temperature of the deposited liquid Train- The cooling of the deposited aerosols provides a heat contribution /ra;n • dp ■ (T0 - Tram) which

Ris0-R-1O3O(EN) 69 is distributed on the remaining fraction of the release 1 — /rain- The release enthalpy is therefore slightly higher than in the absence of liquid rain out.

fTlboil AH0 = / Mc'p dt JT0

f /*^rain T^air + , y...... / Mc'dt — ML(Tboii) + / Mcpdt => 1 - /rain /to A/f0 % —MjL(Tboii) + Mcp • (T0 — Tboii)

—MCp • (Tair - TboiO + - /raf-- • MC; • (To - Train) (170) J- ” /rain The propane experiments to be discussed in chapter 11 involved a cyclone source which provoked liquid rain out. The liquid was separated from the two- phase flow inside the cyclone, where we assume atmospheric pressure and no air content. According to these assumptions the partial pressure must be equal to saturation vapour pressure of 1 atm and the temperature of the rained out material was the atmospheric boiling point Tra;n = Tboii- Liquid deposition is a complicated process, which depends on the aerosol size distribution, the angle of attack between the jet and obstacle and the degree of condensation.

Examples of various substances and source types Table 8 compares the effective relative molar weight deficit AM»/Mair for some chemical substances with various release scenarios. The chemical properties are taken from table 37 in appendix I, and the applied release enthalpies AH0 are the estimates above. The release scenarios chosen are: 1. Isothermal gas releases. The values are negative for gases lighter than air.

2. Blowdown from the gas phase. Tank and ambient temperatures are set to 15°C in the gas phase blowdown case, and the tank pressure is arbitrarily set to the corresponding vapour pressure. In practice gas containers are designed for a wide range of overpressure.

3. Evaporation from a boiling pool. The pool temperature is set to the at­ mospheric boiling point and the air temperature is 15°C.

4. Evaporation pool at minimum pressure. This is relevant when a pool is iso­ lated from the ground below, and the heat of evaporation is supplied from the air through a boundary layer above the pool.

5. Blowdown from the liquid phase with flash boiling and 33% rain out. The tank and air temperature are set to 15° C and the rained out material is at boiling-point temperature.

6. As above except that the rain-out fraction is zero.

The effective relative molar weight deficit AM*/M a;r increases from the left to the right side in the table, and the largest effects on the density are found for substances with large heat capacity, large heat of evaporation and low boiling point. These are also the cases where the density appears to be sensitive to the exact source conditions. Note that the density of two-phase emissions of low- molar-weight compounds such as ammonia are comparable to isothermal releases of high-molar-weight compounds like freon.

70 Ris0-R-1O3O(EN) Table 8. ‘Effective’ relative molar weight defficit AM*/M air for dilute mixtures of various substances and ambient temperature Ta = 15 °C. The source types are: 1) Isothermal gas release, 2) gas-phase blowdown, from 6 Bar, 3) evaporation from boiling point, 4) evaporation from minimum pool temperature, 5) flash with 33 % liquid rain out, 6) flash with no liquid rain out.

Substance Source type Gas Flow Pool Flashing Jet 1) Iso 2) Blow 3) Boil 4) 5) Rain 6) 0% Methane ch4 -0.45 -0.04 0.23 0.27 -0.10 0.14 Ethylene C2H4 -0.03 0.37 0.41 0.50 0.85 1.39 Ethane c2h6 0.03 0.47 0.57 0.70 1.33 1.79 Propylene c3h6 0.45 0.91 0.93 1.22 2.26 2.66 Propane “ c3h8 0.52 0.97 0.94 1.24 2.37 2.76 Butadien a c4h6 0.86 1.03 1.50 3.41 3.55 i-Butane ° iC4H10 1.00 1.26 1.81 3.33 3.55 n-Butane ° nC4Hio 1.00 1.17 1.77 3.55 3.69 Ammoniab nh3 -0.41 0.00 -0.22 -0.05 2.17 2.38

Hydrogen Flouride 0 HF -0.31 -0.32 -0.13 3.44 3.43 Hydrogen Cyanide “ HCN -0.07 -0.13 0.16 3.04 2.95 Hydrogen Sulphide 6 H2S 0.17 0.59 0.48 0.61 2.10 2.41 Hydrogen Chloride 6 HC1 0.26 0.66 0.60 0.70 1.84 2.19 Methyl Chloride “ CH3C1 0.74 0.92 1.13 3.15 3.32 Vinyl Chloride “ C2H3C1 1.16 1.34 1.65 3.71 3.85 Sulphur Dioxide ° S02 1.21 1.33 1.55 4.07 4.20 Chlorine ° Cl2 1.45 1.64 1.80 3.71 3.90 Hydrogen Bromide 6 HBr 1.79 2.20 2.08 2.19 3.63 3.83 Methyl Bromide ° CH3Br 2.28 2.33 2.62 5.07 5.12 Phosgene ° COCl2 2.41 2.46 2.87 5.37 5.41 Bromine “ Br2 4.52 4.33 4.67 8.72 8.23 Nitrogen n2 -0.03 0.37 0.70 0.72 -0.12 0.59 Argon ° Ar 0.34 0.71 0.85 0.86 -3.07 1.09 Carbon Dioxide 6 C02 0.52 0.93 0.90 0.99 3.21 3.65 Freon 12 6 CC12F2 3.17 3.63 3.52 3.83 6.00 6.30 Sulphur Hexaflouride sf6 4.03 4.51 4.95 5.29 5.58 6.38

"Gas phase at 6 bar not possible 1 Adiabatic expansion results in partial condensation. 10 More on box models

The box models in chapter 2 provided a simple integral description dense gas introduction dispersion. The previous description was schematic, but armed with the detailed information from the proceeding chapters we are ready to develop box models to almost an usable state16 and to discuss various extensions. The previous definitions of the main variables (position, horizontal dimension, chapter summary mass, enthalpy, momentum and equivalent fluxes) and the auxiliary variables de­ rived from these are maintained with addition of sub-models for previously un-

16The remaining work required for practical applications are user-friendly computer implemen­ tations with links to source models similar to those sketched in chapter 8 followed by adequate model evaluation. This will not be intended here.

Ris0-R-1O3O(EN) 71 defined auxiliary variables and new momentum equations for boxes with ground contact. Two box models with alternative geometries are presented, ie Webber et al.’s (1993) orange-slice-shaped model for instantaneous releases on uniform slope and Fannelgp & Zumsteg ’s (1986) doughnut-shaped model for a Thorney- Island type of instantaneous releases. Also Cleaver, Cooper & Halford’s (1995) rules for obstacle effects are presented and it is shown how many models super­ impose smooth, usually Gaussian, distributions on top of the box calculations. A few analytical results are presented.

Temperature, composition and density

Previously temperature and density were written as the unspecified functions T = h{H,c) and p = fg(c,T,p). Following the analysis in chapter 9 these sub-models are now expressed as

rp _ rp , c-(H + En=1 6„AH°) + AHcon + AHmix a,r (1 - c)MairCpa + cMcp

_ p (Majr + C • AM) ______1______1______9 ~ ^

The temperature is based on a heat budget where AH is the specific cloud en­ thalpy relative to the ambient air, and AH0, AHcon and AHm\x account for the heats of chemical reaction and phase transition. In the computational convenient limit of homogeneous equilibrium the degrees of gas phase reaction en depend on T and p, ie the composition of a given two-phase mixture is found by iteration. With several condensing components we evaluate the degree of condensation o% for all relevant species, usually the contaminant and air moisture. These degrees of condensation are needed for the mixture density p, the combined heat of con­ densation AHCon = MiLia&i, and the possible heat of reaction in the liquid phase AHm-tx . The variable complexity of possible chemical reactions and phase transitions for individual contaminants makes it practical to implement the f% and f2 sub-models as interchangeable modules for numerical dense gas models, as in the DRIFT model (Webber, Jones, Tickle & Wren 1992). These modules cover the computationally straightforward pure gas-phase mixing to complex non-linear two- phase multi-component models for specific substances like hydrogen fluoride (HF) in moist air. Chapter 9 illustrates the calculation of nitrogen-tetroxide (N2O4) with gas-phase reactions and appendix E contains a phase-transition model for ammonia (NH3) in moist air.

Gravitational spreading, entrainment and heat flux

Most box models estimate the front movement by steady-state front velocity in fronts calm environment uj = Fr/y/gH with the empirical front Froude number set to Frj ~ 1.1, see chapter 3. Laboratory experiments indicate that the front velocity depends on ambient wind. The combined effect of an enhanced velocity at the tail­ wind edge of the cloud and retardation at the opposite head-wind edge is however difficult to discriminate from a global drag on the cloud. Acceleration of an initially still cloud, such as the Thorney Island collapsible tent releases, is usually ignored although van Ulden (1987) presented a model in which the front movement was determined by a momentum balance including non-hydrostatic pressures related to vertical accelerations. This led to an equation of the front acceleration it/ in which the cloud aspect ratio h/r played an important role. Nielsen & Ott (1988) compared the HEAVYPUFF box model with constant front velocity to data from Thorney Island trial 9 and found that the over-prediction of the front velocity of

72 Ris0-R-1O3O(EN) Table 9. Main equations of the box models defined in chapter 2.

Ground-level instantaneous release

dx Position : = u dt dr Radius: = Uf dt dm Mass: = Pair (7rr2ue + 2irrhu() dt dm Enthalpy : = 7rr2y> dt dmu = itair-^jr + T07rr2 + Fd + (n x g) x n ■ ApV Momentum dt

Ground level continuous release dx Position : u dt db Width : 2Uf dt dm Mass flux : Pair {bu e + 2hu{) \u dt, dm Enthalpy flux : ipb\u\ dt dmu Momentum flux : Uair-^- + Tq6|u| + jFdM dt 1 _d_ / Ap(g • n)hm u \ 2 dx V p \u\)

+ (n x g) x n • Aphb

Elevated continuous release

dx Position : u dt dm Mass flux : p a\r2nrue\u\ dt dm Enthalpy flux : 0 dt dmu Momentum flux : tiair*^* - + -Ed 1^1 + ApAg\u\ dt Elevated instantaneous release dx Position : u dt dm Mass: Pair47rr2Ue ~dt dm Enthalpy : 0 dt dmu dm Momentum : Wair-TT + Ed + ApV g dt dt a 1900-kg gas cloud only lasted 5 sec. Edge entrainment in a cloud with ground contact is proportional to the front edge entrainment velocity u{ = 0.14%/ where the coefficient is taken from the laboratory experiment described by Simpson & Britter (1979), see chapter 3. To the casual model user this may give a false impression of the physics, since edge entrainment is larger

Ris0-R-1O3O(EN) 73 at the upwind than at the downwind edge of the cloud. Simpson & Britter (1980) considered the front movement in head-wind and tail-wind conditions and found that the velocity difference between the front and the air above was the relevant measure for mixing. An equation like u{ = a\u/ — «a;r| would physically be more correct than u{ — a-Uf, although this makes little difference in an integral model. The entrainment function ue = f3 (g'h, u, y>) is a matter of some disagreement top entrainment among box models. The new parametrization proposed in chapter 4

3.33 + Rie with Richardson number and turbulence scale set to

Rie = and e = (u3 + O.liu3)2/3

is in good agreement with a range of reference cases. It seems applicable for box models with ground contact although it has not yet been verified by data from dense gas experiments. The turbulent velocity scales u* and w* are affected by internal cloud stability and heat convection ip = f^(T — TSUT,pc p ,u,g'h). Jensen (1981b) estimated iv» and ip by internal Monin-Obukhov similarity theory. This method fails when the gas layer heigh is not sufficiently large compared to the surface roughness zq and in that case it is suggested to use Zeman’s (1982) alternative parameterizations, see chapter 4. It is unnecessary to model the time development of the surface temperature except perhaps for a continuous surface plume of some duration, see chapter 7. The entrainment velocities in elevated plumes and instantaneously released vol­ umes are

0.08 Will + 0.5|uairx| + 1.0(er)1/3

ue = 0.23|tt — uair| + l.O(er)1/3

respectively. These entrainment rates are caused mainly by the velocity shear between the cloud and the ambient. According to Ooms (1972) it is necessary to decompose the wind velocity in its components perpendicular uair_L and parallel «air|| to the plume axis, since the former component is much more efficient in dilution of the plume, see chapter 4.

Momentum equations

The generic ground-level box models in chapter 2 applied a cloud advection u equal to the ambient wind velocity, eg the value of a logarithmic wind profile at the top of the cloud h

(171) or weighted averages like

(172) where c(z) in the last estimate is a suitable vertical distribution, eg

c(z) = cq • exp[-(z/h) p]

Sometimes it is advisable to apply a momentum budget also for ground-level box models, eg in order to model an initial acceleration of a Thorney-Island type

74 Ris0-R-1O3O(EN) release or the deceleration of a jet. Bradley, Carpenter, Waite, Ramsey & English (1983) wrote the momentum equation of the instantaneous release box model in instantaneous release flat terrain as T = + (17% where the surface friction tq and the cloud drag force Fd are evaluated by u t0 = -pu» (174) M

Fd — FDPalr^Th(tiair U) • |Uair (175) with Cd = 0.5. I have simplified these equations slightly. Originally the authors applied a depth integral of the squared velocity deficit and assumed a reduced velocity for the momentum contribution by edge entrainment. The momentum equation for continuous ground level releases in flat terrain is continuous releases dmu dm 1 dg'h2bu dt - U&{T1F + To6N + FdN ~ (176) where the latter term introduced by Bradley et al. (1983) accounts for hydro ­ static the pressure gradients caused by variable plume height. For steady-state dispersions (dx = udt) this may be rewritten as 1 dg'h2bu _ 1 d f mu (177) 2 dx ~~ 2 dt where F>a is the densimetric Froude number, see appendix F. This is often high and pressure-gradient term is therefore of minor importance except perhaps for momentumless release in weak ambient wind. In order to obtain a parabolic dif­ ferential equation for steady-state simulations I suggest either to neglect this term or to approximate it by 1 dmu 2Fr% dt and move it to the left-hand side of equation 176. Bradley et al. (1983) omitted the drag force since plumes normally are parallel to the wind. The drag is however of significance for a jet release in the crosswind direction and it is easily calculated by the perpendicular component of the wind velocity uair± Fd ~ CdP&\r du air .L | tT air -L | (178) similar to the drag on the elevated plume model in chapter 2. Presumably the drag coefficient c<* is ~ 1. Nikmo & Kukkonen (1991) made an obvious model extension for terrain ef­ sloping terrain fects by putting the usual control volume on a slope as sketched in figure 10, see also Kukkonen & Nikmo (1992). The cloud advection was predicted by the usual momentum budget with inclusion of gravity. When describing the terrain by its normal vector n, the projection 17 of the gravitional acceleration g is (n x g) x n and the extra term in the momentum equation become d(mu) + (n x g) x n • ApV (179) dt for an instantaneous release and d(mu) + (n x g) x n - Aphb\u\ (180) dt for a continuous release. Picknett (1981) reported that the instantaneous release in Porton Down trial 10 had an upslope ambient wind. Initially the puff moved down the incline and then reversed in the upslope wind direction after sufficient air entrainment. The model of Nikmo & Kukkonen (1991) is capable of simulating this cloud behaviour, and it accepts any angle between the incline and wind direction. 17Nikmo & Kukkonen (1991) expressed the projection by trigonometric relations.

Ris0-R-1O3O(EN) 75 Figure 30. Box model for instantaneous releases on a slope proposed by Nikmo & Kukkonen (1991).

Figure 31. Box model for instantaneous releases on a slope proposed by Webber et of.

Alternative box models

The problem of Nikmo & Kukkonen’s (1991) model is the assumed cylindric cloud wedge-shaped box model shape which probably is unrealistic. Webber et al. (1993) studied the motion of a dense gas cloud on a uniform slope by simulation using a dynamic shallow-water type model. For releases without ambient wind, surface friction or entrainment the cloud approached the shape of a slice of orange sketched in figure 10. This observation inspired the authors to formulate a box model with a horizontal top surface, and a rear boundary which intersected the terrain. The local front velocity was modelled by u/ = Frfyjg'h, where the local height depends on the slope 6 and on distance L from the rear boundary, i.e. h = TL. This local front velocity was then equated with the projection of the cloud velocity in the direction normal to the cloud boundary giving the kinematic condition

- Frfy/gTL (181)

76 Ris0-R-1O3O(EN) where y is the distance from the centre line and L is the distance from the rear boundary as seen in figure 10. This equation was then transformed to

dL _ jl — L (182) d\y\~ V L where L = L/A and y = y/A are the front coordinates normalized by the cloud dimension in the down valley direction A = w2/Fr‘jg'T. The solution to the shape of the cloud is then f — 2 ~ cos W with the parameter w 6 [-7r, tt] (183) y = w + sinwcosw

It is remarkable that cloud shape is uniform in this model in contrast to the con­ tinuously spreading volume in the model for flat terrain. The down-slope velocity was found to be u = n^Fr/T^Wg'V1/3 (184) where T = tan 0 defines the slope, V is the cloud volume, and is the integral

fig = [ cos6 w duo = ^ (185) J-n/2 16

Figure 32. Perspective of a box gas model for a v-shaped valley.

The model may be extended to valleys with a uniform cross-section (Nielsen 1996a), eg the v-shaped geometry shown in figure 32 in which the cross-valley slope is defined by parameter a. The cloud shape is a wedge with a v-shaped intersection with the terrain and a slightly different front which is determined by

dL _ _ 1 — Z, + a|2/| (186) d\y | "\ L-a|y|

which results in

y = w 4- sin w cos w (187) -2a |-(6a + 2a3)w + 4In [sin w + acosw] — 41na 4(1 + a2)2 a sin 2w + cos 2u — 4 4(1 + a2)2+ 4(1 +a2)

Ris0-R-1O3O(EN) 77 where the first two terms are identified as the original solution and the remaining part vanishes for a — 0. The cloud velocity in still governed by equation 184 and the normalized cloud volume now becomes 5tt 2a In a a(ll + 7a2 + 2a4) fie(Qf) 16 + (1 + a2)4 + 6(1 + a2)3

a2 (35 + 35a2 + 21a4 + 5a6)?r (188) 16(1 +a2)4 which results in a larger advection velocity. Recently Tickle (1996) introduced entrainment in the model and the inertia of the entrained air made the advection speed more realistic.

Figure 33. Toroidal box model for instantaneous releases proposed by Fannel0p & Zumsteg (1986).

Thorney-Island type releases with large-aspect ratios h/r tend to concentrate toroidal box model the gas in a spreading vortex ring with little gas in the centre. This led Fannelpp & Zumsteg (1986) to propose the alternative box model sketched in figure 10. By energy conservations the cloud dimension was shown to develop by r oc f2/5 instead of the usual r oc t1!2 relationship, ie slightly different.

Figure 34- Definition sketch: The effect of an isolated obstacle in the box model of Cleaver et al. (1995).

Obstacles

Recently Cleaver et al. (1995) enhanced a standard box model with a sub-model for obstacle effects, best described as a complex set of rules-of-thumb. The concen­ tration field close to the obstacle was not modelled in detail, but the bulk effect on

78 Ris0-R-1O3O(EN) the gas plume was approximated by a sudden change of the upstream plume width b and height h to the downstream values b' and h'. The model made use of results from two wind-tunnel experiments with a solid fence perpendicular to the wind direction as in figure 10a and a rectangular building with one wall perpendicular to the wind as in figure 10b. The downstream plume dimensions b' and h' were approximated by the equations

f b' f = 6 • (1 + f Ri1/*) Solid fence: \ b!j = max[/i, H] (189) b' b = max[6 + 0.55, B] Isolated building: where B and H are the width and height of the obstacle, and Ri = g'h/u2 is a cloud Richardson number. For an obstacle size comparable to the plume dimensions it is not always obvious whether it should be considered as a fence or a building. In this intermediate cases Cleaver et al. (1995) applied the smallest of the width predictions b' = min[fy, and interpolated between the height predictions, h'f and h'b . The plume expansion behind low obstacles, or partly exposed obstacles as in figure 10c, was further modified by interpolation rules depending on the height ratio h/H and width ratio B\/b', where B± is the width of the exposed part of the obstacle. Similar rules were defined for instantaneous release models. This model covers a wide range of obstacle geometries, but the results should probably be used with caution.

Analytical results Suppose that we have a gas cloud without chemical reactions, aerosol formation or cloud spreading external heat input as in the adiabatic mixing example in chapter 9. For moderate concentrations c < 1, the cloud buoyancy is approximately conserved

ApV to constant (190)

This is inserted in the front velocity for an instantaneous release

5 = Frf = Frf ‘ (191) and we get the solution r = r°V*T, (192) where the slumping time scale Ts is defined by

Ta = Ao (193) yJAng'V Similarly the width of a plume is found from the approximation A pV to constant

3Z = v>iHV2 (194) b = bo (1 + t/T;f/3 with T' —

These considerations show that the plume widening has a time dependence b oc t2/3 and the radius of an instantaneous release has a time dependence r oc t1/2. The passage time Tpass of an instantaneously released dense gas cloud is the passage time

Ris0-R-1O3O(EN) 79 time necessary for the cloud to travel a distance equal to the radius at time t plus the radius at time t + Tpass

— r0^/l + ^ + r0‘\i/l + ti^ 2p„. \ 't^pass = r ^1 + ^/l + T‘+t) (195)

_ 2 r , r2 1 Tpass — u + u* T,+t

i.e. Tpass — 2r/u when the slumping velocity is negligible and longer during active spreading. Consider a relatively large instantaneous release in weak ambient wind, eg 20 example tons of liquefied propane and ua;r=l m/s. The excess effective molar weight for the case of complete flashing listed in table 8 is AM»/Ma;r=2.76 leading to po ~ 1.29 • 3.76 = 4.85 kg/m 3. Taking the initial height equal to the initial radius, this leads to Vo=4100 m3, ro =10.9 m, and Ts = 0.32 s. Now 20 sec after release the radius has grown to 10.9 • (1 4- 20/0.32)1/2 = 87 m and the front velocity is 2.16 m/s giving an effective local velocity of 1.75 m/s. The cloud passage time is therefore Tpass = 2 • 87 + 87 2/V20.4 = 545 sec or 9 minutes. With a rather efficient heat transfer coefficient of % = 0.1 and the calculated effective velocity, the heat-transfer time scale is about 1 hour, see figure 25. The passage time is an order of magnitude less than that of the heat transfer time scale, and a constant soil temperature Tsut is therefore sufficient for heat-transfer models in case of an instantaneous release.

Superimposed distributions

The uniform distribution of cloud properties is a fundamental assumption of box models. Nevertheless this is sometimes moderated by superimposed distributions. Eidsvik (1980) evaluated the friction velocity u* by the spatial average of local effective velocities velocities in the spreading cloud as mentioned in chapter 4. The following local velocities are consistent with the assumed shapes of the ground-level box models:

u £ cos tv + Uf • for instantaneous release . 0 . £cosw u = (196) 1 u 0 + Uf ■ for continuous release . 0 Here, u is the advection, u/ is the front velocity, w is the horizontal angle relative to the wind direction and £ € [0,1] is the relative distance from the centre to the edge. Table 10 lists the first three moments of the velocity distribution. The average velocity (|u|) may be used to estimate the forced heat convection from the ground; the square average of the local velocity (|it|2) can be used to estimate the kinetic energy of the cloud as in Schnatz, Kirsch & Heudorfer’s (1983) box model and the third moment (|u|3) could be used to model the work by friction with the ground. Modern box models in the public domain like DEGADIS, HEGADAS, SLAB, smooth concentration and DRIFT are designed with a smooth transition to passive dispersion and they profiles present their results with superimposed concentration distribution. This may take the form of an undisturbed core and a diffused Gaussian edge zone:

co for the core £ < 77 c(£) = cq exp | — | for the edge £ > 7? (197)

where £ is the distance from the centre, 77 is the radius of the core, and a is the dimension of the edge zone. In order to obtain mass-consistency the spatial

80 Ris0-R-1O3O(EN) Table 10. Average values of local velocities in box models as a function of the advection velocity u and front velocity Uf.

(N> = hy/u2 + u2f + £rj arcoth V1 + 9 Cont. = + H release (hi3) = (l^2 + iu/) '\lu2+u2 f + mjarcoth V1+$

(|tt|) ps yju 2 - 0.14tm/ + |u 2 (Max error=2%) Inst. release = «2 + M

(|u|3) ps u 3 + 0.40u2u/ + 0.29uu 3 + |u3 (Max error=5%)

integrals of the superimposed distributions must equate that of the model distri­ butions. This gives the following relations between model dimensions b or r and the new profile dimensions rj and a:

for 1-D symmetry for 2-D radial symmetry (198)

for 3-D spherical symmetry

It is probably impossible to maintain at the same time the enthalpy and momen­ tum balances, not to mention the unlinear phase transitions. Instead the edge dimension a is modelled by a diffusion equation which expands until the core re­ gion ceases to exist. The use of diffused edges is inconsistent with the initially sharp gravity fronts and it might be argued that the use of superimposed concentration distribution is a cosmetic face-lifting unjustified by the underlying assumptions. On the other hand it gives model users a better impression of the likely concen­ tration field. The vertical concentration distribution of ground level box models may be ap­ proximated by

c(z) = coexp{- 0z/az)p } (199)

where Britter & Snyder (1988) observed that the exponent p was ~ 1 in a momen­ tumless stratified plume in a shear layer and gradually increased to p=1.2-1.4 in the downstream domain of passive dispersion. It is appropriate to require mass- consistency and to relate the length scale to the centre of gravity z as suggested in chapter 4 Cboxh = /0°° co exp {- (z/az)p } dz = 1? (l) crz \Cboxh 2 = /0°° z • co exp {- (z/az)p } dz = a\

2?r(i) Oz (200) rti)2

where F(£) is the gamma function and h and CbOX are the box model height and concentration.

Ris0-R-1O3O(EN) 81 11 Propane experiments with obstacles

Field experiments are labour intensive and involve considerable costs of equip­ introduction ment, test site, release gas, travels etc. They are however necessary since certain phenomena are difficult to model on a laboratory scale, in particular the thermo­ dynamic behaviour of cold two-phase gas clouds and turbulence with a sufficiently wide spectral distribution. The data used in this chapter were obtained in the MTH project BA propane experimental layout experiments with obstacles. Liquid propane was released from a pressurized stor­ age of near-ambient temperature and the source was either a nozzle or a cyclone producing a momentum-free plume. The nominal source strength in the trials se­ lected for analysis in this chapter was 3 kg/s. One third of the emission from the momentum-free cyclone source was however spilled into a pool on the ground and with this source the effective release rate was reduced to approximately 2 kg/s, see appendix A. The obstacle was a 2-m high fence perpendicular to the wind direction at a distance of 48 m downstream of the source. In order to quantify the obstacle effect the fence was removed in the middle of each trial. In some of the selected trials the obstacle line was altered to a line of obstacle elements with a 50% overall porosity. The four selected trials were conducted during the same morning with wind speeds on the order of 2 m/s, humidity conditions and wind direction slowly shifting from one side of the ideal direction to the other. The release conditions are summarized in table 11. Further details are given in appendix A. This chapter is initiated by a description of the selected trials. The section start­ chapter summary ing on page 88 is an analysis of vertical distributions of concentration, temperature, velocity, turbulence and fluxes at two downwind distances during release periods without obstacles. The influence of the two source types are discussed. Based on local enthalpy budgets it is concluded that the mixing process was non-adiabatic, ie that the heat flux from the ground moderated the cloud temperature and den­ sity. The section starting on page 107 is an analysis of the influence of cross-plume obstacles of variable porosity on vertical profiles of velocity, concentration, mix­ ing and turbulence. The last section starting on page 113 is an analysis of the turbulence measurements. This is the first out of four chapters with analysis of dense gas field data. It deals data-analysis chapters with local cloud properties, obstacle effects and effects of source momentum. In the following chapters I shall analyse cross-plume concentration profiles and direct measurements of ground heat flux (chapter 12), plume dimensions, concentration fluctuations, plume meandering and aerosol properties (chapter 13), and enhanced stratification in isothermal dense gas releases (chapter 14). Enthalpy budgets are repeated for all non-isothermal experiments.

Ground-level concentration field

Figures 35-37 are inspired by the multi-plots of Heinrich & Scherwinski (1990). Each curve represents a time series from a catalytic concentration sensor at ground level, and the lower right corner of each frame indicates the sensor position relative to the obstacle, masts and gas source. The scale on the x-axis of each frame is 12 min and the concentration range is 3 %. The response time of the catalytic concentration sensor is *10 s, ie relatively slow. A close study of the figures gives an impression of the time development of the concentration field.

82 Ris0-R-1O3O(EN) Table 11. Overview of the selected trials.

Trial EEC55 EEC56 EEC57 EEC58 Source type Jet ' Jet Cyclone Cyclone Fence type 100% 50% 100% 50% Exit pressure p0 [Bar] 10.0 10.1 9.3 9.3 Exit temperature To [°C] 13.3 13.5 13.3 13.4 Release rate rh [kg/s] 3.0 3.0 fs2.0° «2.0“ Jet momentum Fjet [N] 208 209 — — Effective molar weight M* [kg/mole] 0.099 0.099 0.089 0.089 Wind direction relative to ideal ADir -12° -7° +16° +29° Wind speed at 6-m height item [m/s] 3.2 2.4 2.5 2.8 Air temperature Tajr [°C] 9.9 11.8 13.9 15.5 Relative air humidity 99% 100% 93% 88%

“Corrected for 33% liquid rain out

Jet and solid fence The concentrations in the central part of the jet shown in figure 35 were remarkable steady jet concentrations stable and presumably the jet effect was significant. The signals from sensors at the edge of the cloud were intermittent with gas free periods in the order of 30 sec, eg sensors #21 and 48. This is because the centre-line position was moved by the variable wind direction. The obstacle was removed into the middle of the trial. This is difficult to detect upstream of the obstacle (sensors #18, 19, 21, 26, 28, 43 and 48), whereas the typical downwind concentration increased with a factor of two. Jones, Martin, Webber & Wren (1991) noted that the signal of sensor #24 blocking? disappeared when the obstacle was removed and no longer guided the gas flow. This effect has probably little to do with blocking by stratification as defined by Baines (1984), since the relative obstacle height and densimetric plume Froude number are estimated to H/h fa 1.8 and Fr fa 5 (page 110) which is outside the domain of blocking, see chapter F. The average wind direction was 12° off the ideal direction normal to the obstacle, and this is probably why the obstacle guided the flow toward the left hand side.

Jet and porous fence

Figure 36 is a similar plot of the concentrations observed in the following trial. The experimental conditions were almost identical except that the obstacle this time had gaps giving an overall porosity of 50 %. The concentration increase after obstacle removal observed by the downwind sensors was smaller than in the pre­ ceding trial EEC55. This is not surprising since the jet was able to shoot between the gaps in the obstacle. The obstacle effect for the instrument group around mast M4 (sensors #37, 38, 23, 60 and 63) seems more significant than for the sensor group immediately behind the obstacle (sensors #31, 32, 42 and 35). The plume was able to pass through the gaps in the obstacle line and then the gas was di-

Ris0-R-1O3O(EN) 83 EEC55 - jet source and solid fence

Jk1 Sensor t>4

Sensoroo

bmsor 2I bensSr al

® M4 n Sensor 2d Sensor 23

'ensor 34 Sensor 36

Sensor 43_____jSensor So

® M3, ensor 43 Sensor 41 "■•••Fence sensor ill Sensor 21

0 5 10 15 20 25m Gas source ...... 1.... 1

Figure 35. Concentration time series from the ground based array of catalytic concentration sensors. The lower right comer of each time series indicates the measuring position. The time scale is 12 minutes and the full concentration range is 3 molar percent. The mean wind direction is 10 degree off the ideal perpendicular wind direction. luted by the enhanced turbulence in the wakes of the obstacle elements. This is different from the flow over the solid fence, where the entire plume must pass over the obstacle before intruding the wake.

Momentum-free release

Figure 37 shows concentration time series from trial EEC57 with the momentum- free cyclone source and solid obstacle. The release conditions were comparable to those of trial EEC55 illustrated in figure 35, except that the average wind direction had shifted to the opposite side of the ideal one. The general impression is that the concentration field was more variable than intermittency in the jet case. The intermittent time series measured near the edge (sensors #18, 26 and 28) indicate that the centre-line position was variable. Even the signals

84 Ris0-R-1O3O(EN) EEC56 - jet source and porous fence

ensor 64

Sensor tio

n. Sensor 24 Sensor 0 M4

ensor 26 j .j Sensor 34 Sensor 36

Sensor 43______^Sensor 0 M3, Sensor 41 ""•••Fence sensor

sensor

0 5 10 15 20 25m — Gas source LtaJauJ^UaJaJ_|_LJ^_Lj_LJ^LlaUlaiJ

Figure 36. The same as in the previous figure 35, but for a jet hitting a porous obstacle line. The mean wind direction is almost perfect.

from the core of the plume (sensors #19 and 43) were unsteady, perhaps caused by variable wind speeds. At first sight the results downstream of the obstacle (sensors #32, 34, 35, 38, 23, 60 and 63) indicate a much stronger obstacle effect than in the jet case. The signals from the upstream sensors #19 and 43 near the center line does however also increase at the end of the trial. Figure 38 shows a close-up of concentration signals from a chain of sensors crosswind variation distributed across the plume downwind of the obstacle. As for the jet case we recognize an increase of the mean and variance after the obstacle removal. Before obstacle removal the highest concentrations were detected by sensor #41 at the right-hand edge of the obstacle and this indicates that the gas now passed around the obstacle on this side. After obstacle removal the signals from the neighbouring sensors were correlated whereas signals from opposite edges (sensors #23 and 41) were anti-correlated. This is a sign of plume meander. Figure 39 shows concentration signals from sensors near the plume center line. downwind variation

Ris0-R-1O3O(EN) 85 EEC57 - cyclone source and solid fence

Sensor 6

• . 11 • Sensor 65 Sensor 37

jensoMjO

", l - Sensor ‘24 E Senso^S? 0 M4

Sensor

Sensor^o

• - ~ Sensor 43 ‘••Sensor 35

0 M3 Smsor 41 •••Fence Sensor 1

Sensor 11

0 5 10 15 20 25m •* — Gas source i ■ ■ ' ■ t ■ ■ ■ ■ I ■ i-i-i-i < ' > ' i i i i ■ i

Figure 37. The same as in the two previous figure but with momentum-free source and solid obstacle line. In this trial the mean wind direction is 10 degree clockwise from the ideal perpendicular wind direction.

The transit time from the first to the last of these sensors is «20 sec. With this time lag in mind it is possible to follow characteristic peaks in the concentration, eg the gas arrival. The average concentration decreased in the downwind direction.

86 Ris0-R-1O3O(EN) EEC57 crosswind concentration variation

Figure 38. Crosswind variation of ground-level 'concentrations behind a solid ob ­ stacle in a momentum-free release. The obstacle is removed in the middle of the trial.

EEC57 downwind concentration variation

Figure 39. Downwind variation of ground-level concentrations near the plume cen­ tre line. The obstacle removal in the middle of the trial is detected in the signals of sensors #34, 38 and 60. Note that the scale of plots for sensors #38 and 60 are reduced by a factor 3.

Momentum free release and porous fence

Figure 40 shows concentration time series from a trial with momentum free source and porous obstacle. The wind direction was unfavourable and mast 4 was not properly exposed. Heinrich & Scherwinski (1990) pointed out that obstacle re­ moval is very difficult to detect in signals of the exposed downstream instruments (sensors #23, 34, 35 and 36), ie that the obstacle effect was weak for this exper-

Ris0-R-1O3O(EN) 87 EEC58 - cyclone source and porous fence

Sensor 6c - ■ bensor 65 bensor 37

Sensor 6C

- Sensor ‘M bensor 31 Sensor 38 ® M4

. • bensor 2b Sensor23 Jk :MV1l : Senior 2f Sensor 34

- Sgnso?*3E bensor 18 Sensor 43 -•

® M3

Fence

bensor 21

0 5 10 15 20 25m -«— Gas source i » » » « i-» « « » i » » » » i ■< ■».» » i » r » » i

Figure 40. The same as in the previous figures but with momentum free source and porous obstacle line.

imental set-up. The flow passed through the gaps in the fence and the turbulent kinetic energy generated behind the obstacle elements was probably weaker than in the jet cases.

Vertical profiles without obstacle

In this section I examine vertical profiles measured at the two masts in the period after obstacle removal. The data are taken from trial EEC55 and EEC57 with solid

88 Ris0-R-1O3O(EN) fence and two different source types. Each figure is a comparison of the profiles observed by the two source types and at the masts 35 m and 68 m downstream of the source. The data are averaged over TiiV records #324-520 for EEC55 and #462-718 for EEC57 and the corresponding period in the Risp 10-Hz data set.

EEC55 - jet source EEC57 - cyclone source

Front mast Rear mast

Figure Jtl. Molar Gas Concentration from catalytic sensors • and with the sonic/thermocouple method □. Ground level values is interpolated from nearby instruments.

Concentration

Figure 41 shows concentration sensors measured by catalytic sensors similar to those in the ground level array together with concentration estimates obtained by the sound virtual temperature signal of sonic anemometer with attached ther­ mocouples, see appendix C. The ground level concentrations were not measured at the masts and the values shown are interpolated from nearby measurements in the ground-level array of catalytic concentration sensors. The interpolations c, are calculated with the inverse square distances Axf 2 as a weighting function.

Cint = ■ where AXi = \xi - x 0\ (201) 2_, t±Xi Sensors #19, 28, 43 and 48 were applied for the front mast and sensors #23, 38 and 60 were applied for the rear mast. A catalytic sensor at the 1 m level of the front mast gave much too low concentrations, so observations from this instrument have been rejected. The remaining five sensor pairs produced consistent concentrations in both trials. The ground-level concentrations decreased from the front to the rear mast. Because of the increasing plume depth a similar decrease was not observed by the instruments on the masts. The momentum-free plume was more shallow than the jet. It is of interest to check whether the shape of the concentration profiles is in accordance with the observations by Britter & Snyder (1988). This test is made with the non-dimensional plot in figure 42, where the concentrations are divided by the local surface concentration and the observation heights are divided by the centre of gravity defined by z = f czdzj fcdz using step-wise linear interpolation for the integrals. The best general fit to the vertical concentration profiles is an exponential distribution. The profiles are however not truly self-similar.

Temperature

Figure 43 shows temperature deficits measured by thermocouples. It seems that there was a good local correlation between temperature and concentration for

Ris0-R-1O3O(EN) 89 o EEC55, Front Mast • EEC57, Front Mast □ EEC55, Rear Mast ■ EEC57, Rear Mast

= exp

p'=0.7_

0.20 0.40 0.60 0.80 Dimensionless concentration: c/c,

Figure 42. Observed concentrations compared to distributions discussed by Britter & Snyder (1988).

EEC55 - jet source EEC57 - cyclone source 6 m 6 P m Gj m 6p m

41? 41? 4 3 41? 13 ih 3 2 -h 2 k t n □ . °c □ D1 ' - %- 2 4 2 4 2 4 2 4 Front mast Rear mast Front mast Rear mast

Figure 43. Temperature Deficit. Similarity with the concentration profiles is noted except for the ground level. a given mast and experiment. Concentration and temperature are both results of the mixing process and the thermocouples are capable of measuring the cloud structure. Furthermore they have the advantage of being inexpensive and relatively fast compared to most concentration sensors. Figures 44 and 45 present temperature fluctuations interpolated in time and height between the thermocouple measurements at the front mast. The cloud height is variable and the instantaneous profiles have similar shapes as the mean profile in figure 43. The scale of the horizontal axis represents one minute and the temperature difference between the isotherms is 1 °C with the jet source and 0.5 °C with the cyclone source. The time scale of the characteristic temperature fluctuations is much shorter in the jet case than with momentum-free release.

Enthalpy budget

It is of interest to check whether the mixing process was adiabatic or perhaps influenced by the surface heat flux. Wet adiabatic mixing of ammonia and humid

90 Ris0-R-lO3O (EN) Figure 44• Temperature as a function of time and height in trial 55 with jet release. Temperature fluctuations without momentum

Time [s]

Figure 45. Temperature as a function of time and height in trial 57 with momentum-free release.

Lathen Trial 57, Front mast, lm

0 5 10 15 20

12 -=1---- ,---- r

0 o -20 E -40

Time [min]

Figure 45. Time series of concentration and temperature, a smoothed reference temperature and the derived enthalpy time series.

Ris0-R-1O3O(EN) 91 air was examined in chapter 9 where it was assumed that AH (T - ra!r) - ((1 - c) • Mair • cf + c• M • Cp) + Aflcon = c-AH0 (202)

Propane and water are immiscible liquids and the aerosols are expected to solely consist of water. With an assumption of homogeneous equilibrium the heat of condensation AHcon is simplified to

—Mh 2o £h 20 ((1 - c)«air(l-c) where g air is the ambient humidity and qsat(T) is the saturation humidity at the observed temperature. Figure 46 shows time series of concentration c and tempera­ ture T measured by adjacent sensors. The ambient temperature Ta-,r is represented by a smoothed time series from an unexposed thermocouple at the top of the front mast. In order to obtain zero enthalpy deficit before the trial, each temperature signal is corrected for its pre-trial difference from the reference temperature. The water content of the air g a;r was observed by a psycrometer. The derived enthalpy time series shown below in figure 46 seems to be proportional to concentration al­ though the natural temperature fluctuations also produced enthalpy fluctuations before gas emission.

Concentration [%] Concentration [%]

i'i o -0.05 o -0.05

EEC55 (jet) 1 m level at front mast EEC55 (jet) 1 m level at rear mast

Concentration [%] Concentration [%] 0 1 2

9 -0.05 o -0.05

+ Pre-trial measurements 1= -0.15 O Measurements with fence A Measurements without fence

-0.20 J EEC57 (cyclone) 1 m level at front mast EEC57(cyclone) 1 m level at rearmost

Figure ft. Local correlations between 10 sec block averages of enthalpy and con­ centration. The regression lines are based on the period without fence indicated A forced through (c, AH) = (0,0).

Figure 47 shows scatter plots of 10 sec block-average values of enthalpy and con­ centration. The correlation seems to be linear but not universal. Estimates of the

92 Ris0-R-1O3O(EN) ■1L

local AH/c ratios are obtained by linear regression lines of the type c = /3 • AH, ie lines which are forced through point (c, AH) = (0,0). Similar analyses were made for other measuring positions, and estimates of the AH/c ratio are listed in table 12. In case of perfect adiabatic mixing one expects AHq = AH/c. The uncertainties are estimated by the residual variance between observations and re­ gression line. The uncertainty depends on the range of the observed concentrations and appears to be sensitive to the reference point chosen. Therefore the data from the 4-m level have been excluded from the analysis.

Table 12. Enthalpy to concentration ratio AH/c estimates and uncertaincies. The adiabatic mixing values AHq are calculated by the release conditions.

EEC55 (jet) EEC57 (cyclone) Fence No fence Fence No fence [kJ/mole C3H3] Front mast 1.0 m -14.7±1.1 -14.5=1=0.8 -2.8±1.0 -3.3±0.5 2.0 m -12.5±1.2 -10.0±1.8 -2.3±1.9 -3.6±0.8 Rear mast 1.0 m -8.8±1.1 -8.8±0.8 -2.3±1.7 -3.7±0.9 2.0 m -7.7±0.5 -8.2±1.0 -2.0±1.6 -4.7±2.9 Adiabatic mixing -16.3 -13.3

EEC55 - fence EEC55 - no fence Front Rear Front Rear lm 2m lm 2m lm 2m lm 2m ------0.0

2-7.7 T 1-8.8 £"8 '2 Adia. mix. I--8.8 <>-10.0 £-12.5 £-14.7 1-14.5 kJ -16.3 mole G'sHg

EEC57 - fence EEC57 - no fence Front Rear Front Rear lm 2m lm 2m lm 2m lm 2m 0.0 X"1"3 £-2.3 £-2.0 £-2.8 2-3.3 £-3.6 £-3.7 >-4.7 Adia. mix.

-13.3 kJ mole C3H.8

Figure 48. Observed enthalpy to concentration ratio. The adiabtic mixing value corresponds to the release.

The initial source enthalpy AHq in the jet case is the difference between enthalpy values H(p, T) in the conditions of the release system and in the atmosphere. These are found from a table in Vargaftik (1975, p. 236), which should be more accurate than the linearized integrals in chapter 9. The source enthalpy in the momentum-

Ris0-R-1O3O(EN) 93 free release EEC57 is affected by the liquid fraction which separated from the flow inside the cyclone. Following Heinrich & Scherwinski (1990) I assume that 33% of the aerosols are separated in the cyclone outflow. It is further assumed that the rain-out fraction left the flow with the atmospheric boiling point temperature Tboiij. since the pressure inside the cyclone probably was close to the ambient and the gas concentration close to 100%. The rain-out enthalpy correction is then estimated as in equation 170. Enhanced rain-out fractions and lower liquid rain- out temperatures would further increase the source enthalpy. Figure 48 is a graphical representation of table 12.1 conclude that: Conclusions

• The observed enthalpy to concentration ratios are higher than the source value, ie the mixing is not adiabatic. • The departure from the adiabatic mixing case is larger with momentum free release than with the jet source. This may be because the stronger entrain­ ment reduces the temperature difference relative to the ground.

• With the jet source the enthalpy increases from the front to the rear mast indicating an accumulated heat input. The difference between the two masts is not significant in the momentum-free release, probably because of the modest 0(2) °C temperature deficit.

• The local height dependence is insignificant except for the front mast in the jet case.

• The effect of the obstacle is insignificant.

A very rough estimate of the heat input tp averaged over the ground contact area heat flux A may be obtained from m Pest ~ (204) Mc 3hs • A where m is the effective release rate, Mc3h8 is the molar weight and AHq is the source enthalpy. Using measurements from the 1-m level of the rear mast after obstacle removal with the effective release rates and source enthalpies and contact areas estimated to 1400 m2 for the jet and 2100 m2 for the plume, we obtain ( 3 kg/s (-8.8+16.3) kJ/mole ) 0.044 kg/mole-1400 m2 365 W/m2 for EEC55 (205) | 2 kg/s (-3.7+13.3) kJ/mole 208 W/m2 for EEC57 L 0.044 kg/mole-2100 m2

The surface heat fluxes are probably much higher close to the source.

EEC55 - jet source EEC57 - cyclone source

Figure 49. Relative density surplus. These profiles are quite similar to the concen­ tration profiles.

94 Ris0-R-1O3O(EN) Density

An accurate density calculation should include the heat from possible condensa­ tion of liquid aerosols. The degree of condensation was not measured directly. It may however be estimated by a mass balance and the homogeneous equilibrium assumption. The water vapour content q of the gas phase of the mixture is assumed to be

<7sat(T) q = min (206) 9o • (1 — c) where qo is the water vapour content of the ambient air and g sat is the water vapour content corresponding to saturation. In case of condensation the liquid phase mass fraction a is estimated by the difference between the total water content go • (1—c) and the assumed vapour phase water concentration g = g Sat(T).

[go(l — c) — g sat(T)] • Mah 2o (207) c • Mc3H 8 + (1 — c)[(l — go) • Mair + go • Mah 2o ] The cloud density p is then found by equation 135, which in the present case becomes:

1 p{c- Mc3H 8 + (1 - c)[(l - g) • Mair + Q ' Mh 2o ]} P~l^a Rf (208) where p is the atmospheric pressure, R is the universal gas constant and T is the local mixture temperature. The density of the ambient air is Pair = P{(l-go)-M air + go-MH 2o} (209) -RTair where the air temperature Tkir changes during the experiments. Time series of the local density p and reference air density pair have been calculated from measured temperature and concentration time series, and profiles of the average density surplus time series are plotted in figure 49. As expected the excess density profiles are similar to the concentration profiles, but the density to concentration factor is not universal. The corresponding effective molar weights M* are calculated by A p AM* ------«C' — (210) Pair Mair and listed in table 13. The measurements from the 4-m level are again excluded because of the inaccuracy of finding a ratio between two weak signals. For the same reason the value from the 2-m level of the rear mast in trial EEC57 is prob­ ably inaccurate. The effective molar weights for the two source types (0.110 and 0.098 kg/mole) are shown for comparison. The density effect of aerosol forma­ tion was estimated by a repeated calculation without condensation. The effect on M* was negligible in trial EEC57 and 0(3)% in trial EEC55, which were made with higher relative air humidity. In an isothermal laboratory model of such field experiments the ratio (M* — Ma-,r)/Mair ought to be constant, but the measure­ ments show that this was far from the case. At worst the momentumfree release in EEC57 (M* — Majr)/Ma,r is just 40% of estimated source value. In conclusion the choice of a simulant gas for wind-tunnel modelling of flash boiling releases is very difficult.

Velocity

Figure 50 shows velocity profiles calculated by sonic and cup-anemometer mea­ surements. The profiles from the rear mast are confusing because of a calibration problem of the sonic anemometers at 1, 2 and 4-m levels, which are believed to

Ris0-R-1O3O(EN) 95 Table 13. Effective molar weight M* assuming liquid aerosols in homogeneous equilibrium with gas mixture. Also shown is the error in M, when neglecting the mass of the aerosols. The humidity of the ambient air was 100% R.H. in trial EEC55 and 94% R.H. in trial EEG57.

