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Wind Engineering Terminology
Nicholas Isyumov1 1Professor Emeritus, The Boundary Layer Wind Tunnel Laboratory, University of Western Ontario, London Ontario, Canada email: [email protected]
ABSTRACT: This paper provides an overview of the technical terminology of wind engineering. It is intended to promote its use and to encourage its expansion. The non-dimensional numbers, concepts and ideas which are presented in this paper reflect my interests and should not be regarded as all inclusive. There are other terms which have been given only fleeting attention and some that have not been mentioned at all. Section 2, which presents the terminology used in wind tunnel model studies is the kernel of the paper. It includes such important terms as the Jensen (Je), Reynolds (Re), Scruton (Sc), Strouhal (St), Froude (Fr) and Cauchy (Ca) numbers and discusses their roles in the scaling of wind tunnel experiments and in the interpretation of their results. Also discussed are aeroelastic model studies. Section 3 discusses new additions to our terminology, including the Davenport Chain and the Tachikawa number (Ta). Wind speed scales used to describe and categorize various types of wind storms and their effects on the natural and built environments are discussed in Section 4. Current design procedures and methods of wind tunnel model testing are based on the concept that natural wind can be described as a locally stationary, turbulent boundary layer flow. This model of natural wind has served us well in describing winds in tropical and extra-tropical cyclones. However, the concept of steady “straight line” winds does not capture the effects of severe transient wind events such as tornadoes, thunderstorms and downbursts. Existing analytical and design methods will require extension and modification in order to deal with these phenomena and new types of testing facilities will have to be developed for their study. This will requires new ideas and facilities and will lead to a growth of our technical terminology.
KEY WORDS: Overview; Non-dimensional Numbers and Concepts; Similitude; Wind Tunnel Testing; Scales of Wind; Wind Loads and Responses.
1 INTRODUCTION The objectives of this paper are to identify and explain some of the terminology which is used in wind engineering research and practice. This includes non-dimensional numbers, scale and concepts, which have been named in honour of particular individuals who were instrumental in their development. It is important to mark these individual contributions for posterity and to be aware of their significance and applicability. This may avoid the “re-invention” of the wheel. Wind engineering has become a distinct discipline and its identity and visibility is enhanced by the use of specific technical terminology. In our generation we have seen the emergence of the Scruton (Sc), Jensen (Je) and Tachikawa (Ta) numbers. These are non- dimensional groupings of quantities which govern the similitude of model and prototype processes and influence performance under wind action. The Saffir-Simpson and the Fujita scales have been adopted to categorize the severity of wind storms and the Alan G. Davenport Wind Loading Chain has been introduced in order to summarize the concepts which determine wind induced loads on buildings and structures. Alan Davenport’s chain was formally recognized at ICWE 13 and is the latest addition to our terminology. Wind engineering bridges many disciplines, including structural engineering, fluid mechanics, aerodynamics, meteorology and probability theory. It is natural therefore that we have adopted relevant parts of terminologies formulated by other disciplines. Such terms as the Richardson (Ri), Rossby (Ro), Reynolds (Re), Strouhal (St), Froude (Fr), Keulegan-Carpenter (K- C) and Cauchy (Ca) numbers; the Prandtl mixing length; the Coriolis parameter; the Monin-Obukhov stability parameter; the Kolmogorov inertial sub-range of turbulence; the Beaufort and Fujita scales; and others have become part of our terminology. These terms allow us to communicate facts and ideas in a convenient and unambiguous manner. In a functional sense they provide a form of “shorthand”, much like that used by secretaries to record dictation or the proceedings of meetings. More importantly, familiarity with wind engineering terminology promotes awareness and appreciation of relevant physical laws, their applicability and the limitations which they impose. This paper provides a historical perspective of some of the wind engineering terminology and concepts and presents examples of their applicability and importance. It is not possible to cover all terms and concepts used in our discipline and emphasis is placed on terminology and concepts, which I have used and found valuable in my experience. Some are only briefly mentioned
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others are discussed in detail. The included material reflects my personal experience and that of the Boundary Layer Wind Tunnel Laboratory (BLWTL) of which I have been a member since its inception 50 years ago. Emphasis throughout the paper is placed on terminology which relates to the requirements for achieving similarity of prototype wind loading data and those obtained from small scale wind tunnel model tests. Some similarity requirements are discussed in detail. Also discussed are selected non-dimensional numbers and concepts which influence the effects of wind on prototype buildings and structures and their components. The underlying objective throughout the paper is to provide a historic perspective and to encourage engineers and researchers to become familiar with the existing terminology and interested to further its development.
2 TERMINOLOGY IN WIND TUNNEL MODEL STUDIES 2.1 General Glossaries of commonly used wind engineering terminology can be found in some wind engineering texts [1] and publications [2]. Typically mentioned are various non-dimensional quantities which describe the nature of wind and its action on buildings and structures. Emphasis in this paper is on terminology used in wind tunnel model studies. The paper highlights recent additions with emphasis on the Jensen and Scruton numbers and the Alan G. Davenport Wind Loading Chain. I had the privilege of meeting both Kit Scruton and Martin Jensen and receiving first hand insights into their research and points of view. 2.2 Modeling natural wind 2.2.1 The Jensen number (Je) - Its role in geometric scaling In September 1965 I joined Alan Davenport at the Boundary Layer Wind Tunnel Laboratory (BLWTL) of the University of Western Ontario in the completion of its wind tunnel; its commissioning; and the start of experiments for commercially sponsored projects. Involvement with real engineering projects was judged essential in order to become a recognized wind tunnel testing facility. Also, commercially funded projects were needed in order to pay the bills. We interacted with Dr. Martin Jensen of the Danish Technical University in order to gain confidence in our modeling of natural wind. The success of model studies of the effects of wind on buildings and structures must be attributed to the pioneering work of Dr. Martin Jensen. His published model law [3] clearly states that “The correct model test for phenomena in the wind must be carried out in a turbulent boundary layer and the model law requires that this boundary layer be to a scale as regards the velocity profile”. Jensen’s research indicated that correct modeling is achieved by maintaining h/z0 constant in model and full scale. Here h is a characteristic dimension of a building or a structure and z0 is the roughness length of the flow. Jensen’s pioneering work was recognized by the wind engineering community [4] and the choice of the length scale of model tests in wind engineering wind tunnels has since been based on the observance of the Jensen number (Je) stated in Equation (1) or its equivalent.
