screening reactor for water hammer

8/6/2019 Screening Reactor for Water Hammer

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NUREGICR-6519

Screening ReactorS t e a d a t e r Piping Systemsfor Water Hammer

Manuscript Completed:August 1997Date Published:September1997

MassachusettsInstituteofTechnoloey77MassachusettsAvenueCambridge, MA 02139

D.F3essette,NRC ProjectManager

Prepared forDivision of Systems TechnologyOffice of Nuclear Regulatory ResearchU.S. Nuclear Regulatory CommissionWashington, DC 20555-0001NRC Job Code 56008


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Abstract

A steandwater system possessing acertain combination of thermal, hydraulic andoperational states, can, in certain geometries,lead to a steam bubble collapse induced waterhammer. These states, operations, andgeometries are identified. A procedure that canbe used for identifying whether an unbuiltreactor system is prone to water hammer isproposed.

For the most common water hammer,steam bubble collapse induced water hammer,six conditions must be met in order for one tooccur. These are:

3) the L/D must be greater than 24.4) the velocity must be low enough sothat the pipe does not run full, Le.,the Froude number must be lessthan one.5) there should be void nearby.6) the pressure must be high enoughso that significant damage occurs,that is the pressure should be above10atmospheres.

2) the subcooling must be greater the operation of the reactor system are mide.than 20" C.

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Portions of this documentmay be illegiblein electronic image?prodaeb. h 8 g e S 8reproduced fmm the best availableoriginald0CUXIl-

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ContentsAbstractContentsList of FiguresList of SymbolsList of TablesExecutive SummaryIntroduction 1OSection 2.0 Steam bubble collapse induced water hammers and severefluid transientsSection 2.1

Section 2.2Section 2.3Section 2.4Section 2.5Section 2.6 Pump startSection 2.7 Passive water hammerSection 2.8 ChuggingSection 2.9 Pipe clearing transients

Water hammers due to the stratified to slug flowtransitionConditions leading to SBCIWH due to the transitionAdmitting cold water in down flow into a blocked,vertical stem-filled pipeDraining an inclined pipe which is originally filledwith cold water, the presence of steamColumn separation and rejoining and refillingvoided pipes

to slug flow

Section 3.0 Estimating the severity and duration of a s tem bubble collapseinduced water hammer (SBCIWH)Section 4.0 Pipe clearing transient descriptionSection 5.0Section 5.1

Experience in existing LWR'sScreening an unbuilt system for water hammersSection 5.2

Section 5.21 Surge lineSection 5.22 DVI lineSection 5.23 DVI nozzleSection 5.24 ADS1-3 spargerSection 5.25 CMT drainSection 5.26 PRHR HXSection 5.27 Hot ledcold legSection 5.28 ADS 1-3depressurization valvesSection 5.29 Discussion of the screening criteria used for SBCIWHdue to the stratifieaslug transition

Comments on specific components identified onFigure (5-3)

iiiV

viiixxixiii1

335779991010

1115212127272727272727282828

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Section 5.3Using these criteria to screen a design 29Appendix A Calculating the allowable system pressure to insure that steambubble collapse induced water hammer won't lead to failureReferences

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List of FiguresFig. 2-1

Fig. 2-2

Fig. 2-3

Fig. 2-4

Fig. 3-1

Fig. 3-2

Fig. 4-1

Fig. 4-2

Fig. 4-3

Fig. 4-4

The stratified to slug transition; as it leads to steambubble collapse induced water hammer in a horizontalpipe. Reference (4).The effect of subcooling on the region where steambubble collapse induced water hammer can occur.Reference (5).The stratified to slug transition in a draining pipe. (a)Low velocity drainage. Frd < 44. (b)High velocitydrainage. Frd > 44, Equation (2-3). Reference (14).The stability map for a draining pipe with inclinationangle from the horizontal as the primary variable.Reference (14).A bubble trapped between a column of cold water and aslug of liquid.The variation of the velocity of the slug as a function oftime showing the inertia limit and the wall sheer stresslimits as well as the actual velocity.(a) The actual configuration of water trapped in a lowpoint in a pipe and (b) the assumed configuration whenthe pipe is cleared by a flow of steam or air from the left.References (11)and (12).Force-time data from the pipe clearing experiments ofReference (11). The top figure is a summary of the peakforces measured. The cartoons at the bottom aresamples of the measured force-time traces for selectedinitial liquid fractions upstream of the force transducer.The decay of the peak force as a function of the distancea slug travels. If enough straight pipe is provided afterthe trap or loop seal, the clearing force downstream canbe reduced to manageable values. Reference (11).Impulse durations for pipe clearing experiment.Reference (11).

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12

14

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Fig. 5-1

Fig. A-1

Fig. A-2

Fig. A-3

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Schematic of the AP600 reactor system showinglocations that should be checked for steam bubblecollapse induced water hammers or severe fluidtransients.

25

The velocity of sound in: (a) saturated water andsaturated steam, (b) two-phase mixtures(homogeneous). Reference (2).33

The peak steam bubble collapse induced water hammerpressures observed in the simulated cold leg as afunction of pressure tap location. Reference (13).34

Peak steam bubbble collapse induced pressure measuredin the apparatus shown at the upper right. Reference(16).