M, [kg/mole C3H8] Aerosol effect Front Rear Front Rear Source EEC55 2 m 0.074 0.069 -2.1% -2.3% M„ = 0.110 1 m 0.078 0.068 -3.8% -2.4% EEC57 2 m 0.057 0.071 0.0% 0.0% M* = 0.098 1 m 0.056 0.058 0.0% 0.0%

EEC55 - jet source EEC57 - CO D E

.... . m □ 6 m □ m □

i 4 - • □ 4 - P 4 4 - □ □ - d □

_ 2 - • d 2 2 6 2 - .□ □ □; P O' • □ , . □ , «a □ ms ms rr m/s ...... • 1 i i , .' i i 1 2 1 2 1 2 Front mast Rear mast Front mast Rear mast

Figure 50. Mean velocity. Zigzag profile on the rear mast is an intercalibration problem between sonic anemometers at 1, 2 and 4 m and cup anemometers - cup anemometers are believed to be correct. Circles • indicate readings in the absence of gas. give too high readings. This seems to be a problem at the rear mast only, where the sonic anemometers were of an older type than those on the front mast. A comparison of more sonic measurements from the two masts without obstacle or gas release suggests that the calibration problem was a false offset rather than a false gain, so the variance and flux measurements shown later in this chapter are believed to be valid. Values from a period before gas emission18 are included at the front mast where the obstacle effect presumeably is of minor importance. The average wind profile in the momentum free release is almost equal to the wind in the reference period, whereas the jet effect is evident at the 1-m level of the front mast in EEC55. Nyren & Winter (1990) made test measurements on the release nozzle and jet momentum concluded that the near-exit pressure was very close to the saturation pressure at ambient temperature. With this exit pressure the jet momentum predicted by equation 87 po = p8 at(Tair) is evaluated to F]et = 208 N for EEC55. The jet velocity may be estimated with an approximation of negligible friction, ie treating the momentum as a conserved property of the flow.

(mC3H8 + mair) ' U = mc3H8 • Uo + Thair • Mair =>

c ' MCaHg ' Up _ C • Mc3H8 Fjet H ^air (211) Mair + C • AM Mair + C • AM fhC3H8

lsThe exacts pre-trial periods are defined to EEC55 rec #100-2148 and EEC57 rec #550-1536 in the Rise 10-Hz data set.

96 Ris0-R-1O3O(EN) 0.012 • 0.044 208 N = 1.26 m/s 0.029 + 0.012 • 0.015 3 kg/s where u = velocity at concentration c Mair = typical velocity of entrained air Mo = initial jet velocity (after flash) ■fjet = jet flow force mc3H8 = mass flow of propane Mlair = mass flow of entrained air Mc 3Hb = molar weight of propane Mair = molar weight of air and where the average concentration of 1.2 % observed at the 1-m level of the front mast in EEC55, the estimated flow force Fjet and release rate rhc3H8 are inserted. The 1.26 m/s estimate of the excess velocity is in accordance with the velocity profile measured in figure 50. Unfortunately the velocity profile below 1 m is unknown. Based on cup-anemometer measurements from the rear mast in periods after gas surface roughness release in trial EEC56-EEC57 the surface roughness is estimated to zq=6-6.5 mm. The soil was ploughed and walked upon, so the surface-roughness estimate is in reasonable agreement with Panofsky & Dutton (1984, p. 123). Because of a trench 10 m upstream of the source the profiles were never truly logarithmic at the front mast. EEC55 - jet source EEC57 - cyclone source 6 6 m 6 m

4 □

2 - D • - □ [a . . A m2/s2 m2/s2 j i 0.2 0.4 0.2 0.4 0.2 0.4 0.2 0.4 Front mast Rear mast Front mast Rear mast

Figure 51. Turbulent kinetic energy. Circles indicate readings in the absence of gas. The general stabilizing effect of the dense gas is more than counteracted by the shear production in the jet.

Turbulence Figure 51 is a plot of the turbulent kinetic energy e = |-(cr2+cr2+a2). The circles refer to the pre-trial period representing the atmospheric background turbulence. The accuracy of the data in this and the following figures is not perfect since stable estimates of second-order statistics require longer periods of observations than available. The pre-trial turbulence was slightly reduced in the momentum-free release, though not as significant as in the isothermal Thorney Island continuous release experiments to be discussed in chapter 14. In the momentum-free release case the turbulent kinetic energy was the same at the two masts, probably because the bulk stabilities f Apdz were not that different, see figure 49. In the jet case the turbulent kinetic energy was significantly larger than the pre­ trial energy. At the 1-m level on the front mast the turbulence production was more

Ris0-R-1O3O(EN) 97 important than the stabilizing dense-gas effect. The jet effect was weaker at the rear mast where the turbulent kinetic energy approached that of the momentum- free release. EEC55 - jet source EEC57 - cyclone source m 6 m 6 771 6 m : ___ n # 1 ___

□ • 4 □ 4 .... □ ,

q« 2 □ 2 □ • 2 □ 6 • .

ms ms m/s CO

.i.i., .i.i,, - 0.2 0.4 0.2 0.4 0.2 0.4 0.2 0.4 Front mast Rear mast Front mast Rear mast

Figure 52. Longitudinal velocity variance au. Circles indicate readings in the ab ­ sence of gas.

EEC55 - jet source EEC57 - cyclone source 6 m 6 m 6 m 6 . m ____ □ □ • l i

___ 1 ...... 4 5 □ .... , 1 ' ....

i 6 — i • 6 2 2 to □ • 2 — o □ □ • d ms ms ms m/s .i.i.. ■ i ■ i ■ - ■ i.i 0.2 0.4 0.2 0.4 0.2 0.4 0.2 0.4 Front mast Rear mast Front mast Rear mast

Figure 53. Crosswind velocity variance av. Circles indicate readings in the absence of gas.

EEC55 - jet source EEC57 - cyclone source m 6i m 6 j m 6j m

- □ • 4 - □ 4 B 4 n

- > - £ 2 - □ 2 2 - p ° m/s - m/s m/s *"* m/s .i.i . i . i . r ,1.1 .i.i,, 0.2 0.4 0.2 0.4 0.2 0.4 0.2 0.4 Front mast Rear mast Front mast Rear mast

Figure 5f. Vertical velocity variance aw. Circles indicate readings in the absence of gas.

Mercer & Davies (1987) observed that the turbulent velocity perturbations in the Thorney Island experiments were suppressed in all directions in contrast to the observations in figures 52-54. The largest turbulence suppression observed in the propane experiments was in the longitudinal direction, and the vertical veloc­ ity perturbations was almost unaffected by stratification. This could be related to

98 Ris0-R-1O3O(EN) heat convection from the surface. The velocity time series are rotated to a coordi­ nate system aligned according to the local average flow vector by the method of appendix D.

EEC55 - jet source EEC57 - cyclone source 6 m 61 m 6 m 6 m

4 - □ 4 - P • 4 - □ J

# 2.1* ,V .6 # k m2/s2 m2/s^ m2/s‘ m2/s O 1 1 0.05 0.05 0.05 0.05 Front mast Rear mast Front mast Rear mast

Figure 55. Turbulent stress. Circles indicate readings in the absence of gas. The negative values at the front mast in the jet case mean an upward momentum flux. The surface values indicated by diamonds are estimated.

Shear stress

Figure 55 shows that the turbulent shear stress was significantly affected by the dense-gas release. The measurements indicated by the dots were made before gas release. The pre-trial stress variation with height is unexpected and probably an effect of the trench upstream of the release point. The stress measurements during gas release are much smaller than those made in the pre-trial period. The negative stress at the 1-m level of the front mast in trial EEC55 implies that the momentum flux is directed upward from the jet to the ambient flow.

Dense surface jet in boundary layer Dense cold plume in boundary layer

'11 1 •§> i 1 I ;a ! = 1 i i i l i / i \ / / A...... i \ ...... 7 ...... 7...... "T" V-4~-. \ / i | l / i Cone. Velocity Shear stress T.K.E. Cone. Velocity Shear stress TJC.E.

Figure 56. Interpretation of the measurements in the dense gas releases with and without initial momentum. The lowest part of velocity and shear stress profiles in the jet case are hypothetical.

Figure 56 is my interpretation of the profile measurements. Starting with the profiles in the dense plume at the right-hand side of the figure: 1) the velocity distribution was not much affected by stratification, 2) the shear stress was clearly suppressed and 3) the turbulent kinetic energy was only moderately reduced. Above the gas layer the shear stress approached the ambient shear stress. Because of the finite horizontal dimension of the gas layer, the air above was unaffected by the reduced surface stress, similar to an internal boundary layer resulting from a sudden change in surface roughness, see eg Sempreviva, Larsen, Mortensen & Troen (1990). The interpretation of the profiles in the jet case sketched on the left-hand side of the figure is more speculative. All sonic anemometers were placed above the maximum jet velocity, but since the lower boundary condition for the

Ris0-R-1O3O(EN) 99 velocity is ’no slip at the surface’, the velocity profile must be of the shape as in the sketch. The sketched shear-stress profile should be in accordance with the gradients of the velocity profiles, since the stress profiles must have the same sign as the vertical velocity gradient. This resulting jet shear-stress profile explains the negative observation in figure 55. Unfortunately it also implies that the single negative measurement provides little qualitative information on the stress profile, since the position of the maximum is unknown. The mechanical turbulence production is the product of Reynold stress and turbulence production velocity gradient. —dm 7du —U'W (212) dz

In the momentum-free release the flow profile was almost unaffected by the dense gas, so the significant reduction of the Reynolds stress implies that the shear production of turbulent kinetic energy was reduced. Following this argument the shear stress at the 1-m level in the momentum-free gas cloud was only about 10% of the pre-trial value and 20% on the rear mast. This should be compared with figure 51 in which the turbulent kinetic energy in was reduced to 50% only. The lifetime of the turbulent eddies was short compared to the advection time another source of from the source, and the explanation of the modest reduction of the turbulent turbulence kinetic energy must be sought in one or both of the following hypotheses: a) turbulence was supplied by heat convection

b) turbulent energy was supplied by large eddies above the gas layer

A way to examine the importance of heat convection is to calculate the Monin- Obukhov length scale representative for the gas layer. L _ pul _ —TpCpul ngw'p' Kgip /—280 K • 1.3 kg/m 3 • 1000 J/kgK • (0.1 m/s)3 O (-0.5mX213) V 0.4 • 9.81 m/s2 • 200 W/m2 where the heat flux

Estimates of in-cloud turbulence scales

As explained in section 4 Jensen (1981b) estimated in-plume turbulence by Monin- Obukhov similarity theory using empirical micrometeorological knowledge in com­ bination with the estimate: e = u2 + m2. Table 14 is an attempt to compare this approach with observations. The estimates in the table are generally obtained from the lowest level of observation, except at the front mast in jet trials EEC55 and EEC56, where the temperature and velocities were evaluated at the hypothetical level of maximum velocity. These maxima are estimated to 3 m/s at 0.5 m height, judged by the leftmost velocity profile in figure 50. This is slightly less than a 3.6 m/s maximum velocity which may be found by conservation of jet momentum. Sonic anemometer measurements from the rear mast are corrected for the believed signal offset and some temperatures have been found by interpolation. With these 19 Of course the counteracting density flux by entrainment made the overall cloud stability positive.

100 Ris0-R-1O3O(EN) Table 14. Estimates of the in-plume velocity scales u* and w* and comparison with turbulent kinetic energy e.

Profile data Estimates Fit <1 E i& z u(z) e° u* w* eb Trial Mast [m] [m/s] [m2/s2] [m/s] [m/s] [m2/s2] EEC55 Front 0.5C 4.95" 3.00" 0.261 0.258 0.124 0.269 EEC55 Rear 1.0 2.31 1.94/ 0.116 0.135 0.091 0.084 EEC56 Front 0.5C 4.88" 3.64" 0.249 0.259 0.123 0.269 EEC56 Rear 1.0 3.40 2.19 / 0.097 0.150 0.107 0.106 EEC57 Front 1.0 0.64 1.46 0.109 0.108 0.056 0.048 EEC57 Rear 1.0 0.20 1.69/ 0.111 0.131 0.041 0.063

“Measured at 1-m height 6Least-square-error fit: e = 3.47u» + 2.43tuJ “Estimated height of maximum velocity rfFound by interpolation to z =0.5m “Estimated maximum velocity fCorrected by -0.25m/s values of z, u(z) and AT the model of Jensen (1981b) predicts turbulence veloc­ ity scales u, and w* in the same order of magnitude as the measured turbulent kinetic energy e. The squares of the estimated friction velocities u2 are added as ground-level values in figure 55. The rightmost column shows a quadratic fit of type of some of the entrainment models discussed in chapter 4. The errors are not alarming since the fit is quite sensitive to the estimated velocities at the unknown maximum jet velocity.

EEC55 - jet source EEC57 - cyclone source m 6 m 6 m 6 m

\ -a 4 ° 4 Q

'd 2 d 2 - K 2 - a '□ ‘d ^ d - b ______% ...... % ...... % ...... % 0.5 0.5 0.5 0.5 Front mast Rear mast Front mast Rear mast

Figure 57. Variance of concentration fluctuations crc-

Concentration fluctuations Figure 57 shows variance profiles of the concentration fluctuations. The shapes of these profiles are slightly different from those of the mean concentrations shown in figure 41. Table 15 shows that the signal intensity I = cc/c generally increases with height except in the jet case where a maximum was observed at the 2-m level. The intensities were lower with the jet source than with the cyclone probably because the plume meandering was less significant with this source type. The jet turbulence enhanced the mixing process and diluted the typical strand concentrations which according to the a-/3 model also tend to moderate the intensity, see page 39.

Ris0-R-1O3O(EN) 101 The signal intermittency 7, ie the probability of non-zero concentrations, de­ creased with the height of observation and distance from the source as expected. The intermittencies of the two trials ought to be comparable since the wind mis­ alignments were the same. Likely causes of enhanced jet intermittency are the reduced plume meandering and slightly deeper gas layer.

Table 15. Mean concentration c, signal intensity I = crc/c and intermittency 7 = P(c > 0) in the absence of obstacle.

EEC55 EEC57 jet soucre cyclone source cl 7 c/7 Front mast 1 m 1.16 0.62 0.95 0.47 1.16 0.82 2 m 0.36 1.30 0.81 0.16 1.39 0.59 4 m 0.06 0.75 0.95 0.06 1.41 0.38 Rear mast 1 m 1.16 0.61 0.93 0.34 1.05 0.75 2 m 0.56 0.92 0.73 0.10 2.00 0.44 4 m 0.18 0.65 0.59 0.03 2.21 0.26

EEC55 - jet source EEC57 - cyclone source m 6j m 6 m 6 . m

13, 4 -q 4 -q 4 0

- \ - \ 2 2 -t 2 -q □ w . - h m/s | %-m/s i %-m/s ..... 0.05 0.05 0.05 0.05 Front mast Rear mast Front mast Rear mast

Figure 58. Vertical gas flux.

Gas flux

Figure 58 shows profiles of the vertical turbulent gas flux w'd. As expected from the kinetic energy profiles, the turbulent mixing is much more efficient in the jet case than with momentum-free release. This is one of the reasons why the height of the gas layer was larger in the jet case. At first thought one may wonder why the enhanced mixing did not result in a more diluted cloud than with the momentum- free source. The large effective source strength, higher advection speed, narrower plume width and positive downwind horizontal gas flux u'd does however all tend to increase the jet concentrations at a given downwind position. Some numerical dispersion models apply eddy diffusivities K defined from w'd = Eddy diffusivity —Kdcdz. The plot in figure 59 shows K estimates based on the vertical flux mea­ surements and concentration gradients derived from the measurements shown in figure 41. The mean concentration is only available at 0,1, 2 and 4-m heights, and the estimates of the concentration gradients || were sensitive to the numerical method for the gradient estimate. I have chosen to present results based on either

102 Ris0-R-1O3O(EN) EEC55 - jet source EEC57 - cyclone source 6j 771 6 m 6j m 6j m

4 4 - 4 - ' 4 -

2 □ 2 □ 2 ~ ,-D 2 P Q ■ O'" « 2 o' • 1 ^ , m2/s , m2/s A i m

0.05 0.05 0.05 0.05 Front mast Rear mast Front mast Rear mast

Figure 59. Eddy diffusivity for vertical gas flux. Three-point method: □, and two- point method; •.

1) estimates of |f at 1-m and 2-m levels, based on a second order polynomia of c through the three closest measuring points. 2) an estimates of |§ at the 1.5 m level based on linear interpolation, with w'd taken as the average of the measurements at 1 and 2 m.

In an ordinary surface layer of neutral buoyancy, the vertical eddy diffusivity is Kc = K,u*z/(p c, where k is the von Karman constant and c is the dimensionless concentration defined as 1 in the case of neutral stratification. Thus the eddy diffusivity of a passive tracer would be

0.4 • Voi05m/s • 2m/s % 0.18m 2/s at the 2-m level and its variation should be linear with height. The estimates in figure 59 are »50% of the neutral-flow eddy diffusivity.

Table 16. Entrainment velocity calculated by interpolation at the interface ue = w'dzjc.. and by the integrated vertical gas flux ue — 2 f w'ddz/ f cdz.

Interpolation method Integration method Zi w'c'(zi) cfe) ue f cdz f w'ddz ue [m] [%-m/s] [%] [m/s] [%-m/s] [%-m2/s] [m/s] EEC55 Front 2.05 0.042 0.38 0.112 3.04 0.146 0.096 Rear 2.63 0.030 0.44 0.067 3.05 0.128 0.084 EEC57 Front 1.53 0.020 0.31 0.064 2.27 0.068 0.060 Rear 1.80 0.013 0.15 0.084 1.12 0.053 0:095

Box models usually describe the mixing proccess by a entrainment velocity over entrainment velocity an idealized cloud interface. Following van Ulden (1983) I define this interface height as twice the centre of gravity = 2 fez dzf fcdz. The vertical flux and concentration at this level is then estimated by linear interpolation in the profile data plotted in figures 41 and 58 and the entrainment velocity is calculated as ue = w'd(zi)/c(zi). An alternative method is HI 0 0 9 , 2 fz%dz 4- 2!z^iw'd)dz 2 f w'd dz (214) fcdz fcdz fcdz where the approximations are based on the following arguments:

Ris0-R-1O3O(EN) 103 1. the entrainment rate is evaluated by ue = 2^f. Horizontal flow divergence caused by the lateral slumping process and jet deceleration is considered as part of the mean flow rather than a contribution to the mixing process;

2. the neglect of horizontal flow divergence implies that the denominator is con­ stant; 3. the Lagrangian concentration variation is approximated by the divergence of the turbulent fluxes. The vertical flux divergence is the only one available and presumably also the dominating one;

4. the flux vanishes at ground level and well above the plume.

The integral method does not rely on an assumption of profile similarity. Estimates by both methods are summarized in table 16 using stepwise linear interpolation for the various integrals. The flux profiles shown in figure 58 have been extended by virtual points of zero flux at ground level and at 6-m height. The two methods agree within 10%. It is perhaps surprising that the smallest entrainment velocity at the rear mast was observed in the jet case. This is probably because the jet induced turbulence was less significant at this distance while the f cdz integral was relatively large. Prior to each experiments the momentum flux u'w' was measured to % —0.04m*2 /s1 2. A surface plume of neutral buoyancy would thus have an entrainment rate of ue = Xiu, = 0.75\/0.04 = 0.15m/s so the entrainment rate in these experiments are only reduced by a factor in the order of 2.

Table 17. Entrainment velocities [m/s] in various box models evaluated by either the measured turbulent kinetic energy e or by the estimates of the turbulent velocity scales u*, wm presented in table 14-

Measured e Estimated e, u* & w* Eidsvik SLAB Eidsvik SLAB0 Jensen This report EEC55 Front 0.114 0.120 0.061 0.070 0.052 0.050 Rear 0.065 0.061 0.020 0.018 0.011 0.011 EEC57 Front 0.074 0.078 0.017 0.006 0.011 0.010 Rear 0.084 0.098 0.032 0.016 0.030 0.028

“The excess velocities are set to Su 2, 1, 0, 0 m/s in the fours test cases.

Table 17 contains estimates by some of the entrainment functions discussed in chapter 4 using the following alternative approaches:

1. the turbulent kinetic energy measured at the lowest level of observation was inserted directly in the entrainment functions listed in table 2 regardless of individual model parametrizations. The buoyancy factors g'h were calculated by the f cdz integrals from table 16 and the effective molar-weight estimates in table 13. Both the Eidsvik (1980) and the SLAB models give realistic predictions;

2. as an alternative the turbulent kinetic energy e was calculated by the individ­ ual sub-models e = f(u,,u;„) using turbulent velocity scales from table 14, ie Jensen’s (1981b) in-plume Monin-Obukhov method rather than the individ­ ual parametrizations. All models predict too low entrainments rates in this test.

The largest uncertainty in the entrainment functions are probably those of the sub-models for the in-plume velocity scales u» and w*. Jensen’s (1981b) in-plume

104 Ris0-R-1O3O(EN) Monin-Obukhov approach may have to be calibrated but the available data are insufficient for this purpose. A larger data set is needed with long time series of in-plume turbulence from at least three heights measured in experiments with variable cloud stability and jet momentum.

EEC55 - jet source EEC57 - cyclone source 61 ffl 6 m 6 m 61 772

401- Ct- 401- 4C-

w V d< %-mjs* % • m/s %-m/s ' ' ' " ' ' ' ' i i i «-l t t t 0.1 0.1 0.1 0.1 Front mast Rear mast Front mast Rear mast

Figure 60. Downwind □ and Crosswind • Gas Fluxes.

With the coordinate system aligned according to the streamlines and assump- continuity equation tions of incompressible flow and negligible molecular diffusion the continuity equa­ tion for concentration is simplified to

dc du'^ Udx ~ dxi (215)

The plume height is much smaller than the width, and therefore the dominating flux gradient must be in the vertical direction. In this way the observed negative vertical gas flux gradient in figure 58 corresponds to increasing mean concentra­ tions along the streamlines. A comparison between mean concentrations of the 2 and 4-m level of the two locations in figure 41 confirms this for the jet case, al­ though perhaps not in the momentum-free release. Following the same argument the decreasing ground-level concentrations imply that the flux gradient should be positive in the lowest part of the profile since the ground-level gas flux must have been zero as in figure 146 of appendix G. Finally figure 60 shows horizontal gas fluxes. The downwind flux u'd is of the Horizontal fluxes same order of magnitude as the vertical flux. It is generally negative when the gas plume has a momentum deficit and positive in the case of excess momentum. The lateral gas flux v'd is insignificant in the momentum-free release but not in the jet case. This indicates that the nozzle was not perfectly aligned according to the average wind direction.

Obstacle effect on local wind direction

Figure 61 shows time series of horizontal direction derived from the 3-D velocity measurements. The orientations of the instruments are not known exactly, but each set of measurements is aligned according to the individual mean direction by the method described in appendix D. The flow direction observed at the 1-m level of the front mast during the 2.5- 8.5 min release period appears to be more steady, and removal of the fence causes a distinct difference in the observations from the rear mast. The effect of the obstacle seems to be weak at the front mast. It is noted that the time scale of the fluctuations is quite long and that the correlation between neighbouring instruments is poor.

Ris0-R-1O3O(EN) 105 EEC55 — Derived horizontal wind directions

-90

90

-90

Time (min)

Figure 61. Wind directions with jet and solid fence. The uppermost three time series are from the front mast, and the three lower ones are from rear mast.

EEC55 front mast EEC56 front mast EEC57 front mast

■ Pre-trial - ■ Pre-trial ■Pre-trial - □ Fence □Fence □Fence 50 □ No fence "" □ No fence □ No fence ~

EEC55 rear mast EEC56 rear mast EEC57 rear mast 80 70 ■ Pre-trial ■Pre-trial - ■ Pre-trial - 60 D Fence □ Fence £ 50 □No fence “ □ No fence " % 40 § 30 20 20-- 10 10 T- 0 1m 2m 4m

Figure 62. Standard deviations of wind directions <7Dir calculated from sonic anemometers.

The variability of the local wind directions troir for different periods of trials EEC55-EEC57 is summarized in figure 62. The lengths of the averaging periods are almost equal. The variability of the wind direction is best understood if ap­ proximated by ffDir « crv/u (Panofsky & Dutton 1984, p. 157) where av is the

106 Ris0-R-1O3O(EN) variability of the crosswind velocity perturbations and u is the mean wind speed. The following observations are made:

• outside the wake zone the variance of the crosswind velocity cx v was almost independent of height. The height dependence of the wind direction variability ypir was related to the wind profile u{z)\

• the steady wind direction at the front mast in the two jet releases EEC55 and EEC56 was caused by an increased jet velocity;

• the momentum-free gas release in EEC57 made little difference at the front mast, ie the effect of stratification on the flow direction was modest;

• the upstream variability was only slightly enhanced by the obstacle; • the significant variability downstream is probably both related to the in­ creased turbulence level crv and the decreased mean velocity u.

Wake measurements Figure 63 shows concentration time series at 1, 2 and 4 m in front of and behind concentration time series the obstacle in EEC55. The downstream concentrations are seen to change as the obstacle is removed in the midst of the experiment. The variance at the 1-m level increases after obstacle removal while the mean concentration remains unaffected, ie the intensity of the concentration fluctuations decreases. This implies that the parameters of the a-0 model described in chapter 6 was depending on the presence of the obstacle. The explanation is probably that the enhanced mixing and longer residence time in the wake smoothed out the fine structure of the concentration field. A significant reduction of the mean concentration is observed at the 2 and 4-m levels. The bulk effect of the obstacle was to enlarge the cloud dept and this resulted in lower concentrations near the ground and higher concentrations above. The intensity of the concentration fluctuations at the 4-m level was weaker without the obstacle in contrast to those at the 1 and 2-m levels. Figure 64 shows similar time series from trial EEC56 with jet release and a 50 % porous obstacle obstacle. The width of the individual obstacle elements in the crenelated fence was 2.4 m and the distance to the mast was 15 m. It is believed that the effect on the flow was uniform at the mast position, ie that it is irrelevant whether the mast at a given wind direction is positioned behind a gap or an obstacle element. If we compare the time series from the period with the obstacle in place with those behind the solid obstacle in figure 63, we note that the mean concentration was smaller at the 4-m level. This is probably because the porous obstacle was less efficient in directing the jet upwards. The mean concentrations at the 1-m and 2-m levels were not too different from those with the solid obstacle, but the fluc­ tuations were more intense. Figure 65 shows similar time series from trial EEC57 momentum free release with momentum-free release and solid wall. The concentration fluctuations were reduced in the wake as was the case for the jet release. The mean concentration at 4 m was smaller than in the jet case probably because the jet momentum creates a larger stagnation pressure on the upwind side of the obstacle which enhanced the vertical acceleration.

Wake profiles

Figures 66-68 shows vertical mean profiles measured in the wake of the obstacles. The velocity, concentration, vertical gas flux and turbulent kinetic energy are se­ lected as key parameters. The obstructed period are records EEC55 #114-310, EEC56 #365-525, EEC57 #78-334 in the 1-Hz data set distributed by TiiV and

Ris0-R-1O3O(EN) 107 Concentration EEC55 I

k(L |

n------r ^WvWvW

0.02

OJOt ..t«. l. .i . . .^A»

4 . % 6 Time (min)

Figure 63. Concentration time series at three levels in front of and behind a solid fence with a jet release. The obstacle is removed in the midst of the experiment. corresponding records in the Risp 10-Hz data set. The velocity profiles are ex­ tended to zero velocity at ground level, and the ground level concentrations are interpolated between the nearby catalytic concentration sensors numbers 23, 38 and 60. The velocity profile in figure 66 shows a velocity deficit in the wake. The distance jet and solid fence from the obstacle to the mast was 7.5 times the height of the obstacle which was expected to be just downstream of a recirculation zone behind a two-dimensional obstacle. The concentration profile has a maximum at the height of the obstacle, and the vertical gas flux is in the downward direction from this level and below. The turbulent kinetic energy is enhanced with a factor 0(4) at all levels and the effect of stratification was probably not very important for the wake mixing. The turbulence must have decayed further downstream, where the stratification might have been more significant for the mixing. The vertical mixing in a dense gas model is often predicted from an entrain­ ment equation based on the turbulent kinetic energy budget. The available energy is used by a buoyancy flux gw'p' in competition with the dissipation term. It is therefore surprising to observe a negative gas flux in the wake implying that the downward gas flux buoyancy flux produced turbulence! An interpretation of this observation could be that the dense gas had gained potential energy when it passed the top of the obstacle and used some of this for turbulence production. The order of magni­ tude of this turbulence production mechanism may be estimated by the available potential energy per unit width of obstacle

AEfaii a ApghuH (216) where h and u are the typical height and velocity of the gas flow and H is the height of obstacle. The other relevant production mechanism is the shear stress in

108 Ris0-R-1O3O(EN) Concentration EEC56 ft M3 £ « 0J0Z

o "fit

C 0.00

g 0M ^ 002 | °B>

^ OJOO 0J03

002

a jot

OJOO g 003 ■« OB"

O OBI k, OJOO

•M 0JDZ o 0J3I tt. OJOO

ft OJOO H w OJOZ

O OJOt

«, OJOO

Figure 64■ Concentration time series at three levels in front of and behind a 50 % porous fence with a jet release. The obstacle is removed in the midst of the exper ­ iment. the wake which is the work of the drag force: s

AEdrag OC pCdHu 3 (217) where the drag coefficient % is 0(1). When we take the ratio of these production mechanisms we get

' (218 >

It is shown below that the densimetric Fronde number Fr was well above 1 and the turbulence is therefore primarily generated by shear production. Figure 67 shows wake properties with jet and porous obstacle. The momentum jet and porous fence deficit caused by the obstacle was only half of that observed behind the solid wall. The total drag of the obstacle line was smaller and the increase of the turbulent kinetic energy was only 0(2). As previously discussed the reduction of the ground level concentration was only half of that for the solid wall. The gas flux was in the upward direction at all levels with a maximum flux near the height of the obstacle. In the discussion of the ground-level concentration field of this experiment - see figure 36 - it was suggested that the full impact of the obstacle would appear further downstream than with the solid fence. The strong gas flux at the 2-m level supports this hypothesis. Figure 68 shows wake properties with momentum-free release and a solid fence. momentum free release The velocity profile was reduced similar to that of the wake behind the solid fence in the jet release, and the vertical gas flux was in the downward direction below the height of obstacle. The measured concentrations were rather low probably because the mast was near the edge of the plume during the period with the obstacle in

Ris0-R-1O3O(EN) 109 ConcentTation EEC57 ~l I l l I l I l I | i —i----- 1----- 1----- 1----- 1----- 1----- r~ £ 0J>f

^ OJOO i rmji1 ■ll.M-l -4.

Figure 65. Concentration time series at three levels in front of and behind a solid fence with a momentum free release. The obstacle is removed in the midst of the experiment.

EEC55 - jet and solid fence 6 m 6 m m m

4 - □ ♦ 4 4 - 9 □

2 - P 2 P P - \ 2b f P • P" ..." , P ■ i Cm2/s2 Wr:; ”/s K % % • m/s 1 2 1 2 0.05 0.2 0.4 Velocity Concentration Gas flux T.K.E.

Figure 66. Mean values of velocity, concentration, vertical gas flux and turbulent kinetic energy behind a solid wall in a jet release, with P for the obstacle in place and • after obstacle removal. place. The time series in figure 37 suggests that the plume centre line was near sensor #36, ie 10 m to the right hand side of the rear mast. The turbulent kinetic energy level was even higher than with the jet.

Integrated flow properties

Table 18 shows estimates of integrated flow properties calculated by stepwise linear interpolation between the measurement points with addition of zero concentrations at the 6-m level and zero velocities at the ground. Integrals of fitted curves were

110 Ris0-R-1O3O(EN) EEC56 - jet and porous fence

m 6j 777 6j 777 6j 777

□* 4 B 4 •x 4 - fD ....

2 2 > 2 -♦ □ - • % • 777/s i m2/s2 (fr; I 1 2 1 2 0.05 0.2 0.4 Velocity Concentration Gas flux T.K.E.

Figure 67. Mean values of velocity, concentration, vertical gas flux and turbulent kinetic energy behind a 50 % wall in a jet release, with □ for the obstacle in place and • after obstacle removal.

EEC57 - cyclone and solid fence

61 m 61 771 6| 777 777

@ 418 -c □

- P e .0 tk di n^/s2 777/s % % - 777/S 6-L 1 2 1 2 0.05 0.2 0.4 Velocity Concentration Gas flux T.K.E.

Figure 68. Mean values of velocity, concentration, vertical gas flux and turbulent kinetic energy behind a solid wall in a momentumfree release, with □ for the ob ­ stacle in place and • after obstacle removal.

Table 18. Integrated gas flux, potential and kinetic energy together with typical height, velocity and concentration for the gas flux at the downstream mast.

Obstacle EEC55 EEC56 EEC57 Flux = /o [kg/ (ms)] Present 0.101 0.091 0.015 Removed 0.127 0.077 0.028 EPot = /o 1 m Apgzdz [J/m2] Present 2.22 1.30 0.66 Removed 1.26 0.65 0.43 * — »ii II

[q m cpu 2 dz [J/m2] Present 11.8 10.0 9.3 ■®kin u Removed 15.3 9.6 6.5 5 m cuz dz h [m] Present 2.9 2.1 2.9 “ /«0 m cu dz Removed 2.0 1.4 1.6 -ft5 m cu0 dzj u 6 m [m/s] Present 1.8 2.0 1.6 ■ /

Ris0-R-1O3O(EN) 111 attempted and the difference of the results was in the order of 10 %. Height, velocity and concentration scales h, u and c were defined by:

u-c-h ucdz

~ T u • c • h u2cdz

u-c-h uczdz (219)

The typical height h was increased by the obstacle while the velocity u was re­ duced. If the jet and plume width are set to 30 and 40 m and the effective release rates are 3 and 2 kg/s, we would expect an integrated gas flux of 0.1 and 0.5 kg/(ms) respectively. This is in accordance with the observed gas fluxes from the jet case, whereas some of the material seems to be missing in the momentum-free release. In this trial the mast was probably too far from the plume centre line for the measurements to be representative. The kinetic energy is calculated by an integral weighted by the concentration kinetic energy and it may not be as direct an estimate as that for the potential energy. However there is no doubt that it was an order of magnitude greater than the potential energy. The densimetric Eroude number may be evaluated by supercritical flow Frl = -pi- * (220) Apgh Spot This falls within the range 5-15 so we are clearly in the supercritical flow regime. The potential energy is observed to increase with the obstacle in place. A rough potential energy estimate of turbulent kinetic energy produced by the drag force is found from equation 217. Inserting typical quantities we get

Eprod = O (pc dHu3) = O (1.3 kg/m 3 • 1 • 2 m • (2 m/s)3) = O (20 W/m)(221) for the solid fence and about half of this value for the porous fence. The increase of the potential energy is approximately 1 J/m2 corresponding to an energy flow of 2 m/s 1 J/m2 = 2 W/s for both obstacle configurations giving an overall entrain­ ment energy efficiency around 0.1-0.2. This is in accordance with the observation of Bo Pedersen (1980) who states that the bulk flux Richardson number Rj is in the range of 0.15-0.2 for supercritical flows.

Concentration fluctuations

Tab el 19 shows concentration fluctuation statistics at the rear mast measured with and without obstacle. The intensities I were generally lower with the obstacle in place except for the 4-m level. This may be surprising at first thought since the turbulent kinetic energy was strong in the wake. The reason must be the well- mixed concentration fields in the wake also indicated by the concentration profiles in figures 66-68. A second indicator of steady wake concentrations are the large intermittencies 7 of the wake region. As previously noted the signals had lower intensity I and higher intermittency 7 in the jet release. This was also the case for the wake regions. The differences between the concentration fluctuation statistics of the two types of fence are prob­ ably related to the efficiency of the mixing behind the two types of fence.

112 Ris0-R-1O3O(EN) Table 19. Mean concentration c, signal intensity I = crc/c and intermittency 7 = P(c > 0) at the rear mast with and without obstacle.

With obstacle Without obstacle c I 7 c I 7 EEC55 1 m 0.95 0.28 1.00 1.16 0.61 0.95 jet 2 m 1.15 0.31 0.99 0.56 0.92 0.81 100 % 4 m 0.42 0.83 0.82 0.18 0.65 0.95 EEC56 1 m 0.89 0.44 0.98 1.03 0.65 0.91 jet 2 m 0.83 0.63 0.90 0.25 1.37 0.62 50% 4 m 0.08 2.79 0.40 0.05 1.32 0.36 EEC57 1 m 0.17 0.67 0.83 0.34 1.05 0.75 cyclone 2 m 0.21 0.64 0.86 0.10 2.00 0.44 100% 4 m 0.06 1.94 0.50 0.03 2.21 0.26

Turbulence analysis

This section contains details about the turbulence inside the dense gas cloud. To the best of my knowledge the only other dense gas field experiments in which such measurements have taken place are the Thorney Island experiments, see chapter 14. .

EEC57 Front mast at 1 m

u-ti-u Downwind v-v-w Crosswind w-w-w Vertical

Frequency (Hz)

Figure 69. Turbulence power spectra from a momentum-free release. A -5/3 power law is present in the high-frequency part of all spectra.

Momentum-free flow Figure 69 shows power spectra of the velocity perturbations after obstacle removal in EEC57. The time series are taken from the periods defined in the previous sec­ tion, split into four subsequent parts and Fourier transformed. The shown spectra are the average of the four realizations which are further block averaged in a spectral window with a 10 % bandwidth. This is a standard technique for spec­

Ris0-R-1O3O(EN) 113 tral analysis of atmospheric boundary layer turbulence, see Kaimal & Finnigan (1994). The axes on the plot are both logarithmic, so any power law will appear as a straight line. Appendix G describes how the well-known -5/3 power law corresponds to the Inertial subrange inertial subrange, ie a range of frequencies where turbulence is isotropic and in a state of equilibrium with continuous energy supply from larger eddies and dis­ sipation by smaller viscous eddies. The spectra in the plot are multiplied by the frequency /, so the observed -2/3 slope in the high-frequency range suggests that an inertial subrange does exist. The conclusion is that the fine structure turbulence seems to have followed ordinary scaling laws. The dissipation rate may be estimated from the inertial subrange using equa­ tion G.22 which in the frequency domain reads

S(/) = ai(g)^r=/» (222)

With the Kolomogorov constant cti=0.27, the observed advection speed u—1.46 m/s, and a spectral density 5(1 Hz)=0.003 m2/s we find a dissipation rate of

1.5 2tt 0.003 £ = 5 • 10"3m2s"3 (223) L46 0.27 and the Kolmogorov microscale becomes

T) = y3/4g-i/4 = (Hr5)3/4(5 • 10-3)-1/4 = 0.7 mm (224)

Judged from figure 69, it seems as if we have measured about one decade of the inertial subrange. This part of the spectra could probably be extrapolated to the microscale or ufr\ « 2000 Hz in the frequency domain.

EEC57 Front mast at 1 m

b-b-u Downwind v-v-v Crosswind w w w Vertical

Frequency (Hz)

Figure 70. The same as in the previous figure, but with a linear scale for the energy density.

Figure 70 is identical to figure 69 except for the linear y-axis. As explained in appendix G this makes the area under the curve proportional to the energy. Because of the limited release duration we may have missed some of the low- frequency part of the turbulent fluctuations, whereas the sampling rate was fast enough to detect most of the energy in the high-frequency range of the spectra.

114 Ris0-R-1O3O(EN) The low-frequency part of the vertical velocity spectrum has less energy than vertical velocity the two horizontal ones. This turbulence depression is not just caused by the fluctuations stratification, since the nearby surface has a similar effect. The estimate of the vertical peak frequency fp for unstratified flow given in appendix G is 2zju or approximately 1 Hz which is close to the observed value. Figure 71 compares vertical velocity spectra with and without gas, where the pre-trial reference period is defined as in the previous section. The calculation is the same as above except that the average window is increased to 25% for a better separation of the curves. We note that the integrated turbulent kinetic energy is only reduced by 0(30)% during release, and this depression is mainly related to the low-frequency part of the spectrum.

EEC57 Front mast at 1 m - vertical velocity.

Pre-trial

Release

0.002 -

Frequency (Hz)

Figure 71. A comparison between the vertical velocity spectra before and during release. The advection velocity is virtually unchanged.

The gas release affects the shear stress —u'w', and this effect may also be exam­ momentum flux ined with spectral analysis. Again the reader should be warned that the duration of the available time series is almost too short for this exercise, and the results are qualitative only. The area under the shown cospectra represents u'w', but in order to improve the estimates the time series are again divided into subsequent realizations, and consequently part of the low-frequency spectral energy is lost. The Co uw cospectra in figure 72 are of the same shape as those for neutral stratification. The flux is found mainly in the downward direction, transferring momentum from the flow above to the dense gas plume (and further on to the surface). The significant contribution to u'w' is found at frequencies below the inertial subrange observed in figure 69. This was to be expected, since the theory of the inertial subrange assumes isotropic turbulence. Figure 73 shows similar cospectra from the upstream mast with inclusion of a pre-trial cospectrum from the 2-m level. Pre-trial cospectra from 1 and 4 m are not shown here, and I must admit that some unexpected differences were observed between the three heights, perhaps caused by the downstream obstacle or the trench upstream of the source. The cospectral energy at the two lowest levels are suppressed by the stratification whereas the top level seems unaffected. Reverting to the rear mast in figure 72 the curves are similar at all heights. The two low levels have partly recovered their cospectral energy and show more

Ris0-R-1O3O(EN) 115 EEC57 - Rear mast Co uwspectra

0.010 -

0.005

-0.005

2—2—2 2 m -0.010

-0.015

Figure 72. Cospectra of downwind and vertical velocity.

EEC57 - Front mast Co uwspectra

-0.005

-0.015

Figure 73. The same as in the previous figure, but closer to the source. The dotted line is measured before the release. similarity with the top level. All cospectra seem so have a peak frequency fp 0(0.1 Hz). Using Taylor ’s ’frozen turbulence’ hypothesis this corresponds to a wavelength of 2 ms-1/ 0.1 Hz = 20 m.

Concentration fluctuations

Figures 74 and 75 show power spectra of concentration fluctuation at three levels. These spectra follow the -5/3 power law and the peak frequency fp decreases with height. Presumably this is because much of the concentration fluctuations in the flat wide plume is related to vertical velocity perturbations which have this height

116 Ris0-R-1O3O(EN) EEC57 Rear mast concentration fluctuations

Frequency (Hz)

Figure 7Jt. Concentration fluctuation power spectra at three heights.

EEC57 Rear mast concentration fluctuations

t » » t I II » » t l « t t

Frequency (Hz)

Figure 75. Like the previous figure, but with two logarithmic axes demonstrating the -5/3 power law. dependence.

Mixing Figure 76 shows co-spectra of concentration and vertical velocity Cocw(f), calcu­ lated as the average of four realizations and plotted with a 10 % moving-average filter. The Cocw(f) co-spectrum is a spectral distribution of the turbulent mixing. The bulk of the spectral energy is associated frequencies lower than the peak fre­ quency fp of the w-spectrum in figure 70. Wyngaard & 0. F. Cote (1972) found that similar co-spectra in the neutrally stratified surface layer follow a -7/3 power

Ris0-R-1O3O(EN) 117 EEC57 Rear mast cw-Cospectra

0.005 -

Frequency (Hz)

Figure 76. Co-spectra of concentration and vertical velocity. law in the inertial subrange, see appendix G. The observed co-spectra have some negative values and need a lot of smoothing before they can be plotted in a log-log plot. The results (not shown here) are however not in disagreement with the -7/3 power law. The cross correlation functions Rwc{t) shown in figure 77 are an alternative representation of the relation between the two types of signal. The value at zero time lag RwC(0) is the flux normalized by the standard deviations of each signal. This is seen to be the maximum correlation and it takes the value of « 0.4 for all levels. A repeating period in the order of 10 s is seen at the top level in accordance with the 0.1 Hz peak frequency in figure 72. At the 2-m level the cross-correlations seems to be assymmetrical, eg the concentration is likely to increase four seconds later than an upward movement whereas the motion is likely to be in the downward direction four seconds after an event with high concentration.

Jet effect

Figure 78 shows power spectra of velocity perturbations in the jet case. The energy level is increased and shifted to higher frequencies than in the similar plot of the momentum-free release shown in figure 70. It is also noted that the spectra of lateral and vertical velocity perturbations are almost identical. It was previously found that the momentum flux at the 1-m level of the front mast was in the upward direction. The co-spectra in figure 80 show that this is related to relatively high frequencies, presumably both because of a phase shift by the larger advection velocity and a shorter turbulence length scale in the jet case. The momentum fluxes at the 2-m level are significantly lower than before the gas release probably because of weak velocity shear above the jet. Figure 79 shows that the co-spectra at the rear mast adjusted toward the ambi­ ent conditions with a downward momentum flux at all levels. The peak frequency is still high compared to that of the momentum-free release shown in figure 72. Figure 81 shows that the enhanced turbulent activity in the jet did not increase concentration fluctuations the concentration fluctuations. The peak frequency in the concentration spectra in a jet was higher than in figure 74 and the integrated energy is the same. A similar

118 Ris0-R-1O3O(EN) EEC57 (cyclone) - Rear mast

t (sec)

t (sec)

-0.4

Figure 77. Cross correlation functions of concentration and vertical velocity.

EEC55 Front mast at 1 m

u-u-u Downwind v-v-v Crosswind w-w-w Vertical

0.04 -

S0.03

Frequency (Hz)

Figure 78. Turbulent velocity spectra inside a dense jet.

shift to higher frequencies is observed in the jet co-spectra of vertical velocity and concentration in figure 82. The increased high-frequency spectral energy implies that the viscous destructions of concentration fluctuations must have been stronger in the the jet case. The concentration fluctuation intensities calculated in table 19 are generally smaller in jet case. This is probably caused by suppression of plume meandering, ie a larger fraction of the concentration fluctuations in the jet was related to turbulent mixing. The jet cross-correlation functions in figure 83 should be compared to those in figure 77. The EtoC(t)-functions are clearly assymmetric with significant negative correlations around t = ±1.5s, and the integral time (disregarding the noise) seems to have been shorter than for the momentum-free release. The low concentration level at 4-m height increases the noise level and that curve does probably not

Ris0-R-1O3O(EN) 119 EEC55 - Front mast Co uwspectra

0.010 -

0.000

-0.005

-0.010

-0.015

Figure 79. Jet co-spectra of downwind and vertical velocity at the front mast. The dashed line is observed ahead of the experiment.

EEC55 - Rear mast Co uwspectra

-0.005

2—3—2 2 771 -0.010

-0.015

Figure 80. Jet co-spectra of downwind and vertical velocity at the rear mast. contain significant information. The correlation for zero time lag RwC{0) is close to 0.4 for all levels with both types of release, ie w'd as 0.4 -awac. Figure 84 shows similar cross-correlations from the rear mast. The integral time scale increased compared to that of the front mast, but it was still shorter than in the momentum- free release.

Wake turbulence

The velocity spectra based on wake measurement are similar in all directions. turbulent kinetic energy Figure 85 therefore shows the spectral distributions of the total turbulent kinetic

120 Ris0-R-1O3O(EN) EEC55 Rear mast concentration fluctuations

Frequency (Hz)

Figure 81. Concentration fluctuation spectra at three heights with jet release.

EEC55 Rear mast cw-Cospectra

Frequency (Hz)

Figure 82. Co-spectra of vertical velocity and concentration with jet release.

energy ^(<7^ + cr% + crj,). The scale of the y-axis is larger than that of figure 70, since the overall wake turbulence was enhanced by the obstacle. The distributions followed a -5/3 power law observed for all frequencies above a peak frequency near 0.1 Hz. Presumably the wake produced spectral energy at this frequency. Density effects are probably of little importance in the wake zone since wake spectra from the jet experiments are of the same shape. The vertical mixing process in the wake is examined by the co-spectra of con­ wc-cospectra centration and vertical movements plotted in figures 86-88. The first figure offers an explanation of the observed negative gas flux in the wake. This is related to rather low frequencies near 0.1 Hz close to the peak in the turbulence spectra. This

Ris0-R-1O3O(EN) 121 EEC55 (jet) — Front mast Rw c( t) 4m 0-6'

sA/v t (sec) -Vv ‘ "V" ' ‘W 10 ~20

—0.4 *

2m °-e" iRwc(t)

\ A t (sec) A A -A W /V V f\~. XX y- ----A A ^ /\. ^ v 'v H 10 20

-0.4- 1m °-s" Rwc(t) l t (sec)

,y\) v ,vv;V"‘,vw v u/ \ / \y'V \aa /k/V v‘ m^/^ 2o

—0.4 -

Figure 83. Cross-correlation functions of vertical velocity and concentration at the front mast with jet release. The noise is significant at the top level.

EEC55 (jet) — Rear mast

t (sec)

t (sec)

t (sec)

Figure 84- Cross-correlation functions of vertical velocity and concentration at the rear mast with jet release. frequency might reflect the turn-over time of the wake circulation or a pulsating flow of dense material over the top of the obstacle. The strong negative flux at 0.1 Hz is counteracted by an upward gas flux at the higher frequencies. Figure 87 shows a similar plot for a jet release. The mixing at the top level is very efficient (note the different y-axis) and distributed over a wide range of frequencies. This is also observed at the 2-m level whereas the spectrum of the 1- m level is difficult to interpret. Finally figure 88 shows the wake co-spectra for jet release and porous obstacle. The strongest mixing was observed at the 2-m level. The co-spectra for the 1- and 2- m levels seem to have a low-frequency range of downward gas flux.

122 Ris0-R-1O3O(EN) EEC57 wake turbulence

2--S--2 2 Til-

Frequency (Hz)

Figure 85. Spectra of the total turbulent kinetic energy \ (Su(f) + Sv(f) + Sw(f)) behind a solid obstacle with momentum-free release.

EEC57 Wake cw-Cospectra

-0.002 -

-0.004

-0.006

Frequency (Hz)

Figure 86. Co-spectra of vertical velocity and concentration behind a solid obstacle with momentum-free release.

Ris0-R-1O3O(EN) 123 EEC55 Wake cw-Cospectra 0.020

0.015

0.010

3 0.005 2.

0.000

-0.005

-0.010 10" 10" 10° 10' Frequency (Hz)

Figure 87. Co-spectra of vertical velocity and concentration behind a solid obstacle with jet release.

EEC56 Wake cw-Cospectra

0.000 -

-0.005 -

-0.010

Frequency (Hz)

Figure 88. Co-spectra of vertical velocity and concentration behind a porous obsta ­ cle with jet release.