Je = h / z0 (1)
The addition of Je to the wind engineering terminology occurred prior to ICWE 8 and a tribute to Dr. Martin Jensen appeared in its proceedings [5]. Jensen’s studies were in a turbulent boundary layer, developed naturally over a long fetch of homogeneous floor roughness. The importance of this ratio is illustrated in Figure 1. These comparisons clearly demonstrate the importance of carrying out wind tunnel model tests of buildings and structures at a geometric scale which is consistent with the length scale of the modeled natural wind. In naturally developed boundary layer flows, the modelling of zo assures a consistent simulation of other lengths of the flow, including the depth of the boundary layer and the lengths scales of the components of turbulence or the size of the gusts or “eddies”. Few existing wind engineering wind tunnels have test sections which are long enough to base the selection of the geometric scale on the matching of Je alone. Even in long test section wind tunnels, trips, spires and other flow augmentation devices are used to better match the expected full scale profiles of the mean wind speed and the salient characteristics of atmospheric turbulence [6]. Total reliance on augmentation devices becomes necessary in the shaping of wind flows in short test section wind tunnels [7]. The matching of the model and prototype winds is never exact and usually it becomes necessary to concentrate on what are judged to be the more important properties and to accept mismatches for the less important ones. Limits on mismatching atmospheric turbulence in wind tunnel model tests can be found in manuals of practice [1] and in standards.[8]. A valuable discussion of the consequences of approximations of the flow on various wind effects can be found in Reference [9]. In addition to the simulation of the “approach” wind it is also necessary to include the aerodynamic influence of immediately surrounding buildings, structures and topographic features. The simulation of this “near field” flow in complex surroundings is typically achieved by testing with a geometrically reproduced “proximity” model in place. This assures that the influence of surrounding buildings, structures and geographic features on the mean and turbulent characteristics is allowed for. In most situations nearby buildings and structures provide shielding from the mean or steady wind and their effects are beneficial. However, in some situations, nearby buildings can funnel or redirect the approach wind to cause local speed increase or to increase the turbulence. This can accentuate the wind-induced forces. Figure 2 presents generalized force spectra for the fundamental sway modes of vibration of a tall building located in a complex city terrain, with highly built-up fetches for some directions and more open ones for others. The normalized spectral density is plotted on the vertical axis and the reduced frequency fD /V on the horizontal axis. Here f , D and V respectively are the H H
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frequency, the characteristic frontal width of the building and the mean speed of the approach wind at the height of the building. Figure 2a) shows normalized spectra of the generalized force in the along-wind and across-wind directions for a wind direction for which the upwind fetch is relatively open. The along-wind dynamic excitation is due to the buffeting by upstream turbulence. In this case the dynamic forces and corresponding responses are quite sensitive to the degree to which the ratio of the wavelengths of the spectral peaks in model and full scale corresponds to the geometric scale of the wind tunnel simulation. Wind tunnel tests can significantly underestimate the buffeting action of wind in situations when the generated gusts are not correctly scaled relative to the size of model.
Figure 1. Influence of the Jensen number (Je) on wind-induced time-average pressures, after Reference [3]
Figure 2. Power Spectra of the generalized wind forces for the fundamental sway modes of vibration of a tall building for relatively open and highly built-up fetches of approach terrain
The spectrum of the across-wind force is less influenced by the buffeting action of the approach wind and more sensitive to the effects of the turbulence generated by the building itself. The pronounced peak in the across-wind force seen in Figure 2a) is at the Strouhal number of the building and indicates pronounced vortex shedding. In this case the degree to which the scale of the
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approach turbulence has been scaled is of lesser significance. Figure 2b) shows spectra of the along-wind and across-wind generalized forces for a wind direction where there are many large buildings immediate upstream. The effects of the turbulence generated by the shedding of vortices from the many upstream buildings are clearly apparent in both the along- and across-wind force spectra. In such situations, the consequences of miss-scaling the wavelengths of the approach turbulence are less pronounced. A commonly used approximation for lightly damped structures is to assume that the variance of the wind induced resonant displacements can be expressed as:
2 2 σ x = π f0 S F ( f0 ) /(4 K ζ ) (2) where x, F, K, f0 and ζ are respectively the displacement, the generalized force, the generalized stiffness, the natural frequency and the critical damping ratio. The reduced frequencies of most buildings at their design wind speeds fall into the inertial sub-range of atmospheric turbulence and are higher than the reduced frequency of the normalized spectral peak. In this frequency range the normalized spectral density varies as:
2 η f S F ( f ) /σ F ∝ ( fD /VH ) (3)
The exponent η in this range of the reduced frequency is negative. Fitted values of η are indicated in Figures 2a) and 2b). In this region the dynamic wind forces and responses increase monotonically with increasing wind speed and the RMS displacement of the building can be approximated as:
β 1/ 2 σ x ∝ (VH / f0D) /(M ζ ) (4)
2 where β = 2 −η / 2 and M is the generalized mass which for a particular mode of vibration is defined as M = (2π f 0 ) K . Depending on the nature of the excitation, typical values of β are in the range 2.5≤ β ≤3.5 for situations where the excitation increases monotonically with increasing wind speed. The slope of the inertial sub-range of the normalized power spectrum of turbulence is η = − 2/3. Correspondingly, the lower bound of the power law exponent in Equations (4) is β = 2− (−1/3)=2.33 . Equation (4) does not apply for the across-wind excitation at reduced frequencies lower than the Strouhal number. Considerable differences in the response of aeroelastic wind tunnel models can arise in situations where their geometric scale differs from the length scale of the model turbulence. Current practice suggests that the scale of the longitudinal component of turbulence wind and hence the wavelength at the peak of its normalized power spectrum, can be miss-scaled by a factor of 2 or 3, see References [2, 8 and 9]. In my experience the consequences of such a miss-scaling can become significant in situations where the wind induced dynamic response is primarily due to the buffeting by the approach wind. The incorrect scaling of VH / f0 , which is the wavelength of the turbulence at the natural frequency of the structure, relative to building dimension D implies a shift in the reduced frequency and hence a lower or higher resonant response. In conclusion, a decision on the geometric scale of a wind tunnel model test cannot be solely based on the matching of Je of the model and prototype approach flows. It is also necessary to ensure a consistent scaling of other important “lengths” of the wind. These include the depth of the boundary layer and the salient scales of turbulence. This becomes increasingly more difficult in wind tunnels with short working sections, which rely on various turbulence generating devices and in situations where surrounding buildings modify the approach flow. 2.2.2 The Reynolds number (Re) - Its influence on the flow and flow-induced forces The Reynolds number (Re) is the ratio of the inertia and viscous forces of the flow. It is an important indicator of the characteristics of the flow and the forces which act on objects exposed to the flow. It is named in honour of Osborne Reynolds who lived between 1842 and 1912. He was an engineering professor at Manchester University and made major contributions to fluid dynamics and in particular the influence of turbulence on the flow field and its effect on objects exposed to the flow. The Reynolds number is defined as:
Re = VL /ν (5) where V and ν are respectively the velocity and the kinematic viscosity of the fluid or gas and L is a characteristic dimension of the building or structure. Also named in his honour are the turbulence induced stresses which are independent of the fluid viscosity and are due to the motion of parcels of the fluid or “eddies”. The most significant of these in boundary layer flow is the shear stress due to the vertical momentum transfer by turbulence. This Reynolds stress is defined as:
τ 0 = − ρ u′w′ (6)
