Water Hammer Contents

KSB Know-how, Volume 1

Table of Contents Page 1 Introduction ...... 3 2 General - The Problem of Water Hammer ...... 4 2.1 Steady and Unsteady Flow in a Pipeline ...... 4 3 Water Hammer ...... 6 3.1 Inertia ...... 6 3.2 Elasticity of Fluid and Pipe Wall ...... 7 3.3 Resonance ...... 10 4 The Joukowsky Equation ...... 11 4.1 Scope of the Joukowsky Equation ...... 12 5 Numerical Simulation of Water Hammer ...... 15 5.1 Accuracy of Numerical Surge Analysis ...... 15 5.2 Forces Acting on Pipelines as a Result of Water Hammer . .16 6 Computerised Surge Analysis ...... 17 6.1 Technical Procedure ...... 17 6.2 Interaction between Ordering Party and Surge Analyst . . .17 7 Advantages of Rules of Thumb and Manual Calculations .18 8 Main Types of Surge Control ...... 20 8.1 Energy Storage ...... 20 8.1.1 Air Vessels ...... 20 8.1.2 Standpipes, One-Way Surge Tanks ...... 21 8.1.3 Flywheels ...... 22 8.2 Air Valves ...... 23 8.3 Actuated Valves ...... 23 8.4 Swing Check Valves ...... 24 9 Case Studies ...... 25 9.1 Case Study: Long-Distance Water Supply System ...... 25 9.2 Case Study: Stormwater Conveyance Pipeline ...... 26 Model Parameters ...... 26 Calculation of Actual Duty Data, First Results ...... 27 Surge Control Measures ...... 28 10 Additional Literature ...... 30 Authors ...... 30

Introduction 1

1 Introduction thing is clear: the damage caused • How significant are approxi- by water hammer by far exceeds mation formulas for calculat- Most engineers involved in the the cost of preventive analysis ing water hammer? planning of pumping systems and surge control measures. are familiar with the terms “hy- • Can the surge analysis of one draulic transient”, “surge pres- The ability to provide reliably piping system be used as a sure” or, in water applications, designed surge control equip- basis for drawing conclusions “water hammer”. The question ment, such as an air vessel or for similar systems? accumulator1, flywheel and air as to whether a transient flow or • Which parameters are required valve, has long been state of the surge analysis is necessary dur- for a surge analysis? ing the planning phase or not is art. The technical instruction less readily answered. Under un- leaflet W 303 “Dynamic Pres- • What does a surge analysis favourable circumstances, dam- sure Changes in Water Supply cost? age due to water hammer may Systems” published by the Ger- • How reliable is the surge con- occur in pipelines measuring man Association of the Gas and trol equipment available and more than one hundred metres Water Sector clearly states that how much does it cost to ope- and conveying only several pressure transients have to be rate it? tenths of a litre per second. But considered when designing and • How reliable is a computerised even very short, unsupported operating water supply systems, analysis? pipelines in pumping stations because they can cause extensive can be damaged by resonant damage. This means that a surge System designer and surge vibrations if they are not analysis to industry standards analyst have to work together properly anchored. By contrast, has to be performed for every closely to save time and money. the phenomenon is not very hydraulic piping system at risk Water hammer is a complex common in building services from water hammer. Dedicated phenomenon; the purpose of systems, e.g. in heating and software is available for this this brochure is to impart a drinking water supply pipelines, purpose – an important tool for basic knowledge of its many which typically are short in the specialist surge analyst to aspects without oversimplifying length and have a small use. Consultants and system them. cross-section. designers are faced with the following questions, which we The owners or operators of sys- hope to answer in this brochure: tems affected by water hammer are usually reluctant to pass on • How can we know whether information about any surge there is a risk of water ham- damage suffered. But studying mer or not? the photos taken of some “acci- dents” (Figs. 1-a, 1-b, 1-c) one

Fig. 1-a: Completely destroyed Fig. 1-b: Destroyed support Fig. 1-c: DN 800 check valve DN 600 discharge pipe (wall (double T profile 200 mm, per- following a pressure surge in the thickness 12 mm) manently deformed) discharge pipe

1 Air vessels, sometimes also called “accumulators”, store potential energy by accumulating a quantity of pressurised hydraulic fluid in a suitable enclosed vessel.

3 2 General – The Problem of Water Hammer

2 General – The problem of With a constant pipe diameter or pressure transients. The main water hammer and a constant surface rough- causes of transient flow ness of the pipe’s inner walls, the conditions are: 2.1 Steady and unsteady flow pressure head curve will be a in a pipeline • Pump trip as a result of straight line. In simple cases, a switching off the power supply When discussing the pressure of pump’s steady-state operating or a power failure. a fluid, a distinction has to be point can be determined graphi- made between pressure above cally. This is done by determin- • Starting or stopping up one or atmospheric [p bar], absolute ing the point where the pump more pumps whilst other pressure [p bar(a)] and pressure curve intersects the piping cha- pumps are in operation. head h [m]. Pressure head h de- racteristic. • Closing or opening of shut-off notes the height of a homogene- A pumping system can never be valves in the piping system. ous liquid column which gener- operated in steady-state condition ates a certain pressure p. Values • Excitation of resonant vibra- all the time, since starting up and for “h” are always referred to a tions by pumps with an un- stopping the pump alone will datum, (e.g. mean sea level, axi- stable H/Q curve. change the duty conditions. al centreline of pipe and pipe • Variations of the inlet water Generally speaking, every change crown etc.). level. in operating conditions and every As a rule, system designers start disturbance cause pressure and Fig. 2.1-b may serve as a repre- by determining the steady-state flow variations or, put differently, sentative example showing the operating pressures and volume cause the flow conditions to pressure envelope3 with and rates of flow. In this context, the change with time. Flow condi- without an air vessel following term steady2 means that volume tions of this kind are commonly pump trip. rates of flow, pressures and referred to as unsteady or pump speeds do not change with transient. Referring specifically to time. Fig. 2.1-a shows a typical pressures, they are sometimes steady flow profile: called dynamic pressure changes

MetresKote mabove sea level

stationäreSteady-state Druckhöhenlinie pressure head curve

h NN+m hm

LängeLength

Fig. 2.1-a: Steady-state pressure head curve of a pumping system

2 Not to be confused with the term “static”. 3 The term “pressure envelope” refers to the area defined by the minimum and maximum head curves along the fixed datum line resulting from all dynamic pressures occurring within the time period under review.

4 General – The Problem of Water Hammer 2

hsteady in Fig. 2.1-b is the steady- pipe“) and is, therefore, inadmis- We will come back to the sub- state pressure head curve. Pressu- sibly high. As a rule, vapour ject of macro-cavitation, i.e. re head envelopes hminWK and pressure is a most undesirable liquid column separation, in hmaxWK were obtained from an in- phenomenon. It can have the fol- section 3.1. stallation with, hmin and hmax lowing harmful effects: from an installation without air • Dents in or buckling of thin- vessel. Whereas h and minWK walled steel pipes and plastic h are within the permissible maxWK tubes. pressure range, hmin gives evi- dence of vapour pressure (macro- • Disintegration of the pipe’s cavitation) over a pipe distance cement lining. from 0 m to approximately • Dirty water being drawn into 800 m. Almost across the entire drinking water pipelines length of the pipe, the value of through leaking connecting hmax exceeds the maximum per- sockets. missible nominal pressure of the pipe PN 16 (curve marked “PN

Pipe length L: 2624 m

Inside diameter of pipe Di: 605.2 mm Steady-state flow rate: 500 l/s

Hpump sump: 287.5 m

Houtlet: 400 m Air vessel inlet pipe 3 3 with a bypass and a non-return valve: Vair = 3.8 m , Vwater = 6.2 m 700 hmax

600

PN Pipe 500

hmax WK 400 hsteady hmin WK Elevation of pipe Metres above sea level [m] Metres 300

hmin

200 0 500 1000 1500 2000 2500 Length of pipe [m]