124 Ris0-R-1O3O(EN) 12 Large-scale ammonia experiments

The mixing process was non-adiabatic in the propane experiments described in the introduction previous chapter, and the heat flux from the ground was assumed to be the most likely candidate for the external heat input. The ground heat flux was not mea­ sured in the propane experiments but the ‘Desert Tortoise ’ experiments provide such measurements. The US Lawrence Livermore National Laboratory (LLNL) has made large-scale experimental layout dense gas dispersion experiments with a range of chemicals and release configura ­ tions. The liquefied ammonia releases called the ’Desert Tortoise ’ (DT) series took place in 1983 on the site in Nevada, which later became a permanent test facility for the US Department of Energy. These experiments applied a 81-133 kg/s hor­ izontal flash boiling jet source, and the release durations were 2-6 min. The wind speeds were 5-7 m/s, the air temperature was 30-33°C and the relative humidity was 10-21%. The site was normally a dried-up lake bed, but prior to the exper­ imental campaign the area had been flooded because of unusual heavy rainfall. The surface was dry again during the experiments partly analysed here. Figure 89 shows the experimental set-up. A large number of bi-vane anemometer stations were deployed over a wide area and used for short-term prediction of the wind direction. This technique enabled LLNL to distribute the gas sensors in a fairly narrow array and to await the right moment. The ‘mass flux array ’ at 100-m dis­ tance and the first of the ‘dispersion arrays ’ at 800-m distance consisted of seven and five 10-m masts equipped with gas and temperature sensors at three levels. The experiments are described in a paper of Koopman et al. (1986) and the more detailed data report of Goldwire, McRae, Johnson, Hippie, Koopman, McClure, Morris & Cederwall (1985). This chapter is initiated by vertical cross-wind sections showing a very flat chapter summary dense gas plume. This is followed by an analysis of the heat-flux measurements. In contrast to the theory in chapter 7 the fluxes did not decrease in time as

• the actual surface heat flux maximum was about a factor 2 higher than the measured one, • the actual surface heat flux decayed during release, and

• the actual surface heat flux was in general agreement with the ‘internal cloud Monin-Obukhov ’ estimate of Jensen (1981b). An enthalpy balance similar to the analysis in the previous chapter indicates that the ‘Desert Tortoise ’ dispersions were non-adiabatic.

Instantaneous plume cross sections

Figures 90 and 91 are reconstructions of some of the contour plots in Goldwire et al. (1985) which show nearly instantaneous concentration fields across the plume. A 3-s moving average filter was applied on the signals from the 100-m array in order to reduce the signal noise. The response time of the concentration sensors in the 800 m array was 0(15 s). The two contour plots show that the instantaneous gas distribution was a vertical concentration smooth function of vertical and lateral horizontal distance. At first sight the dis­ profiles tribution looks almost like an ordinary surface plume of neutral buoyancy with maximum concentrations at the plume centre line. It should however be noted

Ris0-R-1O3O(EN) 125 225' Range

Force

Air

Nellis

Figure 89. Figure [2] from Koopman et al. (1986): ‘Diagnostic instrument array for Desert Tortoise and Eagle experiments. ’

DT 4, Concentration field at 100 m

Crosswind Distance [m]

Figure 90. DT4, 10-s average cross stream concentration field 100 m downstream of the source, with the mesh of data points indicated by circles o. After Goldwire et al. (1985).

126 Ris0-R-1O3O(EN) DT 4, Concentration field at 800 m

Crosswind Distance [m]

Figure 91. DT4, 10-s average cross stream concentration field 800 mfrom source, with the mesh of data points indicated by circles o. After Goldwire et al. (1985). that the vertical scale is enlarged, and the plume aspect ratio is just 1:15 at 100 m and 1:100 at 800 m, ie the plume was much broader than usual. In order to calculate the mass flux through each sensor array, Goldwire et al. mass balance (1985) extrapolated the concentration to the surface, assuming negligible vertical gradient at the surface and constructed a parabolic fit through the two lowest measurements as in figure 92. In the light of the propane profiles in figure 41 and the laboratory work of Britter & Snyder (1988), this assumption probably underestimates the ground-level concentrations. Goldwire et al. (1985) then ap-

k;

ii . 10 . 9 . 8 . 7 . 6 , 5 . 4 . 3 .

2 . 1 . i 1 1-- 1 Q 1 1 1 1 2 3 4 5 6 7 [%]

Figure 92. Extrapolation method used by Goldwire et al. (1985). The three mea­ surements are marked with dots •, while the open circles o at the 12 m and at ground level are extrapolated. The concentration profile is then assumed to be lin­ ear between all five points. proximated the concentration profile by a stepwise linear interpolation between

Ris0-R-1O3O(EN) 127 these five points and between measuring points at neighbouring masts. It was at­ tempted to measure the velocity inside the cloud, but the ammonia damaged the anemometers during the first experiment. Instead the jet velocity was estimated to 10 m/s at 100 m distance. Figure 93 shows the accumulated mass passing through each sensor array. The ratios between the detected and the released gas mass were 70% for the 100 m array and 50% for the 800 m array. The linear increase indi­ cates that the mass flux was nearly constant at both distances. This period was however of longer duration at 800 m indicating that the cloud was stretched in the longitudinal direction.

DT3, Mass balance 25000 Spill mass

20000 -

15000 - 100 m row

10000 800 m row

5000 -

Time [s]

Figure 93. DT3 accumulated ammonia mass detected by the instrument array at 100 m and 800 m. The data are read from figure 79 of the report by Goldwire et al. (1985).

The difference between the accumulated mass fluxes at the two distances may be explained by the fact that wind meandering sometimes moved part of the plume out of the 800 m array. The undetected 30% of the emission was probably equal to the volume of the liquid pool in front of the source. The pool area was larger than 2000 m2 and extended up to 90 m from the source. Most of the pool evaporated fairly fast, although a fog was visible over the inner area for at least 20 min. The mass flux from this secondary source is apparent in figure 93 although it cannot account for the entire 30% missing flux. It should however be remembered that the density of ammonia evaporating from a pool is slightly lighter than air (see table 8) and the plume from the secondary source was probably much higher than the sensor array. In DT3 the exit overpressure was p 0— pair=l-03 MPa, the mass flow rate was m=133 kg/s, the liquid density was p0=682 kg/m 3 and the nozzle area was A=0.0071 m2. This information leads to the following jet flow force estimate: 777,2 Fjet = -----2-----k (Po - Pair) ' A0 = 10.9 kN (225) PqAq corresponding to a jet velocity of Fjet/m=82 m/s after depressurization. A crude momentum budget like in equation 212 gives the excess velocity

C * Mg -Pjet Wjet t^air (226) Ma + c • AM mg

128 Ris0-R-1O3O(EN) 0.07-0.017 10.9 kN „ r _ , 0.029 - 0.07 • 0.012133 kg/s “ m/S where the 7% concentration is obtained from figure 94. The ambient wind velocity at 2 m was 7.4 m/s, and if this is taken as a typical velocity of the entrained air, the jet velocity becomes 11 m/s, slightly larger than the 10 m/s jet velocity suggested by Goldwire et al. (1985).

n . 400 Ground Heat Flux

Temperature at 1 m

Concentration at 1 m

Time [sec]

Figure 94 . DT3 100 m from source at ideal plume centre line. Heat flux just below the surface together with temperature and concentration time series at 1 m.

Heat flux Figure 94 shows the ground heat flux at the centre mast at 100 m distance together with the temperature and concentration 1 m above terrain. The heat flux shown in figure 94 increased throughout the experiment in conflict with the prediction in chapter 7. This is because the sensor position was ‘just below the soil surface’. In chapter 7 the surface heat flux was determined by a set of summation coef­ heat flux below surface ficients:

for n = 0 (227) for n > 1

In order to determine the flux below the surface we insert the an constants in equation 65:

> AT / Psoildsoil (p(z,t) A“llTV^w~ oo £ / PsoilCsoiT •][>n-2n.r 1 erfc (228) 2 y Asoilt

where Asou, Psoii and Cs0n are the heat conductivity, density and heat capacity of the soil and the distance from the surface z is positive in the downward direction. Insertion of the summation coefficients an yields:

y(Z; t) — AT\/AsoilPsoilCsoil7heat

Ris0-R-1O3O(EN) 129 00 / f \ (n-l)/2 EH)"- (;' ' / PsoilCsoilPsoilQ ?n—1 erfc (229) \7heat/ 2 Y Asoi: n=0 1* which may also be written oo heat z/z (230) W So Vr; x/t7^heat by definition of an initial surface heat flux ipo = y>(0, 0) and the length and time scales

2Aso nAT Zheat and Theat — ^soilPsoilCsoil (231)

Heat flux for constant gas temperature

surface

Figure 95. Soil heat flux at variable depth when the surface is exposed to cold gas. The surface heat flux is decreasing from the start whereas the fluxes in the soil start from zero and reach their maximum after o time which depends on the depth.

Figure 95 shows the theoretical heat flux

- what was the sensor position z/zheat?

- What was the ratio of the release duration and the heat transfer time scale fpass/Theat) ie for how long should the chosen theoretical curve be followed? - What was the ratio between the measured maximum flux and the surface maximum y>o? An observed 0(20 s) time lag between the gas arrival and the start of the change in the heat flux in combination with the shape of the observed time series indi­ cates that z/zheat — 0.1. This implies that ipo is twice as large as the measured

130 Ris0-R-1O3O(EN) maximum. As a check we calculate the length and time scales 2-0.5 W/(mK).30 K on Zheat - 1000 W/m2 «30mm (232)

Z 30 K V Tiieat = 0.5 W/(mK) • 2000 kg/m 3 • 1800 J/(kgK) 11000 W/m2)

% 1600 s using the soil properties from chapter 7. The ratio between the release duration and the heat-flux time scale 7dur/7heat is 160/1600=0.1, ie the z/zheat = 0.1 curve in figure 95 should be followed until t/Theat = 0.1 and the assumed sensor depth z becomes 3 mm. The corrected heat flux gives a new opportunity to test the ‘in-plume Monin- Obukhov’ approach of Jensen (1981b). To this end we need the bulk convection in-plume M.-O. approach Richardson number Ri&x and the surface roughness zq:

ATgz _ -30 K • 9.8 m/s2 • 1 m Ezat Tu2 ~ 275 K- (10 m/s)2

zo 0.003 m (233)

These parameters are inserted into equation 34 which is solved for the internal cloud stability parameter z/L.

j = 0.00105 ^ ~ (^] •44- — = —0.043 (234) L inln __urns™.1 m ~ * h (f)

In spite of the dramatic temperature deficit the internal cloud boundary layer must have been close to forced convection where the diabatic correction functions ip m and VVi are weak. The stability parameter is used to calculate the heat exchange coefficient 0.42 Ch = = 0.036 (235) [In om-i ’m (-0.043)] [ln 5^3-^ ("0-043)] and finally an alternative estimate of the heat flux.

= 1390 W/m2 (236)

This is in reasonable agreement with the

Pool measurements Ground heat flux and temperature were also measured 3 m from the source. Fig ­ ure 96 shows time series from such measurements during DT4. The jet ripped one of the temperature sensor out of the ground after a period of five minutes.

Ris0-R-1O3O(EN) 131 DT 4, Near-source measurements

I

u

120 240 360 480 600 720 840 960 1080 1200 40 0 u Pool Temperature 1 -40

-80 —i—'—i—'—i— —i------'------i------'------1------'------i------'------1------'------1------'------1 120 240 360 480 600 720 840 960 1080 1200

Figure 96. DT4 near-source measurements, ground heat flux and temperature at 3 m from the source together with pool temperatures at 6 and 9 m from the source.

It is noted that during release all temperatures were well below their boiling point at -33°C. The minimum temperature of an evaporating pool may be esti­ mated by equation 114:

mmin _ rp , Psat(T™rn) ML SUr air p-Psat»)MairC*r

An air temperature Tair = 33° C and pressure p = 0.907 atm lead to T™rm = —68°C, or slightly colder than those of the measurements. The pool temperatures were steady and the ground temperature soon approached a level close to the surface temperature. The slight temperature drop after 320 s is probably caused by changing release conditions.

Enthalpy balance

This section contains an analysis of the enthalpy balance similar to that of chap­ ter 11. Because of the low molar weight, the temperature deficit is more important for the density of an ammonia cloud than for propane. The concentration sensors measured time series at 100 m distance operated on a principle of infra-red absorption and had a re­ sponse time 0(2 s). Both liquid and gaseous ammonia were measured since the mixture passed through a heating apparatus. The temperature was measured by thermocouples mounted adjacent to the sample tube inlet. The thermocouple am­ plifiers had a long-term drift and each time series was therefore base-line corrected using pre-trial temperatures from an upwind meteorological station. The thermo­ couple response time was 0(1) s which is equivalent to that of the concentration sensors. Inspection of the concentration and temperature time series details sug ­ gested that the detailed timing of the two signals coincided, except perhaps at the

132 Ris0-R-1O3O(EN) 1 m level where the thermocouple response slowed down. This thermocouple be­ haviour is typical for liquified-gas dispersion experiments and its cause is believed to be evaporation of wet deposit as discussed in chapter 13. The concentration sensors in the 800 m array were of another type with a slower response time. In order to match these signals with thermocouples I applied a 7 s auto-regressive filter on the faster thermocouple signals. Periods with reasonably high concentrations were selected for the enthalpy bal­ ance, ie 30-210 s in the 100 m array, 120-360 s for mast G22 and 180-270 s for mast G24 in the 800 m array. The period 0-120 s was used as a reference period in the 800 m array, while the 100 m array had to do without a reference period. The air temperature was obtained from the top level on an unexposed mast in each array. The aerosols and surrounding gas phase are assumed to have been in homoge ­ neous equilibrium and the degrees of water and ammonia condensation are calcu­ lated for each data point in the time series using Wheatley ’s (1986) binary aerosol model, see appendix E. The degrees of condensation are then used to calculate enthalpy time series as in chapter 11. For most measuring positions the degree of condensation contributes little to the enthalpy, with exception of the 1 m level on the centre mast in the 100 m array where aerosol formation accounts for 40% of the enthalpy deficit. The binary aerosol model does not predict condensation at the 6 m level, and it is frequently changing between condensating and dry conditions at the 2.5 m level. Goldwire et al. (1985) noted that ‘peaks of visible cloud rose to 6-8 m high as the cloud passed through 100 m row’ so it seems like Wheatley ’s (1986) aerosol model gives a slight under-prediction of the amount of aerosols. The exit pressure and temperature po = 11.4 Bar and To = 296 K corre­ adiabatic mixing enthalpy spond to a release enthalpy of 1069 kJ/kg while gaseous ammonia at the at­ mospheric conditions p air = 0.91 Bar and Ta;r = 307 K has an enthalpy of 2324 kJ/kg (Vargaftik 1975, p. 464). The source enthalpy deficit was therefore AHq = —21.4 kJ/mole NH3.

Table 20. Enthalpy to concentration ratios AH/c [kJ/mole NH3] at well exposed masts in the 100-m array in the DT3. 100 m row G04 (+15m) G05 (0 m) G06 (-15 m) Height 6.0 m -21.6± 5.3 - -15.2± 4.0 2.5 m -19.0± 2.7 -15.8± 2.9 -19.8± 2.1 1.0 m -14.1± 6.0 -18.3± 1.7 -19.2± 4.5

Table 21. Enthalpy to concentration ratios AH/c [kJ/mole NH3] at well exposed masts in the 800-m array in the DT3. 800 m row G22 (0 m) G24 (-200 m) Height 3.5 m -12.0± 3.2 -16.7± 1.2 1.0 m -13.6± 2.4 -14.8± 1.1

As in chapter 11 regression lines forced through origo (AH, c) = (0,0) were results fitted to 10 s block-average values of AH and c. The slopes of these lines AH/c and their uncertainties are listed in table 20 and 21. Poor signal-to-noise ratios made the two estimates from the 6 m level of the 100 m array more uncertain than the rest as shown in table 20. Large uncertainties were also observed at the 1 m level of the edge stations in the 100-m array where visual inspection suggest

Ris0-R-1O3O(EN) 133 evaporation of liquid deposit. The temperature signal from near the plume centre line did not suffer from this problem, probably because the G05 station was well exposed during the entire release. As in the propane experiments the estimated

A jH/c ratios are higher than the source enthalpy AHq with a downwind increase from the row at 100 m to the row at 800 m. The differences within each row are not statistically significant. Weighted averages obtained by • (£) 1/crj)-1 give -18.1 kJ/mole NH3 at 100 m distance and -14.9 kJ/mole NH3 at 800 m distance. The relative effective molar weight ratio AM, _ AM A H/c ■Mair -^air -^airCp* rIair

is a measure of the buoyancy effect. By insertion of the in-situ enthalpy estimates this becomes 1.26 at the 800 m row in contrast to the 1.99 value coresponding to adiabatic mixing, ie the buoyancy effect was reduced by 37%!

DT3 enthalpy to concentration ratio 0 ------1------1------1— 1 1 1 I 1 1 (AH/c)cr=-3.4 -5 -

-10 - - A H/c 0 k J/mole 0 0 - -15 - 0 0

-20 _ 0 AHo=-21.4 - - 0......

-25 _____1_____1_____ 1___ 1 1 1 1 1 0 100 200 300 400 500 600 700 800 900 1000 Distance [m]

Figure 97. All estimates of the enthalpy to concentration ratios as a function of distance. The plume becomes buoyant when this ratio exceeds -3-4 kg/mole NH3

Continued heating will eventually make an ammonia plume buoyant since the plume lift-off? molar weight is lighter than air. The approximate density of diluted mixtures defined in equation 132 gives the following critical value for the transition from negative to positive buoyancy.

(AH/c)cr = AM ■ CpT a

= (0.017 - 0.029)kg/mole • lkJ/(kgK) • 307K

= -3.4 kg/mole NH3 (237)

Figure 97 is a plot of the average A H/c values from tables 20 and 21. The heat transfer was more efficient near the source and the approach to the critical enthalpy gradually leveled off. Presumably the enthalpy development downstream of 800 m was not sufficient to make this plume buoyant before it became so diluted that it dispersed like a passive release. The analysis in chapter 11 did however show that enthalpy conservation was a worse approximation with an momentum-free source than with a jet release. In principle a liquified gas with low molecular may start off as a dense plume and become buoyant after sufficient heating.

134 Ris0-R-1O3O(EN) 13 More ammonia experiments

Toxic gases are sometimes hazardous at small concentrations and a prediction introduction of these may require knowledge of the transition from dense gas dispersion to ordinary passive dispersion. In practice the risk engineer may have to apply a chain of numerical models, in which the output of the first computation is used as input to the next one, etc. This is not an ideal approach since the uncertainty of the calculations accumulates, and it is not obvious exactly where to make the transition from one stage of the dispersion to the next one. Laboratory experimentalists usually focus on accurate modelling of small ed­ dies (by Reynolds number considerations) but the low-frequency perturbations should be of equal interest. In the field these slow perturbations are experienced as variable wind directions which cause plume meandering - much more than in wind tunnels. Most numerical models disregard this effect. In order to facilitate comparison between models and field experiments it is therefore better to detect average dimensions of the meandering plume than those of the average field in a fixed frame of reference. The Fladis field experiments were conducted by Ris0, Hydro-Care(S), FOA(S) experimental layout and CBDE(UK). The main objective was to measure the transition from dense gas dispersion to ordinary passive dispersion. Most of the sensors were placed at positions where the density effect was weaker than in other experiments discussed in this report. The source was a jet of liquefied ammonia similar to that of the Desert Tortoise experiments analysed in the previous chapter. The downwind ex­ tent of the sensor array was 240 m, but the source strength was 0(0.5) kg/s, ie much less than in Desert Tortoise. The experimental design is further described in appendix B. Chains of point measurements are used to calculate cross-wind plume profiles chapter summary at variable distances. Although not attempted here such data are applicable for model evaluation. The analysis is made both in a fixed frame of reference and in a frame of reference following the meandering plume centre line. The downwind gas flux was in general agreement with the measured release rate. Measurements by fast responding concentration sensors are used to calculate probability den­ sity functions of the concentration fluctuations in fixed and moving frames. An enthalpy budget similar to those in chapters 11 and 12 is presented. The ’ballis­ tic’ path of a vertical jet release is in agreement with a model of Ott (1990). The composition of aerosols in a two-phase jet was observed to change rapidly with dis­ tance from the source and this supports the homogeneous equilibrium hypothesis. Dimensions of plume footprints are shown to depend on averaging time.

Plume dimensions

Project partners working with numerical models and wind tunnel simulations needed centre-line concentration, plume height and plume width for intercompari­ son tests. These plume characteristics were deduced from the point measurements available.

Horizontal profiles

Unlike a wind tunnel simulation the atmospheric wind direction and plume centre­ line position are not known a priori but have to be determined by observation. Long-time average plume positions should be in accordance with average wind di­ rections. However in case of short averaging times it becomes increasingly difficult to correlate local wind directions to the plume position, which is determined by a

Ris0-R-1O3O(EN) 135 Figure 98. Concentration time series from trial 16. The map above the series shows the position of the instantaneous plume centre line yc (thick line) and the lateral plume spreading yc ± ay (normal line) as a function of time. time history of wind directions along the plume trajectory. Therefore it is better to determine also the plume position from concentration measurements. At this point of the analysis one may choose either to start calculating local average con­ centrations and then fit the average concentration profile or, alternatively, to find instantaneous plume positions and then calculate plume statistics in a frame of reference following the moving plume centre line. From a risk analysis point of view it may be more relevant to know a typical instantaneous plume profile than the average of a meandering plume. The plume dimensions predicted by most dense gas dispersion models are presumably consistent with average concentrations with­ out plume meandering. The moving frame analysis should therefore be of greater interest in the dense-gas phase. However a longer averaging time, eg 10 min, is usual in dispersion models for passive diffusion and many dense-gas models are designed with a smooth transition to this limit. The best data analysis for a model comparison depends on individual model assumptions. The wind direction in wind tunnels is more steady than in the atmosphere, and the result of the moving frame analysis is expected to better compare to laboratory measurements. The data re­ duction for the dense-gas model evaluation of Hanna, Strimaitis & Chang (1991) applied fixed frame statistics. An experiment like Fladis trial 9 would probably have been rejected by these authors, since the varying wind direction during that trial resulted in a very broad fixed frame profile. On the other hand the moving frame profile from such a trial will still be useful. The concept of a meandering plume has previously been used to predict concentration fluctuations in plumes of neutral buoyancy, see Wilson (1995) for an introduction. Figure 98 shows a set of concentration time series from the lowest level of the first sensor array which in this trial was 22-m downstream of the release point. The variable plume position and width are shown in the map above the concentration time series. The release continued for 20 minutes and the plume was sweeping from side to side with about two excursions per minute. Signals from adjacent sensors are well correlated and it seems as if much of the concentration fluctuation was caused by the variable plume position. The average and standard deviation of each signal from figure 98 are plotted

136 Ris0-R-1O3O(EN) Fixed Frame Moving Frame

300 300 -i x = 238 m x = 238 m z= 1.5 m E 200 : z = 1.5 m

100 -

I ‘ I ' I ‘ I 80 60 40 20 0 -20 -40 -60 -80 80 60 40 20 0 -20 -40 -60 -80 X= 70 m X= 70 m z = 0.5 m z = 0.5 m

U o.l - U 0.1 -

0.0 -n- -10 -20 -30 -10 -20 -30 0.6 x= 20 m x= 20 m r? 0.4 - z= 1.5 m 0.4 - z - 1.5 m

U 0.2 - U 0.2 -

I'M'' 12 9 6 3 0 -3 -"6 -9 -12 0 -3 -6 -9 -12 x= 20 m x= 20 m z = 0.1 m z = 0.1 m

-t-I-tt 12 9 6 3 0 -3 -6 -9 -12 12 9 6 3 0 -3 -6 -9 -12 Distance y [m] Distance y-yc [m]

Figure 99. Horizontal average concentration profiles in trial 16 plotted in 1) a fixed frame of reference, and 2) a moving frame of reference following the instantaneous plume centre-line position yc- in the lower left frame of figure 99 and similar data from other chains of sensors are plotted above this. The Gaussian profiles fitted to each chain of measurements seem to describe the horizontal concentration distribution quite well. The instantaneous concentration profiles were of a variable shape, and each pro­ file is therefore approximated by a stepwise linear variation between neighbouring measurements c() ci+i(y - Vi) + Ci(y»-+1 - v) for yt

Em Svyr

The estimate implicitly assumes that the concentrations at the edges are insignifi ­ cant c(y) y -> 0, since otherwise the estimated yc would be biased toward the ideal centre line. The assumption was not always valid and this source of error will be evaluated below. Another problem is to what extent the concentration signals

Ris0-R-1O3O(EN) 137 should be smoothed before determination of the plume position. Random fluc­ tuations in a finite number of signals could introduce uncertainties in the plume position yc, but too much smoothing would bias yc toward the ideal centre line. The concentration signals were obtained by rather slowly responding sensors, so the instantaneous centre-line position has actually been estimated by the speed-up signals, ie with rs5 sec response time for the sensors in the measuring arrays at 20 and 70-m distance and «15 sec at 238-m distance. The plots on the right-hand side of figure 99 apply a moving frame of reference, where the observations are sorted in bins defined from the distance between the sensor position and instantaneous plume centre line y — yc. The number of bins is an arbitrary choice. As expected the moving frame profiles are more narrow with higher maximum concentrations than the fixed-frame profiles. The intensity of the concentration fluctuations crc//rc is smaller in the moving frame profiles, ie the concentration is more predictable with a known plume centre line. In trials with short release durations the moving frame profiles are often more symmetric than the fixed frame profiles. This indicates less statistical uncertainty since presumably the mixing process is symmetric. In the two moving frame profiles of the first sensor array the jet is seen to be wider near the ground. The reason could be gas which lingers near the surface each time the core of the jet is swept to the other side. The estimated Gaussian curves in figures 99 are derived from an iteration which compares the moments of the stepwise linear profile to moments of a clipped Gaussian distribution, see Nielsen (1996b). In order to avoid the effect of the poor signal-to-noise ratios at the edges of the distribution, the iteration disregards sig ­ nals from sensors which are more than two standard deviations from the predicted plume centre line. The centre-line concentration cmax and plume spreading ay for the fitted profiles are listed in table 22. Here the primary values are found from curve fits to moving frame profiles and the values in parenthesis are from fixed frame profiles. In some trials part of the plume occasionally appeared outside the measuring array. This gave rise to uncertain estimates which were screened out by the following procedure: situations with an obviously poor wind direction were excluded; in case of less obvious problems the calculation was repeated with a con­ ditional sampling disregarding periods during which the 10%- or 90%-fractile of an instantaneous profile was outside the measuring array. If the use of conditional sampling altered the cmax and o y estimates by more than 3% the results were re­ jected from table 22. This is taken as an upper limit of the above-mentioned error caused by occasionally significant concentrations at the edges of the measuring array. On account of the advection time the exposure of the sensors was delayed rel­ ative to the gas emission. The sample periods are therefore individual for each sensor array. Usually these periods T0bS are longer than the release duration Tdur> because the cloud is stretched in the wind direction. A close examination of ta­ ble 22 will reveal that the product CmaxUy is not always the same for the fixed and moving frame profiles. These disagreements have no mean bias, but a standard deviation of 7% and a maximum of 20%. This must be owing to curve fit errors, since the average data are based on identical time series. Indeed a visual inspec­ tion of all curve fits shows that the largest disagreement occurs when the fixed frame profile is positively non-Gaussian. This supports the previous observation that the moving-frame profiles seemed to be more accurately determined by the Gaussian fits and probably more suitable for model comparison.

Vertical profiles

Britter (1988) discuss vertical profiles of grounded dense gas plumes in the form c = Co exp {—azp }. The shape of this profile is quite flexible and may vary from

138 Ris0-R-1O3O(EN) Table 22. Centre-line concentration cmax, plume spreading cry, and vertical centre of gravity z with the correction Az at distance x r and height zr. The primary values of the cmax a.nd ay parameters correspond to measurements in a moving frame of reference, whereas the values in parenthesis are found from the same measurements in a fixed frame of reference. The two values of the Az corrections are for c oc exp{ —z} and c oc exp{ —z3/2} respectively. The ratio of the individual observation period T0bs o,nd release duration Tdur is shown to the right of the table.

x T Zr CmaxO^rj zr) (&r, Zr) Zest 4* Azest Tobs/Tdur [m] [m] [ppm] [m] [m] Trial 9 20 0.1 19600 (12800) 2.66 (4.08) 0.95+0.11|0.05 1.03 70 0.5 2050 (885) 5.70 (15.5) 3.32+0.53|0.29 1.03 238 1.5 138 (57) 13.6 (37.6) ? 1.04 Trial 12 16 0.1 10300 (7740) 4.03 (5.04) ? <1 (vertical) 66 0.5 1180 (1010) 12.6 (16.1) 2.65+0.27(0.12 1.03 Trial 13 22 0.1 24800 (21200) 3.53 (4.03) 0.91+0.10(0.05 <1 Trial 14 22 0.1 24000 (20700) 3.50 (3.93) 0.92+0.10|0.04 1.06 Trial 15 22 0.1 26200 (20700) 2.90 (3.58) 0.85+0.08)0.03 1.08 72 0.5 2360 (1710) 7.21 (10.3) 2.45+0.20(0.07 1.06 240 1.5 166 (127) 19.0 (26.9) ? 1.28 Trial 16 22 0.1 21300 (16700) 3.38 (4.27) 0.83+0.07(0.03 < 1 72 0.5 1810 (1090) 6.77 (11.7) 2.62+0.26(0.11 < 1 240 1.5 179 (127) 16.7 (25.3) ? 1.05 Trial 17 22 0.1 19200 (16900) 3.54 (3.88) 0.83+0.07(0.03 1.06 72 0.5 1570 (1380) 7.68 (7.26) 3.66+0.70(0.42 <1 Trial 20 20 0.1 21600 (12900) 3.00 (4.84) 0.78+0.06(0.02 1.02 70 0.5 1140 (583) 8.86 (18.6) 3.21+0.48(0.25 <1 Trial 21 20 0.1 37600 (30100) 3.05 (3.72) 0.78+0.06(0.02 1.01 70 0.5 5910 (3600) 7.86 (12.9) 1.85+0.06(0.01 1.02 Trial 23 20 0.1 20400 (15100) 2.46 (3.22) 0.91+0.10(0.05 1.03 70 0.5 1880 (1250) 6.97 (10.4) 2.50+0.22(0.09 1.02 238 1.5 92 (62) 20.7 (31.9) ? 1.02 Trial 24 20 0.1 31700 (26400) 3.21 (3.65) 0.77+0.06(0.02 1.08 70 0.5 2560 (1690) 8.57 (14.0) 2.59+0.25(0.10 1.08 238 1.5 113 (74) 24.7 (40.2) ? 1.13 Trial 25 20 0.1 33700 (29000) 3.30 (3.59) 0.76+0.05(0.02 1.03 70 0.5 3270 (2040) 7.73 (12.6) 2.00+0.09(0.02 1.00 238 1.5 146 (98) 21.3 (32.9) ? 1.03 Trial 27 20 0.1 25200 (19500) 4.60 (5.54) 0.62+0.02(0.00 1.07 70 0.5 1850 (951) 8.60 (16.3) 2.58+0.25(0.10 1.08 exponential (p = 1), to Gaussian (p = 2), and top hat (p -+ oo). Diffusion theory with power-law approximations to velocity and turbulent diffusivity profiles

u oc zm and Kz oc zn (240) gives analytical results in accordance with the concentration profile mentioned and results in the relation p = 2 + m — n, see appendix G. The exponent of the velocity profile is often set to m = 1/7, although this depends on atmospheric stability and the ratio between plume height and surface roughness. The eddy diffusivity in a neutral surface layer has linear height dependence n = 1, but

Ris0-R-1O3O(EN) 139 Sutton (1953) adjusted this to n = 1 — m in order to produce a constant stress layer (ie a layer with constant momentum flux) and obtained p = 9/7. Britter & Snyder (1988) measured concentration profiles in a wind tunnel and found that the shape parameter was p « 1.5 for plumes of neutral buoyancy but only p » 1.0 for dense gas plumes. At large distances downstream of the dense gas source the profile seemed to gradually develop into the profile observed for releases of neutral buoyancy p -> 1.5. The propane experiments in chapter 11 showed that in the absence of source momentum the velocity distribution was insensitive to the stratification by the dense gas layer (m rj 1/7). The turbulent kinetic energy was more reduced inside the gas layer than above indicating a concave height dependence of the diffusivity profile n > 1 which might explain the smaller shape parameter p for the typical dense gas concentration profile.

x = 240 m

CT, <|y-yj< 2ct

2ct <|y-y |< 3cr

x = 72m N x = 20m 1

C [%] C [ppm]

Figure 100. Vertical average profiles in trial 16, using conditional sampling de­ pending on the mast position relative to the plume centre line \y — yc\.

Figure 100 shows vertical profiles from trial 16 based on concentration mea­ surements from gas sensors at 0.1, 0.75, 1.5, and 3-m height at 20-m distance, and at 0.1, 2, 4, and 9-m height at 70 and 238-m distance. Each sensor array had a centre-line mast which was sometimes Jut directly and sometimes by the edge of the plume. The estimates of the instantaneous plume centre line yc, based on measurements in the horizontal arrays, makes it possible to evaluate the vertical profile as a function of the distance from the instantaneous plume centre line y—yc- Because of the relatively short release durations the statistical uncertainty does however limit the spatial resolution of this moving frame analysis. The values in figure 100 have been found using a conditional sampling which sorts the observa­ tions into just three bins depending on the instantaneous centre line |y — yc\. The advantage of this' coarse distribution is that each profile in the figure represents at least three minutes of observation. The shape of the profiles from the first two distances is insensitive to the lateral position whereas the profiles from the last distance seem less regular. In the light of the apparent profile similarity for variable plume positions in fig­ ure 100 (most obviously at the 20 and 70-m distances) all available measurements are used to determine the vertical centre of mass z independent of the instanta­ neous plume position yc. Curve fits to the generic concentration profiles described

140 Ris0-R-1O3O(EN) above by least square error methods produced more than a decade of spreading in the shape parameter p, ie the observed profiles are too irregular for estimates of the profile shapes. Even two-parameter curve fits of fixed shapes, eg with p = 1, resulted in great variation, and instead the plume centre of mass was estimated by stepwise linear interpolation

Zest — „/_! with linear extrapolation to the surface:

Z2C1 — Z\C2 Co = ------(242) Z2 ~ Zi Upward extrapolation of the concentration profile was considered to be too inac­ curate, and the profiles were cut off at the highest sensor position. This implies that the plume depth is underestimated by equation 241 - depending on the shape parameter p. The concentration profile of Britter (1988) may also be expressed by f c(z) = Co exp 1 [rrr(2/p)*n (i/p) z\ J (243) where the gamma functions are inserted in order to scale the distribution with the centre of mass at z. The estimated centre of mass zest is expected to have the following relation with the cut-off height zj, the shape parameter p and the true centre of mass z: /0Z,/Zexp{- r(2/P)z]p r(i/P)zJ (244) /z//zexp{- W The cut-off height z/ is known, and this implies that the cut-off error Azest = z-zest is a function of p which may be determined numerically. The two alternative values of Azest in table 22 correspond to the profile shapes typical for dense gas dispersion (p = 1) and for a plume of neutral buoyancy (p = 1.5). It is a good approximation to estimate corrections for shape parameters in the range of 1 < p < 1.5 by linear interpolation. The optimal profile fit is further discussed below. In case of corrections larger than 15% the height estimates zest were rejected from the table. This rules out all estimates from the 238-m distance where the mast was simply too short for an accurate determination of the plume height.

Mass balance

The ground was wet after each trial and a few months later the grass in the ex­ posed area seemed to be more vigorous than the surroundings indicating some fer­ tilization caused by ammonia deposition. However according to the homogeneous- equilibrium estimates described at the end of appendix B the amount of liquid- phase ammonia was insufficiently for the deposition to have a significant effect on the plume mass balance. It therefore seems to be a good check of the measured concentrations to compare the mass flux of the ammonia plume mp i with the re­ lease rate m, which is known to be within 5% of the measurements by the load cell under the release tank. The mass flux is given by the integral mp i = Jj pcu dzdy (245) where the mass ratio is approximated by c- M/Ma-,r since c <1. As an approxi­ mation I neglect correlations in the turbulent signals and insert average density,

Ris0-R-1O3O(EN) 141 concentration and velocity fields estimated by

r(2/p)zlp (y<-Vc)2) c{y,z) co exp (246) {- [r(i/p)zj 2^ J Pair [(1 c) iWa;r + cMeff] ' P(c) (247) -R?air

In (z/zp) cM ”jet u(c, z) (248) 10mln(10/zo) (1 - c)M, ■ + cM m The concentration field is modelled by the product of the vertical and horizontal profiles discussed in the previous section. The ground-level concentration Co is linked to the centre-line concentration cmax in table 22 which was evaluated from the horizontal chain of measurements at height zr.

r (2 /p)zr cq — cmax(zr) exp (249) r(i /P)z For simplicity the mixture density p is calculated as if the release was an isothermal model gas with the ‘effective’ molar weight Meg estimated in table 30. The velocity profile u is essentially logarithmic with a contribution from the jet flow force -Fjet, ie a correction which considers the momentum as a conserved quantity and neglects the no-slip condition at the ground. These estimates are crude, but the magnitude of the density correction compared to p = pa;r is just 1-3% at 20 m distance and essentially zero further downstream. The magnitude of the velocity correction is 15-30% at 20 m distance, 1-3% at 70 m distance, and negligible at 238 m distance.

0.6 -i 13+

0.3 -

1:1 Mass conservation, solid line 20 m distance, +, dashed line 0.1 - 70 m distance, O, dotted line

Release rate [kg/s]

Figure 101. Mass balance between field and source measurings assuming exponen­ tial shape of the vertical concentration profile.

142 Ris0-R-1O3O(EN) The release parameters from table 30 are inserted together with the moving- frame plume dimensions from table 22 and the mass-flux integral is solved nu­ merically. The average plume height is evaluated as z % zest + Azest(p). In cases where the release duration was shorter than the period of gas observation, the estimated mass flux ihp \ is further corrected by the ratio Tdur/Tobs- Figure 101 shows a comparison with the release rate m for vertical profiles of exponential shape (p = 1). The average mass balance is examined by regression lines through data from many trials and the correlation is found to be 1.02 for the sensor array at 20-m distance and 0.90 for the array at 70 m. This is in better agreement than the mass balance of the Desert Tortoise experiments (Goldwire et al. 1985), but it should be remembered that the present procedure makes certain extrapolations and includes only cases where both emax, ay, and z are available from table 22. The estimated mass flux is found to increase with the assumed shape parameter p. In this way the mass flux estimate may be tuned to a 1:1 correlation with the release rate if the profile shapes are described by p = 0.97 at 20-m distance and p = 1.40 at 70-m distance. These shapes are in good agreement with the review of Britter (1988). The mass estimated plume mass flux seems to be in reasonable agreement with the release rate and relatively insensitive to the unknown shape parameter p. If the centre of gravity z had been estimated from curve fits, estimates would have been available also for the third sensor array, but the scatter in figure 101 would increase substantially. This was the reason for use of simple linear interpola­ tion when estimating the plume centre of gravity zest- With the daring assumptions of a vertical shape parameter of p = 1.5 at the 238-m distance, and assuming that the horizontal concentration profiles from table 22 are correct, the mass balance may be used for rough estimates of the plume centre of gravity z. These estimates are zest = 13.5, 9.2, 8.5, 13.7, 12.5 and 13.2 m for trials number 9, 15, 16, 23, 24 and 25 respectively. Trial 16. at (237.5, 0, 9.0)

min Time Close-up: 4-5 [min] 300 '

Figure 102. Concentration measured by a fast responding sensor and the 37.6-ppm .. average concentration.

Concentration fluctuations Figure 102 shows a concentration time series measured by a fast responding Uvic® sensor at the top of the centre-line mast at 237-m distance. The time series were digitized with 1000 Hz and reduced to 20-Hz time series by block averaging. Read­

Ris0-R-1O3O(EN) 143 ings below a threshold level defined as three times the pretrial standard deviation are set to zero. This correction is very small because of the low signal-to-noise ratio. Comparatively long quiescent periods are observed when the plume moves away from the sensor and rapid concentration fluctuations occur inside the plume as shown by the close-up frame in the lower part of the figure. Trial 16, Concentration Power Spectra

Figure 103. Power spectra of concentration time series measured by fast responding sensors at the centre-line mast at 240-m distance.

Figure 103 shows power spectra of the concentration time series from figure 102 and simultaneous measurements by additional sensors at two lower levels of the mast. In order to improve the statistical significance these series are divided into shorter ones with a length of 512 measuring points equal to »25 seconds. The plotted spectra are calculated as averages of the 48 realizations and the esti­ mated spectral energies are further averaged with a 20% relative band width. Low-frequency estimates are excluded when the time series are divided into short realizations. A Fourier analysis without ensemble averaging would on the other hand produce inaccurate low-frequency estimates not worth presenting because of the short release duration. The high-frequency part of the spectra is seen to follow the S(f) oc /-5/3 power law which is a characteristic of turbulence with an inertial subrange, see Panofsky & Dutton (1984). No sign of instrumental smoothing is observed at the high frequencies. The plot in figure 104 shows the cumulated probabilities P{C < c} for each of the Uvic® signals used for the spectral analysis in figure 103. The curve added to each plot is the simple model from chapter 6 which assumes a finite probability of zero concentration and a gamma distribution for the non-zero concentrations, ie

P{C < c} = (1 - 7) + 7 • 1 EMIr(fc)

with

A_ 1°2 + (7 - i)m2 k = and 7a2+(7-1)^2 7P

144 Ris0-R-1O3O(EN) Fixed frame, z=9 m Moving frame, z=9 m 1

0.8 -

y 0.4 V 0.4

0 100 200 300 0 100 200 300 c [ppm] c [ppm] Fixed frame, z—4 m Moving frame, z=4 m

0.4 - r

c [ppm] Fixed frame, z=0.5 m Moving frame, z=0.5 m

Figure 104■ Cumulated probability functions for concentrations in trial 16 measured by fast-response sensors at three heights at 240-m distance. The frames on the left- hand side show fixed frame probabilities and the frames on the right-hand side show moving-frame probabilities marked O for |y — yc\ < ay, A for ay <\y — yc\ < 2ay, and □ for 2ay < |y — yc\ < 3ay, depending on the distance between the mast and the plume centre line. and where F (k,C/A) and F (k) are the incomplete and ordinary gamma functions, respectively, see Davis (1964). The curves added to figure 104 are calculated di­ rectly by the intermittency 7, mean (j. and standard deviation a, ie they are not curve fits. The distributions shown on the left hand side of figure 104 are ordinary fixed-frame statistics. The average plume centre-line position was 22 m away from the mast, ie 0.88 times the fixed-frame plume spreading ay calculated in table 22. Yee, Chan, Kosteniuk, Chandler, Biltoft & Bowers (1994) proposed a concen­ tration fluctuation model based on a Gaussian distribution of the shifting plume centre line and a gamma distribution for non-zero concentrations as above for con­ centrations in a moving frame of reference. The available time series are too short

Ris0-R-1O3O(EN) 145 for high-resolution estimates of such a moving frame probability distributions and for statistical significance the observations are just sorted into three classes, de­ pending on the distance between the instantaneous plume centre-line position and the mast jy — yc\. As for the vertical average profiles in figure 100, the instanta­ neous centre-line position yc is deduced from simultaneous measurements by the horizontal chain of sensors. The derived moving-frame probability distributions are shown on the right-hand side of figure 104. The moving-frame intermittency 7 appears to be variable in contrast to the assumption of Yee et al. (1994), but the shapes are reasonably well described by gamma functions. In the lower right frame, the shape of distribution is seen to become steeper with increasing distance between mast and plume centre line |y — yc|. This is because the shape parameter k decreases with increasing signal intensity I = a/y. A similar change is seen by comparison of the near-centre-line moving-frame distributions (marked by O) for the three different heights.

Trial 20, correlation of concentration time series

£

0.6 -

"■5 o Fit: R(Sy) = exp o O

Cross-plume separation 5y [m]

Figure 105. Spatial correlation between concentration measurements by fast sensors distributed perpendicular to the wind direction 230 m from the source at 2-m height.

In trial 20 the fast concentration sensors were arranged for a study of the spa­ tial structure of concentration fluctuations. The purpose was to study in-plume fluctuations caused by processes other than plume meandering. The instruments were aligned in the crosswind direction at 2-m height and 230-m distance and separated by irregular spacings. Figure 105 shows the spatial correlation of pairs of signals c(y) and c(y + 5y) normalized by their standard deviation

d(y)c?(y + 5y) R(y,y + Sy) (250) o{y)(j{y + 5y) This correlation is evaluated for variable separation using signals from all com­ binations of sensors. The values for small separations are of main interest since the shape of the meandering plume may affect the correlations for large separa­ tions. The curve added to the figure is a best fit of the type R = exp {—{5y/b) a} obtained by linear regression of transformed variables. The value of b probably relates to the plume dimension whereas the exponent a may be of a more funda­ mental interest. The fitted value of a is close to | as in the classic theory of the distance-neighbour function by Richardson (1926), ie with a very fast decay for

146 Ris0-R-1O3O(EN) small separations which cannot be explained by plume meandering. It should be mentioned that periods with zero concentrations are included in the estimate and this tends to increase the correlation. The correlation function may therefore not be a perfect analysis of in-plume structure.

Extinction

Figure 106. Instantaneous crosswind lidar profiles measured with intervals of three seconds in trial 25.

Figure 106 shows ten instantaneous lidar profiles measured with intervals of three seconds. This time increment corresponds to a plume advection of approx­ imately 10 m. The shape of the profiles is far from Gaussian, and sometimes it would be better to describe the plume as several parallel traces. A trace of gas is often located at the same distance for a long time, eg at a distance —30 m in profile number 3 to 8, but sometimes a trace suddenly appears at a new location, eg at a distance +20 m in profile number 5. Topological explanations for this behaviour are either that the plume lifts off at one distance and lands at another, or that the plume is broken into two pieces by a sudden change of the wind. The latter explanation seems most likely. The sometimes abrupt changes of the lidar profiles and point measurements by a fast sensor as in figure 102 indicate that plume meandering is not the only cause of concentration fluctuations.

Heat and temperature

The 8x8 thermocouples on the rig just in front of the source did not measure the detailed temperature field originally hoped for because of a thick layer of deposit. Instead fairly constant temperatures %207 K were measured, ie much below the boiling point of 240 K. This is in accordance with equation 99 which predicts Tmjn=204 K "for a typical combination of Tajr=288 K, pa;r=l Bar, and A#o=-20.5 kJ/mole. The top frame of figure 107 shows the temperature as a function of time and horizontal distance. The measurements were made by 23 thermocouples mounted with a 0.5 m separation on a string which was stretched across the cold jet at a height of 0.5 m. The distance was 10 m from the source, and this was just downwind of the point of jet touch-down. The jet was «3 m wide and moved rapidly from side to side. Steady temperatures about 3°C lower than the ambient air were observed in a wider space around the jet. However this is probably a measuring error caused by evaporation of deposit from previous jet exposure. The frame below is a similar plot of measurements by 16 thermocouples mounted with

Ris0-R-1O3O(EN) 147 Trial20, Horizontal temperature distribution at (x,z) = (10,0.5)

Scale —iC° — 18 — 16 — 14 12 10 ^-8 Time [min] 6 Trial 20, Vertical temperature distribution at (x,y) = (10,0) 4 2 0 -2 -4

Time [min]

Figure 107. Temperature 10 mfrom the source as a function of 1) time and cross- wind distance, and 2) time and height above terrain. The contour levels are plotted for increments of 22 C. a 0.11 m separation on a minimast at the ideal centre line. The exposure of the minimast is in accordance with the horizontal positions of the plume shown by the upper frame. Trial 27, centre line at 20—m distance and 0.1 -m height

Figure 108. Concentration and temperature from adjacent instruments.

Figure 108 is a comparison of concentration and temperature measured at 20- m distance. In order to make the time series more comparable, the temperature signal has been averaged with a first-order auto-regressive filter with a time scale matching that of the concentration sensor. The correlation between the two signals is fair, but temperature fluctuations are present before the gas release. Also at this

148 Ris0-R-1O3O(EN) distance the thermocouple thermometer tends to measure too cold temperatures during short periods with low gas concentration, while the probe probably was wet and the surrounding gas phase undersaturated. In trial 27 the psycrometer on the reference mast had a wet-bulb temperature depression of «6°C (neglecting the ammonia content of the deposit), and this is close to the difference between the pre-trial temperature and maximum temperature during gas release as seen in fig ­ ure 108. One might contemplate to revert the psycrometer equation and estimate the gas-phase temperature from the wet thermocouple temperature and the wa­ ter vapour concentration known from the upstream measurement. This correction would result in discrete temperature jumps whenever the surrounding gas phase is believed to change from saturate to undersaturated states. The correction would therefore be somewhat arbitrary and we cannot assume that a thermocouple cov­ ered by water droplets is in instantaneous thermal equilibrium. I shall therefore not attempt the correction, but note that sometimes the measured temperature is wrong and that the errors at this measuring position and this trial occur for low concentrations c < 1.2%, see figure 108.

Concentration, c [%]

i i i i i i i i i i i i i i i i i i i i i i i i i i i

~z AH/c Symbol [m] [kJ/mole] 0.1 -16.4+2.0 - 1.5 -19.1+4.2 O

Initial enthalpy deficit: AHn= -20.2 kJ/mole

Figure 109. Correlation of 20-sec average enthalpy deficit and concentration. The dashed lines are obtained by linear regression through data from two heights 20 77i downstream of the source. The solid line is the limit of wet adiabatic mixing according to equation 142.