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Cf

DFF *

L

LbLSmP

TSttnt*V

List of Symbols2Cross section area, m

Velocity of sound, m/sVelocity of sound in liquid water, m/sVelocity of sound in water vapor, m /sPipe diameter, mForce, NDimensionless forceMaximum force, NAcceleration of gravity, m/sImpulse, NDimensionless impulseDimensionless stopping constant, 1 for a pipe end,0.5 for a column of liquid

2

Length, mBubble length, mSlug length, mMass, kgPressure, PaSystem pressure, PaTemperature, KSaturation temperature, KTime, sNominal time, sDimensionless timeVelocity, m/s

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aPf

3Bubble volume, mVapor velocity, m/sSlug volume, m3Nominal velocity, m/sVoid fraction dimensionlessLiquid density, kg/m3Vapor density, kg/ m3Slope angle measured from horizontal

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Table 5.1Table 5.2Table 5.3

List of TablesWater hammer events reported in PWR plantsystemsWater hammer events reported in P W R lantsystemsComponents and their associated types of waterhammers (or severe fluid transients

x i

232426

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Executive SummaryThe various causes of @mn BubbleCollapse Induced water Hammer (SBCIWH)are examined and the underlying conditions for

an SBCIWH to occur have been identified.With the exception of filling a long, horizontalsteam-filled pipe with cold water, it appearsthat these water hammers can be eliminatedeither at the design stage or by adoptingsuitable operating procedures. The problemthat remains when a plant is properly designedand operated is how to refill a horizontal oralmost horizontal steam-filled pipe with coldwater without inducing a water hammer. Thisprocess is intrinsic to the advanced reactorpassive safety systems. The conditions thatmust exist for a SBCIWH to occur in thisgeometry are identified and a method proposedfor screening a system at the design stage. Theproposed method is designed to be used withcomputed (RELAP) results for determining thefluid state in various components during thetransients and accidents of interest.The criteria for screening a system forSBCIWH have been identified and are asfollows. For a SBCIWH to occur duringrefilling of horizontal pipes:

1.

2.3.4.

The pipe must be horizontal oralmost horizontal (the slope lessthan 2.4').

The water must be subcooled tomore than 20C.The L/D must be greater than 24.The filling velocity for thecold water, based on the fullpipe area, must be such that the

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Froude Number [V/(gD)% is less than1 .5. There must be void nearby.6. The system pressure must be greatenough so that the water slugs willimpact the affected parts of the systemat a high enough velocity to do damage.This threshold system pressure appearsto be somewhere between 100to 300

psia (1 to 3 x lo6Pa) depending on thecriteria chosen for deciding whatconstitutes an intolerable SBCIWH.An example of how to screen a design (basedon an artist's conception of the layout for theAP 600) is presented. The components andfeatures that might suffer a SBCIWHareidentified and the elimination, mitigation oraccommodation techniques for each componentthat might experience a SBCIWHis suggested.The most important areas for which additionalwork is needed are as follows:

1. The most limiting mode of failure if aSBCIWHoccurs in a steam systemneeds to be identified.2. Some higher pressure and larger pipewater hammer data are needed to see

if we have forgotten anything.3. A decision as to what constitutes asystem that is safe enough needs to bemade as the recommended screeningcriteria are quite conservative.Theywill "predict" many water hammersthat will never occur.4. The subcooling at which SBCIWH is aproblem at elevated pressures is notknown.

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1.0 IntroductionThe proposed advanced light waterreactors differ from existing light water reactorsprimarily in their safety systems. In the eventof an accident, like a LOCA, the advanced light

water reactors are designed to be blown downand then reflooded using a gravity drivinghead. The unique geometries and modes ofoperating this system will insure that someoperating states which have never before beenentered in the existing light water reactors, willbe entered into here.The conditions of concern which arenew include:A partially voided primaryThe presence of subcooled waterA low reflood velocityA variety of potential water hammer-prone geometries.The purpose of this report is to identifythose geometries, operations and states whichlead to water hammers so that, by design oroperational changes, the problem can beidentified and then eliminated, accommodated,or its effects mitigated.Water hammer occurs in piping systemswhich experience rapid changes in velocity.

These changes in velocity occur over such ashort time period that the resulting pressurewaves cannot travel the length of the pipebefore the change in velocity is complete. Abrief description of water hammer can be foundin Marks Handbook (1). A more completedescription is available in Moody (2). For thepurposes of this report however, only thesimplest ideas from these sources will be used.Where two phases are concerned, theuncertainties associated with the two-phaseflow configuration itself, overwhelm the otheruncertainties so that only simple equations orideas turn out to be useful.The most important equation whichwe'll need is the Jukowski equation, Reference1. If a pipe which is filled with flowing wateris suddenly closed at the discharge end, a waterhammer will occur. The resulting pressurewave will travel back to the reservoir where the

1

flow originates at the velocity of sound for apressure wave in that pipe. The resultingpressure rise for a rigid pipe will be

In this equation,AP = the resulting pressure rise inK = a dimensionless coefficient

pascals.which depends on the nature ofthe blockage. K = 1for a solidmetal blockage like a valve or0.5 for a column of liquid.velocity of sound in themedium in m/s (See Figure A- 1for its value in water).

AV = the extinguished velocity in m / s .pf = the density of the flowing liquid

C =

-kglm'.Pipe elasticity, end connections,fittings, wall friction, bubbles andmultidimensional effects all complicate thepicture but because two phase flows have suchcomplex configurations and behavior to startwith, the above equation with an appropriate

velocity of sound is good enough forpractically all our purposes. The uncertaintiesassociated with the configuration of the phaseboundaries and the heat and mass transferprocesses occurring on these boundariesoverwhelm the other uncertainties in thisequation. Much of this report will beconcerned with predicting what conditions leadto water hammer in steam systems and givingrecommendations on how to evaluate each ofthe terms in Equation (1-1).While water hammer is hardly

unknown in nuclear systems, for the currentlyoperating PWR's the way they are built andoperated precludes dangerous water hammersin the primary. The combination of highpressure, void, and subcooled water which isnecessary for a serious steam bubble collapseinduced water hammer to occur is neverpresent. Auxiliary systems such as servicewater, auxiliary feed water systems, and soNUREG/CR-6519