Fig. 2.1-b: Pressure head envelope of pressure transients following pump trip

5 3 Water Hammer · Inertia

3 Water hammer Pressure rise: This is more or less the same as the weight of a truck; v = 3 m/s Pressure transients are also re- • Pipe rupture corresponds to 11 km/h. In ferred to as surge pressure or, if • Damaged pipe fixtures other words, if the flow is sud- referring to water systems, water denly stopped, our truck – to hammer. The latter term suitably • Damage to pumps, founda- put it in less abstract terms – reflects the harmful effects that tions, pipe internals and valves runs into a wall (closed valve) at the hammer-like blows accom- Pressure fall: 11 km/h (water mass inside the panying the pressure surges can • Buckling of plastic and thin- pipe). In terms of our pipeline, have on pipes and system com- walled steel pipes this means that the sequence of ponents. Water hammer causes events taking place inside the piping, valves, pipe fixtures, sup- • Disintegration of the cement pipe will result in high pressures ports, system components, etc. to lining of pipes and in high forces acting on the suffer the added strain of dynamic • Dirty water or air being drawn shut-off valve. loads. The term “water hammer” into pipelines through flanged As a further example of inertia, is used to describe the phenome- or socket connections, gland Fig. 3.1-a shows a pump dis- non occurring in a closed conduit packing or leaks when there is either an accelera- charge pipe. At a very small tion or retardation of the flow. In • Water column separation moment of inertia of pump and contrast to a force, pressure is followed by high increases in motor, the failing pump comes non-directional; i.e. it does not pressure when the separate to a sudden standstill, which has have a vector. Not until a hydro- liquid columns recombine the same effect as a suddenly static pressure starts acting on a (macro-cavitation) closing gate valve, only this time limiting area, is a force exerted in 3.1 Inertia on the downstream side of the the direction of the area normal. gate valve. If mass inertia causes The sudden closure of a valve in the fluid flow on the down- As it is not possible to altogether a pipeline causes the mass iner- stream side of the pump to avoid pressure transients when tia of the liquid column to exert collapse into separate columns, operating a piping system, the a force on the valve’s shut-off a cavity containing a mixture of art lies in keeping the pressure element. This causes the pres- water vapour and air coming transients within controllable sure on the upstream side of the out of solution will be formed. limits. What makes matters even valve to increase; on the down- As the separate liquid columns more complex is the fact that stream side of the valve the pres- subsequently move backward the damage caused by impermis- sure decreases. Let us consider and recombine with a hammer- sibly high surge pressures is not an example: for a DN 200 pipe, like impact, high pressures deve- always visible. Often the conse- L = 900 m, v = 3 m/s, the vol- lop. The phenomenon is referred quences do not become apparent ume of water in the pipeline is to as liquid column separation until long after the event, for calculated by or macro-cavitation4. example a pipe rupture, loose or 0.22 disconnected flanges. The root m = ––––- · 900 · 1000 = 28274 kg (1) water 4 cause of damage then tends to remain in the dark. Some representative incidents caused by water hammer are listed in the following:

4 Macro-cavitation in pipelines is not to be confused with microscopic cavitation causing pitting corrosion on pump and turbine blades. The latter always strikes in the same place and is characterised by local high pressures of up to 1000 bar or more that develop when the microscopically small vapour bubbles collapse. With macro-cavitation, repetitive strain of this kind, or the bombarding of a sharply contoured area of the material surface, does not occur since the pressure rises are considerably lower. 6 Elasticity of Fluid and Pipe Wall 3

1. Steady-state condition prior 2. Formation of a vapour pocket 3. High-impact reunion of separate to pump trip (cavitation cavity) following pump trip liquid columns accompanied by surge pressures

Fig. 3.1-a: Macro-cavitation following pump trip

3.2 Elasticity of fluid and pipe wall The attempt at visualising water hammer resulting from the inertia of a body of water made in section 3.1 is only partly correct, s in t because no allowance was made 1 1 for the elasticity of fluid and pipe wall. As long as safety belts are worn and the barrier impact s2 in t2 speed is not too high, even a head-on collision will not put drivers in too much danger s3 in t3 today, because the vehicle’s momentum is converted to harm- Fig. 3.2-a: Sudden closure of gate valve, visualised by a heavy steel 5 less deformation heat . Contrary spring to the body of a car, however, water and pipe walls are elastic, The front end deformation trav- which is shown in Fig. 3.2-b, even though they are so hard els in the opposite direction to with friction being neglected. that this property is not notice- the original direction of move- The shut-off valve installed at able in every day use. ment at the speed typical for the the downstream end of a hori- What actually goes on inside the steel spring, i.e. wave propaga- zontal pipeline with a constant pipe will, therefore, be described tion velocity a in m/s. In the inside diameter, which is fed using the following example of a compression zone, the velocity from a reservoir at constant heavy steel spring sliding of the steel spring is v = 0 pressure, is suddenly closed: through a pipe. This spring suf- everywhere. fers elastic deformation when it Following these, admittedly is suddenly stopped (Fig. 3.2-a): poor but hopefully helpful, examples chosen to illustrate the subject, we will now go back to the real situation inside the pipe,

5 To withstand the regular pushing and shoving over rare parking spaces, cars have to be elastic. To minimise the damage of a collision at high speed, however, carmakers spend vast amounts of time and money to make their products as inelastic as possible!

7 3 Elasticity of Fluid and Pipe Wall

1 3 1 For t = 0, the pressure profile At t = /2Tr the pressure wave t = 0 L 1 is steady, which is shown by has arrived at the reservoir. the pressure head curve run- As the reservoir pressure p = ning horizontally because of constant, there is an unbal- the assumed lack of friction. anced condition at this point. Under steady-state condi- With a change of sign, the v = v0 1 0 < t < /2Tr tions, the flow velocity is v0. pressure wave is reflected in ∆ 2 the opposite direction. The h 2 The sudden closure of the flow velocity changes sign gate valve at the downstream and is now headed in the end of the pipeline causes a direction of the reservoir. v = v0 v = 0 pulse of high pressure h; 1 t = /2Tr and the pipe wall is stretched. 4 A relief wave with a head of 3 ∆h The pressure wave generated -h travels downstream runs in the opposite direction towards the gate valve and

to the steady-state direction reaches it at a time t = Tr. It is v = 0 of the flow at the speed of accompanied by a change of 1 /2Tr < t < Tr sound and is accompanied by velocity to the value -v0. -∆h 4 a reduction of the flow veloc- 5 Upon arrival at the closed ity to v = 0 in the high pres- gate valve, the velocity sure zone. The process takes changes from -v0 to v = 0. place in a period of time v = -v0 v = 0 This causes a sudden negative 0 < t < 1/2 T , where T is the t = Tr r r change in pressure of -h. amount of time needed by the 6 5 pressure wave to travel up The low pressure wave - h and down the entire length of travels upstream to the reser- 3 the pipeline. The important voir in a time Tr < t < /2Tr, v = -v0 and at the same time, v 3 parameter Tr is the reflection Tr < t < /2Tr time of the pipe. It has a adopts the value v = 0. 6 -∆h value of 2L/a. 7 The reservoir is reached in a 3 time t = /2Tr, and the pressure resumes the reservoir’s v = -v0 v = 0 t = 3/2T pressure head. r Fig. 3.2-b: Pressure and velocity 8 In a period of time 3/2T < t < 7 waves in a single-conduit, fric- r -∆h 2T , the wave of increased tionless pipeline following its r pressure originating from the sudden closure. The areas of reservoir runs back to the v = 0 steady-state pressure head are 3 gate valve and v once again /2Tr < t < 2Tr shaded medium dark, those of adopts the value v . 8 increased pressure dark, those of 0 -∆h 9 reduced pressure light. The ex- At t = 2Tr , conditions are pansion and contraction of the exactly the same as at the

v = v0 v = 0 pipeline as a result of rising and instant of closure t = 0, and t = 2Tr falling pressure levels, respec- the whole process starts over tively, are shown. To give an again. 9 idea of the relationship involved: With a 100 bar pressure rise, the

v = v0 volume of water will decrease by about 0.5%.