Figure 109 shows 20-sec block averages of enthalpy deficit AH and concentra­ tion c based on the time series from figure 108 and simultaneous measurements from another sensor pair above. The block averages follow the linear regression lines with the exception of relatively large enthalpy deficits for low concentration situations at the 0.1-m level. These points are infected by the suspected ther­

Ris0-R-1O3O(EN) 149 mocouple error discussed above, but the data were difficult to screen out by an objective criterion. The deviations from the regression lines are expectable for concentrations less than 1.2% at the 0.1-m level, and this block averaging may also distort the enthalpy for slightly higher average concentrations. As in the pre­ vious chapters the overall enthalpy to concentration ratio for the two heights is estimated by the slope of regression lines which has been forced through zero. The solid line corresponds to perfect adiabatic mixing of the released material. The overall enthalpy to concentration ratio for the sensor pair at the 0.1 m level has a deviation which is 1.9 times its uncertainty. This indicates additional heat input disregarded by the adiabatic mixing assumption in equation 142. The correlation of -16.4 kJ/mole NH3 observed at the 0.1 m level corresponds to an ‘effective’ molar weight Mes = 73 g/mole, which is 15% lower than the value calculated from the source measurements. With Mes = 73 g/mole the relative density deficit Ap/Pair oc AMeff/Mair is 22% less than it would have been in case of adiabatic mixing. The measurements of the sensor pair at the 1.5 m level do not deviate significantly from adiabatic mixing, probably because this mixture has not been in close contact with the ground. There is a theoretical possibility that the ammonia plume could become lighter than air with sufficient heat supply, and according to the approximation of equation 132 this buoyant plume limit corresponds to AH/c >-3.5 kJ/mole. An enthalpy change of this magnitude seems most unlikely also downstream of the measuring point, where the plume temperature deficit and ground heat flux are modest.

Source (40.-7.0.1-5)

• •. Ideal Heavy jet centre line dispersion array

Figure 110. Sketch of the release configuration in trial 12.

A vertical release

Figure 110 shows the set-up in trial 12, where the nozzle was pointed in the vertical direction. Prior to the release the wind direction was not very promising, so the source was moved to a position off the ideal centre line - too much in fact as the wind improved during the experiment. The position of the plume touch down was quite sensitive to the wind speed and direction. On the average this was just in front of the heavy jet dispersion array about 5 m to the right-hand side of the 6-m .mast as indicated in the figure. The sensor distribution was not optimized for this kind of release, but the measurements may still be of interest, since field experiments with dense vertical jets are rare. The ground level concentration in the heavy jet array was much lower than with the horizontal release, and if the gas had been inflammable instead of toxic the dilution in the elevated loop considerably would reduce the area of immediate risk. The large plume width observed at 66-m distance could be related to the momentum of the plume when it hit the ground, but it should also be remembered that the wind speed in trial 12 was less than in the rest of the releases

150 Risp-R-l030(EN) as seen in table 30 of appendix B.

Jet model input Atmospheric conditions Release rate q =0.21 kg/s Pressure Pair=999 mBar Angle to horiz. 9=85° Speed Wio m=2.1 m/s Nozzle diameter do =0.004 m Temperature Tair=289 K Exit pressure Pexit =7.28 Bar Humidity R.H.=75 % Liquid fraction a =0.9978 kg/kg Roughness zq =0.004 m M.-O. length L =-34 m

10.4% 214 K 243 K

205 K 270 K 275 K

0 m 5 m 10 m 15 m 20 m

Figure 111. Numerical simulation of trial 12 with the GReAT model.

Figure 111 shows some results from a simulation of trial 12 with the GReAT model (Ott 1990). The ‘ballistic’ path of the plume is sensitive to the exact re­ lease conditions. According to Vargaftik (1975) the measured exit pressure Pexit is slightly less than the saturation pressure of the 16.5 °G temperature measured inside the nozzle, in fact corresponding to a 1.5 °C lower saturation temperature. These measurements are considered to be fairly accurate, so most likely the flow at the exit had a gas-phase component. The liquid vapour fraction is estimated by a = 1 — d AT/L equal to 0.9978, where c' is the liquid heat capacity, A0 is the dif­ ference between the measured temperature and the assumed saturation pressure at the exit, and L is the heat of evaporation. The calculated jet momentum would be 10% larger for a 100% liquid release. The path and touch-down position of the calculated plume is in good agreement with a video recording, but the calculated centre-line concentration at 16 m is almost twice as much as the moving-frame concentration in table 22. However the measured centre-line concentration might be a little too low because the plume touch down sometimes occurred behind the sensor array.

Aerosol composition In order to measure the composition of the liquid aerosols we took samples of the deposit in the release area. The aerosol collectors in trial 15 to 17 were placed along the ideal plume centre line at heights following the path of the jet from 4 to 12-m distance. The amount of the collected material varied significantly with the distance to the source. Close to the source the collectors contained about 20 g, but at 10 and 12 m they contained only about 1 g, and therefore the uncertainty of the chemical analysis increases with downwind distance. Figure 112 shows the composition of the sampled material as a function of distance from the source. The aerosol content is seen to change within a few metres from almost pure ammonia to almost pure water. The jet swept from side to side, ie not hitting the collectors all the time, and it took 0(1) minute to collect all samples after the release. It is possible that ammonia evaporated or that water condensed from the atmosphere

Ris0-R-1O3O(EN) 151 Aerosol composition

0.27 kg/s

0 0 2 4 6 8 10 12 14 Distance from source (m)

Figure 112. Measured composition of liquid samples in trials 15 and 16 as a func­ tion of the distance from the source. The two ice samples are taken from trials 16 and 17, both with release rates ofm=0.27 kg/s. during periods when the collector was exposed to the ambient air. Thus the con­ centration in each sample is a lower bound of the actual aerosol concentration. In trials 16 and 17 additional pieces of the ice deposit were taken directly from a rig placed 4 m from the source. The ammonia concentration of the ice was almost as high as in the aluminum envelope at this distance indicating that the deposit might have been an ammonia hydrate. Some of the measured concentrations are still quite high which indicates that there was no serious ammonia evaporation from the samples.

Interpolated surface concentrations A feature of many dispersion models for risk assessment is to display a map of the calculated surface concentration field which assist the operator in identifying the risk area. Inspired by contacts at Norsk Hydro we decided to produce similar concentration fields based on observations. A particular objective was to study the dependence of the averaging period. Rather strange results were obtained when using a standard program with in­ terpolation methods like Kriging, inverse squared distance weighting, linear inter­ polation, etc. The trouble was that the sensors were clustered in three chains and the commercial program had no built-in knowledge of the variation between them. Actually this variation is unknown, but in the light of the observed profiles at 20, 70 and 238-m distance it seems appropriate to apply a Gaussian interpolation model

(251)

where the surface centre-line concentration Co, the lateral centre-line position yc, and the lateral spreading ay are functions of the downwind distance x. A specialized plotting program contour.exe was developed by Nielsen (1996b). The procedure was 1) to find block averaged concentrations in three arcs across the plume, 2) to extrapolate these to surface concentrations, 3) to fit Gaussian profiles for each distance, 4) to make longitudinal interpolation of cq , yc, and ay, and 5) to find concentration contours by equation 251. The average concentrations

152 Ris0-R-1O3O(EN) OOl

dd L

Distance x

Figure 113. Contour plot of average surface concentrations during a 1-min period of trial 16. were based on a reduced data set and could be selected to averaging periods of a multiplum of 0.5 min. Extrapolation to the ground was based on the plume centre of gravity z from table 22 and an exponential vertical profile (p = 1) at 20-m distance and shape parameters of p = 1.5 further downstream. The lateral profiles were obtained by matching the moments of stepwise linear interpolation between the observations to the moments of clipped Gaussian distribution as shown in the lower left corner of figure 113. This determines the plume parameters cq , yc and <7 y for three downwind distances. The program also uses the origin of the plume in terms of plume concentration, position and dimension near the source. The initial concentration is approximated by the entrainment needed for flash evaporation at the boiling point temperature of ammonia. The average downwind variation is often described by powerlaws, ie Co oc x n as in Wilson (1995), but for short averaging periods that model seldom fits all reference values at 0, 20, 70, and 238-m distance. Instead of fitting data to an empirical model and to accept some deviation it was chosen to interpolate by a suitable spline function through observation, ie the typical approach of a con­ tour plotting program. The longitudinal interpolation function was selected for its ability to produce ‘a good visual appearance’ of the contour curves. The unscien­ tific term expresses a partiality for positive values of cq and ay with monotonous downstream variations and modest excursions between the reference points. This was obtained by natural cubic spline, see Press, Flannery, Teukolsky & Vetterling

Ris0-R-1O3O(EN) 153 (1989), after transforming the concentrations to a logarithmic scale and the down­ wind distance to a scale with approximately equidistant spacing of the reference points (by f(x) = y/1 + x). The interpolation functions shown in the lower right corner of figure 113 are found in this way. With a short averaging time the surface concentration field will often curve as in figure 113 and the centre-line position for consecutive averaging periods sweeps from side to side.

5000--

= 4000

o 2000

—X—20

Average time [min] Average time [min] Average time [min]

Figure 114■ Average dimensions of the 500 ppm footprint depending on the length of the average period. Each figure has a curve for each trial.

The contour plotting programme was used to investigate the problem: how much does averaging time affect the dimensions of the surface concentration field? This should be of interest to the risk analyst who sometimes has to apply a model with an intrinsic average time, which cannot easily be adjusted. Data for this analysis were derived in the following way: in order to answer the question on the effect of averaging time, a period with durations of a multiplum of 10 min was selected from each not-too-short trial with good wind direction, and shorter periods were defined from subdivision of the long one. Then the area within the 500 ppm concentration contour, referred to as the 500 ppm footprint, was found for all periods except in situations where the concentration contour exceeded a predefined domain of safe extrapolation. Finally the length, maximum width, and triangulated area of the footprints were averaged for each averaging time. As expected the length of the footprint had a tendency to decrease with average time whereas the width generally increased. In most trials these effects counteract each other and the footprint area was independent of average time. Power-low fits of the type Lsoo oc Tn, where T is the averaging time in the range 0.5-10 min, showed that increasing the averaging time by a factor of 10 decrease the footprint length by 8%, increase the footprint width by 12% and the triangulated area increased with a modest +2%.

14 Isothermal freon experiments

The turbulent kinetic energy in the momentum-free propane release (chapter 11) introduction

154 Ris0-R-1O3O(EN) was not damped as much as one might have expected from the significant reduction of the mechanical turbulence production. It was speculated that heat convection may have supplied the additional turbulence. Direct measurement of turbulent heat flux in a dense gas cloud is difficult and it is not practical to manipulate the heat input in the field as in the laboratory experiment of Grobelbauer (1995), see page 9. The Thorney Island experiments do however offer a comparison with isothermal dense gas turbulence. The Thorney Island (TI) dense gas experiments were made by a consortium experimental layout led by the UK Health and Safety Executive (HSE). The test site was a closed- down airfield and the released gas was a mixture of freon and nitrogen. Most of the TI trials were instantaneous releases from a collapsible tent and some of them included obstacles. This chapter focuses on turbulence measurements from the two continuous releases TI45 and TI47, which were conducted by the end of the project (McQuaid 1987). TI45 and TI47 had spill rates re 10 kg/s, duration re 8 min, weak ambient wind velocity re 1 m/s and stable atmospheric conditions. The source produced no momentum. The array of gas sensors and the outline of the plume observed in TI45 are sketched in figure 115. Turbulence data are available from the two masts labeled M2 and M3, ie near the centre line and at the plume edge. The chapter is initiated by a review of a previous external analysis and a scale chapter summary analysis of this and the other experiments analysed in this report (the significance of dense gas effect is variable). Next step is to evaluate concentration estimates from the sonic anemometer signals by a modified version of the method of appen­ dix C. These estimates are faster responding and probably more accurate than those of the regular concentration sensors. The turbulent kinetic energy was much more damped than in the previously analysed cold convective gas clouds and the turbulent gas fluxes were almost horizontal. The combination of these anisotropic fluxes and a variable downdraught associated with the slumping process results in rather uncertain estimates of the vertical mixing rate.

Previous analysis of turbulence data from the TI continuous releases Mercer & Davies (1987) investigated the Thorney Island continuous release data and although they had to fight the same problem of short sample times as I did, see chapter 11, they were able to reach several interesting observations:

• The presence of gas was found to have a pronounced damping effect on both vertical velocity perturbations aw and on the vertical momentum flux u'w', much stronger than observed in chapter 11. • The horizontal turbulence components au and av were also reduced.

• The average velocity at the 1-m level slowed down in the presence of gas, though the wind speed remained unchanged at the 14.5-m level, ie well above the gas layer. The releases had no initial momentum, so a momentum budget like in equation 212 cannot explain this velocity deficit.

• The turbulence and shear stress was reduced just above the cloud, but this did not correlate with the. Richardson number

{P ~ Pair) 9h 10% Riu Pair defined by the local gas density p, the ambient friction velocity u„a and the height of 10% of the surface concentration hio%.

The observation, that the local friction velocity \/—u'w' decreased above the gas vapour blanket effect

Ris0-R-1O3O(EN) 155 S Gas source O Locations of masts 0 Masts at which gas was present Masts with sonic anemometers

Mean wind direction

1,2,3,4,5,6.7 Plume sections

Figure 115. Figure [1] from Mercer & Nussey (1987): ‘Mast array, plume sections and plume outline; Trial 45. ’ cloud, has been somewhat overlooked by dense gas modelers, who often parame­ trize the entrainment with a Richardson number like Riu,a, ie using the ambient friction velocity w*. McQuaid (1983) suggested that the reduced friction in a dense gas layer affects the flow above as if the surface was getting smoother and called the phenomenon the ‘vapour blanket effect’. Stretch, Britter & Hunt (1983) mea­ sured wind and concentration profiles of a slightly dense gas plume in a wind tunnel and observed maximum stability (gradient Richardson number) above the plume.

Intercomparison

A discussion of the differences between the field experiments mentioned in this report requires a scale analysis. Konig (1987) defined the length and velocity scales Lcc and Ucc by the volumetric release rate V0 and the initial reduced gravity g'0. Use of the volumetric release rate only makes sense for iso-thermal gas phase releases unless we substitute the initial density p* with that of an isothermal model release with an effective molar weight M*, ie * M.Pair Po~Ht~

The volumetric release rates used in table 23 are then calculated from the mass release rates, using VQ = m/p*, and the effective molar weight M, are calculated from the release scenarios described in the footnotes of the table. Dimensionless wind speeds uiom/Ucc and dimensionless distances L/Lcc to some of the measure­ ments discussed in this report are shown at the bottom of the table. The small value of the dimensionless wind speed uiom/Ucc in TI45 implies that the dense gas effect in this experiment was very strong in contrast to Fladis trial 16 which had a relatively weak dense gas effect. The high release rates of Desert Tortoise

156 Ris0-R-1O3O(EN) imply that the dimensionless distance to the first array of sensors was rather short in that experiment. The dimensionless velocity and distances are shown by the

Table S3, Comparison of selected dense-gas field trials with continuous release. Each trial is characterized by the length and velocity scales Lcc = and

UCc = Va^g'^51 where the volumetric release rate V q corresponds to the known mass release rate m using an effective molar weight M* evaluated from the release conditions.

EEC57 DT4 TI47 FLADIS16 rh [kg/s] 2.0° 108" 10.5“ 0.27" Tair [K] 287 306 288 289 Pair [atm] 1.00 0.91 *1.00 1.02 Pair [kg/m 3] 1.21 1.04 1.21 1.23 UlOm [m/s] 2.6 8.2 1.5 4.4 Af* [kg/mole] 0.098 c 0.087 d 0.058 “ 0.098 “ P* [kg/m 3] 4.11 3.11 2.42 4.16 Vo [m3/s] 0.486 34.7 4.17 0.065 9o [m/s2] 23.5 19.5 9.81 23.4 Lcc [m] 0.40 2.3 1.1 0.18 Ucc [m/s] 3.1 6.7 3.3 2.0 u10m/Ucc 0.85 1.23 0.45 2.16 *oo oo L/Lcc (see footnote) 449 80 h 112'

“Momentum-free release 6Jet release “Two-phase propane release with 33% rain out ‘'Two-phase ammonia release “32% freon and 68% N2, gaseous isothermal release /Front mast - 35 m from source SG04 station - 100 m from source "M2 mast - 90 m from source •Heavy jet mast - 20 m from source filled-in circles in figure 14. In chapters 11 and 12 it was concluded that the effec­ tive molar weight M» was not conserved, and the closed circles in figure 14 results from a calculation similar to table 23 but using M* values based on observations at the selected measuring positions.

Sonic-anemometer concentration estimates

The anemometers used at Thorney Island were not equipped with an extra ther­ mometer for true temperature. The mixture of freon and nitrogen was however released at ambient temperature, and the distortions in the sound virtual sonic temperature caused by freon were large compared to the natural fluctuations. It is therefore possible to estimate gas concentrations from the sound virtual tem­ perature signal only by an assumption that the true temperature gas release was constant temperature equal to the pre-trial mean temperature. approximation The initial mixing ratios are specified by the relative density ratio po/pair which was 2.0 ± 0.2. The corresponding molar freon concentration Cfreon is

Po Cfreon * M{teon ~H (1 Cfreon) * Pair tt'M* -MN2 Cfreon 0.32 ±0.06 (252) Mfreon - Mn2

Ris0-R-1O3O(EN) 157 2.5-1 °xi Fladis 16 J (Heavy jet mast)

O 1.5 Dessert Tortoise 3 O (G04 Mast)

1.0 Q\ B EEC 57 (Front mast) 0.5 • Thomey Island 45 (M2 mast)

0.0---- 1—■—i—i—|—i—r—i—i—|—i—i—i—i—| 0 50 100 150 L/Lcc

Figure 116. Comparison of selected dense-gas field trials. The filled-in circles use effective molar weights M, corresponding to the release, the empty circles corre­ spond to observations at the chosen distance L - see text.

With this uncertainty in the initial freon content the linearized version of the sonic concentration estimate in equation C.8 should be sufficient. Here this equation is rewritten in order to account for the freon dilution Cfreon at the source.

Tsonic {cfreon - + (4^ 1 + C • (253) ^reai + (1 - Cfreon) ' ^1 + 7^

With the heat capacities and molar weights from appendix I the sonic sound vir­ tual temperature sensitivity to the concentration of the released mixture becomes —3.44±0.61°C/%. The typical concentrations are 0(2%), and the signal-to-noise ratio is sufficient to justify the constant temperature approximation. The gas concentrations in the TI experiments were measured by the HGAS HGAS sensor sensor based on an electrochemical cell measuring oxygen deficit. The oxygen content of the cell responds to the ambient concentration by diffusion through a membrane similar to the low-range ammonia sensors in the FLADIS experiments in chapter reffladis. The cell was equipped with a thermistor in order to correct for the influence of electrolyte temperature. The time response was improved by aspiration on the outer side of the membrane and by electronic enhancing of the signal response (Leek & Lowe 1985). The sensors had problems with drift of the zero-level, and time series were corrected for a linear trend before distribution by HSE. The data to be discussed below were measured by sonic anemometers mounted at the 1 and 2-m levels on masts M2 and M3, ie position (400, 275) and (450, 275) shown in figure 115, and the release rates in TI45 and TI47 were 10.6 ± 1.1 kg/s and 10.1 ± 1.0 kg/s respectively. Figure 117 presents 1-s block averaged time series of velocity, HGAS signal, and intercomparison the concentration estimate based on the sound virtual velocity. The significant events appear simultaneously in the two signals, but the correlation was not per­ fect. The differences may be caused by the 1 m horizontal separation of the two instruments, and Mercer & Nussey (1987) describe the vertical gas distribution

158 Ris0-R-1O3O(EN) Trial 45 - 1m at (400,275) 3 2

0 I fc. 0

-I OS

0.0

-OS 6 4 % tst 2 0

S ■# Co 2 0 0 ZOO 400 600 800 1000 1200 1400 1600 Time (secs)

Figure 117. Velocities, HGAS concentration and derived sonic-anemometer con­ centration time series from TI45 at 1 m on the M2 mast near the plume centre line. by a Gaussian profile with a length scale crz=0.5-0.75 m. Even small differences of the average heights of the two instruments could explain the different mean value of the two concentration time series. Figure 118 shows that the correlation between the two concentration time series from the M3 was poor, but the non-zero concentrations before the release indicate that the HGAS sensor at this position had a fault. Brighton (1987) reviewed the TI data set and found that the nonlinear base-line drift sometimes caused problems. This is a more serious defect in the continuous releases than in instantaneous ones which were the main objective of the project. Similar comparisons from TI47 also show good correlation at the M2 mast and a suspicious HGAS signal at the M3 mast. Both HGAS sensors had a 10 Hz ringing noise in the raw data and it is not absolutely certain that the mean value is correct. The nature of the noise is not known (Mercer, personal communication), and it could be that the characteristics of the electrochemical cells had changed and that the electronic enhancement of the response time therefore did not work properly. It should be remembered that these trials took place by the end of the project, where the electrochemical cells in the HGAS sensors approached the end of their useful lives. Figure 119 shows velocity and derived concentration time series from the 2 m level of the M3 mast. Mercer & Davies (1987) discussed a HGAS concentration time series obtained at the nearby 2.4-m level, but were able to conclude only that the concentrations were below the 0.2% noise level of the sensor. The time series in figure 119 show that the concentrations are significantly different from zero. The weak signal before the gas release was caused by natural temperature

Ris0-R-1O3O(EN) 159 Trial 45 - 1m at (450,275)

Figure 118. Velocities, HGAS concentration and derived sonic-anemometer con­ centration time series from TI45 at 1 m on the M2 mast near the edge of the plume. fluctuations. If we accept the sonic concentration estimates, we obtain additional fast concen­ tration time series with better time response than the HGAS signals. In principle the simultaneous velocity and concentration measurements provides an opportu­ nity to extend the turbulence analysis of Mercer & Davies (1987) with turbulent gas fluxes.

Alignment of local coordinate systems

Figures 120 and 121 show time series of speed, vertical stream-line angle and concentration at the plume centre with a 3-minute moving average filter. The tilt angle is relative to a coordinate system aligned according to the mean wind direction over the entire period using the method of appendix D. The sign of the vertical velocity signal has been reversed20, making a positive tilt angle correspond to an upward movement. The purpose of these figures is to show that the variable tilt angle was variable and that it seemed to correlate with concentration. The downdraft because of plume outline in figure 115 shows that the plume is still widening at this location, slumping? and it is tempting to postulate that the observed downdraft during gas release is related to the horizontal spreading of the plume.

20The instruments were mounted upside-down on the TI mobile M-masts, but not on the permanent A-mast also analysed by Mercer & Davies (1987).

160 Ris0-R-1O3O(EN) Trial 45 - 2m at (450, 275) 3

0 200 400 600 800 1000 1200 1400 1600

fe 0.0

0,0 Time (secs)

Figure 119. Velocity and concentration estimates from Til, 5 at 2 m on the M3 mast near the edge of the plume.

Table 2J,. Non-dimensional turbulence characteristics from 1-m sonic anemome ­ ters.

Propane Freon EEC57 TI45 TI47 Front0 Rear6 Centre Edge Centre Edge Pre-trial u [m/s] 2.26 0.98 1.29 0.76 1.02 y/efu 0.39 0.44 0.34 0.44 0.35 tWVe 0.34 0.31 0.34 0.30 0.36 Fu/e 0.66 0.56 0.61 0.51 0.52 u'w'/Fu -0.18 -0.15 -0.16 -0.14 -0.15 Gas plume u [m/s] 1.46 1.93 c 0.75 1.32 0.56 0.78 Vi/u 0.27 0.17 0.34 0.18 0.38 0.28 aw/y/e 0.34 0.42 0.22 0.31 0.17 0.18 0.38 0.41 0.57 0.46 0.67 0.75 u'w'/Fu -0.03 -0.11 0.02 -0.06 0.05 -0.01 c{%] 0.47 0.34 2.51 0.47 1.94 0.34 acjc 1.16 1.05 0.46 0.53 0.46 0.43 Fc/\feo c 0.15 0.21 0.29 0.06 0.53 0.31 w'c'/Fc 0.67 0.61 0.01 0.25 -0.07 0.02

“A 2 m obstacle is present 10 m downstream in the pre-trial period. ‘Pre-trial values are excluded because of the upstream obstacle. ‘The anemometer offset made this value too high. The turbulence is OK.

Ris0-R-1O3O(EN) 161 TI45 - 1m at (400, 275) 3 min moving average

Cone. _

Time (min)

Figure 120. Three minute moving average of speed, vertical tilt of the wind vector and concentration at plume center line.

Turbulence in isothermal and in cold dense-gas releases

Table 24 compares turbulence properties of TI45, TI47 and EEC57. The results of EEC57 are calculated from the periods previously defined in chapter 11, while the pre-trial and in-plume periods in TI45 and TI47 are chosen to 0-400 s and 600- 1000 s of the time series shown. The turbulence properties are in a non-dimensional form, using the turbulent kinetic energy e, the turbulent gas flux Fc and the flux of longitudinal momentum Fu.

e = u'u' + v'v' + w'w'

Fc — du'2 4- cV2 + dw'2 (254)

Fu = \/u'u'2 + u'v'2 + u'w'2

All measurements are from the 1-m level. The wind speed was lower and the atmosphere more stable in the TI trials. Mercer & Nussey (1987) found that the surface roughness was zq =19 mm and 7 mm in TI45 and TI47. The turbulence statistics in the pre-trial periods of the three experiments are turbulence intensity comparable, and during release the flow becomes less turbulent at all locations in all experiments. In contrast to ordinary plumes of neutral buoyancy (see chap­ ter conflux) the turbulence intensity in the TI experiments was higher at the plume centre line than near the edge. In perfect isotropic turbulence the relative strength of the vertical velocity per­ anisotropy turbations is aw/y/e = 1/V3 = 0.58. In the present experiments the ground re­ duced this to % 0.33 in the periods before gas release. In the TI trials the vertical movements were further depressed during gas release. This damping of the turbu-

162 Ris0-R-1O3O(EN) TI47 - /m at (400, 275) 3 min moving average 1.5

1.0 >CO £ 0.5

0.0 0 4 8 12 16 20 24 28

ci -2

Cone. _

Time (min)

Figure 121. Three-minute moving average of speed, vertical tilt of the wind vector and concentration at plume centre line. lent motions did not occur during EEC57 - probably because of the contribution of heat convection inside the cold gas cloud. Small values of the u'w'/Fu ratio implies that the shear stress u'w' is quite sensi­ momentum flux tive to a vertical tilt of the local coordinate system. This could be the explanation of the unexpected upward direction of the momentum fluxes at the M2 mast near the plume centre line where the downdraft associated with the slumping process tilted the local average wind vector. With this uncertainty in mind" it is hard to comment on the differences between the shear stress at various locations. The intensity of the concentration fluctuations ac/c was higher in the propane concentration fluctuations experiment than in the isothermal freon experiments. The intensity is expected to grow near the cloud boundary, so an explanation for the higher intensity in EEC57 could be that the propane plume was more shallow than the freon plumes. This does however not seem to be the case, since the Gaussian curve fits of Mercer & Nussey (1987) had

Ris0-R-1O3O(EN) 163 Trial 45 - Co uw at 1 m 0.0006

0.0004 (400, 275) centre line

0.0002 (450, 275) near edge

0.0000

-0.0002

-0.0004

-0.0006

Figure 122. Co-spectra of downwind and vertical velocity at two positions.

Spectral analysis This chapter is completed with a spectral analysis. The in-plume data were cho­ sen from the 600-1000 s period, and these time series are divided into sixteen realizations, the average spectra are further averaged with a 10% bandwidth. Following the discussion of the fluxes we start with the Co uw and Co wc co- co-spectra spectra of vertical momentum and gas flux in figures 122 and 123. The sign of the spectral densities is generally negative for Co uw and positive for Cowc, at least for frequencies above 0.2 Hz. The low-frequency range of the co-spectra has little continuity because the release duration was too short to give statistically representative estimates. Figure 124 shows the power spectra of the time series in figure 118. The -2/3 power spectra slope in accordance with an inertial subrange is observed in the high-frequency part of the velocity spectra, but the slope of the concentration fluctuations seems to be steeper. There is significant turbulent variability in the low-frequency range except in the vertical velocity spectrum. This is the reason why Mercer & Nussey (1987) found that 1-min block averages were stable for the vertical fluxes, while the horizontal velocity perturbations needed longer averaging times. From the spectra obtained in figure 124 and those in chapter 11 it is tempting to conclude that dense gas turbulence is almost similar to the turbulence in an ordinary atmospheric surface layer. The spectra in figure 125, which are based strange spectra on the time series from the M2 masts near the plume centre line, do however look unfamiliar. It is noted that the steep slope of the concentration spectrum is observed in two decades, suggesting that it is a real effect. Turner (1973, p. 143) speculated on the existance of a ‘buoyancy subrange ’ in which strongly stratified turbulence would lose energy by work against gravity at a range of frequencies

164 Ris0-R-1O3O(EN)

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45

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Figure do trum N causing Turner signals would in The strongly Ris0-R-1O3O(EN) 0.0010 0,0015 0.0010 0.0000 0.0005 - -0.0015 rw -0.0005 Trial 45 - 1 m at (450, 275) near edge

Downwind

Crosswind

Vertical Concentration times 10'

Frequency 1Hz]

Figure 124■ Spectra of velocity perturbations and concentration fluctuations in the isothermal TI45 continuous release.

166 Ris0-R-1O3O(EN) Trial 45 - 1 m at (400, 275) centre line

Downwind,

Crosswind

Vertical \ A Concentration times

Frequency [Hz]

Figure 125. The same as in the previous figure but close to the plume centre line. The concentrations are higher at this location and the concentration spectrum is scaled by 10~2, ie moved 2 decades down.

Ris0-R-1O3O(EN) 167 15 Conclusions

This thesis is written by a field experimentalist with the intention of relating ob­ servations to conventional model concepts with a minimum of novel theory. Many views were inspired by discussions between Ris0 dense gas researchers and previ­ ous project partners who studied dense-gas dispersion by numerical and laboratory models. During these collaborations we often received questions like:

- What was the width of the plume? - What was the centre-line ground-level concentration as function of distance?

- What was the entrainment rate? It was surprisingly difficult to answer these simple questions on basic model con­ cepts. The plume width and centre-line position were much more variable in the atmosphere, and the entrainment velocity was difficult to quantify both by mass balances and eddy correlation methods. An acurate mass balance requires cross sections with a minimum of two downwind distances. The meteorological con­ ditions implied that the flux measurements seldom were available from neither centre line nor cloud interface which in itself was dificult to assess. Analysis of bulk plume parameters like dimensions and mixing rates must rely on simultane­ ous measurements by arrays of sensors. Many researchers consider field experiments as a tool to calibrate model para­ meters, but it is even more important to check underlying model assumptions and to identify processes which need more attention. The heat flux from the ground is an aspect which needs better description in most dense-gas dispersion models. The observed enthalpy changes were significant and this moderates the cloud density. Furthermore the measurements indicate that heat convection contributed to the turbulence production and entrainment efficiency. The source of a dense-gas cloud of practical interest is usually a liquified storage which because of the heat required for evaporation results in a cold emision characterized by its specific enthalpy deficit. The main conlusions are that:

1. the interaction between flow and thermodynamic processes is of key impor­ tance for dense-gas dispersion; 2. the source parameteres are also very important, eg the momentum of a flash­ ing jet which controls the plume trajectory and generates additional turbu­ lence.

List of specific results Plume profiles: The vertical concentration profile seemed more exponential in the domain of dense-gas dispersion than in a plume of neutral buoyancy (chapters 11,13), which is in agreement with the laboratory experiments of Britter & Snyder (1988). Horizontal crosswind profiles were of a Gaussian shape (chapters 12,13). The stratification had a weak effect on the velocity profiles whereas jet momentum significantly increased the advection speed. It is a reasonable approximation to estimate the jet velocity by momentum conservation of the cloud and entrained air (chapter 11). Moving-frame analysis: A meandering plume seems more narrow with higher average centre-line concentration when observed in a moving frame of refer­ ence following the instantaneous plume centre line (chapter 13). The moving- frame analysis is a kind of high-pass filter on the turbulent measurements

168 Ris0-R-1O3O(EN) and it improves the statistical uncertainty caused by the often limited release duration. Moving-frame results are in better agreement with most numerical models and wind-tunnel simulations which usually does not include plume meandering. The surface concentration field depends on averaging time and a distance to a certain concentration limit eg the lower-flamability distance (LFD) often used in risk assessment, inherits this uncertainty.

Obstacles: The plume in the propane experiments (chapter 11) was not suffi­ ciently stable to block the upwind flow according to classic blocking theory (appendix F). The downward gas flux observed behind solid obstacles was caused by low-frequency fluctuations whereas the contribution from fine-scale turbulence had the expected upward direction.

Concentration fluctuations: The probability distribution of concentration fluc­ tuations are well described by the signal average [i, intermittency 7 and in­ tensity / = a/^i, also in a moving frame of reference (chapters 6,13). The average and intermittency decreased and the intensity increased towards the top and edges of the plume (chapters 11,13). Concentration fluctuations in jets have a shorter time scale and less signal intensity than in plumes (chapter 11). The intensity is reduced in the wake of an obstacle, probably because of the well mixed conditions in that region.

Turbulence: Comparison of turbulence production by shear stress and turbulent kinetic energy level indicates that heat convection was a significant additional source of turbulence in the propane experiments (chapter 11). The turbulence here was not much different from that of the ambient atmosphere in contrast to the almost two-dimensional turbulence observed in the isothermal Thorney Island experiments (chapter 14). The causes of this difference are presumably both the heat convection in the cold propane cloud and the extreme stability of the analysed Thorney Island trials. The anisotropic Thorney Island turbu­ lence makes the flux estimates quite sensitive to the coordinate system which must be aligned according to the local flow lines. The flow lines were however affected by the slumping process. The turbulent kinetic energy was significantly enhanced by jet momentum and upstream obstacles (chapter 11). The combination of a solid cross wind fence and jet momentum was a particularly efficient turbulence production mechanism.

Entrainment: A new entrainment theory was developed (chapter 4) inspired by Jensen’s (1981a) model. This includes turbulence production by heat convec­ tion which, following Jensen & Mikkelsen (1984), is estimated by in-plume Monin-Obukhov theory. The limit of passive dispersion was defined by the growth rate of the centre of gravity of a ground-level plume of neutral buoy ­ ancy (appendix G). Flux measurements were used to evaluate the eddy dif- fusivity and entrainment rate (chapter 11). Estimates based on field exper­ iments are rare, but unfortunately they were not in perfect agreement with the theory.

Heat flux: A model for the ground heat flux was constructed by combining heat conduction in the soil with forced convection in a boundary layer between ground and gas cloud (chapter 7). This model predicts effectively constant surface temperatures during the passage time of an instantaneously released dense gas cloud whereas the duration of a continuous release could be suffi­ ciently long to alter the surface temperature. A close examination of ground heat-flux measurements from the Desert Tortoise experiments with correction for the depth of the sensor position indicates that the surface temperature

Ris0-R-1O3O(EN) 169 decreased by 30% during the 3 min release duration of DT3 (chapter 12). The corrected surface heat flux is in reasonable agreement with Jensen & Mikkelsen’s (1984) in-plume Monin-Obukhov estimate.

Enthalpy budget: The enthalpy deficit of a liquefied gas release affects the cloud buoyancy in a way which, after the stage of aerosol formation, is equivalent to excess molar weight. This relationship is formulated as an ‘effective molar weight ’ (chapter 9) which depends on the gas properties and source type. Simulant gases with actual molar weight equal to this ‘effective molar weight ’ would be appropriate for isothermal laboratory experiments if the mixing was adiabatic - a sometimes questionable assumption. Model simulations (chapter 9) show that the heat-flux effect on buoyancy is weakened by enhanced source dilution, eg in a jet source. Adiabatic mixing was not observed in the field experiments (chapters 11,12,13). The decrease with distance (chapters 11,13) reduced the cloud buoyancy, eg to 37% less than the adiabatic-mixing limit at the second measuring array in Desert Tortoise. This heat-flux effect was weaker in a strong jet (chapter 11) as predicted whereas it seemed insensitive to the presence of obstacles.

Aerosols: Aerosol formation reduces the mixture density in a way which depends on the physical properties of the contaminant and the air humidity (chapter 9). Wheatley ’s (1986) phase transition model (appendix E) was applied to describe binary water-ammonia aerosols. The density-concentration relation­ ship fell into three domains: pure gas phase, almost pure water aerosols and almost pure ammonia aerosols (chapter 9). The simplistic ‘effective molar weight ’ approximation is adequate in the domain of dry mixing. The limit of condensation depends on the relative air humidity whereas the magnitude of the deviation from the ‘effective molar weight ’ approximation depends on ab­ solute humidity, ie on temperature. It may be of interest for model developers to know that even with the meteorological parameters of the most humid of the ammonia trials available, the density calculations of a computionally sim­ pler ‘immiscible-aerosols’ model did not differ much from Wheatley ’s (1986) hygroscopic ammonia model (chapter 9). Wheatley ’s (1986) model was used to prove that the fraction of liquid-phase ammonia was modest in the first measurement array of the Fladis experiments (appendix B). This implies that the measured gas-phase concentration was representative for the two-phase mixture as a whole. In a combination with the mass-balance agreement at that distance (chapter 13) it may further be taken as a sign of insignificant liquid-phase ammonia deposition. The chemical composition of aerosols in the jet was found to change within a short distance (chapter 13), and this supports the often used homogeneous-equilibrium assumption. Miscellaneous: - Measurements of gas arrival and departure (chapters 12, 13) show that a dense gas emission of finite duration also spreads in the longitudional direction. - Temperatures observed in an evaporating pool (chapter 12) and inside a flashing jet (chapter 13) were well under the boiling point as predicted by theory (chapter 8). Measurering technique: - It is possible to estimate high-level gas concentrations from the difference between the sonic anemometer sound virtual temperature signal and the true temperature (appendix C).

170 Ris0-R-1O3O(EN) - Three-dimensional velocity time-series were transformed into a coordi­ nate system aligned according to the local streamlines (appendix D) before eddy correlation. - Temperature measurements in two-phase mixtures, eg by thermocouples, are sometimes too low because of the heat consumption by evaporation of wet deposit (chapter 13).

Acknowledgement

Bent Lundbaek Rasmussen and Leif Tegneby assisted with initial water-flume ex­ periments at Department of Hydrodynamics and Water Resources (ISVA), the Technical University of Denmark. The Danish Research Academy (Forskerakademiet) granted a three month stay at Cambridge University (UK) with Rex Britter as my host. The ‘project BA’ experiments described in appendix A were part of the Ma­ jor Technological Hazards Programme sponsored by the Commision of the Eu­ ropean Communities, contract no. EV4T 0012-DK(B), and Ris0 was granted ad­ ditional support by Danish Environmental Protection Agency (Milj0styrelsen). Erprobungsstelle 91 der Bundeswehr (D) lent us an extra sonic anemometer for the experiments. I would like to thank the staff at Ris0, TiiV Norddeutshland, the Swedish Defence Research Establishment (FOA) for their efforts, in particular the field experimentalists: Manfried Heinrich, Ralph Scherwinski, Andreas Kampen, Fritz Reinken, Niels Otto Jensen, Spren Ott, Finn Hansen and Gunnar Dahlsgard. The ‘Fladis’ field experiments described in appendix B were sponsored by the Environment Programme under the Commision of the European Communities, contract no.: EV5V-CT92-0069. From Ris0 participants in the work were: Mike Courtney, Morten Frederiksen, Ole Frost, Arent Hansen, John Holm, Hans Jdrgen- sen, Spren Lund, Bengt Mogensen, Jan Nielsen, S0ren Ott and Valther Thpfner. Participants from Hydro-Care (S) were: Bo Juhl Andersen, Roland Bengtsson, Sten Bjdrk, Benny Kyngsman, and Bengt Arne Tegner. Participants from FOA (S) were: Kenneth Nyren, Melker Nordstrand and Stellan Winter. Participants from CEDE (UK) were: S. C. Cheah, Wilf Evans, Chris Jones and David Ride. Mike Courtney provided the data acquisition software as in project BA. The ‘Project BA’ and ‘Fladis’ projects involved project partners working with wind-tunnel models, computer simulations and data analysis. Much was learnt from these collaborations of which participants are listed in the final reports by Builtjes (1992) and Duijm (1994). John Davies from the UK Health and Safety Executive retrieved raw sonic anemometer data files from the Thorney Island continuous release experiments and his colleague Alf Mercer answered questions on experimental details. Steve Hanna from Sigma Research Corporation kindly supplied an extensive data set from various dense gas experiments conducted by the US LLNL. I am of course grateful also for the underlying work of the Thorney Island and Desert Tortoise projects. Birthe Skrumsager proof-read this report and Spren Lund created drawings for appendices A and B. My favourite discussion partners Spren Ott and Kenneth Nyren and the supervisors Flemming Bo Pedersen and Niels Otto Jensen made many useful suggestions. The final version includes some of the corrections and additional references suggested by Torstein Fannel0p. Finally I wish to thank the rest of my colleagues at the Wind Energy and Atmospheric Physics Department, Ris0.

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182 Ris0-R-1O3O(EN) Summary

Dense gas dispersion may result from accidental gas releases in industrial envi­ ronments or during transport on rare occasions. Thus dense gas dispersion is no environmental problem, but a potential hazard of explosive and toxic materials. A dense gas cloud has its own dynamics. Because of gravity it collapses to a shallow layer and the turbulent mixing will be reduced by stratification between the gas cloud and the above air. Therefore dense gas dispersion cannot be described by conventional dispersion theory.

Theory

The boundary of a spreading dense gas cloud is sharp, and in a calm environment fronts it propagates with a front velocity determined by the excess pressure inside the cloud (chapter 3). The velocity shear between the spreading gas and the ambient air generates turbulence just behind the head of the front creating a mixing called edge entrainment. The flow around the front is altered by the ambient wind, and this affects the front velocity and edge entrainment. A cloud on sloping ground is influenced by gravity, but the front velocity increases a little only, since a dense gas cloud on a slope tends to entrain more air, both at the front and in the following gravity current. As in ordinary dispersion the mixing through the top of the cloud is driven entrainment by turbulence, although this is moderated by the stratification between the gas and the air above. The vertical mixing process is often modelled by an entrain­ ment velocity ue, which is defined as the turbulent mixing through an interface surrounding the gas cloud (chapter 4). Predictions of entrainment velocity are usually derived from a balance of turbulent kinetic energy, and the entrainment velocity is predicted by a fractional form with some sort of bulk Richardson num­ ber in the denominator, eg Ri = ^-gh/u*. In this way the predicted mixing decreases with increasing stratification. The ideal dense gas entrainment function should take account of the turbulence production by shear stress, production by heat convection and the turbulence in the air above the dense gas layer. It would be well if the entrainment predicts reasonable mixing in the case of nearly neutral cloud buoyancy and in case of jet momentum. The influence of obstacles on the dispersion is complex (chapter 5). If the am­ obstacles bient wind is weak or if the cloud is very dense, the gas layer will flow like a liquid between the obstacles. With certain obstacle geometries (eg a street canyon), the horizontal spreading is reduced by the confinement, and entrainment acts on a much smaller top interface so at a given distance from the release point the con­ centration tends to be higher than in the case of flat terrain. The ambient wind will however generate vortices and turbulence around obstacles which usually will more than compensate for the effect of the confinement. The flow and turbulence field around obstacles depend on the obstacle orientation relative to the wind direction. The turbulence creates concentration fluctuations within a range of length concentration fluctuations scales, from the small internal eddies to shifting wind directions sweeping the plume away from fixed measuring positions. The probability distribution of the concentration fluctuations is well described by mean concentration, signal inten­ sity (ratio between standard deviation and mean) and intermittency (defined as the probability of non-zero concentrations). The intensity increases and the inter­ mittency decreases near the edges of a gas cloud. The release characteristics (chapter 8) is the upwind boundary condition of the gas sources dense gas dispersion. The parameters of interest are the source strength, release

Ris0-R-1O3O(EN) 183 duration, possible initial momentum, initial composition and source enthalpy. In order to minimize the container volume, gas storages are often pressurized or cooled. In many cases the stored material is in its liquid phase and will evapo­ rate after emission. With large pressure differences between the storage and the ambient, the outflow becomes a two-phase flow with tiny airborne aerosols. The density (chapter 9) of a single-phase gas mixture is calculated by the ideal density gas law, using pressure, temperature, composition and molar weight of the compo­ nents. The temperature is determined by a heat budget, and if the mixing between the released gas and the entrained air is adiabatic, the density effect of low source enthalpy is equivalent to an increased molar weight. An ‘effective molar weight ’ M» is defined as the molar weight of an isothermal gas which in the case of di­ luted mixtures result in the same density effect as the actual cold release. It would be convenient if this effective molar weight remained constant during dispersion, since this would allow a cold dense gas cloud to be modelled with an isother­ mal test gas, eg in a wind tunnel. Unfortunately the field measurements shows that the mixing is not adiabatic, probably because of the heat transfer from the ground. Possible chemical reactions and aerosol formation complicate the density calculation. However the calculation of these phenomena is eased by the so-called homogeneous equilibrium assumption, ie when we assume 1) that the saturation pressure of components in the liquid phase are in equilibrium with the partial pressures in the gas phase, and 2) that a chemical reaction momentarily reaches the balance described by the law of mass action. The heat transfer from the ground moderates the cloud density and generates heat transfer turbulence by heat convection. A simple model (chapter 7) applies a transfer coefficient for the heat exchange between the surface and gas layer as well as conventional heat conduction theory for the heat flow in the soil. The temperature of the soil at the ground surface decreases as heat is transferred to the cloud, and therefore the rate of heat transfer will gradually decrease. It is estimated that the heat transfer will change during a typical continuous gas releases, but not within the typical passage time of an instantaneously released gas cloud. Dense gas box models (chapters 2 and 10) define uniform or self-similar distrib­ box models utions of all cloud properties like concentration and temperature et cetera, while the cloud dimensions change in accordance with the front velocity. Some generic models for instantaneous and continuous releases are presented, and it is described how these models may be refined in various ways.

Field measurements

Experimental data have been selected from the four projects listed in table 25. The data main emphasis is on the propane releases with obstacles in the ‘MTH project BA’ (chapter 11). The gas source in these experiments was either a jet or a momentum- free cyclone source, and the release rate was 0(2) kg/s. The obstacle was con­ structed of canvas screens which were removed during each release. In order to compare the flow and concentration field with and without the obstacle the ob­ stacle line was either a solid or a crenelated fence, ie a fence in which every second obstacle element was removed. In the ‘Desert Tortoise ’ experiments (chapter 12) a jet source of liquified ammonia applied with very large release rate 0(100) kg/s. ‘Desert Tortoise ’ included measurements of the heat flux from the ground. In the ‘Fladis’ experiments (chapter 13) an 0(0.5) kg/s jet source of liquified ammonia was applied, and measurements were made in the dense plume close to the source as well as further downstream in the passive plume. The experiments selected from the ‘Thorney Island’ project included continuous releases of 0(10) kg/s mixtures of freon and nitrogen (chapter 14). The temperature of these releases was equal to the ambient, so this experiment was not affected by a heat flux from the ground.

184 Ris0-R-1O3O(EN) Table 25. Field experiments utilized in the report.

Experiment Description Analysis MTH project BA Release of liquified propane - Effect of obstacle with and without initial mo­ - Release momen­ mentum, and with an obstacle tum perpendicular to the wind di­ rection. - Turbulence

- Enthalpy balance

Desert Tortoise Jet release of liquified ammo­ - Enthalpy balance nia, with a high release rate. - Surface heat flux

Fladis Jet release of liquified ammo­ - Plume meander­ nia, with transition to passive ing dispersion. - Aerosols

Thorney Island Continuous release of freon and - Turbulence nitrogen mixtures at ambient temperature.

The selected ‘MTH BA' experiments were configured with a fence perpendicular obstacles to the wind direction. This obstacle increased the cloud height and reduced the mean concentration. The concentration field in the wake became more uniform and the ‘dense gas effect’ was locally weakened by the increased turbulent kinetic energy. Because of the well-mixed wake conditions the concentration fluctuations was not enhanced by the increased turbulent kinetic energy. The mixing efficiency was weaker with the crenelated fence than with the solid one, and the full impact on the ground level concentration was seen at some distance further downstream. The upstream effect of the obstacles was not significant and probably not caused by blocking. The obstacles made the gas flow more sensitive to changes in the wind direction. With similar source strengths and ambient wind conditions, the dense jet be­ release momentum came more narrow and less shallow than the plume. The average gas concentration at the 1 m level was almost equal in the two cases, but the jet had higher con­ centrations above this level and lower concentrations near the ground. In either case the vertical concentration profile could be approximated by an exponential distribution. Changes in the wind direction changed the plume position relative to the mean wind direction, and concentrations near the edge of the cloud were intermittent. The enhanced turbulent kinetic energy in the jet made the mixing more efficient turbulence than in the plume, and the turbulent kinetic energy close to the jet source was ac­ tually higher than in the ambient air. Further downstream in the jet the turbulent kinetic energy approached the energy level of a momentum-free release. In case of a jet release the longitudinal turbulent gas flux was in the forward direction u'd > 0, while the dense material lagged behind in the plume u'd < 0. A spectral analysis of the turbulent velocity and concentration revealed a -5/3 power law in­ dicating the existence of an inertial subrange between the energy producing eddies and the small eddies dissipating energy into heat. The turbulence time scales were shorter in a jet than in a plume, whereas the length scales probably did not differ much since the advection speed was faster in the jet. The shape of the spectral

Ris0-R-1O3O(EN) 185 distribution of vertical velocity was similar to that of the ambient flow, and most of the vertical gas flux was associated with eddies with length scales comparable to the height of the cloud. The turbulence measurements from the momentum free releases had a remark­ able reduction of the turbulent shear stress and consequently also of the shear- stress production of turbulent kinetic energy. However, this was only followed by a modest reduction of the turbulent kinetic energy suggesting a second source of turbulence, which is believed to be heat convection from the surface. From an enthalpy budget of simultaneous concentration and temperature mea­ enthalpy balance surements, it has been shown that other heat inputs than adiabatic mixing were present in both ‘MTH BA’, ‘Desert Tortoise ’ and ‘Fladis’. The overall buoyancy of the cloud was therefore not constant during the dispersion! The heat input cre­ ated heat convection and a crude estimate suggests that mechanical and convective production of turbulence were of equal importance in the propane experiments. Buoyancy conservation seems to be a better approximation in a jet than in a plume, perhaps because the initial mixing in the high speed jet moderated the temperature deficit before the jet touched the ground. When the heat flux measurements from the ‘Desert Tortoise ’ experiments are heat flux analysed in a way which takes the sub-surface sensor position into account, it appears that the measured flux only reached about half of the actual maximum flux at the surface, which is the flux affecting the gas cloud. During the 3 min release duration the corrected surface heat flux from a location near the center of the plume decreased to 70% of its initial value. The release duration of the ‘Fladis’ experiments was sufficient for a statisti­ plume meandering cal representative determination of the cross-wind concentration profiles at three downwind distances. The concentration profiles are found in a fixed frame of ref­ erence and in a frame of reference following the instantaneous plume center line position. The moving-frame profiles had higher centre-line concentrations, smaller plume widths, and less concentration fluctuation intensity than in the fixed frame of reference. The chemical composition of the water/ammonia aerosols were determined by aerosols samples of the deposit in the two-phase jet in ‘Fladis’ experiments and found to change within a few meters. This gives some support for the computational convenient homogeneous equilibrium assumption. The weak vertical fluxes measured from ‘Thorney Island’ are difficult to inter- turbulence in iso-thermal prete, in particular the downward gas flux measured near the plume center line. releases However, time series of concentration and vertical velocity filtered with a 3-min moving average filter, are found to correlate well with each other. This indicates that the slumping of the plume was stronger during periods with high gas concen­ trations giving an unexpected contribution to the vertical gas flux which should not to be confused with entrainment. Spectral analysis shows that the contribution of the small eddies were in the expected direction. Although the ‘dense gas effect’ of the ‘Thorney Island’ experiments was larger than in the rest of the analyzed experiments and therefore not directly comparable to the propane experiments, it is suggested that the large reduction of the turbulent kinetic energy level was partly caused by the lack of heat conduction.