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where τ 0 ,ρ ,u′and w′ are respectively the surface shear stress, the fluid mass density, the longitudinal and vertical time-varying components of turbulence. The over-bar denotes the time average of the product of the longitudinal and vertical time varying components. It is not possible to match the model and prototype values of Re in wind tunnel tests with small scale models using air at atmospheric pressure. A mismatch of Re can result in substantially different flows and flow-induced forces. Fortunately, wind tunnel model tests at lower than prototype values of Re can provide valuable information for most bluff shapes. Nevertheless, careful attention must be given to the consequences of a Re mismatch on the characteristics of the flow itself and on its effects on particular buildings and structures. For tests made to simulate atmospheric boundary layer wind it is important to ensure that the turbulence in the model boundary layer flow is fully developed or “fully rough”. Sutton in his book “Micrometeorology” [10] suggests that the characteristics of turbulent boundary layer flows over rough surfaces become independent of Re when
u*z0 /ν ≥ 2.5 (7)
1/ 2 where u* is the friction velocity equal to (τ 0 / ρ) . Equation (7) is a form of Reynolds number which represents the ratio of the “eddy” viscosity of the flow to the molecular viscosity of the fluid. In other words, it is the ratio of the vertical momentum transfer by “eddies” or discreet parcels of turbulence to that due to molecular motion. This criterion for the Re independence of turbulent boundary layer flows is largely based on the fundamental studies of flow through roughened pipes by Nikuradse [11]. Flow separations for a bluff body with sharp edges is in most situations determined by the geometry of the body rather than the relative magnitudes of the inertia and viscous forces of the flow. Nevertheless, to ensure this independence of viscosity, it important that model tests are carried out at Re values which are above some minimum. For sharp-edged bodies it is common practice to require that
V h D /n ≥Remin (8)
where Vh and D are respectively the time average wind speed at the height of the building or structure and a characteristic 4 dimension of the cross-section, typically taken as the frontal width. For buildings and structures Remin =10 , see Reference [2]. Satisfying the requirements of Equations (7) and (8) does not necessarily ensure complete Re independence of wind tunnel experiments. For example, the dissipation of turbulence is by the action of the fluid viscosity and hence depend on Re. Consequently, there will be distortions of the model spectra at higher frequencies. Achieving Re > Remin is not sufficient for circular cylinders or curved shapes and prismatic shapes with rounded corners. The effect of rounding the corners is illustrated in Figure 3. As seen from this figure, the aerodynamics of circular cylinders in addition their Re dependence are also affected by their surface roughness. Wind tunnel models of circular shapes are often intentionally roughened in order to achieve an earlier transition from a sub-critical Re to a post-critical one. The data shown in Figure 3 are for 2-dimensional infinitely long shapes and exclude end effects. The flow over the top of buildings with cylindrical floor plans with relatively small aspect ratio are 3-dimensional and less sensitive to differences in Re since flow separations over the top occur at sharp edges and is not influenced by the action of viscosity. On the other hand, the similarity of small scale wind tunnel data for high aspect ratios chimneys, stacks and super tall buildings with prototype values is inherently more uncertain. Consequently, the possible consequences of differences between model and prototype Re values require careful consideration. Data at prototype values of Re are rare and in some cases additional tests with models built at a larger geometric scale may indicate likely trends. 2.3 Wind induced loads and response 2.3.1 The Scruton Number Sc - Its effect on wind-induced vibrations I first met Kit Scruton while visiting NPL in the summer of 1966. Subsequently, Kit visited the BLWTL and spent some time here. His work on the aeroelastic modeling of buildings and structures and their aeroelastic stability was of great importance to us as we began our own aeroelastic wind tunnel model studies of tall buildings, observation towers, cooling towers and other wind sensitive structures. The influence of the mass and damping of the structure and on its aeroelastic stability are demonstrated in Figure 4, which is taken from one of Kit’s papers, presented at the 1st conference of this group in Teddington, in 2 1963 [12]. The non-dimensional grouping 2Mδ s / ρ D , plotted on the horizontal axis, has since been dubbed as the Scruton number. In Scruton’s original work the structural damping was most commonly described by the logarithmic decrement δ . In present day usage the Scruton number is usually written as:
2 Sc = 4π mζ s / ρ D (9)
where ζ s = δ s / 2π is the critical damping ratio and m is the mass per unit length of the oscillating body.
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A proposal to coin the term Scruton number first appeared in print in 1982 [13]. The Scruton number Sc was officially added to the wind engineering terminology in time for ICWE 8. Kit Scruton’s many contributions to wind engineering are described in the proceedings of that conference [14]. Kit Scruton’s stability plot shown in Figure 4 is of great relevance to designers of slender flexible structures. At the design stage it is common to use the Sc as an indicator of a potential aeroelastic instability. In the case of slender cylinders such as chimneys and flagpoles, it has been found that excessive vortex shedding-induced effects are unlikely in situations where Sc > 64 [15].
Figure 3. Influence of Reynolds number on the drag coefficient of 2-D square cylinders with different corner radii and circular cylinders with different surface roughness after Reference [1]
There are questions about how to best calculate Sc in specific practical situations. Scruton’s original formulation, as defined in Equation (9) and as shown in Figure 4, uses the mass per unit length of a body which vibrates with a unit mode shape. In actual situations the mass per unit length of a building or a flexible structure is not constant along its height and its motion in a particular mode of vibration follows the shape of that mode. For vertical objects, such as slender chimneys and buildings, a good approximation of the mass to be used in the calculation of Sc is the average mass per unit length over the upper 1/3rd of the height. An improved approximation can be obtained by remembering that Sc corresponds to the product of the mass and damping ratios of the vibrating object. Physically, the mass ratio represents the ratio of the inertia forces of the object to those of the fluid which is displaced by the vibrating object. For an actual structure, vibrating with a mode shape φ( z ) where z is the height above ground, the mass ratio can be expressed as:
∫ m( z )φ( z )2 dz / ∫ ρ D( z )2 φ( z )2 dz (10) where m( z ) and D( z )2 are respectively the mass and the volume of the structure per unit height at height z. To a good degree of approximation the mode shape of a vertical structure can be expressed as:
φ(z) = (z / H )α (11) where the exponent α typically in the range of about 0.8 to 2.
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Consequently a more complete expression for the product of the mass and damping ratios becomes:
= π z φ 2 ρ 2 φ 2 Sc 4 s ∫ m(z) (z) dz / ∫ D(z) (z) dz (12)
If the mode shape were to be constant, namely if α = 0 and if m and D 2 are invariant over the height or length of the structure, the mass ratio would be m / ρ D 2 as used by Scruton, see Equation (9). For typical tall buildings it is reasonable to 2 assume that m(z) = ρ s (z) D(z) and that the building density ρ s is invariant, In that case Equation (10) reduces to the mass density ratio ρs / ρ and the Scruton number becomes:
Sc = 4π ζ s ρ s / ρ (13)
Figure 4. Influence of the Scruton number (Sc) on the dynamic response of flexible slender structures, after Reference [12].
3 For typical tall buildings 200≤ ρ s ≤ 250 kg/m and the damping is in the range 0.015 ≤ ζ s ≤ 0.025 %. Correspondingly, typical values of Sc are in the range of 30≤ Sc≤60 . The reduced velocities which influence the design of tall buildings seldom exceed 15. Consequently, typical tall buildings are not likely to be prone to a galloping type of instability, shown as the upper unstable region in Figure 4. Of greatest practical interest and concern is the potential for excessive resonant vibrations due to vortex shedding induced forces at reduced velocities which are at and near the inverse of the Strouhal number. In Figure 4, this is the lower region of instability denoted as “Aeolian”. Nevertheless, there is an emerging class of very slender super tall buildings where the building mass is deliberately increased near the top of the building in order to achieve a Sc which is high enough to avoid a galloping instability. The detailed form of Sc, as given in Equation (12), is best used in such situations.