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forth have, sometimes, suffered waterhammers (3), but many of the auxiliarysystems that have experienced water hammersare not safety related and thus fall outside thearea of NRC concern. The advanced lightwater reactors, however, are different.The advanced LWRs use safetysystems which involve blowing down theprimary for certain kinds of transients. Highpressure, void, and cold water can coexist atvarious places in the primary during the blowdown or the reffiling process. Thiscombination can lead to steam bubble collapseinduced water hammers which might thenchallenge the primary system in some way.This report is written to provide guidelineswhich will help the NRC to screen a newdesign and identify the design features,possible equipment failure modes and systemoperating procedures which could lead tounexpected and dangerous water hammers.Water hammers in nuclear systems canbe handled using one of three strategies:elimination, mitigation, or accommodation.Often water hammer can be eliminated at thedesign stage by modest changes in thegeometry. This is the best option. Evengeometries which might incur a steam bubblecollapse induced water hammer can often beoperated so that they are eliminated. Forexisting plants, which might actually have a

water hammer problem, operational controlsare often sufficient to eliminate this concern.Under certain circumstances, steambubble collapse induced water hammers areinevitable but their consequences mitigated bythe adoption of clever designs or suitableoperating procedures. Controlled filling orputting in non-condensable gases will oftenmitigate the effects of water hammerssufficiently so that we can live with thepossibility that they will occur.Lastly, a system can be designed so thatthe steam bubble collapse induced waterhammers, even if they are inevitable, can beaccommodated. The piping and supports canbe made robust enough so that the waterhammers cannot damage the system. Thischoice of strategies means that with foresightand good design, steam bubble collapseinduced Eater hammer (SBCIWH) will not bea problem in a nuclear system.

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In the remainder of this report thevarious kinds of steam bubble collapse inducedhammers will be described. Fluid transientscharacteristic of two phase systems, butnormally excluded from classical water hammertreatments will also be touched upon. Thegeometries and fluid conditions that lead tothese water hammers will be identified andvarious elimination, mitigation, oraccommodation strategies will be suggested asappropriate.

Any complex, high-performance pipingsystem, such as a nuclear plant, is designed toride out a wide variety of single phase fluidtransients. These transients are not the subjectof this report. They are already satisfactorilyhandled by procedures universally adopted inthe industry. Single-phase flows are not ourconcern.Our understanding of the processesleading to steam system water hammers andtheir consequences now allows us to constructa screening procedure that can be used on aplant, at the design stage, to identify thosefeatures and procedures that might lead todangerous water hammers. The proposedscreening procedure will be illustrated by anexample which will make the use of thesuggested screening criteria clear.

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2.0 Steam bubble collapse inducedwater hammers and severe fluidtransients: The water hammers that occur insteam systems (which often actually containboth steam and water) can occur for a greatvariety of reasons. In this section we shallcategorize the geometries and processes thatcause these water hammers and provideguidance as to how to predict if they will occur.Several other classification schemes, asidefrom the one chosen here, are in use and couldhave been used to categorize these events. Thesub-system in which it occurs could be used tocharacterize it. (3) The component could beused. (5) The process or physical mechanismcould be used to categorize it. I've chosen tocategorize the SBCIWH by their physicalmechanism. This selection means thatrepetitious descriptions of how they occur areminimized and only a few equations willsuffice to provide the answers we need.

2.1 Water hammers due to thestratified to slug flow transition: Thisis the most common cause of water hammers insteam systems and occurs and reoccurs in avariety of geometries and scenarios. Thismechanism was first identified and described inReference (15) and was subsequently analyzedin Reference (4). For the details of thedescription and analysis, it is recommendedthat these references be consulted. In essence,the processes leading to this kind of waterhammer are as follows.

A horizontal pipe, typically, initiallyfilled with steam and having access to areservoir of steam at one end, experiences aflow of cold water into the other end. Thevelocity of the flow is low enough so that atongue of cold water advances into the steamfilled pipe. This is called a stratified flow.Condensation occurs on this tongue which, ifthe tongue is long enough, leads to acounterflow of steam and water on the tongue.This counterflow becomes sufficientlyvigorous so that first a wave, and then a plugforms. This is the transition to slug flow.These processes are illustrated in Figure (2-1).

the saturation pressure associated with thetemperature of the cold liquid. This pressure isusually so low, that the liquid to the right of thebubble is rapidly accelerated to a velocity highenough to cause a significant water hammerwhen the condensation is complete. A pressurewave, the magnitude of which can be calculatedfrom Equation (1-1) proceeds to the left andright of Figure (2-1)(d). The right travelingwave hits the free surface and is dissipated atthe bubbly interface. A pressure wave, aboutequal to the steam pressure, then proceeds fromthe free surface back towards the point oforigin and then beyond.While this is going on, a similarpressure wave is proceeding to the left. Thesetwo waves act to give rise to large, shortduration forces on the pipes which are often

sufficient to damage them or the pipe supports.The well-established procedures forcalculating the forces resulting from waterhammers in cold water piping systems are notappropriate for typical steam systems.Occasional trapped bubbles of steam or non-condensable gases, indistinct or unpredictableinterface locations and intricate componentgeometries all lead to a rapid amplitudereduction and wave broadening for the pressurewave front. This is why there is very littleexperimental evidence in steam systems of

clean wave reflection from the free surface atthe right of Figure (2-1)(d). In this section thecircumstances leading to SBCIWH will beexplored. In Section (3 ) and Appendix A, wewill describe in detail how to estimate the peakpressure when the slug of liquid, such as theone at the right in Figure (2-1), hits the columnof subcooled liquid shown on the left.

The steam bubble which is shown inthe (c) cartoon of Figure (2-1) is surrounded bycold water. This causes the steam pressure inthe bubble to drop to a value which is close to3 NUREG/CR-65 19


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Steam, r\

Cold Water Rt V

t V

Figure2-1. he stratified to slug transition as it leads to steam bubblecollapse induced water hammer in a horizontal pipe.Reference (4).