Sammendrag — summary in Danish

Titlen pa denne raport kan oversaettes til ‘spredning af tung gas i atmosferen’. En sadan gassky har en indre dynamik, idet den er under indflydelse af tyngdekraften, som far den til at falde sammen til en bred, men ikke saerlig hpj sky. Lagdelingen

186 Ris0-R-1O3O(EN) mellem den tunge gas og luften ovenover daemper desuden den lodrette opblanding, sa resultatet er, at man far daekket et st0rre areal med hpjere gaskoncentrationer. Faenomenet kan optraede ved utilsigtede udslip af luftarter fra opbevaringsanlaeg i industrien eller under transport. Der er ikke tale om et permanent forurening- sproblem, men om ulykker, der kan udvikle sig til brand- eller giftkatastrofer. Pa grund af den tyngdedrevne spredning og den reducerede lodrette opblanding, er det ikke muligt at vurdere konsekvenserne af en ulykke med tung gas korrekt ved hjaelp af konventionel spredningsteori.

Teori

Nar en tung gassky spreder sig ud over terraenet, opstar der ganske skarpe fron- fronter ter, hvis udbredelseshastighed i stillestaende luft kan bestemmes af skyens hy- drostatiske overtryk (kapitel 3). Hastighedsforskellen i forhold til den omgivende luft danner hvirvler bag fronten, og skaber derved en opblanding. Str0mningen omkring fronten pavirkes af modvind eller medvind, og derfor kan man ikke umid- delbart superponere frontbevaegelsen med vindhastigheden. Pa en skranende flade vil gasskyen pavirkes af tyngdekraften, som dog pa grund af inertien fra en 0get indblanding af luft ikke aendrer fronthastigheden markant. Ligesom ved spredning af en almindelig gassky sker fortyndingen gennem skyens- medrivning graenseflade ved hjaelp af turbulente hvirvler, som i en tung gassky daempes af den stabile lagdeling (kapitel 4). Processen beskrives ofte som en blandingshastighed gennem en taenkt flade, der omgiver skyen, og denne hastighed kaldes for medrivn- ingshastigheden 21. Det saedvanlige udgangspunkt er ligningen for turbulent kinetisk energi. Heri indgar det arbejde, som tyngdekraften udfprer nar det tunge materiale lpftes, og ved at vurdere hvor meget turbulens der produceres, kan der udvikles en formel for medrivningen. Sadanne formler indeholder gerne en form for Richard­ son tal i naevneren (fx. Ri = g'h/ul), og pa denne made aftager medrivningen ved 0get stabilitet. Den ideelle formel for medrivning i en tung gassky, b0r tage hpjde for den turbulente energiproduktion fra forskydningspaendninger sa vel som varmekonvektion fra jordoverfladen og turbulens i luftstr0mningen uden for skyen. Det er ogsa pnskeligt, at den forudsagte medrivning konvergerer mod opblanding- shastigheden i en jet og i en almindelig gassky uden tyngdepavirkning. I praksis er det selv for en neutral gassky ganske svasrt at forudsige forhin- forhindringer dringers virkning pa spredningen (kapitel 5). Ved svag vind og stor forskel mellem gasskyen og luftens vaegtfylde vil gassen strpmme som en vaeske mellem forhin- dringerne. I nogle omgivelser, fx et gaderum, vil den vandrette spredning haemmes, og medrivningen foregar gennem en mindre overflade, hvilket betyder, at koncen- tration et givet sted bliver hpjere end i abent terrsen. Imidlertid skaber selv en let vind ganske megen turbulens omkring bygninger, og inddaemningen bliver derfor hurtigt uden naevnevaerdig betydning. Strpmningen omkring bygninger er fplsom over for vindretningen. Turbulensen skaber koncentrationsfluktuationer pa mange lasngdeskalaer, fra koncentrationsfluktua­ hvirvlerne inde i skyen til midlertidige skift i vindretningen, som traskker plumen tioner vaek fra en given maleposition. Sandsynlighedsfordelingen af koncentrationsfluk- tuationerne kan beskrives ved middelvaerdien, intensiteten (standardvariationen i forhold til middel) og intermittensen (som er sandsynligheden for positive koncen- trationer). Intensiteten stiger mens intermittensen falder, nr man bevger sig udad mod kanten af en sky. I studier af tung gas spredning bar man behov for at kende startbetingelserne kilder til tung gas ved kilden (kapitel 8 ). Den vigtigste er selvf0lgelig kildestyrke og varighed; men ogsa impulsen ved nedblaesning fra et eventuelt overtryk; afkplingen i forbindelse

21Jeg oversaetter her udtrykket ‘entrainment* til ‘medrivning*.

Ris0-R-1O3O(EN) 187 med fordampning; medrivning af draber samt stoffets fysiske egenskaber, bar be- tydning for spredningsprocessen. I mange tilfaelde opbevares gasser af pladshensyn pa vasskeform, som fordamper after et udslip. Vaegtfylden af en ren gasblanding kan bestemmes med den ideale gaslov, hvori vaegtfylde indgar tryk, temperatur, sammensaetning samt molvaegten af de enkle bestandele (kapitel 9). Temperaturen kan bestemes ud fra et varmeregnskab, og hvis blandin- gen er adiabatisk, vil et lavt varmeindhold (enthalpi) ved kilden have samme virkn- ing som hpj molvaegt. Man kan definere en ‘effektiv molvaegt ’ M* som molvaegten af den gas, der ved sma fortyndinger uden nogen temperaturforskel fra omgivelserne bar samme vaegtfylde som den virkelige kolde gas. Det ville vaere bekvemt, hvis den ‘effektive molvaegt ’ viste sig at vaere konstant, for sa var det den rette molvaegt for en modelgas i vindtunnelforspg uden temperaturforskelle. Desvaarre viser feltmalinger at dette ikke er tilfaeldet, idet varmeoverfprslen fra jordoverfladen betyder at blandingen med luft ikke er adiabatisk. Eventuelle kemiske reaktioner og dannelsen af svaevende draber komplicerer beregninger af vaegtfylden, men de er overkom- melige hvis man antager, at komponenterne til enhver tid er i termisk og termo- dynamisk balance, dvs. at der er maettede dampes tryk over vaeskepartiklerne, og at kemiske reaktioner meget hurtigt kommer i ligevaegt. Varmetilforslen fra jorden mindsker skyens vaegtfylde og bidrager til turbu- varmeledning fra lensen. Med en enkel model (kapitel 7) beskrives varmeoverfprslen mellem gas jordoverfladen og jordoverflade ved hjaelp af en varmeoverfprselseskoefficient og varmeledningen i jorden med gaengs varmeledningsteori. Generelt vil jordoverfladens temperatur langsomt falde og derfor aftager varmeoverfprslen ogsa gradvist. Det vurderes, at vaxmeoverfprslen typisk nar at aftage i lpbet af et vedvarende udslip, men ikke i lpbet af passagen af en sky fra et momentant udslip. De enkleste tung gasmodeller (kapitel 2 og 10) regner med en ensformet eller simple modeller ligedannet fordeling af alle egenskaber i gasskyen. Nogle prototyper af denne mod­ el type praasenteres og senere diskuteres forskellige modeludvidelser.

Table 26. Feltfors0g anvendt i rapporten.

Forspg Beskrivelse Analyse MTH projekt BA Udslip af flydende propan med - Virkning af en eller uden impuls og med en forhindring forhindring pa tvaars af vindret- - Impuls fra kilden ningen. - Turbulens

- Enthalpibevarelse

Desert Tortoise Jet af flydende ammoniak med - Enthalpibevarelse hpj kildestyrke. - Varmeledning fra jordoverfladen

Fladis Jet af flydende ammoniak der - Plume bevsegelse udvikler sig til en passiv plume. - Koncentration i svaavende draber

Thorney Island Vedvarende udslip af en Hand­ - Turbulens ing af freon og nitrogen ved om- givelsernes temperatur.

188 Ris0-R-1O3O(EN) Feltmalinger

Der er anvendt resultater fra de fire feltfors0g, som beskrives i tabel 26. Hovedvaegt data er lagt pa ‘MTH projekt BA’, hvor der blev udf0rt fors0g med udslip af flydende propan og under indflydelse af forhindringer (kapitel 11). Kilden var nogle gauge en dyse, der gav en kraftig jet, og andre gange en cyklon, der gav en impuls- fri plume. I begge tilfaelde var kildestyrken 0(2) kg/s. Forhindringerne bestod af skserme, som blev fjernet midt under hvert forspg, saledes at man kunne sam- menligne strpmningen og gaskoncentrationerne med og uden forhindring. ‘Desert Tortoise ’ forspgene (kapitel 12) anvendte en jet med flydende ammoniak som kilde der gav 0(100) kg/s. I ‘Desert Tortoise ’ malte man endvidere varmetilfprslen fra jordoverfladen. ‘Fladis’ forspgene (kapitel 13) havde ogsa en jet med flydende am­ moniak som kilde, men her var kildestyrken kun 0(0.5) kg/s. Der blev bade malt i omradet med tung gasspredning og laengere nedstrpms, hvor plumen ikke laengere var tung. De udvalgte forspg fra ‘Thorney Island’ (kapitel 14) brugte vedvarende udslip af en blanding af freon og kvaslstof uden impuls fra kilden. Der var in­ gen temperaturforskel fra omgivelserne, og derfor var disse forspg ikke pavirket af varmekonvektion fra jordoverfladen. De udvalgte forspg fra ‘MTH BA’ havde et hegn pa tvaers af vindretningen, hvis forhindringer hovedvirkninger var en forpgelse af skyens hpjde og en reduktion af middelkoncen- trationen nedstrpms. Koncentrationerne i lae af forhindringen varierede ikke meget med hpjden, og det forpgede turbulensniveau reducerede ‘tung gaseffekten ’ lokalt. De velblandede forhold i lae betpd at koncentrationsfluktuationerne aftog pa trods af det pgede turbulensniveau. I nogle tilfaelde bestod forhindringen af en brudt flade, hvor skaermene kun daekkede 50% af arealet, saledes at det meste af gassen kunne passere igennem abningerne, hvorefter den blev blandet op i hvirvlerne fra skaermene. Derved optradte den fuldstaendige virkning ved overfladen lidt laengere nedstrpms end bag det ubrudte hegn. Den brudte forhindring var lidt mindre ef- fektiv til at fortynde gasskyen. I de udfprte forspg var virkninger af forhindringen svaer at spore opstrpms og skyldtes formentlig ikke blokering. Forhindringer gjorde dog skyen mere fplsom over for variationer i vindretningen - isaer nar der ikke var nogen impuls fra kilden. Ved sammenlignelige vindforhold og kildestyrker blev den tunge jet mindre impuls bred og hpjere end den tilsvarende plume. Der var ikke nogen saerlig forskel pa middelkoncentrationen 1 m over jordniveau, men jetten havde hpjere koncentra- tioner over dette niveau og lavere naer jordoverfladen. Den lodrette koncentrations- fordeling kunne i begge tilfaelde beskrives som et ekspotentielt profil. iEndringer i vindretningen flyttede gasskyen i forhold til middelvindretningen, og koncentra- tionsmalingerne i kanten af skyen blev afbrudt af perioder uden gas. Det forhpjede turbulensniveau i jetten gav en mere effektiv opblanding, og taet turbulens pa kilden var den turbulente kinetiske energi faktisk hpjere end i omgivelserne. Energiniveauet aftog dog gradvis nedstrpms og naermede sig forholdene ved den impulslpse kilde. Den turbulente gasflux i strpmretningen var naturligt nok frem- adrettet u'd > 0 i jetten, mens den tunge gas havde tendens til at sakke bagud i plumen u'd < 0. En analyse af frekvensfordelingen viste at den spektrale energi er proportional med frekvensen i potensen -5/3. Det peger pa eksistensen af et ligevagtsomrade i energikaskaden mellem de hvirvler, hvor den turbulente energi skabes og de sma hvirvler, hvor molekylaer friktion omdanner den kinetiske energi til varme. Den turbulente tidsskala i malingerne i jetten var kortere end med den impulslpse kilde, men laengdeskalaerne var sikkert temmelig ens, idet advektion- shastigheden var hpjere i jetten. Ligesom 1 turbulens under neutrale stabilitets- forhold var de laveste frekvenser undertrykt i den lodrette retning pa grand af den korte afstand til jordoverfladen. Det viste sig, at frekvensfordelingen af de lodrette bevaegelser i propanforspgene havde nogenlunde samme form som under neutrale

Risp-R-1030(EN) 189 forhold, sa den lodrette opblanding skyldtes hovedsagelig hvirvler af nogenlunde samme stprrelsesorden som skyh0jden. Turbulensmalingerne i de impulstose propanfors0g viste en markant reduktion af den turbulente friktion og dermed den mekaniske produktion af turbulens. Dette blev imidlertid kun ledsaget af en beskeden reduktion af det turbulente energiniveau. Turbulensen ma derfor vaere blevet produceret pa anden made - mest naerliggende ved varmekonvektion fra jordoverfladen. Ved at opstille et varmeregnskab for samtidige malinger af koncentration og tem- varmeregnskab peratur kan det vises, at bade ‘MTH BA’, ‘Desert Tortoise ’ of ‘Fladis’ forspgene fik tilfprt vaesentlige varmemaengder ud over blandingen med luft. Skyens sam- lede tyngde minus opdrift var derfor ikke nogen bevaret st0rrelse. Hvis det an- tages at det ekstra varmebidrag kommer fra jordoverfladen, viser et groft over­ slag, at den konvektive og den friktionsskabte turbulensproduktion var af samme stprrelsesorden i propanforspgene. En tilnaermet antagelse om bevarelse af tyngde minus opdrift viser sig at vasre mere korrekt i en jet end i en plume, sikkert fordi den kraftige opblanding i en kogende aerosol jet udligner temperaturforskellen, f0r gassen far kontakt med jordoverfladen. Nar varmeoverfprslen, som i ‘Desert Tortoise ’ forspgene blev malt lige under varmeflux jordoverfladen, fortolkes under hensyntagen til afstanden fra jordoverfladen, kan det vises at det malte maksimum kun svarer til omkring halvdelen af det virkelige maksimum ved overfladen. Det vurderes, at varmefluxen fra en position midt i skyen gennem de tre minutter, som forspget varede, naede at aftage til 70% af fluxen i begyndelsen af forspget. Varigheden af ‘Fladis’ forspgene var tilstraekkelig lang til at give en god sta- beveegelse af en plume tistik pa den vandrette koncentrationsfordeling i tre instrumentkaeder i forskellig afstand fra kilden. Koncentrationsfordelingen kan enten Andes i et fast koordinat- system eller i et bevaageligt system, der fplger plumens bevaegelse. Statistikken for malingerne i det bevasgelige koordinatsystem giver hpjere centerliniekoncen- trationer, en smallere plumebrede og mindre fluktuationer. Den kemiske sammenssetning af vand/ammoniakdraberne i ‘Fladis’ blev malt draber ved at samle prpver af udfaeldet materials. Prpvernes sammenssetning sendredes drastisk inden for fa meters afstand, og det stptter den beregningsmaessige bekvem- me antagelse om at draberne er i termodynamisk ligevsegt med gasfasen. Malingerne af de lodrette turbulente fluxe fra ‘Thorney Island’ er lidt vanske- turbulens uden varmeflux lige at fortolke. Man kan ganske vist konstatere, at de er ret sma, men i midten af plumen er den turbulente gasflux malt til at ga nedad. Ved en nsermere un- derspgelse viser det sig, at glidende middelvasrdier af den lodrette hastighed og koncentration er temmelig korrelerede, nar man anveder et filter med en tidskon- stant pa tre minuter. Det tyder pa, at plumen synker mere sammen nar koncen- trationen er hpj, hvilket giver et uventet bidrag til den lodrette gasflux, som ikke bpr forveksles med turbulent opblanding. En spektralanalyse viser at bidraget fra mindre hvirvler er opadrettede. Virkningen af tung gas var noget stprre i ‘Thorney Island’ end i resten af de underspgte forspg, men den store forskel i turbulensen skyldes efter alt at dpmme ogsa manglende varmekonvektion.

190 Risp-R-1030(EN) A The MTH Project BA propane experiments

The project Research on Instantaneous and Continuous Dense Gas Releases or Major Technological Hazards (MTH project BA (1988-1991) was sponsored by the Commission of the European Communities (Contract: EV4T 0012-DK(B)). Risp’s contribution to this work was co-sponsored by the Danish Environmental Protection Agency (Miljpstyrelsen). The overall objective was to improve the understanding of accidental dense gas releases and the project partners chose some specific problems where it was felt that more information were desirable, such as: - interexperimental variability

- concentration fluctuations - the effects of obstacles The group worked with field experiments, wind-tunnel models, analysis of exper­ imental data and numerical models. The main role of Ris0 was to participate in a series of field experiments with continuous releases of liquefied propane with and without momentum with focus on the effect of obstacles. The field exper­ iments were conducted in collaboration with TiiV, Norddeutschland, Hamburg, Germany. TiiV performed the gas releases and measured gas concentrations while Ris0 measured wind speeds, wind direction, temperature profiles and turbulence. The experiments have been analysed by other members of the project group and ourselves, and they have been used by wind tunnel laboratories as a reference for their physical models. The three wind-tunnel laboratories in the group were: MT-TNO (The Nether­ lands); Univesity of Hamburg (Germany); Warren Springs Laboratory (United Kingdom). They started their work with intercomparison tests and modeled part of the field experiments. WSL made a large number of repetitions addressing the problem of inter-experimental variability. Teoretical work and data analysis were performed by: SRD (United Kingdom); HSE (United Kingdom); Brunei University (United Kingdom); where SRD initi­ ated the work with a literature study. Finally Solvay Industries (Belgium) has worked with the incorporation of dense gas behaviour in their general purpose 3-D dispersion model. A considerable amount of our part of the work was spent on preliminary data analysis, correcting for instrumental errors and presenting the data in a convenient format. A 1-Hz data set containing readings from both Ris0 and TiiV instruments was distributed by TiiV on IMB PC compatible diskettes, and an additional 10-Hz data set containing turbulence and concentration fluctuation records on magnetic tape was distributed from Ris0. Both data sets are available from Ris0 and have later been integrated in the REDIPHEM data base, see Nielsen & Ott (1995) and appendix H.

Objective of the field experiments

Perhaps there was a difference between the Ris0 and TiiV concept as to the pur­ pose of the experiments, and we had to make compromises reflecting two quite different points of view. According to the German philosophy the study of a wide range of obstacle configurations was valuable in order to make the experiments of direct use for industry as a guideline to the design whereever dense gas dispersion is a potential hazard.

Ris0-R-1O3O(EN) 191 Conversely Ris0 wanted to investigate the simplest obstacle to be thought of- a fence perpendicular to the wind direction - in order to obtain detailed information on the ongoing physical mechanisms. It is not a trivial matter to understand the physics even of this simple obstacle or to perform a correct modeling. The relevant parameters for the obstacle mixing effect are:

- wind speed - wind direction

- release flow rate

- source momentum - initial density

- obstacle height

- obstacle porosity The height and porosity of the obstacle, flow rate and momentum were all controllable parameters while the initial density was fixed. A natural but uncon­ trollable variability in wind speed and direction is always present. A series of experiments was made with the perpendicular wall with some varia­ tion of the parameters. In addition to the basical case we made releases in a street canyon (ie between two parallel walls), a wall parallel to the wind direction, semi arches and two perpendicular walls together with vertical jets in the absence of obstacles. These configurations are further explained below.

Side view Top view

and aerosols inlet-=$> 11

Figure 126. The momentum-frees cyclone source used in the project BA experi­ ments, (after Heinrich & Scherwinski (1990)).

Test facility

The test facility was originally constructed by TiiV for a series of experiments with a continuous source of liquefied propane carried out for the German Ministry of

Technology (bmft) in order to determine distances to lower flammability limits(. Heinrich, Gerold & Wietfeldt 1988b, Heinrich, Gerold & Wietfeldt 1988a) A large propane storage with an additional nitrogen container for pressure control was still present. An underground pipeline supplied the source 200 m away. Different sources could be mounted at the outlet - a cyclone for momentum-free releases and nozzles with orifices of different sizes for jet releases. The cyclone source sketched in figure 126 requires some explanation. The momentum because of the expansion by evaporation initiates a rotation of the two-phase mixture inside the cylinder. The net momentum from the source is zero, since the flow escapes in all directions. Part

192 Ris0-R-1O3O(EN) of the liquid aerosols « 1/3 deposits inside the cyclone and leaves the source as a liquid through the holes at the bottom. We normally used release rates « 3 kg/s for both jet and cyclone sources. A 10 m video mast was erected near the source to supervise the release from the control room. A computer/control room, a workshop and a room for general purposes were established in a temporary building. The terrain near the test site was flat with undisturbed wind, and the path of the dense gas clouds was unaffected by terrain slopes. The area is frequently used as a military test site and was easily closed to the public during the experiments. A detailed description of the test facility is found in the final TiiV report (Heinrich & Scherwinski 1990). In order to make use of the existing gas storage and concentration sensors de­ veloped in the previous German experiments for BMFT, we decided to use propane again. The liquefied propane became superheated at the source outlet when the pressure drops to the atmospheric level causing a flash-boiling, fragmenting the material into a mixture of tiny evaporating airborne droplets. The evaporation heat is provided by cooling of the released propane and entrained air. The propane molar weight is 44 g/mol-1 which is dense compared to the average molar weight for atmospheric air of 29 g/mol -1 and the ‘effective’ molar weight - see chapter 9 - is estimated to 98-110 g/mol -1.

Obstacle design

We constructed all obstacles as lines of 2-m high poles placed 2.4 m apart carrying curtains on beams. The beams had a special release mechanism and the curtains could be removed by pulling a wire from outside the gas cloud. In this way we were able to measure dispersion of the dense gas plume or jet with and without the obstacles in nearly the same wind conditions. Our standard procedure in the experiments was to remove the obstacles in the midst of the experiment and to record a period without gas before and after the release. For obstacle configurations consisting of two fences we made an interval before removing the last one. In this way we had two experiments in one where the remaining obstacle served as a new configuration. In some experiments the obstacles formed solid fences and in others we left open every second gap between the poles, giving an overall porosity of 50%. We manufactured a 150 m fence which was distributed in walls with a typical length of 50 m.

Instrumentation and data aquisition

Each mast was equipped with five/eight temperature sensors, three cup anemome­ ters and a wind vane for wind speed and direction, three sonic anemometers for three-dimensional turbulence measurements and three TiiV catalytic concentra­ tion sensors, see figure 127. The temperature sensors were made of 0.1 mm NiCr/Ni wires known as type K thermocouples and had a response time in the order of 0.2 s. We used a real phys ­ ically cold junction inside an isolated copper cylinder with a thermal response time in the order of 30 min and equipped with a thermistor measuring the ref­ erence temperature. Both thermocouples and their amplifiers were developed and manufactured at the laboratory for this project. The cup anemometers had three cups on a rotor with a diameter of 20 cm on a 30 cm vertical axis positioned on booms 1 m away from the mast in order to avoid flow distortion. They were all individually calibrated. Their response time was in­ versely proportional to the wind velocity and for 2 m/s it was approximately 0.6 s. The dimensions of the wind vanes were similar to those of the cup anemometers

Ris0-R-1O3O(EN) 193 SONIC ANEMOMETER WITH THERMOCOUPLE THERMOCOUPLE

CUP ANEMOMETER

CATALYTIC SENSORS

WIND VANE

Figure 127. Instrumentation of the meteorological masts. We used two masts inside the gas cloud in each experiment and a third mast outside for reference. Only the masts inside the cloud was equipped with sonic anemometers which were moved between two alternative obstacle configurations. and response time was a little faster. For turbulence measurements we applied Kaijo Denki ultra sonic anemometers. The principle of these anemometers is to measure the time-of-flight of a supersonic sound signal between a pair of sound transducers in two directions. The difference of the speed in the two directions is taken as the velocity component in that direc­ tion. As it is estimated for three different pairs of transducers, a three-dimensional velocity vector is obtained. For one of the measuring paths, the vertical one, the speed of sound was also evaluated, giving a virtual sonic temperature. In case of a dry atmosphere this is equal to the true temperature. If a foreign substance like propane is present, the virtual sonic temperature will be wrong because of a change in the speed of sound. Therefore, each sonic anemometer was equipped with a thermocouple to measure the true temperature, and this enabled us to estimate propane concentrations as described in appendix C. The instrument was placed 1 m away from the mast like the cup anemome­ ters. One of the three measuring paths was vertical and the two horizontal paths formed a gap of 120°, orientated in the expected mean wind direction to avoid flow distortion. The instrument was cabable of measuring frequencies up to about 5 Hz and our choice of sampling frequency reflects this limitation. The ground-level horizontal mean gas-concentration distribution was measured by TiiV with an array of up to 36 catalytic gas sensors with a response time in the order of 10 s and 8 additional faster sensors based on a principle of infrared

194 Ris0-R-1O3O(EN) light absorption. The sonic anemometers and the array of ground-based concentra­ tion sensors were moved between the two obstacle configurations described below according to the weather forecast. We had to take special precautions in order to eliminate the danger of propane ignition. This meant that we could not use a normal 220 V power supply but had to do with battery power causing some loss of data. TiiV sampled all instruments except the sonic anemometers with approximately 1 Hz. Ris0 sampled the sonic anemometers and some of the in-plume meteorolog ­ ical instruments on a separate faster system. In the first campaign Risp used a Hewlett Packard 3852A datalogger and made 16-Hz measurements. The process­ ing of these data was inconvenient and it was exchanged with a PC based solution. This solution made it possible to sample with 100 Hz and block average down to groups of 10, thus making a digital low-pass filter which reduces the noise. For further description of the Ris0 instruments, see Nielsen (1990). A detailed description of the concentration sensors employed by TiiV is given by Heinrich & Scherwinski (1990).

+ Mast 4

Mast 3 + WALL

+ Mast 2 + Mast 1______+ Source

STREET CANYON

Figure 128. Obstacle configuration in the May 1989 campaign. The configuration includes two 60 degree arches with a 48 m diameter centred around the source.

The general experimental layout

The expected shape of the gas cloud was flat and wide, so long lines of obsta­ cles and low masts were used. The typical flow rate was 3 kg/s and a distance of approximately 50 m from the source was chosen where we expected the gas concen­ tration to be in the order of 1 per cent. We wanted the obstacle and cloud height to be approximately equal and the masts to measure vertical profiles through the cloud, so we chose a height of 2 and 6 m for the obstacle and mast respectively. In the first campaign in October 1988 we checked this design and found it reasonable. A strategic problem in experiments that depend on wind direction is how to orientate the set-up. To be on the safe side as to favourable wind conditions, TiiV persuaded us to use two alternative obstacle arrays with the curtains removed on

Ris0-R-1O3O(EN) 195 + Mast 4

Om 50m l l l l l I

Figure 129. Obstacle configuration in the August-September 1989 campaign. The configuration includes a crosswind wall 48 m from the source and a double wall forming a street canyon.

the side not used. In the second campaign May 1989 the configurations were two 60 degree arches at a distance of 48 m from the source, see figure 128. The masts were positioned 10 m in front and 15 m behind each arch. Figure 129 shows the set-up in the final August-September 1989 campaign which provided the best experiments. The two obstacle arrays were now arranged as a straight wall perpendicular to the gas flow and as a street canyon with the source at one end. The wall setup and adjacent mast were arranged with distances similar to the arches in the May campaign. The street canyon included two 50 m long fences, 2 m high and 4 m apart with the source on the centre line at the entrance. We placed the masts 35 m downwind at the centre line and 2 m outside the canyon.

The field campaigns

The first campaign was conducted in October 1988. The purpose of the trials was mainly to check that the instruments and data aquisition worked when exposed to gas under field conditions. We had little problems during this first campaign. In spite of the successful October 1988 campaign we discovered several new technical problems when we returned in May 1989. The thermocouple amflifiers now had a periodical stability problem and the battery power for cup anemome­ ters and wind vane - a neccesary solution because of the danger of explosion - ran low on far too many occasions. Also the time required to move the six sonic anemometers between the two alternative obstacle configurations was a problem, and we never succeeded in having all the instruments in the ideal position during a gas release. In case of unfavourable wind direction as to the experiments planned, we spent the spare time with additional tests. On one occasion we used the jet to shoot against the wind. It was interesting to see how the jet in this head-wind case was stopped by the obstacle, directed upwards by the stagnation pressure and bended backwards by the ambient wind. The jet contained very high concentra­ tions because the substance above the jet was recycled gas and the dimensions of

196 Ris0-R-1O3O(EN) the built-up gas mountain was 10 m in height with a diameter of 50 m. Because of the large volume of high concentrations this scenario may be a serious hazard with an explosive gas even though an often used risk parameter like the flammability distance is short! The best experiments were made in the final Aug-Sep 1989 campaign where most of the technical problems were overcome. The thermocouple amplifiers were now stable and battery power was checked by routine. The wind direction remained a problem but TiiV developed a mobile source, able to release 0.2 kg/s for about 3 minutes. We made releases from the rear end of the street canyon with this improvised source and even a third type of releases from the north across the two parallel walls. In these double crosswind wall situations the masts were closer to the obstacles than in the perpendicular wall experiments originally planned, so we measured near-obstacle fluctuations. With the small release rate the fence is high compared to the height of the plume. A group from FOA, the Swedish Defense Research Establishment, is experienced in two-phase jet measurements and has developed a model for the release rate and flow force of a flashing jet (Nyren & Winter 1987). A national Swedish contract enabled this group to join our work, and the nozzle source was equipped with a pressure transducer and thermometer. The results presented in Nyren & Winter (1990) are valuable because the flow force of the jet seems to be both an important parameter - see chapter 8 - and a check of the flow rate measurements.

Data processing

In advance of the data distribution to the project partners the data were converted into physical values and obvious instrumental errors were removed. The details of the data processing are described in Nielsen (1990), and a brief summary is given here.

For the first campaign Hewlett Packard packed flies were converted into standard PC binary flies. At a later state we rejected the HP aquisition system and used a more handy PC based system developed at Ris0.

For all signals A visual identification of possible instrumental errors was made.

For the wind vane signals We calculated wind directions from the sine and cosine signals.

For the cup anemometer signals Raw values were scaled, using individual calibration curves obtained in a wind tunnel.

For the thermocouple signals Individual scaling and addition of reference temperature.

For the sonic anemometer signals Strange spikes in the time series were removed (the nature of this error is known to us). The despiked time series were compared to the original ones and differences were reported. Raw values were scaled and the velocity vector was transformed into an ortogonal coordinate system. We made a subsequent transformation to a coordinate system aligned in the mean wind direction, giving a more meaningful data analysis. Two generations of sonic anemometers were used. The old type uses

Ris0-R-1O3O(EN) 197 an approximate formula for the wind speed assuming constant sound velocity. We therefore corrected the velocity measurements from the old sonics for changes in the speed of sound because of the presence of propane.

Concentration We made individual estimates of the thermocouple response times for each ex­ periment. Propane concentrations were calculated from sonic and thermocouple temperatures.

For the data set distributed by Ris0 Packed ascii files for the magnetic tapes were made.

For the data set distributed by TiiV We calculated physical readings from cup anemometers, wind vanes and thermo­ couples. We also interpolated our fast concentration time series in order to match the timing of the 1-Hz system. This caused some difficulties because the TiiV sample rate was not constant.

B The FLADIS ammonia experi­ ments

An accidental release of a pressure liquefied gas often results in a cloud which is heavier than air. If the released substance is sufficiently toxic, the weak con­ centrations in the regime of passive dispersion will also be hazardous. Accurate prediction of these downstream concentrations requires knowledge of the disper­ sion process in all its stages from the source through a dense-gas phase to passive atmospheric dispersion. In practice the risk engineer may have to apply a chain of numerical models, where the output of the first computation is used as input to the next one, etc. This is not an ideal approach since the uncertainty of the calcula­ tions accumulates, and it is not obvious exactly where to make the transition from one stage of the dispersion to the next one. Dense-gas dispersion models available to the public (eg HEGADAS (Witlox 1994), DEG ADIS (Spicer & Havens 1986), SLAM (Ermak 1990), and DRIFT (Webber, Jones, Tickle & Wren 1992)) use similar concepts. The typical dense-gas plume model has an interface to a source module which is selected according to the release type, and the dispersion code is usually designed with a smooth transition from dense-gas spreading to a passive Gaussian plume. Webber & Kukkonen (1990) found that gravitational spread­ ing and jet momentum were likely to co-exist in a typical two-phase jet release and warned against the idea of transition from an pure jet to a momentum-free dense-gas plume. The FLADIS field experiment project was linked to the project Research on the Dispersion of Two-phase Flashing Releases (Fladis) which was part of the STEP Programme of the Commission of the European Communities. Table 27 gives a list of participants. The objectives of the main Fladis project were

- To quantify by numerical modelling the behaviour of the source term of am­ monia with special emphasis on aerosol modelling.

- To quantify the near-field dense gas dispersion behaviour of ammonia and the far-field passive dispersion by wind-tunnel experiments and by ‘simple’ and three-dimensional (CFD) mathematical modelling.

198 Ris0-R-1O3O(EN) Table 27. Participants of the main FLADIS project STEP-CT91-0125, and the FLADIS field experiment project EV5V-CT92-0069 (CEC) and D5226-92-11821 (NUTEK). Institute Activity TNO (NL) Wind tunnel & coordination Building Research Establishment (UK) Wind tunnel Universitat Hamburg (D) Wind tunnel Ecole Centrale de Lyon (F) Wind tunnel University of Thessaloniki ‘Aristotele’ (Gr) Wind tunnel Electricite de France (F) k-e model Gaz de France (F) k-e model Research Center ‘Demokritos ’ (Gr) k-e model Societe Berlin et Cie.(F) k-e model European Joint Research Centre (I) k-e model AEA Technology (UK) Box models Finnish Meteorological Institute (SF) Box- & aerosol models Health and Safety Executive (UK) Statistical analysis Sheffield University (UK) Statistical analysis Cambridge University (UK) 2-D model Institute Activity Risp (DK) Field experiment, 2-D model, & coordination Hydro-Care (S) Field experiment FOA (S) Field experiment CEDE (UK) Field experiment CERC (UK) Source-term modelling

- To quantify the influence of obstacles and terrain effects on the dispersion in the near- and far-field including concentration fluctuations as listed in the final project report by Duijm (1994). Field data on the interaction between a dense gas plume and simple obstacles were available from a previous series of propane experiments presented in appendix A. New data were needed on the behaviour of a flash boiling ammonia jet and on the transition from dense-gas spreading to passive dispersion. The main objective of the Fladis field experiment project was to provide this information. The Fladis project had two reasons for focusing on ammonia releases. First the hazards of ammonia are of interest because of its toxicity and increasing use in industry, eg as an alternative cooling agent substituting freon or as a compound used in smoke denitrification units at fossil fuel power plants. Secondly the den­ sity of an ammonia cloud is a delicate balance which depends on the air moisture and heat input from the ground as explained by Kaiser & Walker (1978). The molar weight of ammonia is less than that of air, and an ammonia plume can only be heavy because of the temperature deficit caused by initial evaporation. Heat transfer from the surroundings, condensation of the water component of en­ trained humid air and possible deposition of liquid aerosols modify the density difference between the cloud and the ambient. The mathematical modelling of si­ multaneous two-phase thermodynamics and dispersion dynamics is greatly simpli­ fied by an assumption of homogeneous thermal and vapour pressure equilibrium between aerosols and the surrounding gas phase. Kukkonen et al. (1994) com­ pared the state of a binary water/ammonia aerosol ventilated by its fall velocity and evaporating into a moist atmosphere to the simple homogeneous equilibrium approximation. An aerosol is of course not in equilibrium during evaporation, but it was concluded that the homogeneous-equilibrium model gave sufficiently accu­

Ris0-R-1O3O(EN) 199 rate results for aerosol diameters less than 100 /um. This condition is met in flash boiling jets from high-pressure liquefied gas storages such as in the present exper­ iments, whereas emission from semi-refrigerated storages may result in aerosols large enough to invalidate the homogeneous equilibrium approximation. Webber, Tickle, Wren & Kukkonen (1992) expressed the phase equilibrium equations in a differential form which linked the rate of temperature and composition change to the rates of air entrainment and aerosol deposition. These formulae were im­ plemented as interchangeable modules for the DRIFT dense-gas dispersion model applicable for contaminants which either 1) are immiscible with water, 2) form ideal solutions, 3) form hygroscopic solutions (ammonia) or 4) involve gas-phase reactions (hydrogen flouride), see Webber, Jones, Tickle & Wren (1992). Hydro ­ gen flouride is hygroscopic like ammonia and its use is of great concern because of the associated hazards and difficulties in dispersion modelling (Lines 1995). The non-isothermal laboratory experiments of Meroney & Neff (1986) and Ruff, Zum- steg & Fannelpp (1988) showed that heat transfer from the ground reduced the excess density of cold gas releases. According to the analysis of Britter (1987) it is however not possible to extrapolate such laboratory results to large scale without violating the scaling laws either for heat transfer or for dense gas dispersion. The most well-known liquefied ammonia dispersion experiments are the Desert Tortoise series (Goldwire et al. 1985). The release rates in Desert Tortoise were 0(100) kg/s, which is much higher than those in the present experiments, and the dispersion was therefore more affected by gravity. In the Desert Tortoise experi­ ments a pool of liquid ammonia formed in front of the spill point, but because of differences in the release system this never happened in the. present experiments. Other differences are the lower ambient temperature and higher air humidity in Fladis, which are more representative for a European climate. Generally the re­ lease durations were longer than those in Desert Tortoise. Resplandy (1969) and Pfenning, Millsap & Johnson (1987) and report on two additional dense-gas ex­ periments with ammonia, but the instrumentation of these were modest compared to those of Desert Tortoise and Fladis. Further large-scale ammonia field exper­ iments, focusing on liquid rain-out after jet impingement, have recently (winter 1996/1997) been carried out by Institute National de 1'Environment Industriel et des Risques, France.

Experimental design

The main objective of the experiments was to provide test cases for dispersion cal­ culations of two-phase jets developing into plumes with passive dispersion. In order to develop a stage of passive dispersion within the boundaries of the test site, the release rates were set much lower than those in the Desert Tortoise experiments. The release durations were longer than those in other dense-gas field experiments because we wanted to obtain better statistics on concentration fluctuations. The ammonia source was designed to produce well-defined release conditions with re­ liable information on release rate, release momentum and thermodynamic state. Deposition of liquid aerosols was avoided by a sufficiently high exit pressure, since the average deposition rate would be difficult to measure and would introduce uncertainty in the downstream dispersion data. This choice may conflict with the interest in aerosol dynamics, but here priority was given to the dispersion aspect. The trials were limited to continuous jet releases in flat terrain without obstacles, and we did not attempt to measure fine details of near-source aerosol dynamics such as droplet size distribution and aerosol temperature deficit relative to the surrounding gas phase. The strong jet momentum affected most of the stage of dense gas spreading. We made use of all meterological conditions with reasonable wind directions and average wind speeds up to 6 m/s.

200 Ris0-R-1O3O(EN) Building heights: 1

Bush O

30cm Grass

30cm Grass 1m Rush Coarse gravel with some vegetation

10cm Gross

10m Water high trees

Figure 130. Map of the test site including the array of measuring positions and a coordinate system aligned along the sensor array.

The test site

The experiments took place at the test site of Hydro-Care in Landskrona which is located in Sweden at latitude 55°53’ N, longitude 12°50’ E, at sea level. This site is currently used for practical training in mitigation of ammonia releases, and it was chosen in preference to a remote area because of the well-established security

Ris0-R-1O3O(EN) 201 organization, workshop facilities, etc. Figure 130 shows a map of the site with indications of measuring positions and a coordinate system aligned according to the sensor array. Also indicated on the map are surface characteristics and the height of upwind buildings. Because of the toxicity of ammonia the sensor array was aligned according to the wind direction which would transport the plume towards the water. This nearby water is a small cove and the open sea is behind an industrial area to the west of the test site. The release rate was restricted by the safety of a marina in the preferred downwind direction. Measurements of local wind speeds show no systematic variation with downwind distance, but the turbulence level was higher near the upwind buildings. In order to assess the influence of the inhomogeneous turbulence field Edmunds & Britter (1994) used the passive dispersion model ADMS to predict a plume of neutral buoyancy without initial momentum and found a significant building effect on 10- min average passive plume concentrations, especially in case of stable conditions. The building labeled 2 in figure 130 was identified as the main disturbance. For model comparison it is recommended to use the measured wind and turbulence fields rather than parameters of a surface layer in equilibrium. A surface roughness of zo=0.04 m was evaluated by measurements from the 10-m mast in the middle of the field using average wind speeds at three heights and a situation with neutral atmospheric stability and wind coming from the unobstructed sector towards the water. This is a typical roughness length for long grass, and the distance from the shore line (x = 170 m) should be sufficient to develop the internal boundary to the height of the mast (h = 10 m) according to the criterion 0.54%/h > ln(h/zo ) — 1 (B.l) found in Panofsky & Dutton (1984, p. 150).

Sensor distribution

Sensors were mounted on the five 10-m masts, a 6-m mast and the poles and tripods indicated on the map in figure 130. The choice of the subtended angle of such a sensor array is a dilemma; The spatial resolution will be reduced when distributing a fixed number of sensors over a wide angle, however a narrow angle will reduce the range of applicable wind diretions. It was decided to distribute the sensors over a sector with an angle of 40°, ie giving priority to the spatial resolution. Apart from instruments near the source, the tripods shown at 150-m distance and the source itself, it was impossible to move the set-up from day to day. We had to await the right wind conditions. Most concentration sensors were distributed on three arcs at 20, 70, and 238 m from the ideal release point. The characteristic dispersion processes at these dis­ tances were intended to be a heavy jet, a near-neutral stage of transition and a fully developed passive plume respectively. The distances were determined in the light of design calculations with the ‘box ’-type GReAT model (Ott 1990), observa­ tions during pilot experiments in the first field campaign and calculations based on the homogeneous equilibrium limit of the binary water-ammonia aerosol model of Vesala & Kukkonen (1992). The position of the second arc of sensors representing the stage of transition to passive dispersion was chosen according to a criterion for dense gas dispersion to dominate over passive dispersion suggested by Britter & McQuaid (1988):

3/Pgas P™JV <0.15 (B.2) Pair 2<7y Here p g3S and pa-,r are the source and air densities, V is the volumetric release rate, 2ay represents the local plume width and itio is the wind velocity at 10-m height.

202 Ris0-R-1O3O(EN) This formula was derived for isothermal gas releases but as an approximation it may be applied for an isothermal simulant gas with the ‘effective’ molar weight, of « 90 g/mole, i.e 3.1 times that of air, see chapter 9. This implies that the typical mass release rate of m — 0.25 kg/s corresponds to an isothermal volumetric release rate of V 0.067 m3/s. With a plume width of 2ay #15m the Britter & McQauid transition criterion predicts dense gas dispersion effects at the second arc of sensors for wind speeds up to 3.0 m/s.

6m i

—r 4.0m

— * 1,5m — • 0.7m

Heavy Gas dispersion array

Figure 131. The heavy gas dispersion array at 20-m distance from the ideal release point consists of a 6 -m mast and several 2-m poles. Groups of concentration and temperature sensors are placed at two levels on the poles and at four levels on the centre mast. Additional instruments on the centre mast are sonic anemometers with attached thermocouples at 0.75, 1.5 and 3 m, a humidity sensor at 1.5 m, short-wave and long-wave radiation sensors at 4 m and a remote sensing surface thermometer at 6 m.

Overview

i i I I l l l 30m 0 -30m

10m i— Masts x4

2m ■ —

—30m

Neutral Dispersion array

Figure 132. The neutral dispersion array at 70-m distance from the ideal release point. The overview shows the array in a 1:1 height to width relation where the heights are exaggerated in the bottom view. Each pole in this array contains a sin­ gle catalytic gas concentration sensor at 0.5 m, and the mast has a profile of four concentration sensors at 0.1, 2, 4 and 9 m. The mast also had three cup anemome ­ ter at 2, 4 and 9 m, a wind vane at the top, a Solent ultrasonic anemometer at 4 77i and two Vaisala humidity/temperature probes at 1 and 9 m.

Ris0-R-1O3O(EN) 203 Overview

For end dispersion orray

Figure 133. The far-end dispersion array at 237.5-m distance from the ideal release point. The top view shows the array in a 1:1 height to width relation whereas the heights are exaggerated in the bottom view. The poles in this array contain a single electrochemical concentration sensor at 1.5 m. The two masts to each side have three electrochemical concentration sensors and a wind vane and cup anemometer at the top. The centre-line mast is further equipped with an extra electrochemical cell, four fast responding concentration sensors, a profile of cup anemometers and an ultrasonic anemometer for turbulence measurements.

Figures 131,132 and 133 show the three arcs of sensors. The first arc had sensors at two levels whereas the second and the third arcs had sensors at one level only. The reason for concentrating the sensors in these few horizontal chains was to obtain a good resolution for the determination of plume width and centre-line position. Vertical profiles were measured by four sensors on a single centre-line mast in the first two arcs and on three masts in the third arc. The three masts in the last arc were placed with a separation equal to the expected plume width with the intention that at least one of them would be exposed during the experiment. Most of these masts were 10 m high and they also had meteorological equipment. Additional temperature measurements were made in the area just in front of the source. A meteorological reference mast was placed 7 m upwind of the source with the purpose of providing upwind boundary conditions for numerical models. Table 28 gives an overview of the sensor distribution. The instruments were connected with micro-computers in the field, each measuring continuously and transmitting data to a master computer which logged all data. More drawings of the experimental layout, sensor specifications and details on data acquisition and processing are reported in Nielsen, Bengtsson, Jones, Nyren, Ott & Ride (1994).

Release system

The two-phase flashing ammonia jet was established by a movable source with mountable release nozzles. The release height was always 1.5 m above terrain and the jet was generally oriented in the horizontal downwind direction, except for a few releases with vertical jets. In order to minimize distortion of the ambient air flow the source was moved away from the storage tank and connected with a hose. The temperature of the storage tank was not controlled and therefore close to ambient temperature. The system was pressurized with nitrogen in order to reduce the likelihood of two-phase flow inside the release nozzle and to avoid pool formation in front of the source. The ammonia was extracted from the liquid phase at the bottom of the tank through a siphon pipe, and the pressure was maintained

204 Ris0-R-1O3O(EN) Table 28. Distribution of instruments with downwind distance.

Measurement Instrument type Number of instruments -7m 0m 10m 20m 70m 238m Pressure Transducer 4 Tank weight Load cell 1 Concentration Catalytic 22 12 Electrochemical 22 Uvic® 10° Sonic anemometer6 3 Lidarc ld Temperature Thermocouple 2 64° 29 Speed Cup anemometer 3 3 5 Direction Wind vane 1 1 2 Turbulence Sonic anemometer 1 1 1 Humidity Psychrometer 1 Hum. k temp. Solid state/PtlOO 1 1 2 Short wave rad. Pyranometer 1 Albedometer6 1 Long wave rad. Pyrgeometer 1 Surface temp. Infrared/ 1 Air pressure Barometer9 1

“occasionally re-arranged Equipped with thermocouple “beam across the plume donly trial 23 & 25 “upward and downward pyranometer /remote sensing ?solid state sensor

Pressure Valve Transducer Valve Release Nozzle

Gaseous Mounteable Valve Nozzle Liquid NH3 Pressure gf'Load Transducers

r * r r * Horizontal Base

Figure 134• 77ie release system consisted of a tank with pressurized liquid ammonia connected to a movable source with mountable nozzles. The nozzle design is shown at the top right comer.