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2.3.2 Aeolian Vibrations - The Strouhal Number St History is full of accounts of both useful and destructive actions of wind. Also there are references to its mystical powers. We often refer to wind action as an Aeolian effect. This is done with reference to Aeolus the god of wind in Greek mythology. In Homer’s Odyssey, Ulysses when sailing through waters known for many past shipwrecks ordered his sailors to plug their ears with wax but to tie him to the mast of the ship so that he could firsthand hear the mysterious noises of that region. Legends described these as the enticing cries of mermaids which disoriented mariners and lured them onto the reefs and their death. All bluff or non-streamline bodies placed into a flow of gas or fluid disrupt the oncoming flow and create a turbulent wake. For some shapes vortices can be shed in a highly regular manner. This phenomenon is an instability of the wake where vortices are shed first from one side of the body and subsequently from the other. A well known example of this phenomenon is the clearly visible pattern of alternating swirls which form behind a row boat. This shedding of vortices is experienced by many bluff bodies ranging from small diameter wires to large chimneys to slender tall buildings to rock formations and islands. The frequency of the vortex shedding from small objects can be high and in the audio range – hence the reference to “singing” wires. For larger objects the frequencies of vortex shedding are low and inaudible to the human ear. However, this vortex shedding produces alternating pressures on the sides of buildings and structures and creates alternating wind-induced forces which act in an across-wind direction. The relationship between the frequency of the shedding of vortices from an object with a particular shape and size when placed into a fluid flowing with a particular velocity is described by its Strouhal number:
St = f D /V (14) where f , D and V are respectively the frequency of the vortex shedding, the cross-sectional width of the object and the velocity of the approach flow. This a non-dimensional parameter is named in honour of Vincenc Strouhal a Czech physicist who experimented with the vortex shedding from wires placed in the wind [16]. As seen from Scruton’s stability plot of Figure 4, the St is of great importance to wind engineers as it results in critical wind speeds at which buildings and structures are forced to vibrate in resonance with the shedding of vortices. This critical wind speed occurs when the vortex shedding frequency approaches f0 the natural frequency of vibration of the building or structure. From Equation (14) the critical wind speed for vortex shedding- 푓 induced vibrations becomesVcr = f0 D / St , where f0 is natural frequency of vibration. Each mode of vibration of a structure has its own frequency and hence its own critical wind speed. Regular or narrow-band vortex shedding at and near a critical wind speed within to the range of design wind speeds can become “Enemy Number One” for designers of flexible and slender chimneys, buildings, flagpoles and other structures. The scientific literature is full information on details of Aeolian or vortex shedding-induced vibrations for various geometric shapes in different flow situations. Examples of St for various geometric shapes are shown in Figure 5a). Figure 5b) shows that St for sharp-edged rectangular shapes varies with the plan aspect ratios. This particular plot is taken from Scruton’s paper at the 1st ICWE [12]. There are uncertainties in St for rectangles with d/h > 2.5. For objects with long after-bodies, vortices which form at the leading edges can re-attach and limit the vortex shedding process. As seen from Figure 5b) the value of St changes abruptly at a plan aspect ratio of d/h = 2.5 and the vortex shedding becomes less regular and of diminished severity. Both Figures 5a) and 5b) are for a wind direction normal to front face. For a square plan form the organized vortex shedding disappears for wind directions skewed at about +/- 20 degrees to the normal. For sharp-edged shapes, with aerodynamic properties invariant with Re, the vortex shedding process is relatively well defined. The vortex shedding diminishes in strength and regularity as the height to width aspect ratio reduces and the flow over the top or end becomes significant. Also the shedding of vortices which is narrow-band and near harmonic in uniform smooth flow becomes less regular and broad-band random in turbulent flow. The spectrum of the across-wind generalized force shown in Figure 2a) is an example of the vortex shedding induced forces acting on a tall building in a relatively open exposure. For sharp-edged bodies with aerodynamic properties which are relatively independent of Re (see Figure 3), the extrapolation of data from small scale wind tunnel model tests to full-scale can be done with certainty. For rounded shapes and in particularly for circular cylinders, whose aerodynamic properties are strongly dependent on Re, as well as their surface roughness, the extrapolation from model to full-scale becomes more difficult and less certain. Most experiments in typical wind engineering wind tunnels are carried out at sub-critical values of Re and while there are some data at post-critical values of Re and some limited feedback from full-scale, the extrapolation to prototype scale is froth with difficulties and is hence uncertain. It is difficult therefore to arrive at reliable wind loading data for tall buildings with circular plan forms. This is clearly evident from data in Figures 6 and 7, which show data on St and the RMS across-lift coefficient for circular cylinders provided in ESDU 96030 [17]. As seen in Figure 6, St at post-critical Re values tends to be somewhat higher than at sub-critical Re values. It is common practice to adjust the wind tunnel model data for this downward shift in the critical velocity at full scale. The extrapolation of the magnitude of the vortex shedding-induced loads from model to full scale is less certain. The magnitude of the across-wind response, as indicated by the RMS lift coefficient, is also influenced by the roughness of the cylinder surface. As shown in Figure 7, much lower values of the RMS lift coefficient are found for smooth circular cylinders at post-critical Re values. Unfortunately, the magnitude of the lift coefficient at Re > 107 remains uncertain and must be judged on a case by case basis. Nevertheless, it is accepted practice to assume that it does not exceed the value of 0.5 found at sub-critical Re values.
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The St also provides a valuable indicator of the potential for Aeolian or wind-generated noise created by exposed objects or their surface details. A potential “noise maker” is identified when the vortex shedding frequency computed from Equation (14) falls into the audible range of the human ear. An inventory of potential “noise makers” for a proposed project can be made by identifying features of its façade for which the vortex shedding frequency may be 80Hz or higher. It may become necessary to devise further studies in order to determine the likely noise intensity. Such studies rely on CFD methods or on wind tunnel experiments. Similarity requirements for acoustic studies with small scale model are uncharted waters. Therefore wind tunnel studies made to quantify the Aeolian noise from small objects are usually done at prototype scale. It is of historic interest, that in the early days of wind tunnel testing, audible vortex shedding from small diameter wires was relied upon to measure the mean wind speed in experiments made at very low wind speeds. Measurements of dynamic pressures with a pitot-static tube become unreliable at very low wind speeds. Also hot-wire measurements are based on Kings Law and also become problematic at low wind speeds.
a) Strouhal numbers for various geometric shapes after Reference [15]
b) Strouhal number for rectangular shapes with different proportions after Reference [12]
Figure 5. Examples of Strouhal numbers St for Different geometric shapes (S is used instead of St in this figure)
2.3.3 The Froude Number Fr – the influence of gravity The Froude number Fr corresponds to the ratio of the inertia force to the force of gravity acting on a moving body. Using dimensional analysis this becomes:
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Fr = V 2 /( Lg ) (15) where V ,L and g are respectively the wind speed, the characteristic body length and the acceleration of gravity. The naming of Fr is in honor of William Froude (1810 to 1879), an English engineer and naval architect, for his work in wave line theory used in the description of how waves affect the motion of ship hulls through water. In model scale studies Fr must be equal to that in full scale. Since the acceleration of gravity in most wind engineering studies remains invariant, the requirement of maintaining a constant Fr constrains the choice of the velocity scale, once a particular geometric scale is chosen. Namely, for experiments where the simulation of the effects of gravity is important and Fr scaling must be observed, the velocity scale becomes:
λV = λL (16)
where λV =Vm / V p and λL = Lm / L p and subscripts m and p denote model and prototype quantities. Equation (16) imposes practical restrictions on wind engineering wind tunnel studies. With typical length scales in the range of 1/ 400 ≤λL ≤1/ 200 , the corresponding velocity scales become 1/ 20≤λV ≤1/ 14 . This requires that wind tunnel model tests are carried out at very low wind speeds. This raises practical difficulties as many wind engineering tunnels do not operate reliably at low wind speeds and exacerbates the scaling of Re effects, as required by equations (7) and (8). The observance of the Fr is paramount for structures, where gravity provides the dominant force which resists deformation. Suspension bridges and many cable-guyed structures fall into this category. Cable supported systems where the cables are “taut” or pre-tensioned , such as in cable-stayed bridges, do not require Fr scaling.