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2.2 Conditions leading to SBCIWHdue to the transition to slug flow.Both Reference (5 ) , the thesis on which it isbased, and Reference (4 ) give stability mapsshowing under what circumstances SBCIWHcan occur. The criteria for SBCIWH weresimplified and worked out numerically for awide range of conditions and published inReference (6). One of the figures fromReference ( 5 ) is reproduced here as Figure (2-2). For a convenient screening procedure,there are far too many parameters in thisproblem to work out all possibilities in detail,so we shall simplifiy these criteria and startwith the minimum subcooling and minimumwater flow rate which are present if a waterhammer is to occur.

condensation events are not vigorous enough tocause one. We did not find water hammers inthis region in our experiments. The benefitsthat these water-hammer-free regions confer ona system will not be exploited in the proposedscreening procedure. Rather, we will assumethat whenever the sub-cooling is large enoughand the filling velocity is less than the criticalvelocity shown at the top of Figure (2-2),hat awater hammer will occur. Let us now focusmore closely on this limit.If a horizontal pipe has a small waterflow rate and the end is open to a steam (orgas-filled volume), the pipe wont run full. Ifthe gas phase is steam, this pipe can experiencean SBCIWH. If, on the contrary, the flow rateis high enough, the pipe runs full and the area

condensation will occur. The counter-currentflow needed to a transition to slug flowcannot be set up. As long as the pipe runs full,SBCIWH will not occur. An approximateconservativecriterion for the pipe full

Let us start Figure (2-2). exposed to the steam is so small that not muchIt is clear, with a little consideration, that somesubcooling is essential if steam bubble collapseinduced water hammer is to occur.something like 20 K of subcooling is present,the range of pipe-filling flow rates over whichA). This subcooling limit, which is basedentirely on experience in low pressure systems,is thought to be generally conservative. Thefirst part of the simplified screening criteria is,therefore:

SBCTWHOccurs is (see so that a water hammer cannot occur is,

(Ts - T)>20Cif SBCIWH is to occur. In equation (2-1),

Ts =Saturation temperature for thenominal local pressure in O K.

T =The actual temperature ofthe water in O K.There is a water-hammer-free region atthe lower left of Figure (2-2),labeled stable ormetastable) where SBCIWH does not occur.This is because the water flow rate and theresulting liquid fraction is so low that atransition to slug flow is not possible. Atransition to slug flow requires a liquid fractiongreater than 0.2. Immediately adjoining thestable region on Figure (2-2) s a metastableregion in which the conditions for SBCIWHare marginal in that the

In equation (2-2),Vfs =The superficial velocity of

liquid water in the pipe in m/s.g =The acceleration of gravity in

m / S 2

D =The pipe diameter in meters.This is one of the most important screeningcriteria for SBCIWH.

Though these criteria were developed inconnection with filling a horizontal pipe, theunderlying mechanism of water hammer whicharises in horizontal pipes, also appears in avariety of other scenarios and geometries. Thenext few sections will describe these.

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0.40

0.30

0.20

0.10

PIPE-FULL LIMIT- L = 2.0 m Ts = 396 K

D = 0.0381 m8 = o

I&= 0 kg 8-l

W a or Ham morRogion

0.000 25 50 75 100

INLET WATER SUBCOOLING (K) 125

Figure 2-2.The effect of subcooling on the region where steam bubble collapseinduced water hammer can occur. Reference (5) .

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2.3 Admitting cold water in downflow into a blocked, vertical, steam-filled pipe. For a small flow rate of coldwater into the top of an empty vertical pipe,one obtains an annular or rivulet flow pattern.As the cold water flow rate is increased, thevoid fraction decreases. Somewhere in therange of void fraction between 0.7 or 0.8, atransition to slug flow occurs. This transitionleads to the trapping of large steam bubbleswhich are surrounded by cold water. A veryrapid condensation of these bubbles canoccur which can lead to a water hammer.(Reference7).

In general, admitting cold waterabove steam is a poor practice because itoften results in trapping a steam bubble.Trapping can lead to a violent bubble collapseand a water hammer. Filling steam-filledpipes or other volumes with cold water frombelow, on the other hand, is usually a smoothprocess. The cold water entering the pipe,quickly acquires a thin layer on top which isclose to the steam saturation temperature.This layer greatly reduces the condensationrate and with it, the possibility of countercurrent, stratified flow. This layer is stabilystratified and no condensation event occurs.(A condensation event, in general, is a rapidcondensation and mixing where the mixing isdriven by the motion due to the condensationitself.) ( 6 ,7).

This kind of water hammer is dueprimarily, to a poor choice of pipinggeometry, and is best eliminated by a designchange. Filling short pipes of any orientationcan lead to problems too. (Reference 7).Whether this will occur in an untestedsystem, however, cannot be determinedwithout examining detailed piping drawingsin the context of a well-defined scenario.Reference (7) gives the details needed forscreening other geometries; a low point inany voided system is prone to this kind ofwater hammer.2.4 Draining an inclined pipe, whichis originally filled with cold water, inthe presence of steam. One of the morecounterintuitive processes that can lead toSBCIWH is draining a pipe which has coldwater in it, while simultaneously refilling it

with steam. This process often occurs whena steam system has been turned off forseveral days. The low parts have filled withcondensate which has had a chance to cool.The drain is opened to remove thiscondensate, the condensate level drops and,for sufficiently rapid draining, the waterwhich is left behind collects into a wavewhich then leads to a transition to slug flow.Figure (2-3), (Reference 14) shows how theflow regime changes in going from slowdrainage to rapid while Figure (2-4) is a mapwhich shows where water hammers occur.

This kind of water hammer can becategorically eliminated by keeping thedraining Froude number, Frd, as defined inequation (2-3), to a value less than 44, andby suitably inclining the pipes. For draininginclined pipes,

(2-3)

where, Frd< 44in order to preclude water hammers. This isa water hammer that should never occur.

In equation (2-3),Frd =The Froude number fordraining, dimensionless

3pf =t he liquid density in kg/mVfs = the liquid draining velocity in

m / S .3p, = the vapor density in kg/m

2g= the acceleration of gravity in m/sD = the pipe diameter in mI=he inclination of the pipe from thehorizontal

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Figure 2-3.The stratified to slug transition in a draining pipe. (a) Lowvelocity drainage. Fr, < 44. (b) High velocity drainage.Fr, >44, Equation (2-3),Reference (14).

o NoHommcrHammert 06 -

UuIn\--- 4 --.-V0 -al>-

I - urve o f ( 1 1 . 0 1-- urve f ro m (21--- urve from (1;)t I # I I I l l

-0 .I25 -250 .375 S O 0 .625 . fSO -875 LODO Ll2SS l o p t , i n 111L 1 I0 I 2 3 4 5

I I t

8 i n Degrees

a.

b.