8 Elasticity of Fluid and Pipe Wall 3

So, one might ask, what hap- condition prevailing at t = 2Tr. If L = 100 m, DN 100, k = 0.1 mm, pened to the original steady-state the gate valve were to be sudden- hinlet = 200 m, linear throttling of kinetic energy of the fluid follow- ly opened at this point, we would Q = 10 l/s at the outlet of the ing the sudden closure of the gate have the old steady-state condi- pipe to Q = 0, starting at t = 0.1 s valve? A closer look at Fig. 3.2-b tion at t = 0 again without in a period of time t = 0.01 s. will reveal the answer. According change, and there would be no Based on Fig. 3.2-b, the reflec- to the law of the conservation of elastic energy left. tion of pressure waves at the up- energy, it cannot simply disap- Without friction, the pressure stream and downstream ends of pear. First it is converted into fluctuations would not diminish. the pipeline can be explained in elastic energy of the fluid and the In actual fact, no system is ever a general manner as follows: pipe wall, then changes into ki- entirely without friction, but the netic energy again as a result of • If a pressure wave p reaches reduction in pressure fluctuation reflection, then becomes elastic the closed end of a pipe, p is relatively small in reality, be- energy again, and so forth. Let’s becomes twice the amount cause the energy conversion into look at Fig. 3.2-b up to the point with the same sign, i.e. p = frictional heat as a result of the where t = 1/2T . The conversion p ± 2· p. The velocity at the r fluid rubbing against the pipe into elastic energy takes place pipe ends is always v = 0. walls, the inherent fluid friction within this period of time. Im- and, finally, the deformation of • At the open end of a pipe with mediately preceding the reflec- pipe walls and fixtures is rela- a constant total head (e.g. res- tion of the wave at the reservoir, tively small. ervoir with a constant water the velocity of the liquid column level), the pressure change al- To show the process in a less is v = 0 everywhere, and it is ways equals zero. totally devoid of kinetic energy. abstract manner, Fig. 3.2-c pro- • At valves, throttling sections, Instead, the kinetic energy has vides the results of a computer- pumps and turbines, pressure been changed into elastic energy, ised simulation of the example and velocity are always found comparable to the situation of a given in Fig. 3.2-b for a real on the resistance or machine compressed steel spring. The en- pipeline with the following para- characteristic curve. ergy conversion in reverse also meters: becomes apparent from Fig. 3.2-b – specifically from the

360

300 Fig. 3.2-c: Pressure head upstream of gate valve. Compared 240 with the situation shown in Fig. 3.2-b, small differences are apparent. For example, the pres- 180 sure flanks are not perfectly per- pendicular, because of the finite 120 closing time of t = 0.01 s. As a result of friction, the pressure planes are not perfectly horizon-

Pressure head above pipe centreline at outlet [m l.c.] 60 tal – this phenomenon will be 0 0.20 0.40 0.60 0.80 1.00 discussed in greater detail in sec- Time [s] tion 4.1.

9 3 Elasticity of Fluid and Pipe Wall • Resonance

Water hammer occurs when the kinetic energy of a fluid is converted into elastic energy. But only rapid6 changes of the flow velocity will produce this effect, for example the sudden closure of a gate valve or the sudden failure or tripping of a pump. Due to the inertia of the fluid, the flow velocity of the liquid column as a whole is no longer capable of adjusting to the new situation. The fluid is deformed, with pressure transients accompanying the deformation process. The reason why surge pressure is so dangerous is that it travels at the almost undiminished speed of sound (roughly 1000 m/s for a large number of pipe materials) and causes destruction in every part of the piping system it reaches.

Surge pressures travel at a very pump. Immediately following sections in pumping installations high wave propagation velocity, pump trip, the air cushion starts are particularly prone to reso- for example a = 1000 m/s in expanding and takes over the nant vibrations transmitted by ductile or steel piping (see 4.1). pump’s job of discharging the the fluid pumped and by the They dampen out only gradually water into the pipeline. Provided piping structure. By contrast, and, therefore, remain danger- that the vessel is properly resonance is all but negligible ous for a long time. The time designed, it will prevent rapid for buried piping. In order to needed to subside depends on changes in the flow velocity in design adequately dimensioned the length of the pipeline. In an the pipeline. Instead, the water anchoring, all pipe anchors in urban water supply installation, level in the vessel and the pumping installations should be they only last several seconds. In undeformed liquid column in examined using structural long pipelines, it can take a few the pipeline will continue to rise dynamics analysis, with the minutes until a pressure surge and fall over a longer period of pump speed serving as the has dampened out. time. The process is kept in exciter frequency. motion by the energy discharged Knowing these facts, the basic by the air cushion each time working principles of all surge fluid flows out of the vessel and control equipment, such as air by the energy absorbed again by vessel or accumulator, flywheel, the air cushion on the fluid’s standpipe and air valves can be return. The energy stored in the deduced. They prevent the dan- air cushion is only gradually gerous conversion of steady- dissipated. That is why it takes state kinetic energy into elastic many minutes for air vessel deformation energy. Air vessels oscillations to die away, in are ideally suited to explain the longer pipelines in particular. underlying principle. The pressurised air cushion in the air vessel stores potential energy. If 3.3 Resonance there were no air vessel, the dreaded conversion of kinetic Resonant vibrations are an energy into elastic deformation exception. These occur when ex- energy following a pump trip citer frequencies of whatever would take place at the pump origin, generated, for example, outlet, which could cause the by the pump drive or by flow liquid column to separate separation phenomena in valves (Fig. 3.1-a). However, this does and pipe bends, happen to not happen, because the energy coincide with a natural frequen- stored in the air cushion in the cy of the pipeline. Improperly vessel takes over the work of the anchored, unsupported pipeline

6 The adjective “rapid” is to be seen in relation to the system’s operating conditions. For example, the pressure transients caused by the closure of a valve in a 2 km long pipeline may well stay within the permissible range, whereas the same closing process could generate unacceptably high pressures in a 20 km long pipeline.

10 The Joukowsky Equation 4

4 The Joukowsky equation with their small diameters and lengths are usually negligible. In The pressure change Dp in a Jou these systems, the kinetic energy fluid caused by an instantaneous levels and fluid masses are very change in flow velocity Dv is cal- small. In addition, it is practical- culated by: ly impossible to close a valve within the very short reflection (4.1) time of a domestic water system. The Joukowsky equation can be used to calculate simple esti- Dv:Flow velocity change in m/s mates. Let’s consider three r: Density of the fluid in kg/m3 examples: a: Wave propagation velocity Example 1: through the fluid in the Nikolai Egorovich Joukowsky In a DN 500 pipeline, L = 8000 m, pipeline in m/s results of his various experi- a = 1000 m/s and v = 2 m/s, a D 2 pJou: pressure change in N/m ments and theoretical studies in gate valve is closed in 5 seconds. D 1898. Calculate the pressure surge. The pJou formula is referred to Calculate the force exerted on as the Joukowsky equation. As It may seem inconsistent that the gate. well as Dv, equation (4.1) con- D pJou in the Joukowsky equation tains the density r and wave (4.1) seems to have nothing to Answer: propagation velocity a. The rela- do with the mass of the flow in- 5 s < T = 16 s, i.e. Joukowsky’s tionship only applies to the pe- r side the pipeline. For example, if equation may be applied. If the riod of time in which the veloc- the water hammer described in flow velocity is reduced from ity change Dv is taking place. If the first example in section 3.1 2 m/s to zero as the valve is Dv runs in opposite direction to had been based on a pipe dia- closed, Dv = 2 m/s. This gives us a the flow, the pressure will rise, meter twice that of the diameter pressure increase Dh = 100 · 2 = otherwise it will fall. If the 2p used, A = D /4 would have 200 m or approximately Dp = liquid pumped is water7, i.e. caused the fluid mass and its 20 · 105 N/m2, which is 20 bar. r = 1000 kg/m3, equation (4.1) kinetic energy to turn out four The valve cross-section measures will look like this: times as large. What seems to be A = D2 · 0.25 · p Ä 0.2 m2. The a paradox is instantly resolved if force acting on the gate is p·A = one considers the force exerted 0.2 · 20 · 105 = 4·105 N= 400 kN. (4.2) on the shut-off valve, i.e. force F = Dp · A, the defining parameter for the surge load. Because g: Acceleration due to gravity of A, it is now in actual fact four 9.81 m/s2 times as large as before. D This shows that one must also hJou: Pressure head change in m consider the fluid mass to judge In 1897, Joukowsky conducted the risk of water hammer, al- a series of experiments on Mos- though that does not seem cow drinking water supply pipes necessary after a superficial of the following lengths / dia- glance at Joukowsky’s equation. meters: 7620 m / 50 mm, At the same time, this explains 305 m / 101.5 mm and 305 m / why the pressure surges occur- 152.5 mm. He published the ring in domestic piping systems