Figure 6. Strouhal Number from spectra (2-D flow) (after ESDU 96030)
Figure 7. Across-wind force coefficient (after ESDU 96030)
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The ratio of inertia forces to those due to gravity in actual situations differs from that given in Equation (15) once an allowance is made for buoyancy and the effective rather than the actual acceleration of gravity is used. This modified form is known as the densimetric Froude number and is expressed as:
2 Frd = V /( Lg(1− r / rs )) (17)
For buildings and structures moving in air ρ s >> ρ and Frd ≈ Fr . The use of Frd rather than Fr is an unnecessary embellishment for most wind engineering situations. This is not the case when objects move through water or some dense gas. An important case where the densimetric Froude number is used is the study of the mixing or dispersion of buoyant exhaust gases in the atmosphere. 2.3.4 The Cauchy number Ca – Influence of elastic forces The Cauchy number is named in honor of the French Baron Augustin Louis Cauchy, who lived from 1789 to 1857. He was a noted mathematician who pioneered analytical studies of time varying flow and elastic motions in continuous media. The original formulation of the Cauchy number related the velocity of motion relative to the speed of sound. The speed of propagation of sound through a medium is E / ρ , where E and ρ are respectively the bulk modulus and density of the medium. The original formulation of the Cauchy number is V 2 /(E / ρ) and corresponds to the square of the Mach Number, defined as M = (speed of motion/speed of sound). In this context the Cauchy number is of limited importance in wind engineering, where the airflows are typically well below the speed of sound in air (340 m/s at standard atmospheric pressure and temperature) and where the compressibility of air can be disregarded and its density be taken as invariant. This simplifying assumption which wind engineers have become accustomed to must be revisited when dealing with the effects of wind during extremely severe wind storms. The sustained wind speeds in a Category 5 Hurricane on the Saffir/Simpson Hurricane Scale are expected to exceed about 69 m/s which corresponds to a Mach number of M ≥ 0.2. The wind speeds during a Fujita Scale F5 Tornado may exceed some 116 m/s or a Mach number of M ≥ 0.34. The air can no longer be assumed to remain incompressible during such extreme wind events. Wind engineers have accepted a modified form of the Cauchy number in studies of flow induced motions of elastic structures. For wind engineering purposes the Cauchy number is taken to be a non-dimensional quantity which represents the ratio of the elastic force which resist the deformation of a building or structure due to wind action, to the inertia forces of the wind flow [2,18,19]. For wind engineering applications, the Cauchy Number it is written as:
2 Ca = Eeff / ρV (18)
where Eeff ,ρ and V are respectively the effective elastic modulus, the density of the flow and its velocity. Note that air density rather than the bulk density of the structure is used in wind engineering applications. This change is made possible by the additional similarity requirement of correctly scaling the inertia forces of the moving structure relative to those of the airstream. This is achieved by maintaining constant the ratio of the bulk density of the structure to the density of air. The variation of the air density at a particular location due to changes in air temperature and weather related changes in atmospheric pressure is small, however, it is important to recognize changes due to differences in elevation. Equation (18) states the requirement for achieving a correct scaling of the elastic stiffness of a structure. The elastic stiffness or resistance to deformation depends on the type of structural system. In the design of aeroelastic wind tunnel models, the 2 4 4 effective modulus Eeff is taken to be the Young’s modulus E for replica models and as Eτ / L, EA/ L , EI / L and GC / L for various types of equivalent structural models where resistance to deformation is due to the action of membrane forces, axial forces, flexure and torsion respectively. The quantities τ ,A, I , G, C and L are respectively the wall thickness of a tube or membrane, the cross-sectional area, the moment of inertia (second moment of area), the modulus of rigidity, the torsional constant and a characteristic dimension or length of the structure. 2.3.5 Aeroelastic studies – Replica models and discreet and continuous equivalent models The scaling of gravity induced effects, as required by the Fr is of secondary importance for structures where the stiffness is predominantly due to elastic resistance. This includes most vertical structures such as tall buildings, chimneys, stacks and towers and structural systems where resistance to deformation is determined by the axial stiffness, shear, bending or torsional action. While gravity does cause the P − ∆ effect which adds to the deformation of a tall slender structure, this is a relatively small effect and can be allowed for by a slight reduction of the elastic stiffness. Replica or exact aeroelastic models at a reduced geometric scale are possible for structures where the elastic properties are concentrated along the exterior geometry, such as in tubular and shell-like structures. Reinforced concrete hyperbolic cooling tower and thin wall box-shaped bridge girders and shafts of tall towers are examples [2,19]. The aeroelastic modeling of most other structural systems at a reduced geometric scale relies on the use of equivalent mechanical analogues which are designed to simulate the prototype elastic stiffness. Such
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equivalent structural models are then enclosed with a non-structural skin in order to replicates the overall exterior geometry and attract the correct aerodynamic forces. In all situations the similarity of the dynamic wind-induced forces which excite a particular mode of vibration of a structure and determine its response relies on the equality of its reduced frequency of vibration, namely:
f L / V = constant (19) 0i where f , L and V are respectively the natural frequency of vibration of mode “i”, a characteristic length of the structure and 0i the wind velocity of interest. This reduced frequency scaling applies for all structures, regardless whether their resistance to deformation comes from the restoring action of gravity or due to elastic action. For elastic systems this requirement becomes physically clear from the initial definition of the Cauchy number. As described above, E / ρs is the speed of propagation of the vibratory stress field through the structure. For mode “i” it is proportional to . Hence the reduced frequency in Equation f0i L (19) represents the ratio of the speed of propagation of the modal stress field to the speed of the wind. The wind-induced resonant response of tall buildings is primarily in its two fundamental sway modes and its fundamental torsional mode. The wind-induced responses in higher modes of vibration are generally of secondary importance and their effects on the peak overall wind forces can be disregarded in most situations. However, the effects of higher modes on the wind induced accelerations cannot be disregarded a priori for super-tall buildings. While the fundamental torsional response can be important for buildings sensitive to eccentric or torsional loads, the modal loads and responses in the two fundamental sway modes are usually of greatest interest. Taking advantage of this hierarchy of importance of the modal responses it not uncommon to use aeroelastic models which only simulated the two fundamental sway modes. Such an aeroelastic model is referred to as a “stick” model and is shown in Figure 8. In such tests aeroelastic similarity is achieved by maintaining the requirement of Equation (19), approximating the actual mode shape by a linearly varying one with height above ground, maintaining the correct generalized mass and the structural damping. This “stick” type aeroelastic model has been successfully used in studies of wind effects for many of the world’s population of tall buildings, including the former World Trade Center Towers in New York City. More complicated mechanical analogues become necessary in situation where the fundamental torsional mode of vibration also becomes important. Such models are referred to as discreet “multi-degree-of-freedom” aeroelastic models. Examples of mechanical analogues relied upon in such models are shown in Figure 9. The development of such analogues is only limited by the ingenuity of the model designer and the available funding. Also there are continuous multi-degree-of-freedom models where the simulation of the elastic stiffness is achieved with a continuous, specially machined elastic spine which is then enclosed by a non-structural skin in order to replicates the exterior geometry. This continuous equivalent aeroelastic model approach is commonly used in model studies of long span bridges. For bridges, such spines can usually be designed to simulate both the flexural and torsional stiffness of the bridge deck. Continuous, equivalent models using a central spine are also used to simulate the flexural stiffness of tall buildings. This permits the simulation of the fundamental as well as some of the higher flexural modes. In the case of tall buildings, it usually not possible to also model the torsional stiffness. Nevertheless, spine type equivalent models which only simulate the flexural stiffness are valuable in studies of tall slender buildings with compact cross- sections, where the across-wind vortex shedding forces are of primary interest and where torsional effects are of secondary importance and can be allowed for by evaluated by other methods. In summary, once the wind has been modeled and the length scale of the structural model has been selected, the scaling of the structural stiffness and the model wind speed are determined in one of the following ways:
1. In situations where the elastic stiffness dominates, the scaling of the model stiffness and the model wind speed are both determined by Ca similarity, Equation (18). 2. In situations where both the gravity and the elastic stiffness are important, the velocity scale is determined by Fr scaling in order to correctly simulate gravity effects, Equation (16) and the elastic stiffness is then subsequently determined by Ca similarity, Equation (18).