Figure 2-4The stability map for a draining pipe with inclination anglefrom the horizontal as the primary variable. The pipe diameter in theseexperiments in 5 cm. Reference (14).

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2.5 Column separation and rejoiningand refilling voided pipes. Thisprocess arises in a variety of systemmaneuvers and operational mishaps. Inessence, this kind of water hammer is due tothe rapid condensation of a bubble which isformed and trapped at the closed end of apipe.Reference (2) describes this processin some detail. Rapid valve action is not theonly cause, however. Any blind ended pipewhich is originally steam-filled and issubsequently filled rapidly with cold watercan experience this kind of water hammertoo. The filling process itself traps the steamin the blind-ended pipe. This might cause

steam to condense rapidly leading to a low,local pressure. This will cause water to flowinto the cavity so rapidly that a water hammerwill result just when the filling process iscomplete. Horizontal, vertical and inclinedpipes are all prone to this kind of waterhammer. This kind of water hammer canusually be eliminated by not maneuvering thesystem too rapidly. The stable, stratifiedpool of water is then not disturbed.The next two mechanisms, pump startand passive water hammer, do not apply to

the primary or high pressure sides of thesecondary though they have occurred in otherreactor systems. At this time, the details inthe design of the advanced reactor systemsare sufficiently indistinct so that a descriptionof these water hammers is included here incase some safety related system is designedso that it can experience one of these.Auxiliary systems in the advanced reactorscan experience these water hammers just asthey can in existing LWRs.2.6 Pump start: Water hammers canoccur if a pump is turned on and fills a pipetoo quickly. Containment spray systems, forinstance, draw water from a sump and pumpit to a high place in the containment where itis then sprayed into the containment to cooldown its contents. If the check valve, whichis normally in the line just after the pump,leaks, that line can, over time, drain. Whenthe pump is turned on, the flow resistance of

the air and resulting back pressure are verysmall. The velocity acquired by the water canbe so great, that when the water hits the sprayhead, an unacceptable hydraulic load or waterhammer can OCCLU-.This problem is eliminated by using akeep-full system on the spray line. A keepfull system is a small (pony) motor and pumpused to circulate a small flow of waterthrough the core spray system all the time.This keeps it full whether the check valve isleaking or not. This should not be a problemfor the safety systems of an advanced reactorbecause there are not any active pumps torefill the system too rapidly. Otherintermittently-operated, non-safety systemson the reactor might use pumps and haveproblems like this, however.

2.7 Passive water hammer: This kindof water hammer has been observed to occurin feed water heater drains and has, perhaps,occurred in other systems too. In essence itarises when a heater drain, which is full ofcold condensate, is opened in the course ofrestarting the plant. When this is done, theflow control or throttle valve between theheater drain line and the condenser must beopened to let the condensate out. To startwith, the condensate is cold and no flashingoccurs. When hot condensate fresh from thefeedwater heater arrives at the throttle valve,however, flashing takes place, the pressuredrop suddenly increases and the flow rate isreduced. This flow reduction causes a waterhammer. References (8 and 9).

This transient can be accommodatedby draining all the cold condensate out of theheater drain line slowly enough so that, evenif the flow is stopped completely, theresulting pressure rise is acceptable. In anycase, suitable starting procedures should besufficient to eliminate this kind of waterhammer as a problem. For the advancedreactors, this kind of water hammer shouldnever be a problem in the primary, either, asin the refilling processes, the flow goes froma cold reservoir to a hot system and such awater hammer is impossible.

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2.8 Chugging: When steam is dischargedinto a pool of cold water at a sufficiently lowmass velocity, a type of water hammer calledchugging occurs. This has occurred in BWRpressure suppression pools and can occur inother systems as well. Early experimentswhich were called "water cannons", arereported in Reference (4).Chugging isessentially unavoidable when steam is ventedinto cold water unless measures are taken tocontrol it. The mechanism is as follows.

As the mass velocity of steamdischarged from a vent in down flow into apool of cold liquid decreases, thecondensation process removes steam morerapidly than it is provided. This reduces thesteam pressure in the vent pipe which sucksup the water from the pool. The cold waterthat is exposed by this flow condenses stillmore steam and soon a rapid reduction of thepressure in the vent pipe takes place. Thepressure typically drops to a value that isclose to the saturation pressure for the pool.This causes the water velocity in the vent torise to a high enough value to cause a waterhammer as soon as a valve or bend isimpacted by the column of water advancingup the vent. The resulting hydraulic forcesare usually unacceptable.

The accepted way of eliminatingchugging is to put a vacuum breaker in thevent line. This breaks the vacuum before thewater has risen far enough in the line to doany damage. Another way to handle theproblem is to add a non-condensable gas tothe steam. This puts a diffusion resistance inseries with the condensing heat transferresistance, thereby reducing the condensingrate, and also diminishes the sonic velocity inthe flow going up the vent. The loweredcondensing rate reduces the velocity, whilethe diminished sonic velocity reduces anywater hammer pressure rise. One percent airin the steam is sufficient to eliminate thesewater hammers (10).2.9 Pipe clearing transients:References (11 ) and (12) describe a variety ofpipe clearing transients. The pipe clearingprocess consists of blowing a plug or pool ofliquid out of a pipe or fitting. As long as the

NUREG/CR-6519

plug of liquid remains coherent, the forcesexerted by this liquid as it travels around thepipe can be considerable. Because theselarge forces are undesirable, the steamsystems should be designed so that pools ofcondensate don't form. If this is impossible,as it often is, the valve should be openedgradually enough so that any liquid trapped inthe pipe is cleared slowly and the peak forcesthe pipe experiences are acceptable. Perhapsa capillary bypass should be used.References (1 1)and (12) describe in detailhow one might do this.