7 Despite the high flow velocities common in gas pipes, these do not experience surge problems, because p · a is several thousand times smaller than for water.

11 4 The Joukowsky Equation

Example 2: Example 3: 4.1 Scope of the Joukowsky A pump delivers water at Q = A pump delivers water at Q = equation 300 l/s and a head Dh = 40 m 300 l/s and a head Dh = 40 m The Joukowsky equation only through a DN 400 discharge into a 2000 m long pipeline DN applies to: pipe measuring L = 5000 m into 400; a = 1000 m/s. The mass • Periods of time which are an overhead tank; a = 1000 m/s. moment of inertia8 of all rotat- equal to or shorter than the The inertia moments of pump ing components (pump, motor, reflection time of the piping T and motor are negligible. Is etc.) is J = 20 kgm2, the speed of r -1 there a risk of liquid column rotation n0 = 24 s and the total • The period of time which falls separation, i.e. macro-cavita- efficiency = 0.9, i.e. 90%. Is within the velocity change Dv tion, following pump trip? If so, there a risk of liquid column • Pipes characterised by friction what is the anticipated pressure separation, i.e. macro-cavitation, losses within the limits typical increase? following pump trip? of water transport systems Answer: Answer: Reflection time Tr: Q = 300 l/s in a DN 400 pipe- For the instant of pump failure, . In Fig. 3.2-b the wave of re- line roughly corresponds to a the change in speed n may be deduced pressure reflected by the flow velocity v = 2.4 m/s. As a rived from the inertia equation tank has arrived at the gate result of pump trip and the loss as follows: valve after Tr has lapsed, and of mass inertia moment, the . Mp = 2· ·J·n evens out some of the pressure pump comes to a sudden stand- increase Dp. If the change in D Assuming as an (extremely still, i.e. v = 2.4 m/s. According flow takes place in a period of rough) approximation a linear to the Joukowsky equation, this D . n0 time t longer than Tr, the rise D speed reduction n = ___ , then, if causes a head drop of h = t in pressure Dp will only occur Jou -100 · 2.4 m = -240 m. Since the M = ______p·Q_____ , p 2·n · at the wave’s source, whereas it steady-state head is just 40 m, 0 we obtain a time Dt in which the will have diminished to the vacuum is reached, the liquid speed has dropped to zero, and, value given by the boundary column collapses and macro- if Dp = 1000 · 9.81 · Dh, condition by the time it reaches cavitation sets in. Following the the opposite end of the pipeline. 2 2 liquid column separation near (2 · n0) · J · n0 · J · t = Ä 4 · = 3.4 s the pump outlet, the two liquid p · 0.001 · Q h · Q Fig. 4.1-a shows the pressure en- columns will recombine with The reflection time of the pipe- velope, which applies to a case of this kind: great impact after some time. line is Tr = 4 s (for a = 1000 m/s), For reasons of energy conserva- which means that the reflected tion, the highest velocity of the pressure relief wave will not backward flow cannot exceed reach the pump until after the the original velocity of the speed has dropped to zero and it steady-state flow of 2.4 m/s. is too late for the relieving effect Under the most unfavourable to take place. It is, therefore, conditions, the cavitation-indu- probably safe to say that macro- ced pressure rise will, therefore, cavitation will develop. be Dh = 100 · 2.4 = 240 m, which is the equivalent to 24 bar.

8 Mass moment of inertia J: J expressed in kgm3 is the correct physical quantity. Flywheel moment GD2, which was used in the past, should no longer be used, because it can easily be confused with J!

12 The Joukowsky Equation · Wave Propagation Velocity 4

hmax ∆ hJou

∆ hmin hJou

Fig. 4.1-a: Pressure head envelope for closing times > reflection time Tr

Friction applies, not even within the reflec- The gate valve in the example tion time of the pipeline. In a case shown in Fig. 4.1-b closes 20 s If the liquid pumped is highly like this, the actual pressure rise after the start of the calculation. viscous or if the pipeline is ex- following the sudden closure of a The first steep increase by ap- tremely long (say, 10 km and gate valve can be several times prox. 20 bar to approx. 55 bar more), the work done by the that of Dp as calculated by the is Dp according to the Jou- pump only serves to overcome the Jou Jou Joukowsky equation! The pheno- kowsky equation; the continued friction produced by the pipeline. menon caused by the pipe friction increase to almost 110 bar is Changes of geodetic head due to is commonly called line packing. caused by line packing. Line the pipe profile, by comparison, The following flow simulation packing is only of significance are of little or no importance. The calculation gives an example of for long pipelines or highly Joukowsky equation no longer this: viscous media. It is unlikely to occur in urban water supply and

120 waste water disposal plants.

100

40 Initial pressure, absolute, in bar (approx.)

20 0 80 160 240 320 400 Time [s]

Fig. 4.1-b: Pressure curve at the outlet of a 20 km long crude oil pipeline following a sudden gate valve closure. Calculation parameters: DN 300, k = 0.02 mm, inlet pressure 88 bar constant, Q = 250 l/s, fluid pumped: crude oil, = 900 kg/m3

13 4 The Joukowsky Equation · Wave Propagation Velocity

Wave propagation velocity contained by the fluid, which equation (4.1) does not take into The wave propagation velocity account, can have a strong im- is one of the elements of the Jou- pact on “a”, as is shown by kowsky equation and, therefore, some examples in Table 4-1: In a vital parameter for defining drinking water supply pipelines the intensity of a surge. It is cal- the gas content is negligible; in culated by solving equation waste water installations it nor- (4.1). mally is not. Further elements of uncertainty with regard to “a” m/s (4.1) mainly concern pipes made of synthetic material. An unknown and varying modulus of elastic- 3 : Density of the fluid in kg/m ity, manufacturing tolerances, EF: Modulus of elasticity of the the age of the pipeline and, in fluid in N/m2 particular, the question whether ER: Modulus of elasticity of the the pipeline is laid in the ground pipe wall in N/m2 or not, all play a part. A buried di: Inside pipe diameter in mm pipeline has considerably higher s: Pipe wall thickness in mm values of “a” than a pipe laid : Transverse contraction num- above ground. ber Equation (4.1) produces a range of values from approximately 1400 m/s for steel pipes to around 300 m/s for ductile plastic pipes. Wave propagation velocity “a” in an unconfined body of water is approximately 1440 m/s. To all intents and purposes, the validity of equation (4.1) should not be over- estimated; surge analyses are often performed without it, in which case the value of “a” is estimated. The volume of air

Gas content a % by volume m/s 0 1250 0.2 450 0.4 300 0.8 250 1 240

Table 4-1: “a” as a function of the gas content at a static water pressure of approximately 3 bar