In situations where the elastic stiffness dominates, aeroelastic model tests in typical wind engineering studies can usually be carried out at or above the minimum Re requirement of Equation (8). Full aeroelastic models of long span bridges, tested in representative simulations of natural wind, simulate the 3-dimensional mode shapes of the structure and assure that the effects of the atmospheric turbulence are correctly included in the modal wind forces. Such full models also permit the inclusion of the participation of the towers, main cables and side spans. Full aeroelastic model studies of long span bridges are typically made at geometric scales in the range of 1/100≥ λL ≥ 1/ 300 . In the case of cable-stayed bridges the model velocities can be chosen based on Ca similarity. However, for suspension bridges the model velocity is determined by Fr scaling. Based on Equation
(16) the corresponding velocity scales are in the range of 1/10≥ λV ≥1/17 . In such situations, Re values can be lower than the minimum value suggested in Equation (8).
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Figure 8. Schematic representation of conventional 2 degree of freedom or “stick” aeroelastic model of a tall building, after Reference [19]
Figure 9. Typical stiffness elements used in multi-degree of freedom models, after Reference [19]
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This raises concerns that the use of small geometric models in bridge studies can results in somewhat exaggerated viscous forces which may suppress possible aerodynamic instabilities. To allay these concerns it is common to conduct companion tests using section models, constructed at a larger geometric scale. Comparisons of the responses of a suspension bridge with a main span of 430 m, which were determined with various wind tunnel models at the BLWTL, are shown in Figure (10). Details of that study have been reported in References [20, 21]. As seen from Figure (10), full aeroelastic model tests made at a geometric scale of λL = 1/ 320 in turbulent boundary layer flows over representative fetches of approach terrain, as well as in uniform smooth flow, indicated that the bridge was aerodynamically stable at wind speeds of practical interest. Companion section model tests made in smooth uniform flow at geometric scales of λL =1/320 and 1/ 40 both indicated a coupled lift-torsional instability. The bridge responses measured with both section models were similar. As a result it was concluded that geometric scale effects and hence differences in Re were minimal and that the differences in the behavior of the model bridge – namely stable in the full aeroelastic model tests and unstable in section model tests – were mainly due to the influence of atmospheric turbulence on the modal forces of the bridge. Section models do not include the effects of atmospheric turbulence and move with a constant or “unit” mode shape. Both of these effects tend to exaggerate the potential for aerodynamic instability.
Figure 10. Summary of various wind tunnel model lift deflections of a suspension bridge predicted with different wind tunnel model tests, after Reference [21] ( wind speed at deck height is in mph units)
3 RECENT ADDITIONS 3.1 The Alan G. Davenport wind loading chain – “Davenport Chain” The Alan G. Davenport Wind Loading Chain is the most recent addition to the wind engineering terminology. Its usage was formally approved and announced at ICWE 13. Further announcements followed in several National Wind Engineering News Letters. Alan Davenport referred to the process of evaluating the effects of wind on buildings and structures as a “chain of thought” where the various necessary concepts, like the ”links” of a chain, are interconnected and where the weakest link limits the final outcome. This chain analogy is illustrated in Figure 11. Its mathematical form, following the notation used in the 1970 Edition of the National Building Code of Canada [22] where it first appeared, is as follows:
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p = qCe C p Cg (20)
where p,q ,Ce ,C p and Cg are respectively the effective value of the wind load, the reference pressure of the hourly mean wind speed in open country terrain, the exposure factor which translates the reference pressure to the project site, the pressure coefficient and the gust effect factor which allows for the presence of turbulent fluctuations of the wind speed and the dynamic magnification of the structure. These correspond to the first 4 links shown in Figure 11. Criteria for judging the acceptability of the predicted wind action are usually stated separately. Details of the various links or concepts of this chain were discussed at ICWE 13 and are included in a follow-up publication [23]. It is important to stress that the specification of wind loads in most building codes and standards follow this “chain” concept. Feed-back, received since the introduction of the term “The Alan G. Davenport Wind Loading Chain”, has indicated that the chosen wording is too long and that this may discourage its use. To encourage greater use it has been suggested to shorten the name of the chain and to refer to it as the “Davenport Chain”.
Figure 11. The Alan G. Davenport wind loading chain – “Davenport Chain” 3.2 The Tachikawa number (Ta) – Wind borne debris The Tachikawa number was named in honor of Professor Masao Tachikawa of Kagoshima University in Japan, who lived from 1929 to 2001. Professor Tachikawa pioneered studies of wind borne debris and developed equations for the trajectories of plate-like debris elements of various types. He presented his approach at the 6th ICWE in 1983. It was also published in the Journal of Wind Engineering and Industrial Aerodynamics [24]. Pieces of debris where described as plate-like elements with a side dimension l taken so that l 2 = A = area and thickness h . The resulting equations of motion due to wind action were written to include a non-dimensional quantity which Professor Tachikawa referred to as the K parameter. In his honor this parameter has subsequently been named as the Tachikawa number (Ta). It is defined as:
Ta = ρ V 2l 2 /( 2mg ) (21) where ρ,V ,l,m and g are respectively the air density; the wind speed ; the side dimension of the plate defined so that l 2 equals 2 the plate area; the mass of the plate is defined as m = ρ m l h , where ρ m is the density of the plate and h is its thickness ; and the acceleration of gravity. The Ta is intended to represent the ratio of aerodynamic to gravity forces acting on the piece of debris. 2 To relate Ta to other non-dimensional numbers, one can substitute ρm l h for m in Equation (21) and obtain the following alternative expression for Ta, namely:
2 Ta = ( ρ / ρm )(V / h g ) (22)
This corresponds to the Fr, formed using the thickness of the plate h , multiplied by the inverse of the density ratio. 3.3 The Irwin Sensor - Measurements of Pedestrian Level Winds in Wind Tunnels In addition to information on wind loads and responses of buildings and structures, typical wind tunnel model studies often also provide information for the evaluation of wind conditions in pedestrian areas. Numerous methods for measuring wind speed in built-up areas have been tried and their effectiveness has been reported in the literature. Such methods included erosion techniques where the local wind speed is inferred from the scour patterns formed on surfaces covered by various types of particles; thermography; visual patterns of tracer gas; hot-wire and hot-film sensors; and others. While shown to provide reliable information most of these methods are time consuming and therefore not cost effective. Dr. H.P.A.H. (Peter) Irwin devised a simple sensor which measures the pressure difference between ground level and the height of a typical pedestrian. This pressure difference is calibrated to provide a measure the horizontal wind speed at the location of the sensor. Dr. Irwin has published details of this sensor and its performance relative to measurements made with a hot-wire anemometer [25].