Of necessity, piping systems oftenhave low points or loop seals in themwhether the designers really want them ornot. Even if they cannot be eliminated, thepiping system should be run in such a waythat the resulting clearing can beaccommodated.

Sometimes the pool forms where it isnot expected as a result of the condensationof steam escaping though a leaky control orcheck valve. Whether this possibility hasbeen considered in the design and operationof the piping system, usually isn't clear sothat important vent and drain lines shouldprobably be operated with this possibility inmind.

10


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3.0 Estimating the severity andduration of a steam bubble collapseinduced water hammer (S BCIWH).For screening purposes a precise descriptionof the pressure-time relation imposed on apiping system due to SBCIWH is not neededand is, in any case, unattainable. Rather, asimplified model that captures the importantphysics and gives a reasonable, but generallyconservative answer, should be sufficient.That is the goal we have adopted here. Westart with the Jukowski equation.

Recommendations for calculatingeach term in this equation will now be madefor the case of a transition from a stratified orannular flow into slug flow in a horizontalpipe. A description of how this equation is tobe used to estimate the water hammerpressure surge and its duration for several

other systems will also be made asappropriate.Let's start with a horizontal steam-filled pipe receiving a flow of cold waterwhich is transitioning to slug flow. This isthe state illustrated in the cartoon which isshown in Figure (2-1). Let us furtheridealize this process by saying the voidfraction in the region in which both phasesare present is 50%. (This assumption turnsout to be almost the worst condition and, forour purposes, makes our analysis particularlysimple). The worst way these phases can bearranged is to have a steam bubble trappedbetween a cold liquid column and a slug ofcold liquid. Figure 3-1 shows this. [This

figure is really an idealization of Figure 2-l(C)]. In order to determine the peakpressure attained when the trapped steambubble is completely condensed, we mustdetermine the velocity attained by the slugdue to the condensation of the steam bubble.

11 NUREG/CR-6519


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Figure 3-1.A bubble trapped between a column of cold water and a slug of liquid.

NUREG/CR-6519 12


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Either the slug inertia or the wall shearstress can limit this velocity. If the inertialimits, the (Pa) work done on the slug by thesteam advancing into the pipe is equal to theincrease in kinetic energy of the slug. That is,

2(Po - P,) 6 = 1/2 mVs .which becomes

(3-1)In these equations:

Po= The existing pressure in the pipein Pa.P, =The saturation pressure of

the water in the pipe in Pa.m =The mass of water trapped in the

slug in kg.V, =The velocity of the slug in m/s .6 = The volume of the bubble in mD = Thepipediameterinm.Lb =The length of the bubble in m.L, =The length of the slug in m.

3

Generally P, e


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)r00c.--8 /---/ -

//\Actual0 VelocityILTime

Figure 3-2. The variation of the velocity of the slug as a function of time showingthe inertia limit and the wall shear stress limits as well as the actual velocity.

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parameter is the liquid fiaction trapped in theloop seal upstream from the bend.Until the liquid fraction exceeds 0.2, ora < 0.8 (4-1)

in the pool, no measurable force due to clearingthe liquid is observed. All the data obtained inthese experiments has been correlated using asimple plug flow model. That model is asfollows Figure (4-1). The peak force iscalculated assuming the liquid is a coherentcylindrical plug of the same volume as theoriginal pool. This plug impacts the bend at thenominal velocity. The idealized peak force thenisF = P f V n 2 A x

In equation (4-2),(4-2)

F =The force exerted at the bend in N3= The liquid density in kg/mPf

V, =The nominal velocity of thedriving fluid (gas or steam) in m / sA, =The cross section area of the pipe

2in mThe idealized force is used to non-dimensionalize the actual force trace.

(4-3)

This peak force is correlated on Figure (4-3) asa function of dimensionless distancedownstream of the pool. The dimensionlessslug length, L,, is defined as

6 sL,= -.AXIn equation (4-4),

(4-4)

NUREG/CR-6519 16

6, =The volume of the liquid slug3trapped, in mThe dimensionless distance is an importantparameter because it reflects how much liquidhas been left behind as the slug advances downthe pipe. After it has gone about 5 sluglengths, the slug becomes an incoherent massof spray.

This is to be expected as the nose of theslug flow bubble advances into the slug at avelocity which is about 20% greater than theflow velocity in the pipe. This increase invelocity for the nose of the bubble reflects,more than anything else, the turbulent velocityprofile in the pipe.The nominal time it takes the slug topass through the bend is,

6,t, =-1 VnAxIn equation (4-5) where,

(4-5)

$, = the nominal time it takes a slug topass through the bend in s.The dimensionless impulse shown in Figure(4-4) is then,

FdtI* =pv ,2Ax tn

in which the dimensionless time is(4-6)

(4-7)

In these equations,I*=The dimensionless impulset* =The dimensionless time the impulse

actsThe duration and magnitude of the force andthe impulse can be obtained from Figures (4-3)and (4-4).


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Q) 1.2ErI2I .o.-E

3 0.82

-.-

\Q)

e 0.6Y

0.4U3VI20.2K*" 0.0

0 56 f V s e c77 t /secI 1 8 . 5 f t I s e cMaximum98.3 t /set

I I A I L0 4 8 I2 16 20 24D = D i s t a n c e T r a v e l e d by S l u g / Slug Leng th

Figure 4-3. The decay of the peak force as a function of the distance a slugtravels. If enough straight pipe is provided after the trap orloop seal, the clearing force downstream can be reduced tomanageable values. Reference (11).

19 NUREG/CR-6519


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1.oain30 I 18.5 f t k e c0.8 9 8 . 3 f t I s e c 0 5 6 f t l s e c-0c.-2 0.6\Q)u)3e 0.4-a010Lg 0.2aIIH* 0.0

0 I 2t*= Average Impulse Duration/Nomina I Impulse Duration

Figure 4-4. Impulse durations for pipe clearing experiment. Reference(1 1).