Ris0-R-1O3O(EN) 205 by adding inert nitrogen gas at the top of the tank as sketched in figure 134. The ammonia tank and the nitrogen supply were placed on a load cell (Toledo) for an independent check of the released mass. For security reasons we used the control valve at the top of the tank and emptied the hose after each trial. The shut-down process involved an 0(30) s period of a not very well defined two-phase flow with decreasing liquid fraction in the release nozzle. The chosen release conditions are representative for accidents from small tanks used for transport or as storage for ordinary consumers. Large storages, eg at a manufacturer, are sometimes semi- or fully refrigerated, and accidental releases from these will result in jets with less flash evaporation or cryogenic pools respec­ tively. Three release nozzles with different diameters and nominal release rates of 0.1, 0.2 and 0.5 kg/s were manufactured. The top right part of figure 134 shows the mountable part of the medium-sized 4-mm nozzle, where the flow direction is from the left to the right through a 45° conical contraction with smoothed edges. Mea­ suring channels and fittings for connections to pressure transducers (Valcom) were drilled just downstream of the nozzle contraction and near the outlet. Connections between the measuring points and the pressure transducers were filled with silicon oil and care was taken to avoid air bubbles. Similar pressure measurements were made in the permanent part of the source just upstream of the contraction and in the gas phase of the release tank. The nozzle temperature T0 was measured just upstream of the contraction by a PtlOO thermometer placed in a thin probe within the pipe. Artificially generated smoke was applied in experiments with lidar measure­ ments. An aerosol generator produced a continuous release of submicron particles consisting of a conglomerate of Si02 and NH4CI which could be detected by the lidar system. Mixing liquid SiCLj and 25% aqueous NH4OH in a neutralizing sto­ ichiometric ratio (1:3.2), the reactions between the two liquids were as follows: SiCl4 + 2H20 -»• Si02 + 4HC1, NH4OH+ HC1 -* NH4CI+ H20.

The flow of chemicals were kept at constant rates, and the plume was visible even downwind of the test area. The two liquids were mixed in a fan mounted on top of the regular ammonia source and the smoke was entrained into the flashing ammo­ nia jet. Earlier experiments have shown the smoke particle size distribution to be log-normal with an average radius of of 0.23 fj.m. The solid smoke particles proba­ bly served as condensation nuclei for liquid aerosols, perhaps changing the aerosol dynamics in the two lidar experiments, but aerosol rain-out had an insignificant effect on the overall plume mass balance. The assumed proportionality between lidar signal and ammonia concentration relies on three hypotheses: proportional ammonia and smoke release rates, homogeneous mixing near the source and a spa­ tially independent smoke particle size distribution. The mass of the added smoke particles was %2% of the mass of the released amount of ammonia. The momen­ tum of the air fan is not accurately known but estimated to ss50% of the flashing jet flow force.

Concentration measurements

Thd purpose of the experiments was to measure the plume dimensions and to study the concentration fluctuations, and this leads to different demands on the sensor response times. Power spectra of concentration data from the previous propane experiments had typical maxima near 1 Hz, see chapter 9. In order to detect at least one decade of inertial subrange in the spectra, the time response of

206 Ris0-R-1O3O(EN) the concentration sensors had to be better than 10 Hz. Determination of plume dimensions did not require equally fast responding sensors. We did however plan to detect the plume position which was expected to meander with a time scale of 5 s near the first arc of sensors and 20 s near the last arc of sensors, and the slow responding sensors should be able to follow this process. Given the uncertainty in state-of-the-art dispersion models, there was no need for extremely accurate sensors although it was desirable to detect the shape of concentration profiles leading to a demand of %10% relative accuracy. A particular aspect of a two- phase release is that part of the contaminant may be transported in the liquid aerosol phase, and for this reason Goldwire et al. (1985) pumped a sample flow through a heating device before measuring the bulk concentration. This was not found necessary in FLADIS since the liquid ammonia fraction was expected to be small at the measurering points and the gas-phase concentration would therefore be representative for the two-phase mixture. At the end of this appendix the liquid ammonia fraction is estimated to be 2% at this distance giving errors of measurement which are less than the sensor accuracy. Three types of concentration sensors were applied. Their principles of opera­ tion were catalytic combustion, electrochemical cells and ionization by ultra-violet light. Additional concentration estimates were obtained from sonic anemometers equipped with thermocouples and by a back-scatter lidar. Their downwind distri­ bution is shown in table 28. The catalytic concentration sensor (Drager Polytron Ex) was the main device to detect the plume shape and position in the first two arcs of sensors. The major­ ity of sensors in the previous propane experiments (Heinrich & Scherwinski 1990) worked on the same measurering principle and the response time of the instrument was similar, ie 0(5) s. The gas entered the catalytic reaction chamber through a porous membrane in a sensor head which pointed downward and shielded the membrane from direct impaction by liquid aerosols. The instruments were cali­ brated in-situ using a reference gas of known concentration. The response time of each sensor was deduced from the individual calibration signals, and numeri­ cal response enhancement was applied as explained in the design report (Nielsen et al. 1994). This speed-up method has a tendency to enhance random noise, so both the original and the ‘improved’ signals were made accessible. The catalytic sensors were known to be sensitive to ambient conditions like temperature, hu­ midity and pressure. These systematic errors resulted in signal offsets which were corrected later on, setting the pretrial concentration to zero. After exposure to high gas concentration, a steady slightly negative signal (% 5% of the previous maximum signal), was occasionally emitted for a period of a few minutes. No correction of this error was attempted. The electrochemical cell sensor (Drager Polytron NH3) detected the plume shape and position in the domain of low concentration in the third arc. The mea­ suring principle of this device is similar to that of the oxygen deficit sensors applied in the Thorney Island experiments (Leek & Lowe 1985), but the response is slower since the ammonia sensor had no built-in electronic response enhancement or as­ piration. The response function was examined as for the catalytic sensors and was found to have a long tail which probably resulted from diffusion in the electrochem­ ical cell. This response function is not a linear autoregressive process, but it may be approximated by a sum of two exponential functions allowing us to filter the long tail leaving the processed signals with first-order response times 0(15) s, see Nielsen et al. (1994). The sensor had base-line drift and slightly negative post-trial signals very similar to those of the catalytic sensors. The fast Uvie® sensor had a better response than 20 Hz which makes it ideal for measurements of concentration fluctuations. The instrument detects any gas which is ionized by ultra-violet light including ammonia. In Landskrona the background

Ris0-R-1O3O(EN) 207 signal was found to be insignificant compared to the relevant range of ammonia detection. It was possible to apply the Uvic® sensor up to « 2000 ppm using the non-linear calibration curve described in Nyren, Ride & Jones (1994). A calibra­ tion curve for each campaign and each sensor was established by reference mea­ surements of several pre-mixed ammonia concentrations. The Uvic® sensors were mounted either on the centre-line mast at 238 m distance or on tripods arranged in various configurations 150 m from the source and further downstream. Additional concentration estimates were deduced from sonic anemometers (Kaijo Denki) with attached thermocouples at 20-m distance. The gas concentration was derived from the difference between the two temperature measurements by the technique in appendix C. This method worked quite well in the previous propane experiments, but the gas-induced response of the sonic anemometer sound virtual temperature is much smaller when exposed to ammonia and the derived concen­ tration time series had to be smoothed with a 1-s moving average filter in order to improve the unfavourable signal-to-noise ratio. Therefore the ammonia concen­ tration estimates by the sonic/thermocouple method are not adequate to detect concentration fluctuations although they are faster than measurements by the nearby catalytic concentration sensors. Two trials included concentration measurements with a mini-lidar (Risp). This instrument fires a short pulse of laser light and detects the range and intensity of the reflection from airborne particles. The lidar was operated 220 m downstream of the source. At this distance the plume was normally invisible, and thus artificial smoke was added to the ammonia plume during these particular trials. The particle size distribution of the smoke is known to be nearly independent of the dilution factor and the initial mixing of smoke and gas seemed to be efficient. With a small correction for reflectivity of the background atmosphere, the detected light reflection is proportional to the particle concentration, which in turn is assumed to be proportional to ammonia concentration. The measuring path was projected across the plume at 2-m height, and laser pulses were emitted with intervals of 3 sec giving instantaneous line profiles of relative concentration with a spatial resolution of 1.2 m along the measuring path. At the plume position the diameter of the laser beam was %0.5 m. The data were processed using optical parameters of artificial smoke, typical background atmosphere and the lidar system itself as determined in previous calibration experiments by Jprgensen, Mikkelsen, Streicher, Herrmann, Werner & Lyck (1997). The background particle concentrations outside the plume were insignificant.

Table 29. Comparisons of signals from prairs of adjacent sensors of different types showing mean and standard deviation (n±cr) of the ratio of average concentrations cl/c2 and cross correlations of filtered signals R(ci,c2), see text for discussion.

Signal types Distance Pairs Trials cT/cJ R{ci,c2) Sonic/Tc & Drager EX 20 m 2 10 1.17 ±0.23 0.71 ±0.16 Uvic®& Drager NH3 238 m 3 1 0.90 ± 0.05 0.95 ±0.15 Uvic® & lidar 220 m 5 2 (1.44 ±0.41)" 0.83 ± 0.04

“The ratios of ammonia and smoke concentration should be uniform, but not necessarily 1:1

Sensor intercomparison

Concentration sensors of different types were occasionally deployed in configura ­ tions which allow intercomparison of in-situ measurements. The two measuring

208 Ris0-R-1O3O(EN) positions of each sensor pair had similar heights (±0.05 m) and horizontal separa­ tions « 1 m, ie relatively close without compromising the measurements by flow distortion or other interference. Such sensor pairs were

- sonic anemometers with attached thermocouples and catalytic Drager EX sensors distributed on the 0.75, 1.5-m level of the centre-line mast at 20 m distance. - Uvic® sensors and electrochemical Drager NH3 sensors at the 2, 4, and 9-m level of the centre-line mast at 238-m distance. - Uvic® sensors placed 2 m above terrain along the lidar laser beam across the plume at 220-m distance.

The different sensor types were calibrated independently and their intercomparison is a check of the measuring accuracy. Table 29 presents basic statistics of ratios of average concentration cf/cg and cross correlation i?(ci, C2) of filtered signals. Time series from the fast responding Uvic® sensors are pre-conditioned for the cross correlation analysis, using appropriate autoregressive filters to match the slow response of the Drager sensors. Similarly the volume averaging of the lidar has been simulated by a moving average filter on the Uvic® signal based on the estimated advection time through the lidar averaging volume. If two ideal sensors had been positioned at a single measuring point they would measure identical average concentrations (except for the lidar which detects smoke not ammonia). In the light of the 10% relative accuracy required in section B, the bias and scatter of the comparisons in table 29 are not impressive. It should how­ ever be noted that these differences are partly caused by the different measuring volumes of the compared sensors and their spatial separation, eg a 1-m horizon­ tal separation decreases the cross correlation coefficient of unfiltered signals to « 0.86 as shown in figure 105. Close examination of thermocouple time series indicates that these signals did not return sufficiently fast to the ambient temper­ ature when the probe was outside the jet, and this explains the positive bias of the sonic/thermocouple estimates. Conlusion: 1) The good overall accuracy suggested by the mass balance in chap­ ter 13 is not accompanied by equally successful intercomparisons of sensor pairs; 2) the sonic/thermocouple estimates have a positive bias; 3) the relatively suc­ cessful intercalibrations for the far-end array provide the quality check which was missing because the masts at this distance were too short for an accurate mass balance.

Temperature measurements

The gas concentration was expected to be correlated by a temperature drop caused by the initial enthalpy deficit. A thermocouple was mounted next to each gas sen­ sor in the arc 20 m from the source in order to detect whether the local concen­ tration and temperature signals were in accordance with an assumption of perfect adiabatic mixing with ambient air. Further downstream the plume temperature deficit was expected to be insignificant compared to the background temperature fluctuations and no thermocouples was mounted in the second or third arc of sen­ sors. In the first pilot field campaign an additional fine mesh of 8x8 thermocouples were mounted on a rig placed 2-5 m in front of the source. The intention was to measure the temperature field across the two-phase jet as in a previous flame ex­ periment by Ott (1993). To our surprise the thin thermocouple wires provoked a lot of ice deposition, and we found that the signals soon approached the constant temperature of the deposit instead of the variable temperature field of the jet. In

Ris0-R-1O3O(EN) 209 Figure 135. A typical arrangement of the near-source temperature measurements. Thermocouples were arranged in a two-dimensional array on a thermocouple rig, on a 2 m minimast, on a string between two poles and on the ground. the subsequent campaigns some of these thermocouples were therefore redistrib­ uted on a 2-m minimast and on horizontal strings in the area 10-20 m from the source, see figure 135. The deposition rate was smaller at these distances, but pre­ sumably they caused too low temperature measurements just after gas exposure and during quiescent periods when the jet moved away from the individual sensor. In a sense this was not an instrumental error, but the measured temperature did not represent the surrounding gas-phase temperature while the probes were wet and the gas-phase temperature was above the dew point. Inside the jet, where the temperature was below dew point, the measurements are assumed to be correct. During the data collection of Nielsen & Ott (1995) this thermocouple problems was observed in every liquefied gas experiment including Desert Tortoise, see the plots in Goldwire et al. (1985).

Meteorological measurements

Participants of the main Fladis project asked for data on the upwind flow pro­ file which was an important boundary condition for numerical and wind-tunnel models. These were made with the reference mast shown in figure 136. More me­ teorological masts were added since the short-term average wind direction was expected to change with downstream distance, and the shelter from the upwind buildings might influence the local flow and turbulence. The wind field was mea­ sured by three cup anemometers (Risp) and a wind vane (Risp) mounted on the centre-line 10-m masts except at 20-m distance, where we were anxious about the corrosive effect of ammonia mentioned by Goldwire et al. (1985). The 10-m masts at the edges of the arc at 238-m distance had only one cup anemometer each. The atmospheric turbulence was measured by ultrasonic anemometers (Solent) at 4-m height mounted on the upstream reference mast and on the centre-line masts at 70 and 238-m distance. The measured effect of upwind buildings is discussed above. Air humidity was measured by an automatic psychrometer (Frankenberger) at

210 Risp-R-1030(EN) Reference mast

Figure 136. The upstream reference mast measures the wind profile with three cup anemometers, at 1.5 m, 4 m and 10 m. The turbulence is measured by a ultrasonic anemometer at 4 m, and the wind direction is measured with a wind vane at 10 m. At 1.5 m the downward short-wave radiation is measured by a pyranometer, and the humidity is measured by a solid-state probe and also by a psycrometer equipped with a pump.

the upstream reference mast. Additional solid state humidity sensors (Vaisala) were distributed at the centre-line masts of the first and second sensor arrays and for comparison next to the upstream psychrometer. Atmospheric short and long ­ wave radiation sensors (Kipp & Zonen) were mounted at 20-m distance and the atmospheric pressure was measured by a barometer (Vaisala) inside a cabin. In­ formation on heat flux from the ground to the cold ammonia plume was desirable but difficult to obtain. As a substitute a remote sensing infra-red thermometer (Hiemann) was mounted on the top of the 6-m mast at 20-m distance and di­ rected toward the ground 18 m downstream of the source. The surface tempera­ ture measured by this instrument is only reliable before and after each trial owing to obscuration by aerosols in the plume

Aerosol samples An attempt to measure the concentration by a catalytic sensor 4 m downstream of the source was no success. The instrument was covered by a thick layer of water/ammonia deposit and measured ammonia for hours after the actual release. Every obstacle as close as rj 10 m to the source was covered by this deposit

Ris0-R-1O3O(EN) 211 1 2 3 4 5

T-----1 i j i i i \y w

Figure 137. Construction of the aerosol collectors. The envelope is folded from a piece of aluminum foil and the weight is less than 1 gram. especially in case of high air humidity, and it was decided to collect samples in order to analyse the composition. The collectors were made from ordinary aluminium foil folded to an envelope with a weight less than 1 g and a capacity for 20 g of liquid, see figure 137. The envelopes were placed on pieces of steel wire mounted on small movable masts following the height of the jet centre line. The envelopes were collected immediately after each trial and dropped into bottles containing known amounts of pure water. The bottles were sealed and stored in a refrigerator before analysis in order to reduce the rate of ammonia evaporation from the sample. The ammonia content of each sample was determined from the concentration in the bottle and from the weight of the sample and water originally in the bottle.

Description of the experiments Release conditions

Three field campaigns with a total number of 27 trials were conducted. Data from pilot tests and trials with obviously bad wind conditions or unsuccessful data acquisition have not been processed, and this limits the set of processed data to 16 experiments. Table 30 provides an overview of release conditions for these and adequate input data for most dense-gas dispersion models. The exit pressure po is measured two nozzle diameters from the outlet whereas To is the temperature measured upstream of the nozzle contraction. The release rate m is calculated from the pressure drop through the conical nozzle contraction where the flow was into liquid phase. The time integral of this is slightly less than the corresponding weight loss of the ammonia tank with an average disagreement of 2% for the 4-mm nozzle and 5% for the 6.3-mm nozzle. The wind speed «io and wind direction Aoir relative to the one preferred are average values of measurements from four masts in the field. Their standard de­ viations cr„ and uoir are calculated as mean of the local standard deviations, ie the contribution from spatial variation of the mean values is not included. The friction velocity u, and the Monin-Obukhov length L are based on measurements by the sonic anemometer at the 4-m level of the upstream reference mast. The turbulent fluxes are found by eddy correlation of time series which are transformed into a coordinate system aligned according to the local wind vector by the method described in chapter D. Because of the upwind buildings the average flow profile

212 Ris0-R-1O3O(EN) Table 30. Overview of release conditions. All parameters are calculated over the release period of each trial, and the standard deviations of wind speed and direction are therefore not directly comparable. The wind direction is measured at 10-m height, except in trials 6 and 7 (campaign 1) where it was measured at the 4 m level. 0 h 85 — — 131 134 660 606 653 390 674 448 239 326 247 509 [m]

[°C] [mBar]

69 52 86 75 60 62 63 54 54 54 50 67 57 52 53 59 R.H. [%]

] length 2

9 8 16 16 18 17 19 16 16 17 17 16 17 19 20 21 ^air pressure

[W/m

temperature humidity — —

999

Pair 1018 1019 1020 1019 1020 1020 1012 1013 1013 1019 1008 1008 1017 L 59 138 -25 -77 -16 -22 -28 -61 -53 -51 348 271 -201 -164 -112 -174 Monin-Obukhov Atmospheric Ambient Relative Insolation

m

U 0.38 0.43 0.29 0.48 0.50 0.41 0.31 0.34 0.53 0.41 0.25 0.44 0.15 0.45 0.36 0.34

Pair R.H. /j. L Pair 9.6 9.7 9.5 8.0 9.6 9.5 13.6 11.7 12.8 10.0 11.8 19.6 14.2 18.5 18.7 12.3 CDir

[Deg] o-„

1.03 1.15 1.24 1.35 0.72 0.70 0.84 0.87 0.48 0.91 0.87 0.78 0.51 0.64 0.62 0.57

[m/s]

[Deg] 5 2 4

-6 -8 -7 -7 -6 -7 -7 24 -31 -28 -10 -27 -31 Aoir [m/s]

direction speed

ideal m

3.0 5.5 4.4 3.7 4.0 6.6 4.9 4.5 2.4 6.1 2.2 5.2 5.9 4.3 2.7 2.9 [g/mole] Uio to 10

wind wind

at

of of 3 5 5

10 10 15 10 10 15 40 22 21 20 25 40 20 ^dur [min] weight [m/s]

relative

speed IT

86 87 87 88 88 88 88 90 90 86 89 88 88 89 92 92 Me molar deviation deviation

’

wind velocity duration

direction 18 12 18 15 18 13 13 21 34 32 34 29 28 24 27 24

^*jct Effective ‘ Average Friction in Release Wind Standard Standard 0.23 0.46 0.21 0.50 0.47 0.51 0.27 0.27 0.57 0.43 0.46 0.22 0.42 0.40 0.20 0.42 9 9 7 7 15 18 17 18 17 16 12 16 14 16 20 20 To u Anir CTDir Miff Tdur Mio -> -> -> -> -> -> -> -> -> -> -> -> [°C]

[mm]

0 6.3 6.3 6.3 4.0 6.3 6.3 6.3 6.3 6.3 6.3 4.0 4.0 4.0 4.0 4.0 6.3 [N] [Bar]

[kg/s]

force 14:39 15:31 14:25 16:06 16:38 14:49 16:41 release 13:25 14:00 15:51 19:18 19:51 12:29 11:56 16:50 Time 21:09 rate

diameter temperature

of pressure

flow direction

Date Jet Exit Jet Nozzle Release Start Nozzle 7/4/93 7/8/93 7/4/93 10/8/93 13/8/93 13/8/93 11/8/93 11/8/93 13/8/93 23/8/94 30/8/94 30/8/94 30/8/94 31/8/94 31/8/94 23/8/94 7 6 9 12 13 16 17 14 15 26 27 20 21 23 24 25 L To m -Fjet 0 Time Po Trial Headings:

Ris0-R-1O3O(EN) 213 was not in equilibrium with the turbulence at the reference mast. The magnitude of the deviation may be evaluated by comparison with the log-linear flow profile for an equilibrium boundary layer:

(B.3)

Here k = 0.4 is the von Karman constant, and $m is an empirical diabatic cor­ rection function, see Paulson (1970). When inserting the measured turbulence parameters u, and L and the estimated surface roughness of zq = 0.04 m we obtain velocities which on the average are 15% and sometimes considerably more in excess of the real velocity. Additional turbulence data are available from the sonic anemometers at 70 and 238-m distance, and it is recommended to use these measurements rather than equilibrium boundary layer theory. Model users in need of a Pasquill-Turner stability class may interpret the measured Monin-Obukhov length L by a Colder (1972) diagram. The ambient temperature T0, relative hu­ midity R.H. and short-wave downward radiation Tj. are measured at the 1.5-m level of the upstream reference mast. All parameters are averaged over the individual release period of each trial. It may be argued that stable statistics of the friction velocity u* and the Monin- Obukhov length scale L require longer average periods than those in some of our trials, but it was felt that also these parameters should represent the actual release period. The spectral representation of the horizontal wind speeds contains significant variability on time scales % 10 min, see Panofsky & Dutton (1984). Short observation periods will remove part of this variability, and the different duration of individual experiments implies that the standard deviations of wind speed and direction presented are not directly comparable. Table 31 contains a brief characteristic of each trial. Experiments with long release durations and good average wind directions should be of greater interest to analyse. In principle trials with short release duration could provide interesting information on longitudinal cloud dispersion like the recent experiments at the Nevada test site, see Hanna & Steinberg (1996). Our instrumentation did however involve sensors with slow response times and the source had a finite shut-down time. In selecting experiments for analysis it should be noted that in trials 6 and 7 we used a limited instrumentation during the first field campaign and that the durations of trial 12 and 15 were relatively short. We made a variable deployment of the fast Uvic® concentration sensors, near-source thermometers and aerosol samplers, and the lidar instrument was applied only in trials 23 and 25. The vertical jet source of trial 12 makes this release different from the rest. A further description of each experiment is given in electronic text files distributed together with the data.

Source diagnostics

The exit pressure po, ie the measurement at the tip of the nozzle and the nozzle temperature To are directly applicable as input to a numerical dispersion model with a built-in source module. Estimates of the source dynamics will be of greater interest to other purposes, eg wind tunnel modelling. The first step in the source diagnostic is to check the thermodynamic state of the emission. In about half of the trials the boiling point corresponding to the exit pressure Tb0;i(po) was slightly less than the temperature measured near the nozzle contraction To- This indicates the beginning of a two-phase flow near the outlet, and the outlet liquid fraction by mass a may be estimated by the simple enthalpy balance

AHnh3(1 - a) = ciiq • [T0 - Tboii(po)] (B.4)

214 Ris0-R-1O3O(EN) Table 31. Comments on individual releases.

Trial Comments 6 Good wind condition, but limited instrumentation. 7 As for trial 6. 9 A drizzle just stopped and the ground was wet, but apparently the measurements were not disturbed by moisture. Gradually shifting wind direction. 12 Vertical release. 13 Poor wind direction. Low air humidity. 14 As for trial 13. 15 Good wind direction. Interrupted for security reasons. 16 Best trial in the second campaign. Analysed by participants of the main Fladis project. 17 Less ideal wind direction than that of trial 16. Stable atmosphere. 20 Good average wind direction, but sometimes the plume was too far to the left-hand side. Uvic® concentration sensors placed in a close formation. 21 Plume close to the right-hand edge of the sensor array. 23 Good average wind direction, but sometimes the plume was too far to the left-hand side. Artificial smoke added to the plume and detected by a lidar system. 24 Good wind direction. 25 Artificial smoke and lidar as in trial 23. 26 Unfavourable wind direction. Low wind speed. 27 Low wind speed and highly variable wind direction. Low humidity. where ci;q is the liquid heat capacity and AHnh3 is the latent heat of ammonia vapourization. The temperature drop was 0(1) °C and the maximum vapour fraction was 0(1) %. The small initial vapour fraction reduces the jet flow force which is estimated by the model of Nyren & Winter (1987)

Fiet« ^ • ((1 a)^"M + + (m-W' A (B.5)

where A is the nozzle cross section, R is the universal gas constant, /9j,- q is liquid density and pair is ambient pressure. The unknown velocity distribution of the flow is neglected. The ‘effective’ molar weight Mes is used as a simple way to characterize the approximate density effect. The background for this concept is a discussion among participants of the main Fladis project on how to model two-phase releases with isothermal model gas. Model experiments with an isothermal simulant gas with Mefr approximate the density of a two-phase release after aerosol evaporation. The ‘effective’ molar weight Meff approximation is not valid for high aerosol loads, and at worst (near the first sensor array in trial 9) it results in a 78% overprediction of the density difference relative to the ambient Ap. The deviations are less severe for other trials and often limited to the near-source area where jet momentum dominates the dispersion process.

External data analysis

The analysis carried out by participants of the main Fladis project is described in the joint final report edited by Duijm (1994).

Ris0-R-1O3O(EN) 215 The University of Sheffield used the fast Uvic® measurements to validate a new model for the statistical distribution of concentration fluctuation time series, see Lewis & Chatwin (1995). Hamburg University made a wind-tunnel simulation of trial 16, and Electricite de France and Gaz de France made a comparison with the 3D k-e MERCURE model, see Gabillard & Carrissimo (1994). Both the wind- tunnel measurements and the numerical predictions were in excess of the field measurements. The comparisons were however based on fixed-frame statistics and it seems as if the moving-frame statistics from table 22 are in better accordance with the model predictions, probably because the plume meandering was relatively weak in the wind-tunnel and not included in MERCURE. NSCR ‘Demokritos ’ compared the temperature-concentration relationship near the source to predic­ tions by the 3D k-e ADREA-HF model, see Andronopoulos et al. (1994), and concluded that the model had difficulties with the degree of condensation in bi­ nary water-ammonia aerosols. The EU Joint Research Centre compared their ID shallow-layer type model with trial 16 data, see Wtirtz (1993). More references to these and previous works are listed by Duijm (1994).

Data distribution

The data base was organized to match the needs of the main Fladis project. In practice this meant a hierarchy of information with different degrees of detail since some researchers asked for complete time series whereas other wanted data analy ­ ses like ‘average surface concentration at the plume centre line’. It was pointed out that background information, eg accurate sensor positions, should be accessible. The available information include measured time series, block statistics, writ­ ten documentation and a set of utility programs. All successful measurements are included with corrections for non-linear sensor response and known errors as re­ ported by Nielsen et al. (1994). A set of 1-min block statistics written as comma- separated files may easily be imported into commercial data-base-, plotting- or spreadsheet programs. The documentation was divided into general notes and notes on individual trials. The general information include descriptions of surface roughness, instrument response times and drawings. The volume of the specific information vary, but a description of release conditions, source position and a list of signals are repeated for each trial. The signal list provides information on sensor position, sample frequency, measured property, physical unit and a short comment like ‘a slight noise from ... ’ or simply ‘ok’. Utility programs were distributed with the data and accessed through a program shell. Groups of time series, eg signals from a row of sensors, may be plotted on a PC screen or exported to hpgl and postscript graphics. More than 700 of these plots have been predefined and each of them is accompanied by written comments. This system is intended to substitute a lengthy data report and our visual inspection of the time series is a good check of the measurement quality. The user may calculate average profiles and probability density functions in selected periods and translate binary time series to ascii files. Computer animations show the variable concentration field, sequences of lidar profiles, wind trajectories and the concept of moving frame profile analysis. The utility programs may be run from the program shell with the interface shown in figure 138. The information are prepared for FTP distribution (for free) and also available on CD-ROM and Magneto-Optical disks (with a distribution charge). The volume of the installed system is 122 MB distributed on 20740 MS-DOS files. Further details are found on the internet at

http://www.risoe.dk/vea-atu/densegas/fladis.htm

216 Ris0-R-1O3O(EN) Shell for FLADIS Utility Programs:

Data Program TRIAL006 FI: Plots of time series TRIAL007 F2: Translation of time series to ASCII files TRIAL009 F3: Probability density functions TRIAL011 F4: Precalculated Statistics TRIAL012 F5: Animations TRIAL013 F6: Two-phase mixtures (Vesala+Kukkonen, Atm. Env. 26A) TRIAL014 F7: Mean Profiles TRIAL015 F8: Surface Concentration Contours TRIAL016 Ctrl+Fl: Read general information TRIAL017 Ctrl+F2: Read information on selected trial TRIAL020 Ctrl+F3: Read information on sensors in the selected trial TRIAL021 TRIAL023 TRIAL024 TRIAL025 TRIAL026 TRIAL027

Up/Down: Select Run Esc: Quit FI... F8: Execute program Alt+Fl... Alt+F8: Documentation

Figure 138. Display of the shell for the distributed utility programs. The up and down arrows are used to select an experiment, and the utility programs are executed by pressing one of the hot keys.

Relative density difference Liquid ammonia fraction

!'V Meff approximation Radis 9 Radis 27 Desert Tortoise 4 (very dry)

Hadis 27 (dry)

Hadis 9 (humid)

0.1 1 10 100 0.1 1 10 100 Mixture Concentration, c [mole%] Mixture Concentration, c [mole%]

Figure 139. Results of Wheatley’s binary phase-transition model: 1) Relative den­ sity difference as a function of concentration and comparison with the simplistic Mc r approximation, and 2) liquid ammonia fraction as a function of total ammo ­ nia concentration.

Ris0-R-1O3O(EN) 217 The significance of the density effect by aerosol formation

Figure 139 illustrates the significance of aerosol formation in Fladis 9, Fladis 27, and Dessert Tortoise 4. The plot to the left-hand side of the figure is similar to that of figure 28 in chapter 9. It shows the relative density difference as a function of concentration with addition of the Meff approximation for Fladis 27 for com­ parison. As in chapter 9 the curves are based on Wheatley ’s hygroscopic ammonia model although the simpler immiscible-liquids model produced only slightly higher densities.

Table 32. The limit of condensation and the maximum error of the Meg approxi­ mation for each of the Fladis trials.

Trial 6 7 9 12 13 14 15 16 Condensation [% NH3] 0.62 0.85 0.25 0.48 1.05 1.05 0.86 0.80 Max. Meff error [%] 33 22 78 59 29 32 40 40 Trial 17 20 21 23 24 25 26 27 Condensation limit [% NH3] 0.77 0.65 0.93 1.00 1.04 1.00 1.09 1.18 Max. Meff error [%] 41 59 47 33 35 33 34 31

The Meff approximation is sufficiently accurate in the domain of dry mixing. The question is to what extent the deviations for higher concentrations affect the dispersion process? There are two aspects to consider, 1) the distance from the source to the limit of condensation and 2) the magnitude of the error in the domain of liquid aerosols. The strong jet in Fladis dominated the mixing in the domain of high concentrations, so the deviation of the simple approximation for concentrations higher than, say 10% NH3, was unimportant. Furthermore we observed ice not liquid deposit in the near-source area so Wheatley ’s model could be unrealistic in this area. The main concern is the deviations in the intermediate domain of almost pure water aerosols. The typical concentration was «10% NH3 where the jet first touched the ground about 10 m from the source and «2% NH3 in the first measuring array 20 m from the source. In the humid Fladis trial 9 the limit of condensation was 0.25% NH3, ie almost as low as the typical concentration in the second measuring array, and the Meff approximation predicted a Ap difference which was up to 78% larger than in Wheatley ’s model. In the dry Fladis trial 27 the limit of condensation was ssl.2% NH3 and the maximum relative error was «31% near %3.9% NH3, ie the modification of the density effect owing to condensation was less significant in this trial. Table 32 shows the limit of condensation and the maximum error of the Meff approximation compared to Wheatley ’s model for c <10% NH3. The Meff ap­ proximation should be avoided or used with care for high relative air humidities, which may be interpreted as Fladis trial 9,12 and 20. Wind-tunnel modellers may consider to apply a model gas with a lower molar weight than Meg in order to reduce the near-source error, but this will be at the expense of too high densities further downstream. The right-hand side of figure 139 shows the liquid ammonia fraction as a function of the total ammonia concentration. It is seen that »90% of the ammonia was in the gas phase where the jet touched the ground increasing to «98% in the first measuring array. It is therefore unlikely that a significant amount of the ammonia was lost by liquid deposition, and the gas-phase measurements at 20-m distance detected most of the total ammonia content.

218 Ris0-R-1O3O(EN) C Gas concentrations from sonic anemometers

For the experiments described in appendix A we developed a method which en­ abled us to estimate concentrations from the temperature signal of our sonic anemometers. The idea22 is that the sound virtual temperature signal from a sonic anemometer is influenced by the gas concentration and this is utilized for a concentration measurement. Nussey, Davies & Mercer (1985) noted of this relation but merely used it in a disscussion of the response time of regular concentration sensors. i

Instrument principle

The measuring principle of the Kaijo Denki ultra sonic anemometer - or sonic for short - is detection of the travel time of ultra sonic sound pulses between pairs of sound transducers. From these measurements the wind velocity component along the measurering path is assessed by the Doppler shift which is calculated inside the instrument. The total wind vector is then obtained from three measuring paths and a vertical measurement path provides average speed of sound, giving a sound virtual temperature equal to the true temperature in case of 20°C and dry conditions. It is well-known that a small correction on this temperature signal must be applied when water vapour enters the dry atmosphere and changes the speed of sound and this is true also for any foreign gas component. Relatively fast respond­ ing thermocouples were mounted on the anemometers for measurements of the true temperature. The path length between the sound transducers is 0.2 m and the measurements are spatially averaged over this distance. With this physical filter - plus some electronic ones - the instrument should be able to measure frequencies up to about 5 Hz depending on wind velocity.

Theory

Let us define the distance between two sensors in a single measuring path as l, the wind component along the axis as va, and the wind component normal to the axis as vn. The times-of-fiight ti,t2 of the sound pulse from one sensor to the other and vice versa are then :

ti = h = (C.l) \/c2 -v* +Va “ y/c2 -v2 - Va

It is straightforward to deduce the velocity va and the speed of sound ca from these equations.

(C.2)

22The credit for this idea is given to N.O. Jensen

Ris0-R-1O3O(EN) 219 where

Cp“x = (l-c-q)-C™ + c-Cfs+q-C**°

C„mix = {l-c-q)-Cf + c-Clas+q-C*>° (C.4)

Mmjx = (1 — C — q) ' Mair + C • Mgas + q • Mh 20

where C* = molar heat capacity of substance i at constant pressure Cl = molar heat capacity of substance i at constant volume M* = molar weight of substance i

The sonic measures the speed of sound from equation C.2 but a temperature Tronic is returned as if the mixture consisted of pure dry air. This is equal to the speed of sound written as a function of the real temperature Treai and the unknown molar concentrations of gas and water vapour like c and q

I C™ix • -RTreal Cf ■ RTsonl (C.5) Cf - Mair leading to

^sonic 1 + 9- (g pH2°/Cg ir - 1) + c• (CfVCf - 1) real 1 + 9- (c2a0/c* - l) + c• (cr/cf - 1)

1 (C.6) 1 + 9 ■ (Muso/Mair — 1) + C • (Mgas/Mair — 1) or, changing from molar heat capacities C* and Cl to heat capacities per mass c* and c'v, which are easier to find in literature.

1 + 9- (c«*0MH* 0/c»irMair - 1) + C • (c|asMgas /CpirMair ~ l) ^real 1 + 9- (c{?2°MH*°/q; irMa-ir - l) + C• (cTMS“/^rMair - 1)

1 (C.7) 1 + 9 - (Mn-jO/Mair — 1) + C • (Mgas/Mair — 1)

220 Ris0-R-1O3O(EN) Equation C.6 provides the relationship between the two temperatures and the concentrations assuming ideal gas with no aerosols or particles present. In general heat capacities depend on temperature - eg modeled with the polynomia presented in appendix I - but this is no serious complication as the true temperature is measured. A time series of humidity q is usually not available and we have to apply the mean value. For the typical concentrations the terms including humidity were less important than the terms including gas concentration, and the humidity fluctuations must be an order of magnitude smaller than the mean humidity. For a quick estimate we may use a linearized version of equation C.6 z*H 20 1 + q • I 1 + Afn2o -1 2real ■Mair cf Mgas + C • ( 1 + (C.8) Mdr 'Wir which for the propane experiments is ^sonic 1 + 0.31 • q - 1.12 • c (C.9) 2real by insertion of physical constants at 20° C. A gas mixture of 2% propane and 65% relative humidity at 20°C equal to sensitivity to propane 1.5 % molar water concentration, gives a sonic temperature depression of 5.2°C from a combined effect of a 6.6°C temperature depression caused by the presence of propane and a 1.4°C temperature increase from the water vapor. The large temperature depression meant that the signal was sufficient to derive propane concentrations with good resolution in the range of interest. The method can also be used for high concentrations of other gases and the other gases efficiency is proportional to the difference between the speed of sound of gas and air. The sensitivity analysis of the response of different substances in table 33 was presented by Ott, Nielsen & Jensen (1989). That paper also contains a calculation of the speed of sound in a mixture of air and aerosols and concludes that the aerosol effect is a negligible sensitivity for large aerosols > 1.5pm and less than -0.3°C/% for smaller aerosols.

Table 33. Sensitivity of the thermocouple/sonic anemometer method for gas con­ centrations of various substances from Ott et al. (1989).

Propane -3.2 °C/% Water vapour +0.9 °C/% Carbon dioxide —1.8 °C/% Ammonia +0.9 °C/% Freon 12 —n.o°cy% Argon -0.8 °C/% Chlorine -4.4°C/% Methane +0A°C/%

Matching instrument response times

Analysis of time series acquired with different time filters may lead to erroneous the problem results as pointed out by Kristensen & Lenschow (1988). Consider two time series xi[t] and X2[t] and two time series yi[t] and yzlt] defined as the result of two first- order autoregression processes on ii[f] and zzM- The covariance of the filtered

Ris0-R-1O3O(EN) 221 series will then have a contribution from the co-spectrum as well as the quadrature spectrum of xi[t] and 22M - unless the time constants in the two processes forming 2/i [£] and 7/2 [£] are identical. If we want to avoid contamination from the part in the signals that is out of phase in the initial series, we have to match the response time of the two signals. In our case the thermocouple response was slower than that of the sonic tem­ perature. Consider an instantaneous increase in the concentration level coincident with a true temperature drop. This is sooner detected by the sonic than by the thermocouple, and direct application of equation C.6 would over-predict the con­ centration for a period equivalent to the thermocouple response time. The opposite is true for sudden concentration drops leading to too low and even negative con­ centrations. An autoregressive filter is a simple model for the response of a thermocouple: thermocouple response dTtc(t) ^ Tair(i) - Ttc(t) (C.10) dt Ttc This is integrated to the thermocouple temperature Ttc(t) as a function of the surrounding temperature Ta;r(t)

(C.ll) 0 A way to match the sensor response times is to apply a filter on the fast sonic numerical filter temperature with a time scale similar to the response time of the thermocouple. Accordingly we make a numerical approximation to the integral above, inserting the sonic temperature instead of Tair(i)

-•slow I sonic [*1 = sonicl [i] • (l - exp (“))

(C.12)

and the equivalent, more convenient recurrence formula

rpTs iZ\i]Slow = exp(-a) • - 1] + (l - exp (-|)) • Tsonic[i] 1 sonic

+ (exp (--) - exp(-a)) • Tsonic[z - 1] (C.13)

where

/ sample frequency 71c response time for the thermocouple temperature a (/71c)-1 record # i in the raw sonic temperature time series record # i in the filtered sonic temperature time series

222 Ris0-R-1O3O(EN) Equation C.13 produces time series with a cut-off frequency corresponding to the time constant chosen. Fast ambient temperature fluctuations may also be estimated from the thermo­ speed-up method couple response model in equation C.10.

Tt'W = TtcH + +1] - Ttc[i - 1]) (C.14) where the fluctuations of the Ttc time is magnified for a < 1. The speed-up ther­ mocouple time series is then used together with the unfiltered sound virtual time series. The advantage of this procedure is that the obtained fast concentration times series may be correlated with the unfiltered velocities. The drawback is however that the prediction amplifies the noise of the thermocouple signal. If the sensitivity to noise noise is considered to be a stochastic variable with no autocorrelation and a vari­ ance of ot1c , the noise variance ot in the time series predicted by equation C.14 is

(C.15)

However for sampling frequency /=10 Hz and response time Ttc = 0.2 s this amplified factor is only 1.7. Periods just before the gas release were used to find the individual thermocouple data processing response times. Each response time Ttc was optimized to give maximum correlation between thermocouple speed-up temperature and sonic temperature (showing true temperature with no gas present) and used in the data analysis. The response time for the individual sensors was of the order of 0.15 s corresponding to a thermocouple cut-off frequency of 1 Hz. We have other filters than the thermocouple itself, eg electronic filters inside the instrument, but a second-order model with two time scales provided no significant improvement. The thermocouple temperature is changed by forced convection and the re­ sponse time depends on wind velocity. In certain humid situations the thermocou­ ple seemed to be very slow, indicating water condensation on the sensor.

Accuracy of the method The method of estimating concentrations from the sonic anemometer and attached thermocouple was evaluated by two independent tests. First a small laboratory test was performed (Ott et al. 1989). A sonic and some laboratory test thermocouples were placed in a box. Three different reference gases were pur­ chased which contained known mixtures of propane and air (propane and nitrogen for flammable propane concentrations). The box was filled with ambient air of a known humidity, and the sonic and thermocouple temperatures were measured. This measurement was necessary because of the adjustable sonic temperature off­ set. After the measurement with humid air the box was filled with a reference gas, and the propane concentration was calculated. The reference gas with the highest concentration was mixed with ‘synthetic air’ ie pure nitrogen and the analysis was made with a slightly different speed of sound. The procedure was repeated for mixtures of 1.04 ± 0.04, 2.04 ± 0.04 and 4.84 ± 0.10 %V propane for an old and a new anemometer type and the results are plotted in figure C. The standard deviation of the relative error is 5 %. The worst-case result was a 5.5 %V estimate for a 4.84 %V reference gas. This result might however be explained by a wet box interior caused by a rain shower. Figure C shows an intercomparison under field conditions of the sonic/-thermo- field conditions couple concentrations and concentration measurements from catalytic type con­ centration sensors applied by our project partners from TiiV Norddeutschland.

Ris0-R-1O3O(EN) 223 Laboratory test

Figure 140. Results from the laboratory test comparing measurements with the sonic anemometer to the known concentrations of reference gas. Some of the points are falling on top of each other.

Field comparison

EEC55 O EEC57 +

catatytic

Figure 14I. Comparison of mean concentrations from sonics and catalytic concen­ tration sensors under field conditions.

The readings were taken in the field from six sonics and six catalytic instruments placed at equal heights but 1.2 m apart. The two outliers are taken from the same group of instruments and presumably the catalytic instrument is defective since the concentration at this level should be higher than that of the 4-m level. If we exclude these two points and compare with the laboratory test in figure C, we see no alarming discrepancies. The accuracy of the catalytic instruments is probably better than with the sonic/thermocouple method, but there seems to be no scaling problems between the two concentration measurements.

224 Ris0-R-1O3O(EN) 0.010

0.008

0.006

0.004

0.002

0.000

Frequency (Hz)

Figure lJt2. Spectral analysis of turbulence fluctuations measured by 1) the cat­ alytic concentration sensor and 2) the faster responding sonic anemometer. The instruments were located at 2-m height on the front mast of trial EEC57.

Dynamic response of catalytic sensors Figure 142 is a comparison of spectra from adjacent sonic anmometer and catalytic sensors on the 2-m level of the front mast using a single realization23 of the entire release period in EEC57. The plot is smoothed with a 15% block averaging filter. The catalytic sensor response is simulated by a first-order autoregressive filter.

dc^t = C-Ccat (c.16) dt /cat For a given frequency f the energy density of the recorded signal will be damped with a factor of (1 + (/T^at)2)"* 1- Thus the energy density is damped with a factor of 50% at the frequency Tff), probably near 0.04 Hz corresponding to a response time 7^at=25 s. The area under the curves represents the total variance of the two time series. different intensity Chatwin & Goodall (1991) found lower intensity 1(c) = a(c)/p,(c) in time series form catalytic concentration sensors, but this is of course owing to the variance reduction of the slow sensor. Furthermore they detect poor point-to-point corre­ lation of the two time series. With the different response times this was to be expected (Kristensen & Lenschow 1988). In conclusion the concentration estimates from the sonics are in accordance with the measurements of the catalytic sensors. The later instruments were meant to monitor the spatial gas distribution not concentration fluctuations.

23Unlike other analyses in this report the low-frequency components were not removed.

Ris0-R-1O3O(EN) 225 D Anemometer coordinate trans­ formations

The three-dimensional velocity measurements from a sonic anemometer are ob­ tained in a coordinate system relative to the instrument. R:om a turbulence analy ­ sis point of view we are normally interesting in statistics relative to the mean flow, and this depends on the observation period. The coordinate system can be rotated to a new frame of reference, and this transformation has three degrees of freedom. The natural choice is to use an orthogonal system aligned according to the mean wind direction, but this only determines the first two degrees of freedom. Raima! (1988) discussed some suggestions for determination of the last degree of freedom, which could be fixed by one of these constraints: • horizontal y-axis • y-axis parallel to nearby surface

• shear stress in the new (x , z)-plane

• z-axis normal to mean wind direction of subsequent averaging periods

Actually none of these suggestions are perfect. Ideally the y-axis should follow a surface of the mean flow stream function, but this information is not available from a single point measurement. In the following we will just specify that the y-axis lies in a plane prescribed general transformation by its normal vector n. This leads to a basis with the unit vectors ei, 62 and eg given by

_ u _ n x u _ u x (n x u) (D.l) |u| 62 |re. x u| 63 |m||ti X u|

where we assumme that |w| ^ 0 and u [f n. If the coordinates of u and n in the old basis are written (u,v,w) and (711,712,713), a point (x,y,z ) gets the new coordinates (x,y,z ). T r u mw—nzv nifv2+tu2)—u(niv+nsw) 1 |7lx7Z| |W||7lxM| X M X IS) — nau-niu; n 2(u2+w2)—v(ni u+ns w) (D.2) y FT \nxu\ |w||7XxU| z W m U—Tl2U n3(u 2+v2)—w(niu+ti2v) L fEj |7lXll| |U||7lxU| J where

M y/u2 + v2 + w2

\n x u\ y/(n2w - n3v)2 + (713U — Tiiui)2 + (niv — 712u)2

The computations are simpler if we introduce the restriction that the instru­ simplification ments is positioned with its z-axis normal to the relevant surface, ie that n = (0,0,1) in the instrument basis.

U V w \U\ |7t| M ' X " X —« « n y = |7lxU| |7Zxlt| u • y Z — uw —vw \7hxVL\ Z L |u||nxu| \u\\nxu\ |u| J

226 Ris0-R-1O3O(EN) where we now have |nxit| = \At2 + v2. The simplified transformation is equivalent to a rotation 6 in the (x , y)-plane followed by a tilt in the (x , z)-plane where

6 = Arctan2(v,u)

= Arctan2(w, |n x it|) (D.4)

The tilt should be modest in uniform terrain with n normal to the surface. The third degree of freedom is fixed by choosing the last rotation to zero.

Application for covariance matrices

A convenient computational method for covariances is to calculate both u'ku[ and mean velocity directly in the old basis and then transform the covariance matrix into the new system. The advantage is that data only need to be read once from storage into computer memory. The transformation matrix A in equation D.2 or D.3 is then used to transform the covariances into the new basis aligned in the wind direction. u) = AA5lui } ^ UK = AikAjiuM (D.5) where we use the summation rule of tensor notation, ie the right-hand side of the equation contains nine terms. The arrangement of the anemometer measurement paths is designed to minimize flow distortion, and a transformation described by the matrix B is need for an orthogonal system. The two transformations can be done in one operation by

u'jUj = AikAjiBknBimUffl (D.6) where the product matrix A-B is calculated in advance. The A transformation is calculated from the mean wind u in the first orthogonal system = Bknun. As a curiosity an orthogonal basis could be formed from the principal axes in the covariance matrix, but this alternative would probably lead to limited physical insight.

E Thermodynamic background

The physics of dense-gas dispersion include processes like heating, phase transi­ tion and chemical reactions. This appendix will review the necessary background information mainly found in Zemansky (1968) and Zemansky & H. C. van Ness (1966).

Basic equations The main equation is the ideal gas law giving the relationship between pressure, ideal gas• law temperature and volume.

pV = nRT (E.l)

where

p = pressure V = volume n = number of moles R = universal gas constant = 8.314 K-|^ole T = absolute temperature.

Ris0-R-1O3O(EN) 227 The moderate pressure and temperatures in the atmosphere allow us to consider the gas to be ideal. The ideal gas law depends on the mole number n and not on the gas type, so for a mixture of I types of gas with n* moles each, we have / pV = RT-J2ni (E.2) i=1 The partial pressure pi of is defined, as the pressure excerted by each compound Dalton ’s Law if left alone. From the ideal gas law we recognize Dalton’s Law, which states that the sum of partial pressures is equal to the total pressure. i UiRT (E.3) Pi = V i=i

The mole fraction of a gas X{ (or molar gas concentration or concentration by concentration volume) is related to the partial pressure

Xi = Pi (E.4) P

The mass of one mole of a gas is called the molar weight Mi, and then the total mixture density mass of a mixture is Y^niMi- This enables us to calculate the mixture density as the total mass divided by the mixture volume

niMi (E.5) f Hi"; 1=1

The sum 52 ahMi is the effective molar weight of the mixture. Even pure gases are combined of slightly different isotopes, but we only need to consider the effective molar weight. For dry air it more is convenient to use an effective molar weight of Ma=29 g/mole rather than to sum up from the contributions of nitrogen, oxygen, argon et cetera in each application. The composition of air is fairly constant except for variations of the water vapour content. The change of the internal energy in a gas dU depends on the heat supply dQ internal energy and on the work of pressure forces. For ideal mixtures the internal energy U is only a function of temperature.

dU = dQ — pdV (E.6)

The total internal energy of an ideal gas mixture U is equal to a weighted sum Gibbs ’ theorem of partial energies u, that each component would have if they occupied the total volume V at the temperature T. According to Gibbs’ theorem, this is also true for all of the thermodynamic properties defined below. U = Hi UiUi Cp = Hi TliCpi Cv = TliCyi Hi (E.7) H = Hi mhi S = Hi 72j$oi G = Hi TliQOi The two latter properties S and G are pressure dependent and the subscript o is a reminder that the partial property is evaluated at the partial pressure (so; y- Si). Capital letters for thermodynamic properties like Gp refer to overall mixture properties, while small letters Cp; refer to molar partial properties. The ratio between the heat supply and resulting temperature change is called heat capacity

228 Ris0-R-1O3O(EN) heat capacity. This depends on the specific heating process, and we define two heat capacities - one for heating under constant pressure Cp and one for heating with a constant volume Cv.