14 Numerical Simulation of Water Hammer Accuracy of Numerical Surge Analysis 5

5 Numerical simulation of water hammer

In current theory, the dependent (5.1) model variables are the pressure p and the flow velocity v in the two partial differential equations (5.1) for every single pipe of a piping system; the time t 5.1. Accuracy of numerical The real energy losses due to and an unrolled reach of pipe x surge analysis friction, and the degree of warp- are independent variables. ing of pipeline and pipe fixtures Computer programs based on the Equations (5.1) are generally valid are somewhat larger than the characteristics method produce and cover the effects of both forecast supplied by simulation. solutions whose accuracy by far inertia and elasticity. Mathema- The first pressure peaks and val- exceeds that which is called for in tically, the pipe ends serve as the leys, therefore, tend to be simu- practice. This is evidenced by boundary conditions of equations lated very precisely, whereas the numerous comparisons with (5.1); different types of boundary pressures further down the line actual measurements. Significant conditions are introduced to in- are on the whole depicted with differences were only found for clude internal components such as an increasing lack of dampen- calculations aimed at predicting pipe branches, vessels, pumps and ing. But imperfections of this macro-cavitation or dampening of valves in the model. For example, kind are negligible compared pressure waves inside a pipe. the creation of a complete piping with inaccuracies caused by system by connecting a number of For example, the pressures com- entering wrong or insufficient individual pipes is done by taking puted using the standard model input data. a pipe node to be the boundary of vapour cavitation derived Some of the potential sources of condition. The starting condition from equations (5.1), i.e. the error are: of equation (5.1) is the steady- assumption of a simple cavity of state flow inside the pipe con- low pressure following liquid • Inaccurate valve and/or pump cerned before the onset of the dis- column separation, are always characteristics. turbance. Equations (5.1) are higher than what they are in real- • Lack of knowledge about the solved by means of the character- ity. However, the advantage of actual wave propagation istics method, which provides the the conservative outcome is that velocity inside the pipeline. basis for almost all surge analysis one is always on the safe side. • Lack of information about software available today. tapping points in a main pipe. The time frame covered by • Unawareness of the degree of equations (5.1) is less appro- incrustation inside the pipes. priate for computing resonant vibrations. These can be calcu- This shows that the quality of lated much more precisely using the surge analysis stands or falls the impedance method, or, in with the accuracy of the input other words, by looking at the data. frequency range.

A surge analysis can only be as accurate as the system data entered as inputs. Only if the input is accurate, and the computation model is a faithful reproduction of the real system conditions, will the analysis yield a high degree of accuracy.

15 Accuracy of Numerical Surge Analysis · 5 Forces Acting on Pipelines as a Result of Water Hammer

In practice, it is often impossible 5.2 Forces acting on pipelines to obtain exact data. If this is as a result of water the case, one has to estimate the hammer required inputs. After computing the time-depen- An example: dent pressure gradients, it takes For a valve manufacturer, a small a further separate step to calcu- individual loss coefficient in the late the forces acting on the el- open condition of a valve is a bows and connections of un- powerful sales argument. By supported pipes. The interaction contrast, for a surge analysis the between fluid and pipe wall does values obtained immediately not enter into the computation preceeding total closure of a (separate calculation). Apart valve are of the essence, and from the odd exception, which measuring these is a time-con- is of no relevance in the field of suming and complex affair. As a water supply and waste water result of this, many individual disposal anyhow, this method loss characteristics available for tends to produce forces which valves do not extend far enough are somewhat higher than what into the closing range. For cost they are in reality, so that the reasons, the individual loss conclusions drawn from the cal- curves provided by most manu- culation results will definitely be facturers are extrapolations, on the safe side. rather than curves plotted on the basis of original measurements. When designing a plant with the aid of surge analyses, inaccuracies of this kind should be ac- counted for by designing the surge control equipment slightly on the conservative side.

16 Computerised Surge Analysis 6

6 Computerised surge analysis 6.2 Interaction between - Piping elevation profile ordering party and surge 6.1 Technical procedure - Lengths analyst A surge analysis will not provide - Diameters First of all, a distinction has to direct solutions for the required be made between the quotation - Wall thickness parameters, such as, for exam- phase and the calculation itself. ple, the optimum air vessel size, - Materials of construction, lining During the quotation phase, the compressor settings, valve clos- material, pipe connections surge analyst requires the ure characteristics, flywheel di- - Pressure class, design pressure following information from the mensions, etc. Instead, the surge head curve plant engineering contractor to analyst must specify the type of compute the cost involved: - Permissible internal pipe pres- surge control to be employed sures (p , p ) and provide estimates of the 1. A rough flow diagram of the min max relevant parameters. After installation indicating all im- - Method used to lay the pipes: checking the outcome of the portant equipment, such as buried or placed on supports surge analysis, the original para- pumps, valves, additional in- - Modulus of elasticity of pipe meters are suitably adjusted and let and outlet points, as well materials a complete re-run of the surge as any existing safety devices, analysis is made for the system. such as aerators, air vessels, - Surface roughness coefficient After several runs, the values etc. The flow diagram can by - Provision of air valves at the supplied will come very close to all means be in the form of a highest points of the piping the technical and economical quick sketch, which does not - Branch connections optimum. As surge analyses take more than a couple of necessarily need to be performed minutes to draw. - Zeta or flow factors as well as by surge specialists, they remain valve closing characteristices 2. A rough list of all main para- time and labour intensive de- meters, i.e. principal pipe - Characteristic curves or perfor- spite the use of modern compu- lengths, diameters and flow mance charts and characteristic ter technology. rates. data of all hydraulic equipment Considering that powerful surge 3. A list of all major operation - Mass moments of inertia of all analysis software is now com- and downtime periods. hydroelectric generating sets mercially available, users may wonder whether they cannot do 4. A list of all known incidents - Characteristic curves and data their own analysis just as well. that could have been caused on surge control equipment al- As reliable9 surge analysis soft- by water hammer. ready installed in the system ware is far from a mass product, 5. Irregularities observed during - Characteristic values of all ae- the low sales volume makes it operation. ration and deaeration equip- expensive. Add to this the high ment If a surge analysis is to be per- cost of training and hands-on formed, additional data to be - Settings of control equipment practice. Also if the software is specified by the surge analyst not used for some time, opera- - Water levels in tanks and reser- will have to be obtained. Some tors usually have to brush up voirs examples of additionally re- their skills. So, if users require quired data are: - Rates of flow in the individual fewer than, say, ten analyses per piping branches year, the cost involved in doing their own will probably not be - Degrees of opening of all shut- worthwhile. off and throttling valves – Operating pressures

9 Users are in the uncomfortable position of not being able to verify the workings of surge analysis software. It is, therefore, important that a reput- able manufacturer vouch for the quality of the product. Surge analysis software, as a rule, is developed by specialist university institutes. There are some examples of programs that were bought by commercial enterprises and provided with a sophisticated user interface, which makes them easier to handle for the user. 17 7 Rules of Thumb and Manual Calculations

7 Advantages of rules of A simple example shows why: It takes lots of experience to be thumb and manual calcula- The only difference between two able to judge whether approxi- tions otherwise completely identical mation formulas can be used to water supply systems are the reliably calculate transient flow A rough estimate can be a very elevation profiles of the main conditions. For every day en- useful tool to quickly assess the pipes; one system has a high gineering purposes, approxima- risk of water hammer. This leads point, the other does not. The tion formulas should be used ex- us to the validity of rules of system without the high point clusively to roughly estimate the thumb and to the question can be safely protected by an air potential risk in a system (exam- whether the surge characteristics vessel. A vessel of the same size ples, see section 4). Using them of one system can be applied to will not adequately protect the as a basis for a serious surge another, similar installation (scal- second system, however, because analysis or, even worse, for de- ability). To answer that question, the falling water level in the air signing the surge control equip- we should start by pointing out vessel would cause the minimum ment, would have to be regard- that there is a great variety of dynamic pressure head to inter- ed as highly irresponsible. A water supply and waste water sect the pipeline’s high point. brief description of all known disposal plants, and that these are The low pressures thus created processes of approximation and so different from each other that would pose a risk of dirty water estimation formulas is given approximation formulas cannot being drawn into the system. below: be applied. Even if the characteristic values of different systems are very similar, i.e. same rates of flow, same pipe lengths, they cannot normally be scaled.