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This sensor, is now commonly referred to as the “Irwin Sensor”. Its simplicity has made it the instrument of choice for most commercial wind tunnel testing laboratories. These sensors are inexpensive and measurements of pedestrian level wind speeds can be carried out as part of the pressure tests made to determine the local pressures on the cladding and curtain wall. It is not surprising therefore that the use of “Irwin Sensors” is routinely mentioned or implied in request for proposal issued in the commercial wind engineering community. While I was initially apprehensive about the accuracy this sensor in areas of strong updraft and/or downwash, I became a convert to the use of this device. It is very difficult to argue in favour of hot-film anemometry, which has been the previous standard method of measurement, once it was shown that the “Irwin sensor” provided comparable information at a fraction of the effort and cost. To the best of my knowledge, Dr. Peter Irwin is the only living individual to have been thus honoured during his lifetime. Dimensionless numbers, methods of measurement and analysis, chains, etc. are usually named posthumously.
4.0 WIND SPEED SCALES 4.1 General It is fitting to close this paper with reference to the terminology which is use to describe and categorize different types of wind storms and to indicate their severity and potential impact on the natural and built environment. Readily available electronic search engines can provide historic perspectives of various types of wind and the scales which are used by weather forecasters, the news media and the public to describe their effects. No further references are therefore provided. Currently used scales to describe wind storms are limited to wind speeds experienced in extra-tropical and tropical cyclones and in tornadoes. No scales are yet available to categorize other types of wind. 4.2 The Beaufort scale The Beaufort scale was formally introduced in 1805 by Sir Francis Beaufort, a Rear Admiral in the British navy. It was intended to help mariners to gauge the severity of the wind and its effect on the state of the sea. The scale ranges from a Beaufort Number 0 which corresponds to calm conditions to a Beaufort Number 12, which corresponds to hurricane force winds with a sustained speed of 64 knots or 74 mph (33m/s) and higher. The initially proposed scale of wind speed over water was subsequently extended to also describe wind speeds and their effects over land. Also, the sustained wind speeds quoted at the standard anemometer height of 10m were adjusted downwards to height of a typical pedestrian (1.7 to 1.8 m). This land based version has been a valuable point of reference for criteria and guidelines which are used by various commercial wind tunnel testing laboratories to judge the acceptability of wind conditions in pedestrian areas. Extracts from the Beaufort scale are helpful in conveying the consequences of different wind speeds to architects, developers and the public. For example, this scale suggests that a “light breeze” with a sustained pedestrian level wind speed of about 2 m/s is “felt on the face and causes leaves to rustle”. A “strong breeze” with a corresponding speed of about 10 m/s “causes large tree branches to move and makes the use of umbrellas difficult”. A valuable overview of winds in cities can be found in Reference [26] 4.3 The Saffir-Simpson Hurricane scale The Saffir-Simpson Hurricane scale is an extension to the Beaufort scale and describes wind speeds in hurricanes and their consequences after they make landfall. This scale was developed by Herbert Saffir, a Florida civil engineer, from observations of damage to buildings and structures in the aftermath of specific hurricanes. The intention of this scale was to describe the damage potential of hurricanes a way similar to how the Richter scale describes the damage potential of earthquakes. This hurricane wind scale was formally proposed in 1971 by Herb Saffir and Robert Simpson, a meteorologist and Director of the U.S. National Hurricane Center. The scale was named in their honour. The scale underwent several modifications before its final adoption. I am fortunate to have personal recollections of the gestation of the scale. Herb Saffir regularly reported on its progress at meetings of the Aerodynamics Committee of the ASCE Aerospace Division. I too, was a member of that committee. Herb was a productive and highly motivated member of our committee and he chaired a special Sub-Committee on Wind Damage Investigation. Herb Saffir died on November 23, 2007 but will be remembered for his dedication to bring clarity to the description of hurricanes and their effects on the built and natural environments. The Saffir-Simpson scale starts with a Hurricane Category 1 which is a continuation of Beaufort scale Number 12 and is expected to packs sustained wind speeds in the range of 64 to 82 knots (74 to 95 mph). A Category 1 Hurricane is expected to create dangerous winds which can cause some damage. It is assigned a damage potential of “minimal”. The most severe wind storm on the Saffir-Simpson scale is a Category 5 Hurricane, which is classified to have sustained wind speeds of 135 knots and higher (> 69 m/s or >155 mph) and a damage potential referred to as “catastrophic”. 4.4 The Fujita scale The Fujita or sometimes called Fujita-Pearson Tornado Scale is intended to categorize wind speeds in tornadoes and the resulting damage to the natural and built environments. It was introduced in 1971 by Professor Tetsuya Theodore Fujita of the University of Chicago. The wind speed intervals of the scale were determined from the analysis of many recorded tornado events and the ensuing damage. Apparently, Professor Fujita wanted to devise a continuous scale which would extend the Beaufort scale to wind speeds upwards towards a Mach number of M = 1. The speed of sound at sea level and at standard atmospheric pressure is about 340 m/s. Constrained by available damage information the Fujita Scale ended up with a scale
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with 5 categories. It started with a F0 tornado with estimated speed of 40 to 72 mph (18 to 32 m/s) which could cause “light” damage and continued to a F5 tornado with estimated speeds of 261 to 318 mph (117 to 142 m/s) which was expected to cause “incredible “ damage. This Fujita scale was revisited as more data became available and was re-issued as the Enhanced Fujita Scale with 6 categories. Wind speeds in an EF0 tornado are expected to range from 29 to 37 m /s. Wind speeds in an EF5 tornado are expected speeds of exceed 90 m/s. Wind speeds expected during an EF2 tornado are in the range of 50 to 60 m/s and are comparable to basic wind speeds which are used for the design of structures. However, the difference in the performance of buildings and structures in tornadic versus “straight-line” winds remains unclear. 4.5 Straight-line versus tornadic winds Tornadoes are transient wind phenomena in which an intense vortex with a vertical axis moves horizontally with a translational velocity which is relatively low in comparisons with the maximum horizontal wind speed within the vortex. The width, track length and duration of such storm events are relatively short and details of their flow field are distinctly different from those of tropical and extra-tropical cyclones. These cyclonic storms are large scale low pressure systems in which the flow at any particular location can be approximated by a “straight-line” turbulent boundary layer flow, which has been shaped by the surface roughness of the terrain over which they pass. The consequences of both tropical and extra-tropical winds can be effectively studied in conventional wind engineering wind tunnels. On the other hand the effects on buildings and structures during the passage of a tornado, which is a cell of rotating or “swirling” wind a core pressure much lower than the atmospheric pressure, are still not fully understood. So far the studies of tornadic winds have relied on CFD (computational fluid mechanics) methods and physical experiments in facilities referred to as tornado simulators. This is a relatively young but rapidly growing branch of wind engineering. It is important to point out that while current methods for the design of buildings and structures are based on the action of straight-line winds, tornadoes, downbursts and other intense types of local wind storms very much contribute to the wind damage inflicted on our built and natural environments. Details about such unusual storms still lie in uncharted waters and the development of rational methods for estimating their effects remains an important challenge for wind engineers. One aspect of this challenge will be to decide how to best allow for the compressibility of air in experiments carried out at a reduced scale. The prototype Mach numbers for Category 5 Hurricane winds are M = 0.2 (M = 69/340 = 0.2) and higher. The prototype Mach numbers for winds in EF5 tornado winds are M = 0.26 (M = 90/340 = 0.26) and higher. Compressibility effects can no longer be disregarded at such Mach numbers and the air density can no longer be treated as invariant. I look forward with interest to the keynote address on the subject of tornadic winds and their effects which will be presented at this conference by Dr. Horia Hangan, Director of the WINDEEE Research Institute of Western University in London, Ontario, Canada.