Ideal gas heat capacities depend only on temperature, and it is sometimes conve­ nient to approximate them by polynomials like

cp na + b-T + c-T2 + d-T3 (E.9)

Molar parameters are assumed in this appendix as the formulae becomes shorter with molar concentrations. However literature data and physical parameters else­ where in this report are given per unit mass (eg [cp]=J/kgK ), and in order to maintain the use of molar concentrations we have to multiply by the molar weight. PYom the definitions of internal heat and heat capacities it is seen that the absorbed heat may be written

dQ = CvdT+pdV or dQ — Cp dT — V dp (E.10)

A process with no heat supply dQ = 0 is called an adiabatic process. In this adiabatic process particular case equation E.10 and the ideal gas law give

' d(p.y?) 0 dV dp dQ = 0 ■ =$■ <£> < d(r • p^ j 0 (E.11)

. d{p-p~ lh) 0 where 7 = Cp /Cv. If dQ is added to a system in a reversible manner, the entropy entropy change dS is defined by:

(E.12) and from equation E.10 and the ideal gas law it follows that

dT ,dp and dS = Cvf+nRf dS — Cp — ni2— (E.13)

We are now able to calculate the difference in the partial entropy at mixture pressure s, and at partial pressure so;.

ds = -R& Si — soi = —2? In — = i?lnxf (E.14) Pi According to Gibbs’ theorem in equation E.7, the mixture entropy then becomes / / S = n ■'^XiSi — nR-^^Xilnxi (E.15) :=1 i=l If we allow two separate gas volumes to form a mixture, the second sum in equa­ tion E.15 implies that the overall entropy will increase (Inaq < 0). Such a mixing process is considered to be irreversible and therefore not covered by equation E.12. The definition of the enthalpy is enthalpy

H = U + pV (E.16)

Taking the derivative of this and inserting the ideal gas internal energy change dU two useful expressions for the enthalpy change dH are provided. dH = Cp dT dH = dQ + V dp =»• (E.17) dH = TdS + Vdp

Ris0-R-1O3O(EN) 229 where the final steps are obtained by equation E.10 and E.13. The last state variable, that we need to introduce, is Gibbs’ free energy G. Gibbs ’ free energy

G = H-TS (E.18)

Differentiation and the second part of equation E.17 give

dG = Vdp - SdT (E.19)

Gibbs’ theorem may be written i ii G = ^2 n«" {hi ~Tsi + RT In a;*) = ^2 ni9i + RT ^2 n« X{ (E.20) i=l i=l i=l Gibbs’ free energy is applicable in the description of phase transition or chemi­ cal reactions. The equilibrium condition at a given temperature and pressure is minimum Gibbs’ free energy dGr,p = 0.

Chemical equilibrium in ideal gas

Consider a chemical equilibrium in an ideal gas. Rather than writing the equations stoichiometry for the general case, an example of two components and two reaction products is shown. The chemical symbols for the four components are A, and the stoichio­ metric coefficients are z/,.

V\ Ai + vih-i ^—\ v3K3 + 1/4A4 (E.21)

If we change the balance to the right-hand side with de moles times the stoi­ degree of reaction e chiometric coefficients, we would alter the composition of the mixture with

dn\ — -vide dn 2 = -z^de dn 3 = v3de d% = z^de (E.22)

The equilibrium at a given temperature and pressure is the composition where the Gibbs free energy is minimal, and we will investigate the conditions for dGp,p = 0. In order to discriminate the pressure effect from that of the temperature on standard state Gibbs’ free energy, it is convenient to define a standard state, which has the same temperature but a reference pressure arbitrary set to 1 atm. Integrating equation E.19 with dT = 0 we get

r9 dg= fp ----RT dp =$> g~g°„ =-firingn (E.23) JgO JpO P P where the suffix 0 refer to the standard state. Introducing this new variable in equation E.20 gives

G = (nidi + RTrii In x, + niRT In (E.24) i=l ' P and we get

-vi-(g<> + RTlnx 1+RT\n$!) (E.25)

~V2 ■ ^52 + RT In x2 + RT In ■jp'j

+v3 ■ (g° + RT In x 3 + RT In

+^4 • ^5$ + RT In X4 + RT In

Note that the signs are positive for components to the right-hand side in the stoichiometric equation and negative for the components to the left-hand side.

230 Ris0-R-1O3O(EN) The requirement of dGx,p = 0 leads to

J/3+I/4—J/l —^2 Vi9i + ^292 - Vzdi - vi9i In (E.26) ^2 RT

The right-hand side of this equation contains properties only at the standard state law of mass action and consequently it only depends on temperature. This leads to the law of mass action: V3 x 3 v\ -V2 = K(T) (E.27) x 1 For many reactions temperature dependence K(T) or pK(T) = —logK(T) is found directly in chemical handbooks. We may also evaluate it from the enthalpy change of the reaction. The temperature variation of the standard Gibbs free energy is related to the enthalpy change by reaction.

dG — Vdp — SdT =+ => 9i = h% + TM (E.28) g0=h0_Ts0 dT

where A denotes the changes of various properties caused by reaction > = ^39° + vAg\ - vx gl - v2g°

Ah = z/3/13 +1/4/14 — 1/4/11 — v2h2 < = V2Cp 2 + I/4 Cp4 — VlCpi — V2Cp 2 A a = Z/3Q3 + Z/4O4 — vx ax — v2a2 (E.29) A b = z/363 + Z/4&4 — vx bi — 1/362 Ac = Z/3C3 + Z/4C4 - Z/lCi - v2c2 Ad = v2d2 + 1/46/4 — V\ d\ — Z/2C?2 where a, b, c and d refer to polynomial fits of Cp. The standard enthalpy change enthalpy change of reaction Ah0 may be integrated from equation E.17

A h°(T) = A/i0 + J A CpdT (E.30) where the index o now refers to a standard state at a reference temperature often chosen to 25°C. The enthalpy change affects the mixture temperature after reac­ tion and thus the density, but here we shall use it for the equilibrium temperature function K{T).

In K =

A/io+ f A CpdT ; flT3 dT -^ + ^inT + (E.31) A general formulation of the law of mass action, standard enthalpy change of reaction and related equations can be written 11* W K(T) —Ag° In AT RT (E.32) Ag° Y,Vf9°f-T, vi9i Ah0 X>//io/-£>tM et cetera

Ris0-R-1O3O(EN) 231 where the suffix / refers to compounds to the right-hand side of the stoichiometric equation, and refers to the left-hand side. The theory is only applicable for ideal systems. For non-ideal systems like not non-ideal systems too diluted aqueous solutions, the Gibbs functions are no longer proportional to the concentrations Xip. More refined theories building on the idea of activity coefficients is available, but it is beyond the scope of this introduction.

Phase transition Evaporation from the liquid phase requires the enthalpy change L called latent latent heat heat, and the same amount of heat is released during condensation. The entropy difference between the two states is the supplied heat divided by temperature. L s" - s' (E.33) T where we use double suffix " for the gas phase and single suffix ' for the liquid phase. The latent heat is temperature dependent and it may be approximated by

L(T) ~ L0 + ACp(T - r0) (E.34) where Lq is the latent heat at the reference temperature T0 and Acp = c" — c'p usually is negative. At the equilibrium pressure there is no driving potential for further phase transition, and thus the Gibbs’ free energy in the two phases must be equal.

g" = g' (E.35)

This holds for any temperature T and corresponding saturation pressure pSat(T), including the nearby equilibrium psat + dpsat at temperature T + dT. This means that

dg" = dg' (E.36)

Now, since dg = —sdT + vdp sat the equilibria on the saturation pressure curve are described by

dpsat _ s" - s' (E.37) dT v" — v' Inserting the entropy difference from equation E.33 we get Clapeyron ’s equation. Clapeyron ’s equation dpsat _ T (E.38) ~W ~ T{v" - v')

For the pressures and temperatures encountered in the atmosphere the specific volume is much larger in the gas phase v" v'. Neglecting the specific volume of the liquid phase and inserting the ideal gas law for v" we get dpsat ^ Lp sat dT ~ RT2 (E.39)

With the latent heat approximation in equation E.34 the temperature variation saturation pressure curve can be integrated to

Psat f Lq — AcpTp /JL_JA ~ exp *3" Psat (To) 1 R VTo TJ

(E.40)

232 Ris0-R-1O3O(EN) where the last line is a slightly weaker approximation derived from a Taylor ex­ pansion in AT/T. As a further approximation we may insert a constant latent heat and obtain

(E-41) which is sometimes called the Antoine equation. Empirical saturation vapour pres­ sure curves for common substances like water are found in literature.

Measures of air humidity

The water vapour pressure in the atmosphere e is often quantified by indirect air humidity measures, eg relative humidity RH defined by M=dk'100% (E42) or the dew point temperature Tdew, defined as the temperature at which the water starts to condensate

fi — ^sat(Tdew) (E.43)

Sometimes the water content is measured by a psycrometer using a dry and a wet psycrometer equation bulb thermometer Tdry and Twet- The principle of this measurement is that the heat supply from the temperature difference between the incoming air and the saturate air leaving the wet thermometer provides the necessary heat for evapo­ ration.

(Tdry - Twet) = - |) • L

e _ eSat(Twet) , cpir ■ (Tdry Tvet) —------1------(E.44)

Equilibrium of liquid aerosols A cold dense gas cloud is often a two-phase mixture of gas and liquid aerosols. It is a computational advantage to calculate the degree of condensation as a function of concentration, i.e. to assume that the aerosols are in thermal and vapour-pressure equilibrium with the surronding gas phase. This is will be refered to as the ho­ mogeneous equilibrium assumption. Webber, Tickle, Wren & Kukkonen (1992) homogeneous equilibrium considered a selection range of phase-transition models for dense gas dispersion, which were later implemented as interchangable modules of the DRIFT model (Webber, Jones, Tickle & Wren 1992). The modules of the homogeneous liquid phase applied the saturation vapour pressure curves in equation E.41, whereas binary aerosol models had two vapour pressure curves binary aerosols

Xh 2o (P,T) = ^ • ATh2o • exp + 5h2o| (E.45) Xgas (Pt T) = • -Xgas • exp | jT" + 5gas| where x and X are equilibrium concentrations in the gas and liquid phase, po is a reference pressure, and A and B are a shorthand notation for L/R and L/RTq. In accordance with Raoult’s law valid for ideal mixtures each vapour pressure curve Raoult ’s law is multiplied by its liquid-phase concentration. Liquid mixtures are however not always ideal, eg a hygroscopic substance like ammonia which reacts with water:

NH3(aq) + H20 NEtf + OH" (E.46)

Ris0-R-1O3O(EN) 233 Wheatley (1986) developed a semi-empirical extension of equation E.45, where A and B become functions of the liquid-phase concentrations X.

Ah2o = A§2q + (1 + |ra + ra-X"H2o) • (1 — Ah2o)2 • wa ■Bh2o = #&2o + (1 + + r6XH2o) • (1 - XH2o)2 • m

Agas — Ag^ + (1 + ra — TaXgas) • (1 — -Xgas) 2 ' Wa Bgas = Bgas + (1 + rb ~ TbXgas) ' (1 ~ Agas) 2 ' Wb

The ra, rb,w a, and Wb parameters are empirical; table E contains values of am­ monia found by (Wheatley 1987). The heat of mixing per number of moles in the liquid phase is also related to these constants:

Hmix = —R ■ Xgas ■ (1 — Xgas) ■ (1 + rn — —raXsas) ■ too (E.48) where R is the universal gas constant. Normally the two liquid concentrations add to unity Xgas + %y 2o = 1, but if imiscible liquids the liquid components are imiscible, two sets of pure aerosols may form where both X h2o — 1 and Xga$ — 1.

Table 34■ Constants for a binary aerosol model with water and ammonia NHg, accurate for Xsas <0.4 and T > 5°C and within a factor of two for Xgas >0.4 and T > 5°C. After Wheatley (1987).

Ah2o = 5314 K ■®h2o = 25.9 Agas = 2747 K % = 23.0 Wa = -185 K ra = -14 Wb = -0.34 n = -14 Po = 1 N/m2

The assumption of homogenerous equilibrium equilibrium is not trivial, and homogeneous equilibrium? Kukkonen (1990) pointed out that the aerosols of interest to dense-gas disper­ sion evaporate during the dilution process. The vapour diffusion away from each aerosol must be driven by a concentration gradient, and thus the aerosol satu­ ration vapour pressure is higher than the partial pressure outside the boundary layer surrounding the aerosol. Also the heat of aerosol evaporation must diffuse through this boundary layer, and for these reasons the homogeneous equilibrium model might underpredict the lifetime of aerosols in a diluting mixture. In order to investigate this problem, Vesala & Kukkonen (1992) made the AERCLOUD model for the time-dependent evaporation of a binary water/ammonia aerosol in a moist atmosphere ventilated by its fall velocity. Later on Kukkonen et al. (1994) compared AERCLOUD results to Wheatley ’s (1987) solution, as implemented in DRIFT. The conclusion was that homogeneous equilibrium gave sufficiently accurate results for aerosol diameters less than 100 /mi. This condition is met in flash boiling jets from high-pressure liquefied gas storages, but emission from semi-refrigerated storages may result in aerosols large enough to invalidate the homogeneous equilibrium approximation.

Microcroscopic aerosols

The saturation pressure above describes the equilibrium between a single compo­ nent in the gas and liquid phase. For aerosols in a dense gas cloud both phases could be mixtures and the surface tension of very fine droplets becomes significant because of the large surface curvature.

234 Ris0-R-1O3O(EN) Suppose there is another inert gas present in the gas phase. This will not affect absolute pressure the partial pressure or free energy of the gas directly, but the higher total pressure p will increase the free energy of the liquid phase with the amount v'dp. We still require a minimum in the total Gibbs free energy, so the partial pressure in the gas phase must increase. The path between the state of equilibrium with the total pressure p and partial pressure p, is described by

v'dp = RT— (E.49) Pi This can be integrated from the initial equilibrium in equation E.40 in which P — Pi — Ps at dk)= exp {I (^ ■ f) } •exp {”

where the second factor is the correction factor because of the total pressure. At modest atmospheric pressures v'/v" < 1 we will generally ignore this effect. During the formation of a droplet the surface tension a results in the extra work surface tension

Wsur = 47rr2 • a (E.51)

where Wsur is called the surface energy. The mass of a spherical droplet may either be expressed by the number of moles n' and the molar weight M or by the density p' and droplet volume. From this equality we find the droplet radius

n'M 1/3 n'M = p'jirr 3 4* r = (E.52)

Inserting this in the surface energy we can estimate the change of surface energy for a condensation of dn' moles. dWsur _ dWsur r _ ^ M _ 2crM (E.53) dn1 r dn' p"~irr 2 p'r

This is an extra contribution to free Gibbs’ energy of the liquid phase, so the partial pressure in the gas phase tends to increase. We will evaluate the effect of a foreign component in the liquid phase. For dilute solution diluted mixtures the liquid phase approximates an ideal solution and the change of the Gibbs free energy of the solvent becomes

Agx = RT In X (E.54)

where X is the mole fraction of the solvent and 1 — X Cl. The combined effect of surface tension and foreign component in the liquid phase gives a change in the Gibbs free energy which must be followed by a change in the partial pressure of the gas phase. 2oM dr = RT— (E.55) p'r 2 Pi The boundary condition in the initial equilibrium without surface tension and negligible solution of a foreign liquid phase component is X = 1, r = oo and Pi = Psat- Integrating from this state we get 2cxM Pi = Psat • X • exp (E.56) p'RTr This formula shows that the equilibrium pressure would go to infinity for decreas­ ing droplet size if the liquid phase was absolutely pure. However aerosols in the atmosphere usually form on a condensation nuclei, which could be a solid particle condensation nucleus

Ris0-R-1O3O(EN) 235 of finite radius r or soluble salt particles. Wallace & Hobbs (1977, p. 162) cal­ culated an example of an atmospheric aerosol forming on a soluble condensation nucleus of ns moles with the molar weight ms. The linearized result was

2 crM nsM Pi — Psat 1 + (E.57) p'RTr p'^nr 3 where the point is, that the effect of salt concentration is oc r~3 while the effect of surface tension energy is oc r-1. This means that the concentration effect becomes the stronger one when the aerosol becomes very small. The maximum saturation pressure for realistic condensation nuclei in the atmosphere is close to the satura­ tion pressure over a plane surface (Wallace & Hobbs 1977, p. 163). In conclusion we need only to worry about supersaturated moist air if there is a lack of conden­ sation nuclei. Dense gas accident are most likely to occur in industrialized areas or maybe at sea where there is plenty of condensation nuclei.

F Fluid mechanical background

This appendix starts with the basic flow equations which are modified for tur­ bulence analysis and turbulent mean flow. The gravity currents in dense gas dispersions have some resemblance with open-channel hydraulic, so the shallow- water equations and the theory for hydraulic jumps are presented. A list of non- dimensional numbers is included at the end.

Basic flow equations

Tensor notation has the advantage of being compact yet reasonable simple to tensor notation read. The fundamental rule is that any index appearing twice in a term refers to summation over the directions whereas single indices indicate that the equation could be read for any direction. Thus

(F.l) refers to either of the equations du du du du * +“te+”sJ + ”’&=0

dv dv dv dv Tt+uTx +vTy+wTz=a

dw dw dw dw dT+,1te+"g?+”8l = 0 where u, is any of the three velocity components (u, v, w) and Xi the corresponding direction among (x,y,z ). The standard meteorological coordinate system is (north, east, upward) - a left- coordinate system handed system - while the preferred orientation in turbulence theory is mean wind direction x, lateral direction y (either horizontal or following the local terrain) and the direction perpendicular to these z (approximately upward). The conservation of matter is written flow continuity dp dpuj (F.2) dt dxi and the budget for a conservative compound of the fluid with the concentration c tracer continuity

236 Ris0-R-1O3O(EN) is quite similar dcp dcpuj = 0 (F.3) dt dxi Navier-Stoke’s equation describes the flow momentum. It is derived from Newton’s Navier-Stokes equation second law for a fluid parcel with the assumption that the viscous forces are proportional to the shear of flow. Fluids which have this linear viscosity are called Newtonian fluids. dui dui dp d (dui duj\ p lt + w,+ (F.4)

In order to find an equation for the kinetic energy we may elaborate a little on this equation. The first step is to multiply by a velocity U{. dui dui dp _(dui + dui\ (F.5) ■j \dxj dxi J The left-hand side is then reformulated to dui dui d\puiUi 8\pUiUiUj + ■ (F.6) dt dxj where we made use of the continuity equation F.2. We now have the kinetic energy kinetic energy equation dhpuiUi d\pu iUiUj dpui d f dui , duj —dT + —d^—=ims,-TzT+pm< tei + (F.7)

Bernoulli equation For stationary, incompressible, and frictionless flow equation F.4 is simplified to: du du du 1 dp "s+'%+'"te pdx dv dv dv 1 dp pdy dw dw dw 1 dp = ~9~Wz (F.8) which for each fluid element has the solution u2 + u2 + w2 + gz + - = const (F.9) P This is called the Bernoulli equation. In a stationary flow this is true for any stream line. Bernoulli equations may also be derived in compressible or accelerating flow, but we shall need it in the present simple form only.

Turbulent flow equations

The equations above describe the instantaneous flow fields, but we are actually Reynolds’ approach more interested in the mean turbulent flow field. This statistical approach may be built into the equations splitting each variable into a mean and a fluctuation part like u = u + v! (F.10) where the time average of the fluctuations u' = 0. Introducing this in the continuity equation for the tracer and average the term we get dc dcui _ ddu\ (F.ll) dt dxi dxi

Ris0-R-1O3O(EN) 237 where the density p is taken constant. It is seen that a flux divergence will change the balance of the mean quantities. A similar treatment of Navier-Stoke’s equation F.4 provides us with the relevant Reynolds ’ equation flow equation for the mean velocities in a turbulent flow. This is called Reynolds ’ equation and the additional momentum flux terms are called Reynolds stresses. dvTi _dul dp d (dWi duj\ duty P~RTdt +' ' 3 dxj -P9i-aT_+dxi ' Pv~dxj (\dxj — +‘ dxi ) “ P-r -----dxj (^ ■*• )

The laminar viscosity term is usually negligible compared to the Reynolds stress except close to a rigid surface. The energy equations are derived by the same method as above. Reynolds ’ equation is multiplied by the mean velocity vj and mean kinetic energy after time averaging we arrive at

dhpm Ui dkpUi Ui Uj _ dim __d2ul __duty ------4------^------= puiQi — + pvui (F.13)

The equation for the average total kinetic energy is simply the average of equa­ tion F.7. dhpUiUi d^pUiUiUj __ dpul d2Ui (F.14) —dT~ + a*, =

P^iPi-^S- • Pu'ty^ + put£; (§%- du'.i) + dx This may also be written a little shorter as de duje , dtyuty __ 1 dp'u\ -j-rdm — + ---- 1------^------= p'u'-Si------z—- - u',m------(F.17) dt dxj dxj 1 p dxi 1 3 dxj with introduction of the turbulent kinetic energy e and the dissipation rate e defined by du'f f du[ du'- e = -uty £ — V (F.18) dx. dxj + dxj Consider the latter term in the mean energy equation F.13. This is related to the mechanical turbulence Reynolds ’ stress which may be written as production __dutyx dutyu'x ——dui ~PUi~d^~ ~ ~P~te~+pUiU 3d^ (F.19) where the latter term is recognized with the opposite sign in the turbulent kinetic energy equation F.17. The physical interpretation is that energy in the mean flow is transformed to turbulent energy. The volume integral of the remaining part of the Reynolds ’ stress work is L dvTiu'ty -dv’ = / putyu'jdaj (F.20) iv dxj J A where A is the surface surrounding the volume V. This is an energy transfer to the surroundings. Appendix G contains more statistical turbulence theory including empirical knowledge of the atmospheric boundary layer.

238 Ris0-R-lO3O (EN) Pressure and gravity

In a fluid at rest the Navier-Stokes equation reduces to dp = P9i (F.21) dXi When the motion of a fluid is predominantly horizontal and the vertical accel­ hydrostatic approximation erations are insignificant, we may assume to a good approximation that the mo­ mentum balance across the stream lines is close to being hydrostatic. This means that the pressures are determined by the density distribution. In case of ambient flow we may still call the part of the pressure determined by equation F.21 for the hydrostatic pressure and the residual for the dynamic pressure. The gravity related forces on a body with density po + Ap submerged into a reduced gravity fluid of density po is the direct gravity force plus the ambient hydrostatic pressure forces on the surface area of the body. If the fluid is quiescent these pressure forces balance the weight of the replaced fluid, as realized by Archimedes (according to tradition). With use of Green’s theorem we transform the surface integral into a volume integral.

/ pgdv- / pda = / [(/?0 + Ap)g - grad(p)] dv (F.22) Jv Ja Jv where a is the unit vector pointing away from the surface. The hydrostatic balance in the ambient may also be read grad(p) = —pog so

/ pgdv - / pda = / A pgdv (F.23) Jv Ja Jv We see that that the net gravity related forces depends on the density difference from the ambient. It is convenient to simply replace the normal gravity acceleration 5 by a reduced gravity

9' = ^9 (F.24) and apply open-channel hydraulic theory for the description of internal currents with the addition of terms related to the mixing between the fluids. The reduced gravity means that internal waves are in slow motion compared to free surface waves of similar dimensions. When the ambient fluid is moving relative to the body, the local accelerations lift and drag will affect the pressure forces on the surface. The net flow induced pressure force acting on the body in the flow direction is called the drag force while the force in the perpendicular direction resulting from an asymmetry is called the lift force.

Shallow water equations

Shallow water equations are useful approximations to describe flows with pre­ depth integrated equations dominantly horizontal variations. They are the vertical integrals of the basic flow equations but they may also be deduced directly. For clarity we leave the tensor notation and assume that u, v, p and c are uniformly distributed over a layer with the height h. The mass in the layer is increased by entrainment through the top interface ue. dph duph dvph = uepi (F.25) dy where pi is the density at the interface. We may add various sources like pool evaporation to the right-hand side. The mass of a contaminant is normally con­ served dphc ^ duphc ^ dvphc _ ^ (F.26) dt dx dy

Riso-R-1030(EN) 239 but again we may add various sources and sinks to the right-hand side. The layer integrated momentum in the x- and y-directions is affected by:

- momentum of the entrained air which has the velocity components (%«,%;) at the interface;

- friction at the interface Tj and at the surface tq;

- horizontal gradients in the integrated hydrostatic pressure. This is determined by the slope of the top interface, i.e. the combined effect of the variable layer height h and variable surface height ho', - drag and lift forces from movements of the ambient fluid modeled by changes of the dynamic interface pressure pi. Even without wind these dynamic pres­ sures will result from the slumping process. The two momentum equations are then

“+- - - - (F.27,

-ta +^+CP*)

If we consider sinks or other sources than entrainment, we should include their momentum. In dense gas dispersion we want to model the layer averaged enthalpy H since this enables us to describe the layer temperature, phase composition and density. Choosing the ambient temperature as the reference temperature, see chapter 2, the enthalpy H is not affected by entrainment but only by heating from the surface

These are the main principles of the shallow water equations but they may be gen ­ eralized in several ways. Webber, Tickle, Wren & Kukkonen (1992) have a more rigorous description of source and sink processes including chemical reactions and phase transitions. In reality the variables are not uniformly distributed over the height but if the distributions are self-similar we may correct this with distribu­ tion coefficients. Some of the terms to the right-hand side of the equations needs parametrization, eg the entrainment velocity ue which was discussed in chapter 4. The surface exchange processes may be written

tx o = Cdu\u\

TyO = Cd v\v\

Ifo = ChVu2 + v2(To - T)pCp (F.30) where the coefficients Cd and c& will be estimated in appendix G, the layer temper­ ature T is a function of concentration and enthalpy and the surface temperature To was discussed in chapter 7.

Sub- and supercritical flow

Consider the Bernoullis equation u2 p — + gz + - = const (F.31) l p If we assume that the flow has a uniform velocity and density profile, a free surface at height h and a hydrostatic pressure distribution ^ = —pg, the Bernoulli

240 Ris0-R-1O3O(EN) constants are identical for all stream lines and the flow is characterized by an energy height E defined by

E = ^- + h (F.32)

For a fixed flow rate V = uh the energy height depends entirely on h

(F.33)

The minimum for a given flow rate q is found when

(F.34) where the left-hand side is the square of the Froude number u/y/gh. This flow condition is called critical flow and it is the largest possible flow rate for a given energy height. Flow conditions with Fr < 1 and Fr > 1 are called subcritical and supercritical respectively.

Figure 143, Definition sketces: a) hydraulic jump, b ) partial blocking, c) patial blocking with upstream hydraulic jump, d) partial blocking by crenelated fence.

Hydraulic jump

A. hydraulic jump is a discontinuity, where a fast shallow flow transforms to a deeper slow one. This is essentially a conversion from kinetic to potential energy with some dissipation into turbulent kinetic energy. Without friction forces the momentum balance becomes

^pgh% + ph 0u% = ^pghl + ph x u\. (F.35) where ha and uq are the upstream height and velocity, and hi and are the conditions downstream of the jump - see figure 143a. It is convenient to make the equation non-dimensional with the introduction of the Eiroude number Fr = u/y/gli. This leads to the dimensionless equation

(F.36)

Ris0-R-1O3O(EN) 241 where Fr\ may be eliminated using the continuity equation uoho = uihi Frlhl = Fr\h\

2 /, /7 \ —3 \ «- (9 - (§+(9 Sr2

(fe-i)'((£) +^™2Fr«)=o ' (F.37)

Formally this equation has three real solutions hi , hi -1 ± \/l + 8Srg - -1 and 5 ' (F.38) but the only non-trivial and physically meaningful one is corresponding heights

hi _ + SF tq — 1 (F.39) ho ~ 2 which could also be expressed as fe + 1 1 f ho\ f ho fri = o r hi+1 (F.40) 2 Vhi. It is seen that one of the Froude numbers must be smaller than unity and the other one larger. A lot of turbulence is produced in the jump and this results in an energy loss. gi AE=m+h° -hi (F.41) 2^h? Using the Froude number formulation and continuity we get

AS = -Froho + ho ——Frfhi — hi

= =-Fr?21'r° ‘ hf (F.42) By insertion of equation F.40 we obtain energy loss (hi — hp) AS = (F.43) 4h0hi The energy loss is seen to be highly dependent on the increase of flow depth, and the transition is always from supercritical to subcritical flow since we must require that hi > ho- A propagating hydraulic jump (sometimes called a bore) may be analysed as propagating hydraulic an ordinary jump if we choose a frame of reference travelling with the velocity of jump the discontinuity Ujump- The transformed velocities are then

U0 — Uq Ujump

Ui — Ui 4" Ujump (F.44) and the relevant Froude numbers are r-i _ u0 + Ujump Fr°-~7&r

JP 1 _ UX + Ujump 1 Vgh ' (F.45) The condition for the propagating hydraulic jump is (uo + Ujump) (F.46) gh0 2 ho Vho ) not too different from the ordinary hydraulic jump equation. For a propagating jump the energy difference in equation F.43 is incorrect and we apply equation F.41 directly with

242 Ris0-R-1O3O(EN) Blocking

When an open channel flow (or a dense bottom current) meets an obstacle, the buoyancy forces may prevent passage of all or part of the flow. In this situation the fluid piles up in front of the obstacle and the flow is reduced downstream of the obstacle. The phenomenon is known as blocking and it is observed near mountain ridges or sills at the sea floor. It has also been studied in towing tank laboratory experiments in which a stratified fluid remains stationary and the obstacle is dragged through it. A recent literature review of theory and observations is given by Baines (1987), who identified the flow regimes shown in figure 144 Simple

0

Figure 144■ Blocking criteria for a hydrostatic flow over an obstacle (Figure 1 from Baines (1987)) - see text for discussion. blocking criteria may be derived when

- the flow is in steady state

- the velocity and density profiles are uniform

- the vertical pressure distribution is hydrostatic, i.e. that the effect of stream­ lines curvature is negligible - friction forces are negligible The main idea is that the upstream energy height must be just sufficient for the flow to climb the obstacle, i.e. that the flow is critical with Fr = 1 at the crest of the obstacle. Consider a flow over an obstacle with upstream height ho, upstream velocity uo, partial blocking obstacle height H, layer thickness hi and velocity ui at the crest of the obstacle. With these definitions the surface height is H + h\ at the passage of the obstacle - see figure 143b. Introducing the Froude number definition (see below) in the continuity equation we obtain

(F.47)

The Froude numbers are also inserted in the Bernoulli’s equation.

(F.48)

Ris0-R-1O3O(EN) 243 and the height ratio hi/ho is eliminated using the continuity equation

(F.49)

In the blocking situation we have Fr\ = 1 and this leads to the criterion for partial blocking

£il + 5*- (F.50) which corresponds to line B'A'E' in figure 144. To the right-hand side of this curve the flow will be partly blocked. For larger ratios of obstacle height and initial layer height a steady solution does not exist. Instead the fluid will pile up in front of the obstacle and the height will adjust itself with and upstream propagating hydraulic jump. In a certain flow regime close to the criterion for partial blocking two solutions possible partial blocking with and without blocking exist. Actually the energy is sufficient to for the entire flow to pass the obstacle, but if an upstream hydraulic jump is established anyway, this will involve an energy loss and the energy height becomes too low. Using the notation in figure 143c with hi and Fri as the surface height and Froude number downstream of the jump the partial blocking criterion is f - l + Frr (F.51)

At the limit where partial blocking is just possible, the upstream hydraulic jump is stationary and we may insert the relationship Frl/Frl = h\/h\

H_ h (F.52) ho ho where the height ratio hi/ho is given by equation F.39.

= yi + SF-rg-l (F.53) h o 2 This criterion corresponds to line A'F' in figure 144. The region between line A'F' and line A'E' has two alternative solutions which both have been observed in laboratory (Baines 1984). The condition for complete blocking where all the dense fluid is stopped by complete blocking the obstacle is zero velocity downstream of a propagating hydraulic jump. All incoming fluid is stored in front of the obstacle and the continuity equation reads:

hoUo — {hi /lo) ‘ Ujump ^ Uq + Ujump — ^ ^ Uo (P.54)

This is inserted in the propagating jump condition equation F.46.

(F.55)

The minimal obstacle height H which causes complete blocking is equal to hi, so the condition for complete blocking is:

1& + 1 (F.56) 2 P-h0 This complete blocking condition is shown with line B'C' in figure 144. The flow through a line of obstacles elements with gaps in between is three- crenelated fence dimensional, but an approximate blocking criterion will be derived for this case

244 Ris0-R-1O3O(EN) 5

4

3 £ fc. 2

1

0 0 1 2 3 4 5 Relative obstacle height H/ho

Figure 145. Blocking criteria for partial blocking of a line of obstacles depending on the porosity (3. too. Consider a line of obstacles with an overall porosity /?. The continuity equation for this

Uoho = (1 — 0)Uihi + 0Ulh2 (F.57) where u2 and hi are the velocity and height of the flow in the gaps and u\ and hi are the velocity and height of the part of the flow which passes over the obstacle elements. The Froude numbers are called Fro for upstream flow, Fr\ for flow over the obstacle and Fri for flow in the gaps- see figure 143d. These are inserted in the continuity equation Fr0 = (1 - P)Fn ' + pFn ' (F.58)

Without blocking the energy is conserved both at the crest and in the gaps

ifrg + l

+1 \H (F.59) and the blocking condition is that the flow is critical both in the gaps and over the obstacles Fr± = 1 and Fri = 1. This fixes the height ratios hi/ho and hi/ho and the continuity equation becomes

rq /1 it\13/2 Zi o\3/:i3/2 ■ Fro = (1-/3) [3 -M- —jj +0 + 3J (F.60)

This is solved for the relative obstacle height H/ho and the partial blocking cri­ terion for a porous line of obstacles is found to be

3/2' 2/3 va<-\ — Frn + 1 — — (F.61)

Ris0-R-1O3O(EN) 245 This blocking criterion is seen to approach the solid wall criterion in equation F.50 for P -> 0. The right hand side of the inequality is only real when

(\ 2\3//2 Fr0 - (3 ^-Ftq + 3 ) > 0 =>

Frl — ZP~2!3F tqZ 4- 2 > 0 (F.62)

The discriminant of this third order equation in Fr2/3 is negative, i.e. there are three real roots. FYo/3 = 2/T1/3. cos0±P27r (F.63) where

6 = arccos(—P) => 6 e [pz‘/2,pi] (F.64) and n = 0,1,2. Using cos3 x = 3/4 cos X + 1/4 cos 3% we solve for the Froude number and get

6 9 + n2?r Fro _C£>5__----- 2 (F.65) with real solutions for n = 0,2. The conclusion is that the blocking criterion is only meaningful in the range of

]j^C0St~2 - Fr° - \J fcos ~ 2 (R66)

The explanation for this restriction is that obstacle height is unimportant outside this range, because the energy is sufficient for the entire flow to pass through the gaps. Figure 145 shows the criterion for partial blocking by a porous fence. This family of curves corresponds to B'A'E' in figure 144. The figure can be used to estimate whether a group of obstacles of similar height can partially block a dense gas flow. A criterion for complete blocking does not exist as part of the flow will always be able to pass through the gaps.

Dimensionless numbers

Sometimes the relevant processes in a flow problem are identified but the de­ tails is either unknown or very complicated. In this situation a useful engineering approach is to study the effect of dimensionless numbers which expresses the relative strength of two types of forces or processes. Table 35 is a list of such non- dimensional numbers where it should be noted that some of the numbers, eg Ri numbers, exist in many variations in literature while the fundamental ones, like Pr, are used with more consistency.

G Micrometeorological background

In the discussion of dense gas dispersion we need to determine the ambient wind conditions and to compare the turbulence observations with atmospheric turbu­ lence. This appendix contains surface layer theory, an introduction to turbulence spectra, and two examples of dispersion in a boundary layer with sources at the surface. More information on basic micrometeorology may be found in Panofsky & Dutton (1984) or Kaimal & Finnigan (1994).

246 Ris0-R-1O3O(EN) Table 35. Some common dimensionless numbers, u is relevant velocity, h is layer thickness, p is density, a is surface tension, r is surface curvature, 5 is boundary layer thickness, v is viscosity, a is molecular diffusivity of heat, K is molecular diffusivity of the contaminant and k is the time constant of a first-order chemical reaction. Non-dimension number Balance

Fr = -)= (Fronde) velocity B gravity wave

Fr& = -y= (densimetric Froude) velocity B internal wave

RigT = pf 'My (gradient Richardson) stability B velocity shear

Ri = (layer Richardson) integrated stability B velocity shear

Rif = (flux Richardson) gravity work B shear production

Rif (bulk flux Richardson) entrainment efficiency ratio

We= (Weber) surface tension B inertia

Re = ^ (Reynolds) inertia B viscosity

Pr = % (Prandtl) viscosity B thermal diffusivity

Sc= jg (Schmidt) viscosity B contaminant diffusivity

Da — oc zzh (Damkohler) Turbulent diffusion B chemical reaction

Surface layer theory

A boundary layer is the transition zone between the free flow and surface condi­ tions. In an equilibrium boundary layer the profiles of velocity and temperature profiles are determined by the vertical fluxes of momentum and buoyancy. These fluxes will vary over the boundary layer but near the surface we can assume that they are close to the actual surface fluxes. This lowest part of the boundary layer is called the surface layer and its height can be taken to 10% of the total bound­ ary layer height. The typical height z, of atmospheric boundary in equilibrium is 0(1 km), ie far beyond the heights of interest in dense gas dispersion. Surface layer theory is therefore adequate in describing the ambient wind in dense gas dis­ persion with the exception of possible spatial or temporal changes of the surface conditions. Changing surface conditions result in a new boundary layer growing within the existing layer. A simple but important result from the surface layer hypothesis is the logarith ­ neutral velocity profile mic velocity profile for neutral flow. The vertical flux of downwind momentum can be used to define a constant velocity scale called the friction velocity

u, = y/—u'w' (G.l) and the only relevant length scale for the velocity gradient is the height above surface z. Dimensional arguments then suggest that

du u. / \ U* i z u(z) = — In — (G.2) k z0

Ris0-R-1O3O(EN) 247 where the von Karman constant k has been found to be approximately 0.4 and the roughness length zo characterizes the momentum exchange near the surface. A buoyancy flux w'p' in the surface layer affects the vertical mixing and change Monin-Obukhov scaling the flow profiles. This may be expressed by an additional length scale called the Monin-Obukhov length

vjpo (G.3) Kgw'p' The general idea of Monin-Obukhov scaling is to consider the buoyancy effect as a minor perturbation from neutral flow. This is described by correction functions •4>(z/L) where the stability parameter is the height relative to the new length scale. This also applies to other properties such as temperature T, humidity q and concentration of a contaminant c.

u{z) = t- [lnt -iMi)]

T(z)-T0 = (G.4) q(z) - go = £ ‘ sf; - A (f)]

c{z)-co = IT-

The new scales T*, g* and c* are defined from the turbulent fluxes.

T*u* = -T'w' q*u* = ~q'w' and c*u* = —dw' (G.5)

The exchange processes at the surface are not similar for momentum, heat or contaminants and there are two ways to describe these differences; either we let the roughness lengths differ z0/i i1 zoq # z0c # zo or accept that the offsets To, qo and Co are slightly different from measurable surface values. The review article of Brutsaert (1982) demonstrates how the surface process may be incorporated in the roughness lengths Zoh, zoq and zqc. If the surface is smooth with a laminar sublayer the two ratios zok /zq and zqc/zo are expected to depend on ratios of the molecular diffusivities. These parameters are called the Prandtl and Schmidt numbers Pr and Sc, where Pr is the ratio of viscosity to molecular heat diffusivity (% 0.7 in air) and Sc is the ratio of viscosity to molecular diffusivity of the chemical substance in question. The Monin-Obukhov theory is semi-empirical since the correction functions V>(z/Z,) need to be found from measurements. An often used correlation for veloc­ ity and temperature is found in Paulson (1970).

f ]n _ 2 arctanm + | for f < 0 for%>0

f 2 In #46- for l < 0 (G.6) 1 —5f for f > 0

The auxiliary parameters (f>m and h are non-dimensional gradients which for unstable conditions have been found to *-(§) - (^r *(i) = Mzf

Note that the correction functions approach zero for z/L 0, ie when the buoy ­ ancy flux is insignificant. The assumptions behind Monin-Obukhov surface layer theory are that

248 Ris0-R-1O3O(EN) - the flow is turbulent,

- the variations in the horizontal direction are negligible,

- all vertical fluxes are constant, ie the measurement height is small compared to the height of the boundary layer, ie z 4C z,,

- the measurement height is not too close to the boundary, ie z > zq

- and the buoyancy only causes a modest perturbation from the neutral loga ­ rithmic boundary layer, ie z/\L\ < 5.

Empirical correlations have also been found for other variables like variance and turbulent spectra. The large eddies in a convective atmosphere have dimensions of the order of the total boundary layer height This is felt as low-frequency contributions to the horizontal velocity fluctuations, and the theory for these prop­ erties is expanded with parameters like z/z, or Zi/L. Large scale turbulence in the vertical direction is inhibited by the nearby surface.

Suppose that the surface conditions zq , zo/t, zoq, zoq, To, qo and cq have been surface exchange settled. We may then define bulk transfer coefficients coefficients

(G.7) ? [in —V'm(r)] [in )J

which relates the fluxes to the mean parameters u, T, q and c at a given height z.

u'w' = -Cd • u(z)2 w'T' = c/t • u(z) • [T(z) - To] (G.8) w'q' = cq • u(z) • [q(z) - q0] w'd = cc • u(z) • [c(z) - Co]

The exchange coefficients depend on the correction functions so the Monin- Obukhov length must be assessed. From appendix 9 we know that the density of an ideal mixture is

P • [Mg + q(Mg - Mg) + C(M - Mg)] P = (G.9) RT The density disturbances dp result from perturbations in the rest of the variables dp, dT, dq and dc as seen from the total derivative. dP ~ %dp + §%dT + dq + §^dT (G.10)

From this we see that the buoyancy flux p'w' has several contributions and the stability parameter z/L is written

z_z _ Kzgp'w' L pul

where the correlation of pressure and velocity p'w' is omitted since it is very difficult to measure. Now the friction velocity u, and the fluxes are eliminated in

Ris0-R-1O3O(EN) 249 order to obtain and an implicit equation for z/L. The correlation of pressure and velocity p'w 1 is omitted since this is very difficult to measure.

z (M - Ma) • (c - cp)gz [ln f0 ~ (l)]

L Mm\xu 2 \n-^ — ipc (^)

, (.M„-Ma)-(g-g0)gz fln 177-^"(t)]2 (G.12) Mmix« ln

(T-Ta)gz [ln^-^m(f)]2 '»*-*(*) It should be mentioned that the expansion of the buoyancy flux equation G.ll is more elaborated than usual. The most significant atmospheric process is ussually the heat flux T'w'. The correction functions ip (z/L) in equation G.4 are therefore referred to as diabatic corrections. The humidity flux is sometimes also be signif ­ icant, eg when a dry wind blows over a saturated surface and temperature is not too low. If humidity flux is unknown its ratio to the heat flux q*/T* may be eval­ uated from the ratio of the differences to the surface Aq/AT with the assumption that ip q(z/L) ~ iph(z/L). The contaminant flux dw' is included for its relevance in the boundary layer over an evaporating pool of liquefied dense gas.

Free convection

For large numerical values of z/L the surface friction forces u* become irrelevant. In case of strong instability we define a new turbulent velocity scale from the convection 1/3 -w'p' 0gzi\ w, (G.13) Po J where z, is the height of the convective boundary layer. As the surface buoyancy flux in the atmosphere usually is a heat flux, we may rewrite this to w, = (gziW'T1 /T)1^3. As mentioned above the time scale of atmospheric convective turbulence is rather long. The turn-over time Tw, of a convective eddy may be estimated form nzi/w*, eg

9.8 m/s2 • 500 m • 100 W/m2 —1/3 Tw, = 0 I 7T • 500 m 24min(G.14) 300 K • 1.3 kg/m 3 • 1000 J/kgK

The smallest eddies

Viscous dissipation is only efficient for steep velocity gradients related to small- Kolmogorov microscale scale turbulence. The length and time scales of the eddies influenced by viscosity 77 and v are estimated from the energy dissipation rate e and viscosity v

T) = z/3/4e-1/4 and v = vl/2e~1/2 (G.15) since the dimensions are [e] =m2s-3 and [v\ =m2s-1. These scales are called the Kolmogorov microscales and the length scale 77 is O(lmm) in the atmosphere. The production of turbulent kinetic energy is related to the much larger length scales of mean flow such as height above the ground or obstacle dimensions. The large eddies are not influenced directly by molecular viscosity but they interact with eddies of a slightly lesser scale, and this way they loose turbulent kinetic energy. The hypothesis is that the energy transfer continues in a cascade process to smaller and smaller eddies until the dimension is in the order of the Kolmogorov microscale 77 and then the viscous dissipation digests the energy.

250 Ris0-R-1O3O(EN) Correlation functions A way to describe turbulent structures is to consider the correlation of fluctuations separated by a time lag r. This may be found for all types of fluctuations, eg for two velocity perturbations u\ and it'-.

1 f7’/2 Rij(r) = lim — / u'i(t + T)u'j(t)dt (G.16) T-»OC> 1 Jjy 2

The correlation Rij (r) is within the range ±<7Ui aUj and equal to the covariance u'jUj for r = 0. The correlation in a stochastic stationary process will vanish for large time lags limT_>±00 Rij(r) = 0 and the autocorrelations (z = j) are seen to be symmetric while this is not the case for the cross correlation (z ^ j). A microscale Tm is defined from the behaviour of the correlation function at microscale small time lags.

Tm = (G.17) while an integral scale is defined from integral scale

roo Te = / R(t)cLt (G.18) Jo In practice the integration period T will be finite, and estimates of the integral time scale are sensitive to the exact duration since more synoptic variability is included in longer observation periods. It is sometimes argued that a spectral gap near 1 Hr-1 separates micrometeorological turbulence from synoptic scale variability, but measurements indicates that in practice it is hard to make this discrimination (Courtney & Troen 1990). Instationary time series are often a problem in the analysis of atmospheric turbulence. A spatial correlation function of a homogeneous turbulence field may be defined in a similar way 1 rL/2 RijiO = I™ T / u’iix + £)u'j{x)dx (G.19) L-yoo L JL/2 where a; are the positions of the observations and £ is a spatial separation between tow measuring points. A spatial correlation function Rij($) may also be defined using the vectors x and £ instead of distances x and £ and by averaging x in all directions.

Spectral analysis

An alternative tool for turbulence analysis is turbulent spectra in the wave number or frequency domain. The wave number power spectrum .^-(k) is the Fourier transformed spatial velocity correlation function Rij(Q

1 roo

4>tj (*) = Js///2 Riitty^dhdbdb (G.21) where £ and k now are vectors. If the length scale of the turbulence production mechanism is sufficiently larger inertial subrange than the Kolmogorov scale r], a frequency range exists where turbulent kinetic

Ris0-R-1O3O(EN) 251 energy is neither produced nor dissipated and this is called the inertial subrange. Dimensional analysis of the spectral energy distribution E(k ) assumes that the spectral energy depends only on the wave number k and the energy transfer equal to the dissipation rate e. With the dimensions [S(/c)]=m3s-2, [k] =m-1 and [e] =m2s-3 it follows that

E(k ) = ae2/3K~5'3 (G.22) where a ~ 1.6 is called the Kolmogorov constant. In an inertial subrange we can use equation G.22 to evaluate the dissipation rate s, and if the turbulence is in local balance this is close to the turbulence production. The energy spectrum E(k ) is linked to the three autocorrelations, ie to u(n) where the double index a indicates summation of the three dimensions. Therefore to find E(k ) from

(G.23)

This relation is convenient since the energy spectrum E(k ) is difficult to measure in practice. With integration over two of the dimensions in the wave number space the energy spectrum may even be related to the two independent one-dimensional spectra. Panofsky & Dutton (1984, p. 79) find the relation

(G.24) for the longitudinal power spectrum and

(G.25) which links transversal and longitudinal power spectra to each other. From these two equations we see that the longitudinal power spectrum has the same wave number dependence as that of energy

as well as the transversal one but with a factor 4/3 stronger energy density.