Fig. 7-1: Graphical method developed by Schnyder-Bergeron

18 Rules of Thumb and Manual Calculations 7

• Before the days of modern These are the only manual cal- computer software, the graphi- culation methods. This apparent cal Schnyder-Bergeron method lack is more easily understood if was often employed and pro- we take another look at the air duced relatively reliable surge vessel, our representative exam- analysis. For practical reasons, ple of before. Reading the total use of this method is limited to volume of the vessel from a systems comprising a single design curve is not all that is re- pipeline. Friction can only be quired. The way the air vessel taken into account by complex works depends to a large extent procedures. Besides, it takes a on the ratio of water volume to specialist to apply this method air volume in the vessel, or, in and obtain the desired results. other words, on the question Fig. 7.1 is an example of a whether pre-pressurisation of typical Schnyder-Bergeron dia- the vessel is “hard” or “soft”. gram, which shows how the The pre-pressurisation level has pressure wave propagation an impact on the total vessel due to the closure of a valve is volume required. The pipeline determined by graphical profile also plays a significant means. part. For example, if it has a high point which should not be • Application of the Joukowsky intersected by the minimum equation for rapid changes in dynamic pressure head curve flow velocity v (examples un- following pump trip (area of der 4). low pressure), the basic condi- • Graphical method to deter- tions for designing the vessel mine the required air vessel will be different, even if the sizes.*) plant parameters are otherwise • Graphical method used to the same. The vessel will have to estimate the condition of line be considerably larger. In many packing.*) cases, the swing check valve and throttle installed in a bypass will • The largely ideal valve closing keep the reverse pressure wave characteristics for the ex- from causing an impermissible ceptional case of a single-con- rise in pressure levels in the air duit pipeline can be calculated vessel. It is impossible to de- by approximation.*) termine these crucial variables using rules of thumb or graphical design methods.

*) Expertise required.

19 8 Surge Control Systems

8 Main types of surge control 8.1 Energy storage 8.1.1 Air vessels The purpose of surge control is With air vessels and standpipes, Air vessels come in the form of to stop kinetic energy from energy is stored as pressure en- compressor vessels (Fig. 8.1.1- being converted into elastic ergy; when a flywheel is instal- a), [bag-type] accumulators (Fig. deformation energy. This can be led, the energy stored takes the 8.1.1-b) and vessels with a vent done by the following basic form of rotational energy. There pipe. Compressor- and accumu- methods: is a sufficient amount of energy lator-type air vessels basically stored to maintain the steady- work on the same operating – Energy storage state flow for a relatively long principle. The reason for choos- – One-way surge and venting time and to make sure the de- ing one or the other is based on facilities crease in flow velocity due to dis- technical or commercial conside- – Optimisation of valve closing sipation will be slow to take full rations. Because of their design, characteristics10 effect. A rapid pressure drop is accumulators are only suitable thus prevented. If air vessels and for small volumes. – Optimisation of the strategy standpipes are installed upstream designed to control the piping As explained earlier, the vessel of a pump in a long inlet pipe, system volume is not the only impor- they not only prevent a pressure tant factor. If the water-to-air transient by means of energy dis- volume ratio is carefully chosen, sipation, but also the other way a vessel with a substantially around, by absorbing energy. lower total volume may be used.

Va Compressor on 100 mm HWIN Compressor off

Vw WSH

Z1 Hgeo

D 1 D2

Fig. 8.1-a: Schematic layout of a compressor-type air vessel. To avoid excessive pressures on return of the vessel water, the connecting pipe may have to be fitted with a swing check valve with a throttled bypass.

10 The valve closing characteristics describe the closing angle of a valve as a function of time.

20 Surge Control Systems 8

• The bag-like enclosure in an Membrane accumulator would be punc- tured by the sharp objects Gas contained in the waste water, such as razor blades, nails, etc. • There is a major risk of in- crustations, deposits and blockages. Grid to limit the expansion of the membrane Provided they are adequately Liquid monitored, the operating reliability of air vessels is high. Dur- Fig. 8.1.1-b: Schematic of an accumulator ing their operation, attention has to be paid to the following: To make sure compressor vessels in a piping system. For example are always filled to the correct in long inlet pipes, an additional • Monitoring of the water level levels, they can be equipped air vessel at the inlet end of the in the vessel. with sensors which will switch pump provides effective surge • For reasons of hygiene, the the compressor on or off as re- control. If the pump fails or water volume must be conti- quired. Bag-type accumulators trips, an upstream vessel will ab- nuously or regularly replaced. are typically adjusted by pre- sorb energy, while a down- pressurising the gas inside the stream vessel will dissipate en- • The compressed air must not bag or membrane enclosure to a ergy. contain any oil. certain initial pressure prior to Air vessels or accumulators are • To be able to take the air installation. not suitable for waste water dis- vessel out of service for an Air vessels are not just installed posal systems11, because inspection, spare vessels at the pump discharge end to should be available. • With waste water, it is not guard against the consequences possible to measure the water • It must be possible to lock the of pump trips. They can also be level needed to set the com- shut-off valves in the connecting installed in other suitable places pressor. pipeline against unintentional closure; the open position has to be monitored. • Maintenance of the compressor (compressor vessel). 8.1.2 Standpipes, one-way surge tanks Standpipes can only be installed at points of a piping system characterised by low-pressure heads. As a rule, a standpipe cannot replace a downstream air vessel. Fitted with a swing check valve in the direction of the flow and a filling mechanism (one- way surge tank), it is used to stop the pressure falling below atmospheric at the high points Fig. 8.1.1-c: Accumulators

11 An exception is a vessel fitted with a vent pipe; this arrangement, comprising an air vessel, a standpipe and a vent valve, is very rarely used in Ger- many.

21 8 Surge Control Systems

of long clean-water pipelines. Because of the possibility of malodorous fumes, standpipes are rarely found in waste water installations. Standpipes and one-way surge tanks are highly reliable pieces of equipment provided the following points are observed: • Continuous or regular changes of water (problem of hygiene). • Filtering of air flow. • Functional tests of the check valve on one-way surge tank arrangements. Fig. 8.1.3-a: The V-belt pulleys in this arrangement are solid discs • Monitoring of water level or filling device on one-way surge which is suitable for a relatively checked in advance that the tank arrangement. short pipeline, or, put different- flywheel will not interfere with ly, with a short reflection time the starting procedure of the 8.1.3 Flywheels Tr. The limits for employing a pump driver. Flywheels are flywheel are in the region of 1 to probably the safest and most Mounted on the driver, a fly- 2 km pipeline length. Example 3 elegant types of surge control. wheel prolongs the rundown ti- in section 4 includes a rough Their reliability beats that of all me of a pump to standstill by estimate performed to check other surge control methods. means of the stored rotational whether a flywheel can be used. With the exception of the bear- energy: For reasons of design, the fly- ings of larger-scale systems, they wheel solution is not suitable for do not require any in-operation 1 2 E = – · J · (8.1) submersible motor pumps. On monitoring. kin 2 other pump types, it must be J: Mass moment of inertia of flywheel in kgm2

: Angular velocity s-1 For a homogeneous solid disc with a radius r and a mass m, for example, the mass moment of inertia is

m · r2 J = –––––– 2

Figs. 8.1.3-a and 8.1.3-b show several practical applications. However, with a type of flywheel that is economically and technically feasible, one can only achieve a prolongation of the Fig. 8.1.3-b: Vertically mounted flywheel (driven by means of cardan running down time of the kind shaft, D = 790 mm)