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5.0 Experience in existing LWR's:Before going to the specific example, which isbased on a proposed advanced light waterreactor design, it is appropriate to review andsummarize what has been learned on existingBWR's and PWRs. Virtually all the waterhammers observed in existing LWR's haveoccurred in the auxiliary systems, not theprimary. Most of these can be traced to one oftwo overriding causes:1) Inexperienced operators because theplant is new so that the procedures that mightcause a steam bubble collapse induced waterhammer have not all been identified or,2) A piece of equipment like a checkvalve, fails and starts to leak.

This causes steam to be present where onlywater should be or perhaps causes condensateto collect in a pipe that should contain onlysteam. Reference (3) classifies the waterhammers in such a way that the auxiliarysystems that are most prone to water hammerscan be identified and appropriate design andoperating precautions taken. The details on theprecautions provided in Reference (3), will notbeduplicated here. We will focus only on theproblems that are unique to the advancedreactors because these are the only designs inwhich water hammers might occur in theprimary.

Tables (5-1) and (5-2) from Reference(3) summarize the experience utilities have hadwith water hammers obtained on existingLWR's. These two tables are inserted here as areminder that a plant can experience waterhammers in the auxiliary systems as well asprimary and some of these water hammers mayhave safety implications. Steam bubblecollapse induced water hammers are not theonly possibilities. References (3) and (15)describe some other possibilities as well. Mostof the information in Reference (3) wasprovided in licensee event reports submitted tothe NRC in the course of operating thesereactors. Even though this data is for existingLWR's, it can tell us a lot.

Feed water systems and steamgenerator nozzles are particularly prone to

water hammers. This is because they are theparts of the system which would normally havecold water in them and yet are at high pressure.During certain transients, however, they mayalso have steam in them. The combination ofcold water and steam is the most commonprecursor of a steam bubble collapse inducedwater hammer. Their presence is, indeed,essential if a SBCIWH is to occur at all.Components in the advanced reactors thatusually have cold water but may have steam inthem are the first places to look for waterhammer problems.

The feature that makes the advancedlight water reactors different from existingLWR's is that they are designed to be blown-down and then refilled with cold water usingnatural circulation. The automatic-epressurization System (ADS) and the & c t-essel bjection systems (DVI) whichaccomplish these processes are unique to theadvanced reactors and thus are the likely placesto find any new problems. The ADS wouldmost likely have a problem during blowdownwhile the DVI system would be most likely tohave one during refill. The core makeup tanksare new as well so their performance must alsobe examined. Most of the other components inthe advanced LWR's are also in existingLWRs and are thus less likely to haveproblems. We now know how to operate thesesystems.5.1 Screening an unbuilt system forwater hammers: The specific examplechosen to illustrate the suggested screeningprocedures is based on the AP600 conceptualdesign and is illustrated in Figure 5-3. (Thisfigure was provided to the NRC byWestinghouse). It is not a final design and iscertainly not complete. Many details such asvalves and their locations, stress-relievingloops, pipe inclinations, instruments, drainsand vents and so forth are all omitted from thispicture. None-the-less, this figure is useful foridentifying the places where problems mightarise and suggests what the problem might be.Only a detailed examination based on pipingisometrics, the study of component details likevalve geometries and a knowledge of the statespassed through from the computer simulationsof the transients will allow one to see if there isactually a SBCIWH problem.

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Looking at Figure (5-1), we canidentify a number of places where problemsmight arise. Table (5-3) gives a key to thenumbers on Figure (5-1) along with the sectionin this report where the likely process leadingto a water hammer in the identified componentis described.Not every process mentioned in section(2) of this report is referred to in Table (5-3).This is partly because Figure (5-1) is notcomplete and some of the drains, vents and

NUREG/CR-6519 22

other components that are present in thecomplete plant are missing. The refillingprocess in short pipes of various orientationsand blind-ended components are possiblesources of water hammers and should bechecked for too. We just don't know wherethese blind-ended pipes are. In most cases,however, the water hammers that result fromthe processes not mentioned in Table (5-3) arewater hammers best eliminated at the designstage or managed by operational means such ascontrolled refilling rates.


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t4urn8efO fEvents

i iI t0

PWR Plant SystemsPLANT SYSTEMS EVENTS

AFW -ASW -CCP -ccw -CON -m -cvcs -FPS -R N -FWHD -MS -RCS -RHR -SCW -SG -SGB -SI -

Auxiliary Feed WaterAuxiliary SaltwaterComponent Cooling WaterCondenser Circulating WaterCondensate SystemContainment SprayChemical 6 Volume ControlFireProtectionFeedwater SystemFeedwater Heater DrainsMain SteamReador Coolant SystemResidual Heat RemovalService Cooling WaterSteam GeneratorSteam Generator Blowdown

111214271

2718673306

Safety Injection 6Total PW R Events 123

Table 5-1. Water hammer events reported in PWR plant systems.Reference (3).23 NUREG/CR-6519


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IRWST\

Figure 5-1 . Schematic of the AP600 reactor system showing locations that should be checkedfor steam bubble collapse induced water hammers or severe fluid transients.