<£22 («0 = a2e2/3K~5/3 with a2 = ^|a = |ai (G.27)

Turbulence time series in a fixed point are easier to obtain than wave number Taylor ’s hypothesis spectra of an instantaneous spatial distribution. To overcome this difficulty it is often assumed that the turbulence is changing slowly and that it may be considered as a ‘frozen pattern’ carried by the mean velocity u. Since the integrated variance

252 Ris0-R-1O3O(EN) is the same in the spatial and temporal domains, the wave number and temporal spectra, 4>{k ) and S(/) respectively, are linked by (j)(K)dn = S{f)df (G.28) for the corresponding wave number k and frequency / = uk /2tt. The temporal power spectra in a fixed point with ‘frozen’ inertial turbulence is then

&(/) = ((3 29)

The total variance is the integral of the spectral energy density in either wave total variance number or frequency domain. a\ = f°° dK = r Si(f) df (G.30) Jo Jo As the energy containing frequency range usually is several decades wide, it is log-linear spectral plot convenient to plot frequencies on a logarithmic scale. It is easily shown that the area under the curve of such a plot still represents the integral variance if the spectral density is multiplied by the frequency fS(f). I S(f)df = I fS(f) din f (G.31)

A log-linear plot gives an idea of the variance distribution while a log-log plot is useful to check power laws. Close to the surface the vertical spectrum will peak at a higher frequency than vertical velocities near the the two horizontal spectra. A simplistic model for the vertical velocity perturba­ surface tions is a field of eddies with horizontal axes carried by the mean flow. Eddies of diameters much larger than the observation height will not contribute much to the vertical motions but diameters two times the observation height are quite efficient in producing vertical velocity perturbations. The frequency corresponding to this length scale would be 2z/u, and this is a useful estimate of the peak frequency in the vertical velocity spectrum. For increasing positive values of the stability parameter z/L the low-frequency stability effect part of the three spectra is damped and the peak shift to higher frequencies. For increasing negative stability with heat convection more low-frequency energy is added to the two horizontal spectra. The lower frequencies in an unstable surface- layer spectrum are still affected by the nearby surface. Dimensional analysis may also be used for the inertial subrange of co-spectra in co-spectra the surface layer. The co-spectrum is a spectral representation of a flux so Wyn- gaard & 0. F. Cote (1972) included the mean gradient in their scale analysis. The dimension of the vertical temperature gradient is [^]=Km-1 and the dimension of the spectral densities in the co-spectrum of temperature and vertical velocity perturbations is [Cowt{k )\ = KmV1 leading to CowT{k ) = -7^e1/3/c 7/3 (G.32) and using Taylors hypothesis

(G.33)

This and the similar momentum flux co-spectrum Couw(f) were observed in the atmospheric boundary layer. Note that the power of frequency has changed to -7/3. This indicates that the high-frequency contribution is less significant than in the power spectra, ie that mixing is related to relatively large eddies. This implies that reasonable flux estimates are obtained by the eddy correlation method from somewhat slower measurements than needed for estimates of the power spectra. The spectral energy df the low-frequency part of the co-spectrum increases with increasing instability z/L.

Ris0-R-1O3O(EN) 253 Eddy diffusivities

A simple approach to diffusion modelling is to take the flux proportional to the concentration gradient, eg w'd = —Kdc/dw, where K is called eddy diffusivity. With this model it has been possible to derive analytical solutions to a number of problems and it works very well with molecular diffusion, where the transport is the sum of a large number of small random steps. For atmospheric dispersion K- modelling usually fails, because the turbulent transport is a result of eddies with dimensions comparable to the global length scales of the dispersion problem and a limited number of random events. The plume from a stack is a good illustration of this difficulty. The application of Af-theory on an elevated continuous point source predicts a plume with Gaussian cross stream distribution but the turbulence in a convective boundary causes the plume to loop up and down, and sometimes the instantaneous maximum concentration is found at the ground. The Gaussian plume model is a better approximation of the mean distribution when the average time is much longer than the turbulent time scale, ie on the order of an hour. With these limitations in mind Af-theory will be considered only for surface releases and when the vertical diffusion is our main interest. In this situation Af-theory gives reasonable results because the vertical dimension of the turbulent eddies are limited by the nearby surface. We simplify the general diffusion equation to a two-dimensional stationary problem where the flow transports the tracer downwind, and diffusion is predominant in the vertical direction.

(G.34)

Following Sutton (1953) the wind velocity and diffusivity are approximated by power laws

u = u\ ^ and Kz = K\ (G.35)

Of course the wind is better described by a logarithmic profile but the power laws are necessary for the analytical solutions below. The approximation with minimal errors near the reference height z\ has m = 1/ln (z/zq ), so the value m = 1/7 often mentioned in literature is optimal for zi/zq = O(103) only. The vertical momentum flux pKdu/dz should be constant in a surface layer, and thus n = 1 — m = 6/7. Ideally the eddy diffusivity K should be proportional to the distance from the wall, ie n = 1, but this was a necessary compromise because of the power-law approximations. The diffusion downstream of a surface line source with strength Q at (x, z) = surface line source (0,0) has the following boundary conditions

c -> 0 for x,z-t oo -» 0 for z -> 0, x > 0 (G.36) c —> 00 for x,z 0 /0°° uc(x, z)dz = Q for all x > 0 and with the profiles in equation G.35 the solution to equation G.34 becomes

S ■ Uiz\ ' Q-P z?~mzp ] c(x, z) = exp r «i (G.37) uiZiT(s) p 2K\x p 2Kix where p = m - n + 2 and s = (m + 1 )/(m - n + 2) (Sutton 1953, p. 281). The solution can be verified by insertion into the differential equation and the boundary equations. The shape of the vertical concentration profiles is seen to be exponential for s = 1 and Gaussian for s = 2 and choice of m and n gives s = 8/9, ie closer to an exponential distribution than a Gaussian one. It is of interest to calculate the

254 Ris0-R-1O3O(EN) average height z — f zcdz/ f cdz and advection velocity u = f ucdz/ f cdz of the plume.

where we have made use of the definite integral

x° exp {-ax6} dx = ^a~^~ r j (G.39)

Assuming m = 1/7, n = 6/7 and p = 9/7 we get u oc x 1/9 and z oc x 7/9 ie nearly linear growth of the plume height and a weak change of the advection velocity. With insertion of u and z in the concentration field, we find the vertical gas flux

dc QKz(z)P*^ (P) fz\m+1 Kzdz uz2 • exp (GAO) ar (i) and with m = 1/7 the gas flux becomes w'd oc (z/z)8/,7 exp [-0.688(z/z) 9/,7 j, i.e the shape plotted to the right-hand side of figure 146.

Concentration Gas Flux

N I |M

0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 c w'd Cmax w'd max

Figure 146. Shape of the vertical concentration distrubution and gas flux in a plume with a surface-line source, according to the model of Sutton (1953). The concentration and flux profiles are normalized by their maximum values and the vertical distance is normalized by local average height z.

In the development of entrainment functions for stably stratified surface plumes passive ‘entrainment rate’ we need to consider the transition to passive dispersion. If the separation between the plume and the air above is characterized by an interface height z,-, we define the passive entrainment velocity ue from

“' = iU 'udz} = i{-0w} (G.41)

The definition of Zj is a bit artificial with the smooth concentration profile in equation G.37 but it could be taken proportional to the average gas height z, = j3z.

Ris0-R-1O3O(EN) 255 Insertion of z and differentiation with respect to x lead to: m+1 UjZi r uiz\ i_s ue (G.42) px b2Jifix.

The constant K\ is linked to the friction velocity by v% = Kdu/dz = mKiUi/zi so

Finally u\ = u«//dn(zi/zo) and m = 1/ln (z/z0) so u«/ui = m/c. This leads to:

(G.44) where the usual values of m, p and s have been inserted. This implies that z\ « IOOOzq or typically a few meters. The range of interest for x/z\ is something like 20-200 and we obtain 0.38-0.29 for the center of gravity (/? = 1) 0.84-0.65 for twice the center of gravity (/? = 2) (G.45)

The variation with downwind distance x is seen to be weak. Another problem analysed by Sutton (1953) is the evaporation from a surface evaporation where the concentration is supposed to be fixed. The background concentration upstream of x = 0 and far from the surface is zero while the surface concentration is cs for x > 0.

C -> cs for z -*• 0 and x > 0 c —y 0 for x -> 0 and z > 0 (G.46) c -> 0 for z oo and x > 0

The result is taken from Sutton (1953, p. 306) with a few changes in the notation for a better comparison with the line-source problem above.

L sin(sir) r(s) r 'uiz\-mz? m c(x,z) = Cs } (G.47) p^K-ix ’ p where e r(y,p) = / ip-1e~$di (G.48) o is the incomplete gamma function which approaches the ordinary gamma function for 6 -> oo. The integrated evaporation from the surface 0 < x < xq is equal to the advection at the vertical cross section at xq .

r OO V(x 0) = / pu(z)c(x 0,z)dz Jo = pc,pi/P^M (G.49)

Now the eddy diffusivity is not just a function of height but also of velocity. The original paper (Sutton 1934) modelled the autocorrelation function for vertical

256 Ris0-R-1O3O(EN) velocity and derived a turbulent mixing length from the approximated wind profile. This led to an eddy diffusivity which with the present notation may be written 1 —m 2 2m 1 *+"* ['.2K /1+m 1+mJ Ki 2~2m ■UiZi (G.50) l=jn [_2_1 *+"* 1+m I 1+m I where u/uiZi is the Reynolds number. When this is inserted into the evaporation formula, we get

y(%o) oc u^p x o = Ui'78X q'89 for m = 1/7 (G.51)

As a first estimate, one might expect E oc Ui^o but, because of the growing boundary this is incorrect.

H Literature guide

Table 36. Some dense-gas field experiments.

Experiment Gas Keywords B. la Bertrand “ nh3 jet Bureau of Mines6 LNG pool on water KNMI c Freon puff from evaporation Porton Down d Freon puff from collapsible tent Maplin Sands e c3h8 plume with ignition Thorney Island ^ Freon puff or plume with obstacle Burro 3 LNG pool on water Coyote h LNG pool on water, rapid phase transitions Desert Tortoise* nh3 jet Eagle J N2O2 pool on soil, chemical reaction Falcon LNG pool on soil, vapour barrier Goldfish k HF jet, chemical reaction, air humidity BMFT 1 C3H8 jet or plume Project BA m c3h8 jet or plume with obstacles FLADIS n nh3 jet, transition to neutral dispersion

“(Resplandy 1969) ‘(May, McQueen & Whipp 1983) c(van Ulden 1974) ‘'(Picknett 1981) '(Puttock, Colenbrander Sc Blackmore 1983) /(McQuaid & Roebuck 1983, McQuaid 1987) 9 (Koopman et al. 1982) ‘(Goldwire et al. 1983) ‘(Koopman et al. 1986) ■'(McRae et al. 1987) t(Blewitt, Yohn, Koopman Sc Brown 1987) '(Heinrich et al. 1988b) "•(Heinrich Sc Scherwinski 1990, Nielsen Sc Jensen 1991) "(Nielsen et al. 1994)

Table 36 summarizes previous dense-gas field experiments. The most well-known field experiments are the Desert Tortoise and Thorney Island experiments which were well instru­ mented with simple experimental configurations ideal for comparison with wind- tunnel simulations and numerical models. Recent experiments tend to focus on

Ris0-R-1O3O(EN) 257 special effects like mitigation procedures, complex thermodynamic behaviour, or the effects of obstacles. This complicates the interpretation, and it is probably the reason why recent data sets have been given less attention than earlier ones. Model developers often should be critical about data interpreted from published tables and figures since the data processing of the original researchers, eg their averaging time and interpolation methods, are often incompatible. It is on the other hand time consuming to obtain access to measured time series and read the private file formats of available data sets. A good compromise is to make use of existing data collections from previous model evaluation projects, eg one of the following:

- Hanna et al. (1991) collected time series from seven of the experiments in table 36 plus two neutral dispersion experiments. The release parameters were described in a standard format and Gaussian profiles were fitted to the plume. This condensed data set, called Modellers’ Data Archive (MDA), is available from the authors. - Nielsen & Ott (1995) were grateful to recieve raw data Hanna et al.’s (1991) and added recent European field and laboratory measurements. It was de­ cided to avoid preliminary data reduction and instead prepare 1-Hz time series in a unified format. The data collection (% 150 MB DOS files, called the REDIPHEM data base) includes a systematic description of the instru­ mentation, relevant remarks by the experimentalists and utility programs for data browsing. We encourage future experimentalists to publish dense-gas data in this format like Muller (1997). Read more at http://www.risoe.dk/vea-atu/densegas/rediphem.htTn Journals with frequent dense-gas-dispersion articles are journals

- Journal of Hazardous Materials with special issues in vol 6, 11, 16 and 30.

- Journal of Loss Prevention in the Process Industries,

Less frequent articles are found in Atmospheric Environment and Boundary Layer Meteorology. The following selection of proceedings from symposia or conferences were avail­ proceedings able to me:

- Heavy gas and risk assessment. Frankfurt am Main, September 3~4 1979, edited by S. Hartwig.

- Heavy gas and risk assessment II. Frankfurt am Main, May 25-26 1982, edited by S. Hartwig.

- Heavy gas and risk assessment III. Frankfurt am Main, November 12-13 1984, edited by S. Hartwig.

- Atmospheric dispersion of heavy gas and small particles. Delft, August 29- September 2 1983, edited by G. Ooms and H. Tennekes.

- Stably stratified flow and dense gas dispersion. Chester, April 1988, edited by J.S. Puttock.

- International Conference on vapor cloud modeling. Cambridge Massachusetts, Nov 2~4 1987, edited by J. Woodward, COPS. - International conference and workshop on modeling and mitigating the con­ sequences of accidental releases of hazardous materials. New Orleans, May 20-24 1991, COPS.

258 • Ris0-R-1O3O(EN) - International conference and workshop on Modeling and Mitigating the Con­ sequences of Accidental Releases of Hazardous Materials-New Orleans, Sep ­ tember 26-29 1995, CCPS. Krogstad & Jacobsen (1989); Britter (1989); Brighton, Jones & Wren (1991) literature reviews review dense-gas-dispersion research. The latter focus on obstacle effects. It is recommended to try ‘heavy gas dispersion’ as well as ‘dense gas dispersion’ Internet when searching the internet. I have a few links at

http://www.risoe.dk/vea-atu/densegas/address.htm

I Substance properties

Thermo dynamical data

Thermodynamic data are quite important to the prediction of dense-gas source terms. Table 37 is based on Harris’ (1987) selection of toxic or inflammable gases used by industry with the addition of harmless gases suited for dense gas experi­ ments. Heat capacities of the vapour phase are found in the handbook of Kaye & Laby (1966). These are presented at a reference temperature of 20° C and when possible also at the individual atmospheric boiling points. Some compounds cannot exist in a liquid phase at atmospheric pressure and in these cases the sublimation data are listed instead. Accurate enthalphy balances may involve temperature dependent heat capaci­ ties. The traditional way to express this variation is by empirical third-order poly- nomia, like the curve fits in tables 39 and 38 obtained by Touloukian & Makita (1970). Extrapolation should be avoided outside the temperature ranges given.

Inflammability Table 40 presents lower and upper inflammability limits of ignitable gases. The reason for the upper limit is the need for atmospheric oxygen in the combustion process.

Toxicity Wunderlich (1987) assembled the toxicological data shown in table 41. These are statistics from experiments where a know concentration of gas was inhaled by a population, a certain percentage of which was poisoned. Dangerous effects cannot deliberately be tested on human beings and human response may differ from that of experimental animals. The response is unlinear and (Griffith 1991) suggests to model the toxic load of a fluctuating concentration by weighted integral like

(1.1) where n may be quite different from 1, eg 2.75 for chlorine. This method is also sensitive to the response time of the concentration sensor. Official guidelines usu­ ally ignore fluctuations and specify a limit concentration. An inspection of the table suggests that the safety margin between this and the experimental evidence is variable.

Ris0-R-1O3O(EN) 259 Table 37. Physical parameters for density determination of potential dense gases. After Harris (1987) but with some corrections and with addition of gas phase heat capacity c'p and values for harmless model gases. All values are taken at the boiling point except the gas phase heat capacity cp ° taken at 20 ° C.

Substance M TB L ft $ g P' kJ kJ kJ kJ mol K fcq ktjK koK koK & Methane ch 4 0.016 111 510 3.77 2.00° 2.23 415 Ethylene c2h 4 0.028 169 426 2.79 1.12= 1.55 570 Ethane c2h 6 0.030 184 489 2.49 1.43“ 1.75 546 Propylene c3h 6 0.042 225 4406 2.56 1.52“ 1.52 609 Propane CgHg 0.044 231 4266 2.64 1.42" 1.67 585 Butadiene c4h 6 0.054 269 415 2.21 1.36“ 1.47 620 i-Butane iC4H10 0.058 263 3676 2.54 1.53 1.67 600 n-Butane nC4Hio 0.058 272 387 6 2.51 1.57 1.68 600 Ammonia nh 3 0.017 240 1374 4.44 2.01 2.10 682 Hydrogen Fluoride HF 0.020 292 1562 3.02 1.45 967 Hydrogen Cyanide HCN 0.027 303 935 3.68 1.33 688 Hydrogen Sulphide H2S 0.034 2116 550 1.99 0.98 1.00 993 Hydrogen Chloride HC1 0.037 189 6 443 1.65 0.80 “ 0.79 1193 Methyl Chloride CH3C1 0.051 249 427 1.49 0.76" 0.80 1003 Vinyl Chloride c2h 3ci 0.063 260 360 1.38 0.86 969 Sulphur Dioxide S02 0.064 263 390 1.36 0.62“ 0.62 1455 Chlorine Cl2 0.071 239 288 0.93 0.46 0.48 1563 Hydrogen Bromide HBr 0.081 206 210 0.50 0.36 2160 Methyl Bromide CH3Br 0.095 277 250 0.84 0.45 1732 Phosgene COCl2 0.099 281 6 253 1.05 0.61 1380 Bromine Br2 0.160 332 194 1.18 0.23 0.22 3110 77c Nitrogen n 2 0.028 187= 2.05 1.04“ 1.04 810 Argon Ar 0.039 87 160 0.53 1400 Carbon Dioxide C02 0.044 195 c 595= 1.85 0.78 “ 0.84 910 Freon 12 CC12F2 0.121 244= 216= 0.97 0.54 0.60 1410 Sulphur Hexafluoride sf6 0.146 209 161 1.85 0.67 1880 Dry Air 0.029 1.00

“Extrapolation 1 Corrected value “Sublimation

Notation a Chapter 10: Coefficient of front entrainment a Appendix C: The time step parameter (/7tc)-1 a, 6, c, d Appendix E and I: Coefficients of expansion of Cp(T) an Coefficients of temperature development in the soil A An area, eg the cross section of a pipe or the contact area be­ tween gas cloud and surface

Ai Stoichiometric equations: chemical component no i A, B Appendix E: variables in Wheatley ’s (1986) aerosol model

260 Ris0-R-1O3O(EN) Table 38. Polynomial variation of liquid-phase heat capacity dp [,J/kgK\ according to Touloukian & Makita (1970). The polynomia are valid only within the specified temperature [K\ ranges!

Substance cp = a + b-T + c-T2 + d-T3 Range a b- 103 c-10& d-108 Tmin Tmax Methane ch4 94.8 -1071.8 773.7 -1463.5 95 150 Ethylene C2H4 20.1 58.7 -70.2 217.0 105 170 Ethane c2h6 15.7 52.5 -40.1 120.1 91 230 Propylene ° c3h6 10.1 10.0 0.0 0.0 169 223 Propane c3h8 9.84 8.90 -4.96 23.38 89 230 Butadiene ° c4h6 4.79 62.93 -37.69 78.59 165 230 i-Butane 1C4H10 2.51 63.80 -27.85 50.07 0 0 n-Butane nC^Hio 6.10 27.19 -13.67 29.95 140 366 Ammonia nh3 -53.2 1333.4 -524.6 711.4 197 377 Hydrogen Sulphide h2s 812 -12013 6021 -10046 190 211 Hydrogen Chloride HCl -36.5 879.1 -546.4 1134.6 163 173 Methyl Chloride CH3CI 7.83 -4.21 -2.54 12.39 223 323 Sulphur Dioxide S02 5.00 0.33 0.00 0.00 223 323 Chlorine CI2 1.87 19.27 -9.05 13.31 179 237 Bromine Br2 1.53 -4.67 0.46 6.11 266 300 Nitrogen n2 -18.9 1379.7 -1776.4 7779.1 67 117 Carbon Dioxide C02 -1060 13288 -5506 7613 223 283 Freon 12 CCI2F2 0.08 19.18 -8.04 12.36 194 294

“Curve fit of values found in Vargaftik (1975).

Aij, Bij Appendix D: coefficients of coordinate transformations b Width of a gas plume b' Chapter 5: width of plume downstream of obstacle B Chapter 5: width of obstacle c Concentration of contaminant gas - volume by volume c Appendix C: the speed of sound c Chapter 11: concentration scale - defined in equation 219

Cl,C2,C3,C4 Chapter 4: parameters in entrainment model

Cc Surface exchange concentration coefficient Co Drag coefficient

•-freon Chapter 14: initial freon concentration

Ch Surface heat exchange coefficient cint Chapter 11: interpolated concentration Cp Heat capacity at constant pressure per mass unit

Heat capacity at constant pressure per mole

Heat capacity at 20° C

Cpi Partial heat capacity at constant pressure for component no i

Ris0-R-1O3O(EN) 261 Table 39. Polynomial variation of gas-phase heat capacity c" [J/kgK] according to Touloukian & Makita (1970). The polynomia are valid only within the specified temperature [K] ranges!

Substance C" = a + b-T + c-T2 + d-T3 Range a b • 103 c ■ 105 d • 108 Tmin Tjnaz Methane ch4 30.97 -32.85 16.97 -11.03 178 511 Ethylene C2H4 4.00 29.56 1.23 . -2.03 178 610 Ethane C2H6 10.88 -16.32 11.79 -9.12 189 603 Propylene “ c3h 6 2.35 21.75 -0.23 0.00 298 373 Propane CgHg 3.36 10.50 4.10 -3.94 240 693 Butadiene ° c4h6 2.27 4.02 5.09 -5.59 273 413 i-Butane iC4Hio 0.59 23.09 -0.45 -0.35 233 710 n-Butane nC4Hio 0.97 21.05 -0.17 -0.47 270 790 Ammonia nh3 27.40 -11.58 7.65 -5.10 223 630 Hydrogen Sulphide h2s 7.03 -2.80 1.19 -0.73 200 620 Hydrogen Chloride HC1 5.30 -0.41 0.05 0.03 250 770 Methyl Chloride CH3C1 1.57 7.76 -0.02 -0.19 270 782 Sulphur Dioxide S02 1.50 3.27 -0.18 0.01 298 770 Chlorine Cl2 1.13 2.60 -0.39 0.21 200 640 Bromine Br2 0.26 0.46 -0.09 0.06 200 590 Nitrogen n2 9.33 -3.22 0.64 -0.25 250 780 Carbon Dioxide C02 3.11 4.89 0.16 -0.36 220 540 Freon 12 CC12F2 0.23 4.70 -0.58 0.27 100 600

“Curve fit of values found in Vargaftik (1975).

Table 40■ Limits of inflammability in volume percentage of gas mixture with at­ mospheric air according to Weast (1987).

Substance Inflammability limits Lower Upper Methane ch4 5.0 15.0 Ethylene c2h4 2.75 28.6 Ethane c2h6 3.0 12.5 Propylene c3h6 2.0 11.1 Propane C3Hg 2.12 9.35 i-Butane iC4H10 1.80 8.44 n-Butane nC4Hio 1.86 8.41 Ammonia nh3 15.5 27.0 Hydrogen Sulphide h2s 4.3 45.0

Acp Difference in heat capacity, either between two gas components or between the liquid and gas phase of a component cq Humidity exchange coefficient at the surface Csoii Heat capacity of soil

c„ Heat capacity at constant volume per mass unit Cv Heat capacity at constant volume per mole

cvi Partial heat capacity at constant volume for component no. i

262 Ris0-R-1O3O(EN) Table 41- Acute Toxic data for inhalation of gases according to Wunderlich (1987), eg toxic concentration (TC), lethal concentration (LC) and lethal dose (LD). The index shows the percentage of the population that respond in these ways. TCL0% indicates the smallest toxic dose observed, ie a lower limit for the effect. The concentration under the substance name is the human exposure limit recommended by the US federal register, Vol. 36, No.105 - after Weast (1987).

Substance Measure Exposure Ammonia LCioVo human 30000 ppm in 5 min NHg TCiq% human 20 ppm 50 ppm LDc ,q% rat 2000 ppm in 4 hours ld50% mouse 4837 ppm in 1 hour TCL5o% cat 1000 ppm in 10 min Hydrogen Fluoride TCio% human 50 ppm in 30 min HF TCi0% human 110 ppm in 1 min 3 ppm LC$q% monkey 1774 ppb in 1 hour Hydrogen Cyanide LCiq% human 120 mg/m 3 in 1 hour HCN 10 ppm LCiq% human 200 mg/m 3 in 10 min Hydrogen Sulfide LCLq% human 600 ppm in 30 min H2S lc 50% rat 444 ppm LCsoYo mouse 673 ppm in 1 hour Hydrogen Chloride LCW% human 1000 ppm in 1 min HC1 5 ppm L^50% rat 4701 ppb in 30 min Sulphur Dioxide LC\o% human 400 ppm in 1 min S02 LCio% human 3 ppb in 5 days 5 ppm LCio% mammal 3000 ppb in 5 min Chlorine LCLm human 373 ppm in 30 min Cl2 rat 293 ppm in 1 hour 1 ppm LCso% mouse 137 ppm in 1 hour Phosgene human 3200 mg/m 3 COCla TCL0% human 25 ppm in 30 min 0.1 ppm LCLo% rat 50 ppm in 30 min Bromine mouse . 750 ppm in 9 min Br2 LCio% cat 140 ppm in 7 hours 0.1 ppm LCio% rabbit 180 ppm in 6.5 hours LCio% guinea pig 140 ppm in 7 hours Methyl i-cyanide TCL0 human 2 ppm C2H3NO LC5q% rat 5 ppm in 4 hours 0.02 ppm LCL0% mouse 37 mg/m 3 in 1 hour Ethylene Oxide TCL0% human 12500 ppm in 10 sec c2h4o cat 1462 ppm in 4 hours 50 ppm LCso% dog 960 ppm in 4 hours ■ Phosphine LCiq% human 1000 ppm PH3O.3 ppm LCio% mammal 1000 ppm in 5 min Propylene Oxide LCiq% rat 4000 ppm in 4 hours C3H60100 ppm Arsine TC\q% human 3 ppm AsH3 0.05 ppm LC10V0 human 25 ppm in 30 min

Ris0-R-1O3O(EN) 263 Cyis Chapter 8: limit of visible concentration c, Scale of concentration fluctuations defined by c*u* = —dw' Co(/) Coherence spectrum di Chapter 8: hydraulic radius of pipe section i e Turbulent kinetic energy defined by | yu'u' + v'v'+w'w', ie without density p e partial pressure of water vapour

61,62,63 Appendix D: unit vectors in an aligned coordinate system

E Energy head in fluid mechanical calculations

E{k ) Spectral distribution of turbulent kinetic energy

Skin Kinetic energy

Spot Potential energy

Sprod Production of turbulent kinetic energy A E Loss in energy head by dissipation

ASdrag Chapter 11: energy dissipation by drag effect

ASfall Chapter 11: energy dissipation by ‘waterfall’ effect erfc(z) Complementary error function JJ° e~^d^ / Frequency Chapter 2: unspecified temperature function

/2(c,T, a,s) Chapter 2: unspecified density function f3(g'h,u,tp) Chapter 2: unspecified entrainment function fi{T — Tsur, pCp,u,g'h ) Chapter 2: unspecified ground heat flux function

/rain The mass fraction which rains out a two-phase jet

Fu Turbulent momentum flux y u'u'2 + u'v'2 + u'w'2

■Pjet Jet flow force

Turbulent momentum flux \Ju'u'2 + u'v'2 + u'w'2 Fu Fr Froude number u/^fgh

Fr& Densimetric Froude number u/y/gH

F t f Front Froude number Uf/y/gH Turbulent momentum flux \Ju'u'2 + u'v'2 + vj^2 Fu 9 Gravity acceleration 9 Vectorial expression of the gravity acceleration 9' Reduced gravity acceleration ^-g

G Appendix E: Gibbs’ free energy of a thermodynamic system G(W) Chapter 13: gamma distribution

9i Partial Gibbs’ free energy for component no i

264 Ris0-R-1O3O(EN) h Height of a gas layer ti Chapter 5: height of gas layer downstream of an obstacle hio% Plume height at which the concentration is 10% of cmax (sy 2.15crz with Gaussian distribution) applied by Spicer & Havens (1986) and Mercer & Davies (1987) hi Partial enthalpy of component no i h Chapter 11: length scale - see equation 219 H Chapter 5 and appendix F: height of obstacle A H Specific enthalpy relative to ambient conditions A Hcon Enthalpy contribution from condensation of aerosols AH0 Enthalpy in a pre-trial reference period

(A H/c)cr The enthalpy to concentration ratio giving neutral buoyancy A Hcon Heat of condensation for an aerosol

AHmi* Heat of reaction inside a binary aerosol Aijmix Heat of reaction in aerosols per number of moles in liquid phase

AJTrain Chapter 8: heat contribution from cooling liquid aerosols before rain out

AH A, AH A Chapter 9: heat of reaction for reactions A and B AH Chapter 2: integral cloud enthalpy difference relative to ambient conditions I Number of components in gas mixture

t ^21 • • • Chapter 4: integrals of the terms ti,t2,... in equation 24

1(c) Signal intensity 1(c) = a(c)/fi(c) in erfc(i) The nth integration of the complementary error function k Chapter 13: shape parameter in gamma distribution k Chapter 3: energy loss coefficient I< Eddy diffusivity

I

Length scale of a continuous dense gas release Vq^q'q-1^5

Length scale of an instantaneous dense gas release

Ris0-R-1O3O(EN) 265 LCi o% Appendix I: lethal concentration for 10% of a population m mass m Flow rate by mass m,n,p, s Appendix G: constants in Sutton’s dispersion model

77lair Air component of the flow rate

?h.gas Contaminant component of the flow rate rhcr Choked flow rate in pipe or nozzle M Molar weight M* ‘Effective’ molar weight, ie the molar weight of an isothermal stimulant gas which models the density approximately

AM Difference in molar weights n Dimensionless frequency fz/u n Appendix E: number of moles n Chapter 12: index in a time series n Normal vector of a surface n Appendix F: unit vector normal to a stream line

Tli Number of moles of component no i ni,U2,n3 Appendix D: components of the three-dimensional vector n

•^block Chapter 11: number of blocks in a time series

P Pressure

Po Reference pressure

Per Pressure of choked flow conditions in pipe or nozzle

Pi Partial pressure of component no i

Pi Appendix E: partial pressure of component no i Psat (r) Saturation pressure at temperature T Ap Pressure difference

Pr Prandtl number -

9 Humidity, ie the water vapour concentration Q Appendix E: heat supplied to a thermodynamic system

9evap Chapter 8: evaporation from a pool

Qsat(T) Humidity at saturation, ie p^2t° (T)/p

9sink Chapter 8: liquid drainage from a pool by processes other than evaporation

9source Chapter 8: liquid supply to a pool

9storage Chapter 8: liquid accumulation in a pool

9. Humidity fluctuation scale defined by = —q'w' r Radius, eg the radius of a box model or an aerosol

266 Ris0-R-1O3O(EN) Chapter 11: distance in an interpolation scheme ra,n Appendix E: variables in Wheatley ’s (1986) aerosol model R The universal gas constant, 8.314 K.^ole Rij (T) Correlation between ui and Uj with time lag r

%(() Correlation between ui and Uj with spatial separation £ RiiiO Vector formulation of Ry(£) Re Reynolds ’ number ^ RH Relative humidity, ie q/qs&t{T) Ri Layer Richardson number where Au is a velocity differ­ ence and Ap is a density difference Rie Layer Richardson number used by Jensen (1981a)

Ri/ Flux Richardson number pu'ui'ff Rtf Bulk flux Richardson number used in Bo Pedersen (1980) de­ fined from depth integrated turbulent kinetic energy budget dp Rigv Gradient Richardson number

Riu. Layer Richardson number in the limit of negligible heat convec­ tion Apgh/pul applied by Jensen (1981a)

Riu. a Layer Richardson number lp ~p l[r% applied by Mercer & Davies (1987)

Riw. Layer Richardson number in the limit of free convection Apgh/pw applied by Jensen (1981a)

Ri&T Bulk heat convection Richardson number A^r Ru Layer Richardson number Ri, = Apgh 10%/pul applied by Spicer & Havens (1986) S Entropy

Si Partial entropy for component no i 3(/) Spectral energy distribution of a power spectrum Sc Schmidt’s number t Time hi h Appendix C: time-of-flight for sound pulses iii hi • • • Chapter 4: terms in turbulent kinetic budget - see equation 24 t Appendix F: unit vector parallel to a stream line T Temperature

Tair Temperature of the ambient air

Tboil Boiling point temperature ^max Maximum temperature ^inin Minimum temperature Train Temperature of liquid raining out of a two-phase jet

Ris0-R-1O3O(EN) 267 -*-real Real temperature (in contrast to measurement) Tsonic Temperature measured by a sonic anemometer Ttc Temperature measured by a thermocouple TsoilC 2! i) Soil temperature at depth z and time t T. Turbulent temperature scale defined by T«u* = —T'w' AT Temperature difference

^Cio% Concentration where 10% of a population is poisoned r Time scale

Teat Response time of a catalytic concentration sensor / -v \ 1/5 Tee Time scale of a continuous dense gas release

It \1/2 Tci Time scale of an instantaneous dense gas release ( ^)

Tdur Duration of gas release Te Taylor ’s integral time scale

Theat Time scale of the development of surface heat flux Tm Taylor ’s micro time scale Tobs Observation period Tpass Passage time of a cloud Tie Response time of a thermocouple

Twake Appendix 5: wake resistance time r«. Appendix G: turn-over-time for a convective eddy

Tt Time scale of the temperature development of a cloud u Downwind velocity u Velocity vector u0 Chapter 11: initial jet velocity just after flash boiling

MlOm Wind speed at 10-m height UQ Ambient velocity

Ue Entrainment velocity

«/ Front velocity

M/0 Front velocity in calm environment Uj Appendix E: partial internal energy for component no i

Mi Velocity component (ui,U2,us) = (u,v,w)

4 Velocity perturbation of u;

Mjump Velocity of a propagating hydraulic jump

U Chapter 11: velocity scale - see equation 219 U. Friction velocity defined by v% = —u'w'

K Chapter 8: friction velocity in boundary layer above pool

268 Ris0-R-1O3O(EN) Ambient friction velocity

U Appendix E: internal energy of a thermodynamic system Velocity scale of a continuous dense gas release V^5g'^^5 uci Velocity scale of an instantaneous dense gas release (Aciflo)1^2

V Velocity in the horizontal lateral direction va, vn Appendix D: flow along and normal to measurement path V Volume V Flow rate by volume w Vertical velocity component w. Velocity scale of free convection w, = [—gziw'p'/po )1^3

Wa,Wb Appendix E: variables used in an aerosol model Appendix E: work done by surface tension

We Weber number x Downstream direction

X Appendix D: first direction in the original coordinate system

X Position vector x 0 Appendix G: fetch in Sutton’s evaporation model

Xi Appendix E: mole fraction of component no i

Xi Appendix F: nirection, (xi,X 2,x s) = {x,y,z)

X Appendix E: liquid phase concentration in an aerosol model y Lateral horizontal direction y Chapter 10: front coordinate for a box model on slope

Ve Position of plume centre line y Chapter 10: dimensionless coordinate y = y/A a Appendix D: second direction in the original coordinate system z Vertical direction normally upwards except in the model of soil heat flux in chapters 7 and 12 where z is the depth into soil z Appendix D: third direction in the original coordinate system

Zo Surface roughness 4 Chapter 8: aerodynamic roughness above a pool

ZOc Surface roughness of concentration profile ZOh Surface roughness of temperature profile z0q Surface roughness of humidity profile Z\ Appendix G: reference height in Sutton’s dispersion model

Zheat Length scale of temperature distribution in the soil Zi Interface height, normally height of the gas cloud, but in ap­ pendix G Zi is the height of the atmospheric boundary layer

Ris0-R-1O3O(EN) 269 a Liquid mass fraction, degree of condensation a Appendix F: thermal diffusivity a Appendix G: Kolmogorov constant <*1,0% Appendix G: Kolmogorov constants of the 1-D longitudinal and transversal power spectra

P Chapter 13: scale parameter in gamma distribution P Appendix F: porosity of an obstacle

7 Ratio of heat capacities Cp/Cy r(p) Gamma function r(o,p) Incomplete gamma function x v~1e~x dx 5 Chapter 8: boundary-layer height over evaporating pool

£ Degree of reaction in chemical equilibrium e Dissipation rate of turbulent kinetic energy

C Appendix B: friction coefficient in nozzle contraction c Chapter 3: normalized height in a mixing layer behind front V Kolmogorov length scale e Surface slope e Appendix D: horizontal rotation angle K von Karman’s constant % 0.4 K Appendix G: wave number

K Appendix G: wave number vector k Uk 2> K3 Appendix G: three components of vector k -^1,^2, A3, A4 Chapter 4 and appendix G: parameters specifying empiric en­ trainment limits.

Asoil Heat conductivity in soil

A Chapter 10: length scale of wedge shaped box model

P Mean value, eg mean concentration fic z/ Viscosity

Appendix E: stoichiometric coefficient of component no i

L Chapter 8: single loss resistance factor

V>c Monin-Obukhov correction of concentration profile Iph Monin-Obukhov correction of temperature profile 1pm Monin-Obukhov correction of velocity profile Monin-Obukhov correction of humidity profile

P Density

P Mean density

P' Density perturbation

270 Ris0-R-1O3O(EN) p' Liquid phase density p" Gas phase density

Po Initial density of isothermal model gas

Ps oil Soil density Ap Density difference a Appendix E: surface tension

°Txc Appendix C: standard deviation of thermocouple signal o c Standard deviation of concentration time series

O'Dir Standard deviation of wind direction OH Standard deviation of enthalpy time series Ou, Ov, Ow Standard deviation of downwind, lateral and vertical velocity

°V Chapter 13: horizontal dimension estimated by Gauss fit

Oz Chapter 14: vertical dimension estimated by Gauss fit or Appendix C: standard deviation of sonic temperature signal

Ti Chapter 8: friction factor in pipe section %

T0,T< Appendix F: surface and interface friction

V Kolmogorov velocity scale

y ’conduct Chapter 8: heat conduction from the surface below

‘pev ap Chapter 8: heat consumed by evaporation

V’long Chapter 8: net heat received by long-wave radiation

^sensible Chapter 8: heat contribution from entrained air

V’short Chapter 8: net heat received by short-wave radiation

V’sink Chapter 8: heat loss because of liquid dainage

^source Chapter 8: heat contribution from supply of liquid material

V’storage Chapter 8: heat accumulation in pool

Appendix G: tensor formulation of the power spectrum

0c Monin-Obukhov dimensionless concentration gradient 4>h Monin-Obukhov dimensionless temperature gradient 0m Monin-Obukhov dimensionless velocity gradient

09 Monin-Obukhov dimensionless humidity gradient X(T) Gas concentration at saturation, %(T) = psat (T)/p

Riso-R-1030(EN) 271 UJ Chapter 10: integration parameter in Webber et ah' (1993) slope model

Use of indices In turbulence theory: perturbation of a property from its mean value defined by u = u 4- u' In association with gravity g: reference to reduced gravity g' =

/ In thermodynamic theory: reference to the liquid phase, eg c'p // Reference to the gas phase, eg c" 1...9 Reference to location, eg hi, see definition sketches air Property of dry air, either in the ambient fluid or as a compo­ nent in a gas mixture, eg Cpir cat Measurement by catalytic concentration sensor, eg ccat con Reference to condensation, eg AJJcon

C3H8 Property of the propane component of a gas mixture dew Reference to dew point temperature, eg 7dew dry Measurement with a wet bulb thermometer, eg Tdry est Estimate, eg mass flux mest freon A property of the freon component of a gas mixture gas A property of a contaminant, eg c®35 H20 A property of the water component of a gas mixture i Reference to component no i, eg partial pressure pi i,j,k,l For velocity and direction: indices 1.. .3 correspond to down­ wind, lateral and vertical respectively. NB: repeated index in­ dicates summation, ie A,kUk = AnUi + Ai2U2 + A^uz max Maximum value of a measured property min Minimum value of a measured property mix A property of a mixture, eg c£*lx

NH3 A property of the ammonia component of a gas mixture o Reference value, eg the initial value in an integration o Appendix E: parameters in Wheatley ’s (1986) binary aerosol model have ° as a reference to the limit of zero chemical inter­ action o Appendix E: reference to the standard state of a thermody ­ namic property, eg AH0. NB: superscript is reference to the specific standard state at temperature 25° C, eg AH° real The real value of a property in contrast to the measured one sat Reference to saturation, eg saturation pressure p sat(T) slow A measured property which has been filtered

272 Ris0-R-1O3O(EN) soil Reference to a value in the soil sonic Measurement by sonic anemometer sur Reference to a value at the surface tc Thermocouple measurement wake Property in the wake of an obstacle wet Measurement by a wet-bulb thermometer

Miscellaneous

A A difference of a property, eg density difference between the density of a gas mixture and that of the ambient fluid Ap = p mix _ p 3.iT

A A change of a thermodynamic function associated with a chem­ ical reaction, eg Ah = 1/3/13+1/4/14—vihi — z/2/12 for the reaction z/iAi + Z/2A2 ^_ 1/3A2 + 1/4A4

( ) An average in space, eg average of the local velocity in a spread­ ing gas cloud (|u|)

A bar denotes the average value of a fluctuating time series, eg c is the mean value of c Correlation of two fluctuating values, eg the correlation of two velocity perturbations u'v'

1 1 The absolute value or norm of a vector, eg |u| for the length of the velocity vector m Record number i in a time series MT Transposed matrix

Bold Bold-face typesetting is reference to vectors and tensors, ie u is the velocity vector

Bis0-R-1O3O(EN) 273 Index

adiabatic mixing, 18, 60-63, 79, 90, Modellers’ Data Archive, 258 133, 150, 209 MTH project BA, 197 aerosols, 46, 50, 55, 57, 61-64, 133, REDIPHEM data base, 258 151, 199, 211, 233-236 signal speed-up, 138, 207, 223 effect on sound, 221 eddy correlation, 212, 253 buoyancy, 17, 25, 60, 108 eddy diffusivity, 22, 24, 37, 102, 139, 254 chemical reaction effective molar weight, 60,70,95,134, degree of, 66, 72, 230 142, 150, 156, 215, 228 effect on density, 66-68 energy kinetics, 67 conversion, 20 Clapeyron ’s equation, 49 dissipation, 24, 238, 250, 252 concentration in front, 12 centre-line, 152 in hydraulic jump, 242 distribution Gibbs’ free, 230 effect of obstacle, 107 internal, 228 footprint, 154 kinetic, 62, 237 front wake, 13 potential, 19 horizontal, 137 surface tension, 57, 235, 247 superimposed, 80 turbulent kinetic, 24, 162, 238 vertical, 89, 140, 158 enthalpy, 7,46-58,60-70,72,90,132, fluctuations, 37-40,101,112,116, 149, 229 143, 163 entrainment, 7, 18-30, 74, 101, 112, intensity, 38,101,107,119,138 163, 239 inflammable, 259 edge entrainment, 8, 13, 73 sensor effect on front velocity, 18 Drager catalytic, 207 passive ‘entrainment rate’, 255 Drager electrochem., 207 entropy, 57, 229 EGAS electrochem., 158 exchange coefficient, 27, 42, 54, 131, lidar, 147, 207 249 sonic, 157, 194, 208, 219-225 TiiV catalytic, 82, 194, 224 field experiment UVIC, 143, 207 Desert Tortoise, 125-134 toxic, 259 Fladis, 135-154, 198-218 visible, 13, 63, 128, 206 intercomparison, 156 photographer ’s dilemma, 64 list of, 257 coordinate system MTH project BA, 82-122, 191- alignment, 99,160,197,212,226- 198 227 Thorney Island, 154-165 moving frame, 38, 145, 216 free convection, 22, 250 front velocity, 12 front, 7,11-18, 72 critical flow Froude number, 13, 35, 57, 72, 83, compressible, 48 112, 241, 246 gravity, 20, 34, 112, 240, 243 densimetric, 35, 75, 246

Dalton’s Law, 228 Gibbs, 228 Damkohler number, 246 data heat capacity, 220, 228, 259 Fladis, 216 heat flux, 8, 74, 100

274 effect on density, 65 SLAM, 18 effect on front velocity, 17 Wiirtz, 18, 216 effect on turbulence, 28 Wheatley ’s aerosol, 63, 133 in soil Monin-Obukhov scaling, 212, 248 measurements, 129 in-plume, 27,100 theory, 40-46,129 pool boundary, 54 Monin-Obukhov estimate, 27 moving frame, 135-141 pool evaporation, 52 turbulent, 249 Navier-Stoke’s equation, 237 homogeneous equilibrium, 8, 49, 50, obstacle, 30-36,105-112 58, 62, 72, 92,133,199, 233 blocking, 34, 83, 243 hydraulic jump, 241 box model, 78 hydrostatic pressure, 35, 239 effect on front velocity, 34 ideal gas, 47, 59, 220, 227 effect on turbulence, 120 MTH project BA setup, 193 Kolmogorov, 114, 250 rain out, 51 laboratory experiment passage time, 44, 79 Britter & Linden, 16 plume Grobelbauer, 17 height, 8, 19, 140,158, 255 Heidorn, 34 effect of obstacle, 79, 112 Konig, 35 meandering, 38, 101, 119, 128, Simpson & Britter, 13 136, 216 Vincent, 33 touch down, 150 latent heat, 232 width, 8 law of mass action, 66, 231 effect of averaging time, 38,152 lift off, 134, 147 effect of obstacle, 79 Prandtl number, 246 mass balance, 127,141 profile similarity, 21,138 model psycrometer, 92, 149, 233 a-p, 39 k-e rain out, 46, 70, 82, 94,193, 200, 206 ADREA-HF, 18, 216 Raoult’s law, 233 FEM3, 18 reduced gravity, 16, 35, 156, 239 MERCURE, 18, 216 response time, 82,125,132,138,159, AERCLOUD, 62, 234 193, 206, 259 box matching, 221 Cleaver’s obstacle, 78 review articles, 259 DEGADIS, 6, 24, 80,198 Reynolds number, 15, 16, 135, 246, DRIFT, 6,62,67,80,198,233, 257 234 Reynolds stress, 19, 25, 238 Fannelpp’s toroidal, 78 Reynolds ’ decomposition, 237 FMI’s sloping-terrain, 75 Reynolds ’ equation, 238 GReAT, 10, 51,151, 202 Richardson number, 246 HEAVYPUFF, 72 HEGADAS, 6, 80, 198 scaling law, 16, 35, 200 Corns’, 10, 29 Schmidt number, 246 Schnatz’, 80 self-similarity, 89 SLAB, 24, 80,104 slumping, 104, 160 SLAM, 6, 198 time scale, 79 Webber’s sloping-terrain, 76 source, 46-58 evaluation, 136, 258 cyclone, 82, 192 shallow layer gas phase outflow, 47 equations, 239

Ris0-R-1O3O(EN) 275 instantaneous two-phase release, 57 jet, 50, 69, 128 effect of momentum, 82-122 effect on turbulence, 118 entrainment into, 29 interaction with obstacle, 107- 112, 120 rain out, 51 vertical, 150 liquid phase outflow, 47 pool, 51, 69,128, 256 two-phase outflow, 48 surface roughness, 248 Desert Tortoise, 131. effect on density, 65 effect on front, 15 effect on heat flux, 28 Fladis, 202 MTH project BA, 97 Thorney Island, 162

Taylors hypothesis, 116, 252 tensor notation, 227, 236 terrain box models, 75 effect on front, 16 turbulence, 237-238, 247-253 co-spectrum, 117, 164, 253 effect of averaging time, 164 intensity, 162 isotropy, 114, 162, 252 spectrum, 113-122,164-165,251- 253 buoyancy subrange, 164 effect of sensor response, 225 inertial subrange, 40,114,144, 164, 251 vapour blanket effect, 155 vapour pressure, 233 over aerosols, 62, 199, 233

Weber number, 246

276 Ris0-R-1O3O(EN) Bibliographic Data Sheet Ris0-R-1O3O(EN) Title and author(s) Dense Gas Dispersion in the Atmosphere

Morten Nielsen

ISBN ISSN 87-550-2362-2 0106-2840

Dept, or group Date Wind Energy and Amospheric Physics September 21,1998

Groups own reg. number(s) Project/contract No.

Pages Tables Illustrations References 276 41 146 189

Abstract (Max. 2000 char.) Dense gas dispersion is characterized by buoyancy induced gravity currents and reduction of the vertical mixing. Liquified gas releases from industrial accidents are cold because of the heat of evaporation which determines the density for a given concentration and physical properties. The temperature deficit is moder­ ated by the heat flux from the ground, and this convection is an additional source of turbulence which affects the mixing. A simple model as the soil heat flux is used to estimate the ability of the ground to sustain the heat flux during release. The initial enthalpy, release rate, initial entrainment and momentum are discussed for generic source types and the interaction with obstacles is considered. In the MTH project BA experiments sourcee with and without momentum were applied. The continuously released propane gas passed a two-dimensional remov­ able obstacle perpendicular to the wind direction. Ground-level gas concentrations and vertical profiles of concentration, temperature, wind speed and turbulence were measured in front of and behind the obstacle. Ultrasonic anemometers pro­ viding fast velocity and concentration signals were mounted at three levels on the masts. The observed turbulence was influenced by the stability and the initial mo­ mentum of the jet releases. Additional information were taken from the ‘Dessert Tortoise ’ ammonia jet releases, from the ‘Fladis’ experiment with transition from dense to passive dispersion, and from the ‘Thorney Island’ continuous releases of isothermal freon mixtures. The heat flux was found to moderate the negative buoyancy in both the propane and ammonia experiments. The heat flux measure­ ments are compared to an estimate by analogy with surface layer theory.

Descriptors INIS/EDB ANEMOMETERS; BOUNDARY LAYERS; BOX MODELS; CHEMICAL EF­ FLUENTS; CLOUDS; COMPLEX TERRAIN; DISPERSIONS; ENTRAINMENT; EVAPORATION; FIELD TESTS; FLUCTUATIONS; GAS FLOW; HEAT TRANS­ FER; JETS; LIQUEFIED GASES; MIXING; PLUMES; TURBULENCE; TWO- PHASE FLOW

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