22 Surge Control Systems 8

8.2 Air valves The reliability of aerators /deaerators depends on their design Air valves should not be used and is the lowest of all surge until every other solution has control equipment. They have to been ruled out. Their drawbacks be tested for proper functioning are: in regular intervals and it may • They require regular mainte- be necessary to filter the in- nance. coming air. • If arranged in the wrong place or mounted incorrectly, they 8.3 Actuated valves can aggravate pressure variations instead of alleviating Suitable actuation schedules for them. the opening and closing of valves are calculated and veri- • Under certain circumstances, fied by means of a surge analysis operation of the plant may be Fig. 8.2-a: Duojet*) two-way air on the basis of the valve limited, because the air drawn valve with a medium-operated characteristic. into the system has to be re- single-compartment valve. moved again. The valves will give very reliable Large vent cross-section for service if, on valves with electric • The handling of waste water drawing in and venting large actuator, adequate protection is calls for special designs. amounts of air during start-up provided for the actuating times Air valves (Fig. 8.2-a) have to be and shutdown of pumping and the break points of the actu- carefully designed. On large dia- systems. ation schedules or if, on valves meter pipelines, one has to ar- Small cross-section for removing with hydraulic actuators, ade- range air outlet valves on top of small amounts of air during op- quate safety elements, such as domes, to make sure that the air eration against full internal pres- orifice plates or flow control drawn into the system will col- sure. valves, are used. Proper valve lect there. As long as the fluid functioning has to be checked at flow has not reached the steady regular intervals with regard to state, air drawn into pipes can, and out through a small cross- the actuating times and closing under unfavourable conditions, section. characteristics. have a very negative effect. Air cushions normally have a dampening effect. However, the air drawn into the pipeline can also give rise to dangerous dynamic pressure increases. It has to be pressed out of the piping slowly; a large air outlet cross-section would lead to sudden pressure variations towards the end of the air outlet operation. For this reason, aerators and deaerators have different nominal diameters depending on which way the air flows. Air normally flows in through a large cross-section Fig. 8.3-a: Motorised shut-off butterfly valve

*) With the friendly permission of VAG-Armaturen GmbH.

23 8 Surge Control Systems

8.4 Swing check valves unfavourable effect, because manner after the pump trips. they take a long time to close, This feature is important on The dynamics of swing check which means reverse flow sets in pumps operated in parallel, valves often have a major in- while they are still partly open, when one pump fails whilst the fluence on the development of and the valve disc re-seats with remaining pumps continue to surge, because the valve’s clos- considerable impact. The pheno- run and deliver flow against the ure, after reversal of flow, gener- menon is known by the term tripped pump. In a case like this, ates velocity changes which, “check valve slam” and is much controlled closing is achieved by according to Joukowsky’s equa- dreaded. Since the closing time adjustable hydraulic actuators tion (4.1), produce pressure is the main criterion for check without external supply but variations. valve slam, limit position dam- with a lever and counterweight, Check valves generally have to pers will improve the situation, with the free-swinging valve disc meet the following two contra- but not eliminate the risk alto- opening in the direction of the dictory requirements: gether. In waste water systems, flow and, upon actuation, • bring the reverse flow to a nozzle check valves cannot be closing in one or two stages standstill as quickly as used because they tend to clog according to a set closing possible, up. This means that valves with characteristic. free-swinging discs and limit po- The operating reliability of • keep the pressure surge gener- sition dampers are the only re- check valves is relatively high. In ated during the process as maining option, despite their operation, they have to be small as possible. drawbacks. checked for proper functioning Drinking water pumping instal- Pump check valves installed in at regular intervals. lations protected by air vessels the cooling pipes of a power should ideally be equipped with station are designed to throttle nozzle check valves. Free-swing- the reverse flow in a controlled ing valve discs can have a very

Fig. 8.4-a: Swing check valve equipped with a hydraulic actuator and counterweight

24 Case Studies 9

9 Case studies a schematic diagram of the op- Fig. 9.1 shows the head and erating principle is shown in Fig. flow curves of the system pro- The case studies below were 8.1.1-a. In the present case, the tected by an air vessel arrange- taken from surge analyses throttling action is achieved ment plotted against time (heads performed by KSB. Although we with the aid of a short length of expressed in m above mean sea have altered the system para- DN 200 pipe fitted with a stan- level). meters, so that the installations dard DN 80 orifice. Fig. 2.1-b concerned remain anonymous, shows the calculated pressure the problems involved and the envelope with and without air way these were resolved have vessel. The maximum head not been altered. curve obtained with an air vessel h is now only slightly above 9.1 Case study: long-distance maxWK the steady-state head curve h water supply system steady and the associated minimum head

The system parameters are indi- curve hminWK runs at a wide safety cated in Fig. 2.1-b. A steady- margin above the peak point of state flow Qsteady = 500 l/s is the pipe. pumped through a DN 600 pipeline of ductile cast material with a total length of L = 2624 by three centrifugal pumps operating in parallel at a total head H inlet [m above MSL]:KN=1/Pipe No. System with air vessel of the pumps hsteady = 122.5 m into an overhead tank. The disturbance under investigation, which leads to excessive dynamic pressures, is the simultaneous failure of all three pumps. The dynamic pressure peaks Time s produced by far exceed the per- Q inlet [l/s]:KN=1/Pipe No. 1 System with air vessel missible nominal pressure of PN

16 (see hmax curve) in Fig. 2.1-b; the minimum pressures drop to vapour pressure in wide areas of the system (see hmin curve) in Fig. 2.1-b. The system can be protected by installing an air vessel at Time s Water vol. [m3]:KN=1/Air vessel No. System with air vessel the inlet of the long-distance pipeline. Although the vessel dimensioned as shown in Fig. 2.1- b will initially prevent the development of areas of low pressure, the water column in the pipeline swinging back will still produce Time s dynamic pressure peaks in Fig. 9.1: Time plots for the long-distance water supply pipeline (Fig. excess of 16 bar. Therefore, the 2.1-b); the example shows the head and flow curves of an air vessel- reverse flow into the air vessel protected system as functions of time (heads expressed in m above has to be additionally throttled; mean sea level)

25 9 Case Studies

9.2 Case study: stormwater conveyance pipeline Starting from a waste water pumping installation, a new DN 350 stormwater pipeline with a total length of L = 590 m was Aerator laid to an aeration structure.

Pumping operation was by Improved system with aeraor and means of three identical pumps bypass running in parallel, each equipped with a non-return valve and a motorised gate valve to control Fig. 9.2-a: Schematic diagram of the stormwater conveyance pipeline pump start-up and run-down. When a surge analysis was final- Model parameters The first 100 m of pipe made of ly ordered, its objective was: high-density polyethylene were Besides the parameters indicated laid under ground, the remain- • to determine what caused the in Fig. 9.2-a, the following sys- ing 490 m were of steel and laid surge pressures and forces that tem data were entered into the above ground supported on pipe had been observed, calculation: bridges. Fig. 9.2-a shows a sche- • to devise some protective meas- Pump characteristic shown in matic of the model installation. ures or surge control equipment Fig. 9.2-c The nodes connecting the above- that would prevent the excessive Model pipeline L1: ground single pipes of the model dynamic pressures produced by Material: high-density polyethy- are 90° elbows. The engineering a pump failure from occurring, lene (HDPE) firm in charge of planning the and to prove their effectiveness D : 354.6 mm plant neither performed nor or- mathematically. inside dered a surge analysis to accom- k: 0.1 mm pany the project planning phase. a: 600 m/s (estimated value) Min. permissible pressure: vacuum During the first operating tests Pressure class: PN 6 following the plant’s comple- tion, several incidents, among them a power failure which caused all three pumps to fail at the same time, caused the part Stormwater pump 1470 rpm of the piping laid above ground to shake considerably, damaging pipe fixtures and tearing off some pipes altogether.