5 CONCLUDING REMARKS This overview paper has presented aspects of the wind engineering terminology which have been selected to reflect my interests and experience. These include estimates of wind-induced loads and responses of buildings and structures, their modeling in wind tunnels and the subsequent prediction of design values. There are other areas of wind engineering, such as atmospheric diffusion and air quality; wind energy; meteorology; and CFD modeling, which have received only scant mention but which are also important parts of our discipline. The main purpose of this paper was to present the background of specific parts of our terminology; to draw attention to their physical meaning; to discuss the practical limitations which they impose; and to comment on the consequences of not observing recommended limits. Familiarity with of our terminology is important in order to improve communications and to better convey and explain ideas. In this process, it is important to look back and recognize past achievements. It is also important to remain flexible and to make adjustments to our terminology, as needed. For example, based on the feedback from the wind engineering community the term “The Alan G. Davenport Wind Loading Chain” which was adopted at ICWE 13 is judged to be too long and cumbersome. In response, it is proposed to shorten the name of this term to be simply known as the “Davenport Chain”. It is hoped that this simplification will encourage greater use. Finally, it is expected that future developments in wind engineering will generate new concepts and methods of solution. It is important that we properly recognize and honour such future contributions and expand our terminology accordingly.
ACKNOWLEDGMENTS The efforts of Ms. Karen Norman, Administrative Assistant to the Boundary Layer Wind Tunnel Laboratory, towards the preparation and submission of this paper are gratefully acknowledged. Also acknowledged are contributions made by my colleagues Drs. Peter King and Eric Ho and Messrs. Peter Case and Steven Farquhar.
REFERENCES [1] E. Simiu and R. H. Scanlan, Wind Effects on Structures, John Wiley & Sons, New York, 1986. [2] ASCE Manual of Practice No. 67, Wind Tunnel Studies of Buildings and Structures, Reston, Virginia, 1999. [3] M. Jensen, The Model Law for Phenomena in Natural Wind, Ingenioren, International, Edition,2,121-128 [4] N.J. Cook, Jensen Number: a proposal, Journal of Wind Engineering and Industrial Aerodynamics, 22 (1986) 95-96. [5] A. G. Davenport, Martin Jensen: An Appreciation, Journal of Wind Engineering and Industrial Aerodynamics, 41-44, 1992, 15-22, Elsevier. [6] J.E. Cermak, Physical modeling of the atmospheric boundary layer (ABL) in long boundary layer wind tunnels (BLWT), Wind Tunnel Modeling for Civil Engineering Applications, Cambridge University Press, Cambridge 1982.
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[7] N.J. Cook, Simulation techniques for short test-section wind tunnels: roughness, barrier and mixing device methods, Wind Tunnel Modeling for Civil Engineering Applications, Cambridge University Press, Cambridge, 1982. [8] ASCE Standard ASCE/SEI 49-12, Wind tunnel testing for buildings and other structures, Reston, Virginia, 2012. [9] D. Surry, Consequences of Distortions in the flow including mismatching scales and intensities of turbulence, Wind Tunnel Modeling for Civil Engineering Applications, Cambridge University Press, Cambridge, 1982. [10] O.G. Sutton, Micrometeorology, McGraw-Hill Book Company, Inc. New York, N.Y., 1953. [11] J. Nikuradse, Verhandl. Deut. Ing. Forschung, 361, 1933. [12] C. Scruton, On the wind-excited oscillations of stacks, towers and masts, Proceedings International Conference on Wind Effects on Buildings and Structures, NPL, June 1963. [13] M.M. Zdravkovich, Scruton Number: a proposal, Journal of Wind Engineering and Industrial Aerodynamics, 10, 1982, 263-265. [14] L. R. Wooton, C.S. Scruton Memorial Lecture, Journal of Wind Engineering and Industrial Aerodynamics, 41-44 1992, 3-14, Elsevier. [15] R.D. Blevins, Flow-induced vibrations, Van Nostrand Reinhold, New York, 1990. [16] V. Strouhal, Ueber eine besondere Art der Tonerregung, Annalen der Physik und Chemie, 3rd Series, 5(10): 216-251. [17] ESDU 96030, Response of structures to vortex shedding. Structures of circular or polygonal section section, [18] R.E. Whitbread, Model simulation of wind effects on structures, Proceedings International Conference on Wind Effects on Buildings and Structures, NPL, June 1963. [19] N. Isyumov, The Aeroelastic Modeling of Tall Buildings, Wind Tunnel Modeling for Civil Engineering Applications, Cambridge University Press, Cambridge, 1982. [20] A.G. Davenport, N. Isyumov, D.J. Fader and C.F.P. Bowen, A study of wind action on a suspension bridge during erection and on completion, Boundary Layer Wind Tunnel Laboratory Research Report BLWT-3-69, University of Western Ontario, London, Ontario, Canada, May 1969. [21] A.G. Davenport, N. Isyumov and T. Miyata, The experimental determination of the response of suspension bridges to turbulent wind, Proceedings 3rd International Conference on Wind, Tokyo, Japan, 1971 . [22] Associate Committee on the National Building Code, “National Building Code of National Canada 1970”, National Research Council of Canada, NRC No. 11246. [23] N. Isyumov, Alan G. Davenport’s mark on wind engineering, Journal of Wind Engineering and Industrial Aerodynamics, Vol. 104-106, pgs. 12-24 (2012), Elsevier. [24] Masao Tachikawa, Trajectories of flat plates in uniform flow with application to wind-generated missiles, Journal of Wind Engineering and Industrial Aerodynamics, 14, 1983, 443-453. [25] H.P.A.H/ Irwin, A simple omnidirectional sensor for wind tunnel studies of pedestrian level winds, Journal of Wind Engineering and Industrial Aerodynamics. Vol. 7, 1981, pp. 219-239. [26] ASCE Task Committee on Urban Aerodynamics, Urban aerodynamics, American Society of Civil Engineers, Reston, Virginia, 2011.
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