Fig. 9.2-c: Characteristic curve of the pump used in the stormwater conveyance system

26 Case Studies 9

Model pipeline L2 to L10: Pump failure without surge control Material: steel

Dinside: 349.2 mm k: 0.1 mm a: 1012 m/s (from equation 4.1) Min. permissible pressure: vacuum Time s Pressure class: PN 10 H inlet [m]:KN=1/Pipe No. 1 Pump failure without surge control Nothing was known about the pump check valves. For the purpose of the model, it was therefore assumed – correctly so, as it turned out – that the valves would suddenly close upon reverse of the flow direction. Time s

Q [l/s]:KN=1/Pipe No. 1 Pump failure without surge control Calculation of actual duty inlet data, first results The steady-state flow calculated by the surge software for the parallel operation of three pumps amounted to Qsteady = 187 l/s. The first surge calculation of the Time s simultaneous failure of all three Fig. 9.2-d: Operating characteristics of the stormwater line without pumps showed that macro- surge control plotted over time cavitation and, as a result of it, dynamic pressure peaks as high LongitudinalLängskraft auf force L8 acting ohne onDruckstoß L8 without -Sicherungen surge control as 15 bar would occur inside the 40 HDPE pipeline, i.e. considerably in excess of the given nominal 20 pressure of the pipe of PN 6. 0 0 5 10 15 20 25 30 35 40 45 50 The calculation showed that the -20 pipe bridges between each pair -40 of 90° elbows had to temporari- Force kN Force Kraft kN ly withstand longitudinal forces -60 of just under 100 kN, or in -80 terms of weight, the equivalent -100 of a thrust somewhere in the re- -120 gion of 10 t. Figs. 9.2-d and 9.2-e Zeit s Time s show some examples of the sys- Fig. 9.2-e: Longitudinal force acting on L8 if the stormwater line is tem behaviour without surge without surge control control plotted over time. Fig. 9.2-d shows the pump speed, head and flow at the entrance of ing on L8. This explained the model pipe L1 (head in m above violent shaking and resulting pipe centreline); the curve in Fig. damage observed. 9.2-e shows the axial forces act-

27 9 Case Studies

Pump failure in a system equipped with an aerator Surge control measures and a bypass as surge control devices To eliminate the macro-cavitation developing after pump failure, a second simulation calculation was run with a DN 150 aerator at the outlet of L2, the highest point of the piping. De- Time s spite the addition of a surge con-

H inlet [m]:KN=2/Pipe No. 1 Pump failure in a system equipped with an aerator trol device, the HD-PE pipe was and a bypass as surge control devices still found mathematically to contain unacceptably high pressure increases a few seconds after pump failure. In order to eliminate these highly undesirable pressure peaks, it was eventually Time s decided to add a shut-off valve with a bypass between the inlet Q inlet [l/s]:KN=2/Pipe No. 1 Pump failure in a system equipped with an aerator and a bypass as surge control devices of L1 and the pump suction tank which would be automati- cally opened by a maintenance- free electro-hydraulic lever and weight type actuator if all three pumps were to fail at once. To

Time s valve manufacturers today, systems like this are more or less Fig. 9.2-f: Operating characteristics of the stormwater line with part of their standard product surge control plotted over time range. After adding surge control devices, i.e. an aerator and a bypass fitted with an automati- cally opening shut-off valve, the simulation finally showed that the dynamic pressure peaks re- Longitudinal forces acting on L8 if the system is protected by an aerator/bypass combination Längskraft auf L8 mit Belüfter und Bypass mained below the steady-state 40 initial pressure, and that the longitudinal forces acting on the 20 pipe bridge sections laid above 0 ground had diminished to no 0 5 10 15 20 25 30 35 40 45 50

-20 more than 5% of the initial value. The calculation further

Karft kN -40 Force kN Force revealed that the existing check

-60 valves could be dispensed with. Fig. 9.2-f shows – on the same -80 scale as in Figs. 9.2-d and 9.2-e

-100 to facilitate comparison – the n, timeZeit {s} s H and Q curves of the surge- protected system plotted over Fig. 9.2-g: Longitudinal force acting on L8 if the stormwater line is time; Fig. 9.2-g shows the forces suitably protected

28 Case Studies 9 of the surge-protected system plotted over time. The global pressure envelope of the rehabi- litated installation, as well as the curves of the system without surge control, are shown in Fig. 9.2-h.

PressureDruckeinhüllenden envelope with mitand und without ohne Druckstoß-Sicherungen surge control equipment (DS) (SC)

220

200

180

hmaxmaxwithout ohne DS SC 160

140

120 Kote müNN

100

hhmax with mit SC DS 80 max Elevation in m above mean sea level in m above Elevation

60 hhmaxminwithout ohne DS SC ElevationRohrkote of pipeline hhmaxminwith mit SC DS 40 0 100 200 300 400 500 600 Pipelineabgewickelte section in m covered Rohrlänge by the manalysis

Fig. 9.2-h: Pressure envelope of the stormwater conveyance pipeline with and without surge control

29 Additional Literature 10 Authors

Additional literature Authors 1. Dynamische Druckänder- Prof. Dr. Horst-Joachim Lüdecke, ungen in Wasserversor- born in 1943, Diplom-Physiker, gungsanlagen (Dynamic developed process engineering pressure changes in water and fluid dynamics software supply systems), Techn. whilst employed with BASF AG, Mitteilung, Merkblatt Ludwigshafen; professor at Hoch- W303, DVGW, Sept. 1994 schule für Technik und Wirtschaft 2. Horlacher, H.B., Lüdecke, (HTW) des Saarlandes (University H.J.: Strömungsberechnung for Technology and Economics of für Rohrsysteme (Flow mod- Saarland) since 1976; numerous elling for piping systems), publications on the subject of flu- expert Verlag, 1992 id flows in pipelines; co-author of the book “Strömungsberechnung 3. Zielke, W.: Elektronische für Rohrsysteme” (Flow model- Berechnung von Rohr- und ling for piping systems) (expert Gerinneströmungen (Compu- Verlag); as a member of the Water ter analysis of flows in pipes Hammer Committee of DVGW and channels), Erich Schmidt (German Association of the Gas Verlag, 1974 and Water Sector), involved in the 4. Wylie, E.B., Streeter, V.L.: revision of Surge Guideline W Fluid Transients, FEB Press, 303; currently supports and Ann Arbor, MI, 1983 advises KSB in the field of surge 5. Chaudry, H.M.: Applied analysis. Hydraulic Transients, Van Dipl.-Ing. Bernd Kothe, born in Nostrand Reinhold Com- 1955; graduate from “Otto von pany, New York, 1987 Guericke” Technical University at 6. Sharp, B.B.: Water Hammer, Magdeburg; joined Pumpenwerke Edward Arnold, 1981 Halle as a development engineer 7. Parmarkian, J.: Water- for power station pumps. From hammer Analysis, Dover 1993 to 1998, whilst employed in Publications, 1963 the engineering division of KSB 8. Publication of all papers AG, in charge of surge analyses presented at the Internatio- and complex flow modelling for nal Conference on “Pressure waste water systems. Since 2002, Surges” held by bhra fluid Manager Sales Support of the engineering, Great Britain, Waste Water Competence Center in the years 1976, 1980, at Halle. 1986, 1992, 1996, 2000 9. Engelhard, G.: Zusammen- wirken von Pumpen, Armatu- ren und Rohrleitungen (Inter- action between pumps, valves and pipelines), KSB 1983 Edited by: 10. Raabe, J.: Hydraulische KSB Aktiengesellschaft, Maschinen und Anlagen Communications (Hydraulic machines and systems), VDI Verlag, 1989 Dipl.-Ing. (FH) Christoph P. Pauly

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