25 NUREGKR-6519


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Table 5.3 Components and their Associated Types of Water Hammersor Severe Fluid Transients

LocationNumber Location Type of Water Hammer(Refer to this section) Discussion

12345678

NUREG/CR-65 19

PZR Surge LineDVI LineDVI NozzleADSl-3 SpargerCMT DrainPRHR HXHot Leg/Cold LegADS 1-3DepressurizationValves

26

2.42.1,2.22.1,2.22.82.1,2.32.3,2.42.1,2.2

2.9

5.215.22,5.29523,5295.245.255.265.27,5.29

5.28


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5.2 Comments on specific componentsidentified on Figure (5-3): Beforeproceeding to the screening problem associatedwith filling a horizontal line, we should takethis opportunity to discuss the components andprocesses appearing in Table (5-3)with theintent of making the screening process easier.5.21 Surge Line: The geometry of thesurge line is almost exactly that studied inReference (14). The greatest difficulty incalculating whether this is really a problem isprobably getting the subcooling correct.SBCIWH would only occur if there issubcooled liquid in the pressurizer at the timewhen it is drained in such a way that thesteadwater interface retreats into the surgeline. It isn't obvious in what transient thismight occur, but an overcooling transient mightdo it. Inclining the surge line certainlydecreases the likelihoodof such a waterhammer but even if the line is inclined, there 'still exists a drainage velocity which can lead toSBCIWH. A very large pressurizer, which hasother benefits too, might eliminate thisproblem.5.22 DVI Line: Inclining a nominallyhorizontal pipe more than 2.4" and filling frombelow are the best ways to avoid this kind ofSBCIWH. Under normal operation or for aLOCA anywhere but in the DVI line itself, thisline should remain filled with liquid. It is notclear, however, what the temperature of thisliquid is. If it is hot enough, it can flash duringblowdown and when it refills, the line couldpass through a state where it contains coldwater and steam. These are the most importantingredients leading to SBCIWH.

If the DVI line is suitably inclined andthere is a check valve immediately behind thenozzle leading into the vessel, SBCIWH maynever be a problem in this line.If the DVI line experiences a LOCA, itwill certainly drain and refill with cold waterbut the pressure level at which this happenswill be so low that the resulting SBCIWHs areunlikely to further damage the plant. For thiscomponent it is important to identify all thetransients which lead to voiding in the DVI andmake sure any refill with cold water occurs at a

low enough pressure such that no damageresults.5.23 DVI Nozzle: The problem here isvery similar to the problem in the DVI line.The geometry illustrated in Figure (5-3) isalmost identical to the geometry in the IndianPoint steam generator which experiencedasevere water hammer some years ago. Voidingin the down comer might lead to a similar eventhere. The procedures and results reported inReferences(4) and (15) give ample guidanceon how to avoid this problem. Most importantis to slope the DVI line down from the vesseldropping the DVI line one pipe diameter ormore, in less than 24 L/D's.5.24 ADS1-3 Sparger: The sparger andvent line is probably the product of a lot ofdevelopment work in the past and is likely towork as designed. Here the items to check are:first, does it have a vacuum breaker andsecond, has the system been tested over theentire range of pressures and vapor flow ratesat which it is expected to operate? It isparticularly important that the chugging regimebe amply tested. The precise conditionsleading to chugging are reported in Reference(10). A low enough mass velocity for thesteam being released into a cold pool willalways lead to chugging and the system mustbe designed to accommodate it..5.25 CM T Drain: Under normalconditions, the CMT is filled with cold water.It is piped in such a way, however, that itdischarges into the DVI line. If the cold waterin the CMT is discharged into a partially voidedDVI line at high pressure, a serious waterhammer can result. I don't know if thiscombination of states ever arises or even if thisis a problem at all but it is worth looking at thecomputer printouts to see if this kind of waterhammer is ever expected to happen.5.26 PRHR HX: For almost any conditionwhich the PRHR HX is expected to operate, itis vastly over-sized. This means any steamwhich enters it will soon be condensed and thecondensate will acquire lots of subcooling.These are exactly the conditions which lead toSBCIWH, steam and cold water. Dependingon the inclination and transient time, theprocesses in this component could also be like

27 NUREG/CR-6519


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draining a line filled with cold water in it (14)or even filling a steam filled vertical pipe withcold water (7). In general, I believe thesewater hammers, if they occur, will occur withso little subcooling that the pressures will notbe damaging. I think though, that the PRHRHX s should be tested over the entire range offlow rates, pressures, and inventories at whichit will operate in the plant to insure that we havenot missed anything.

When the cold condensate from thePRHR is returned to the primary, the pressuremight be high and the condensate very cold sothat a SBCIWH could occur. Figure (5-3)does not show how this is done but the samecautions mentioned in the discussion of theDVI line apply here.5.27 Hot Leg/Cold Leg: The hot or thecold legs can drain and refill at a high enoughpressure so that water hammer might be aproblem. The screening criteria assembled laterin this section address both hot leg/cold legproblem and the DVI problem in considerabledetail. I regard these three components as theones most worthy of our close examination.

5.28 ADSl-3 Depressurization Valves:The depressurization valves illustrated onFigure (5-3) indicate no problems. Apparentlyno loop seals are present and the lines can besloped so condensate doesn't collect. On theassumption that this figure is not a completerepresentation of the actual installation, thispotential problem is included here. The issuethat needs to be addressed is the pipe clearingproblem. Are there any traps or loop sealsfilled with water upstream of the ADS valves?The water in these traps might lead tounacceptable forces downstream of the A D Svalves when the pipe is cleared.

As it is easier to seal a valve which isbacked up with cold water than one backed upwith steam, I expect the valves are actuallydesigned with a trap upstream which fills withcondensate under normal operation. When thevalve is opened, a slug of cold water is releasedinto the discharge pipe and possibly causes asevere fluid transient. Section (2-9) andreferences (10) and (11) will provide all the

information needed to check the adequacy ofthese designs. Programming the valve openingcorrectly, if there is a loop seal upstreameliminates this problem.

5.29 Discussion of the screeningcriteria used for SBCIWH due to thestratifiedhlug transition. By far the mostpersistent steam bubble collapse induced waterhammer problem is filling a steam filled pipewith cold water. A number of components arepotentially prone to this problem. At the veryleast, the DVI line, the hot legs and the coldlegs are possible problem areas. A number ofconditions need to be met if such a process is tolead to a damaging water hammer. These arelisted and described below. Most of them canbe gleaned from reference (4) or the thesis thatreference (4) is based on. First, let us look atthe geometric conditions.

The first condition is that the pipe belong enough. For a steam bubble collapseinduced water hammer to arise, the horizontalpipe L/D must be more than 24. Longhorizontal pipes with L/D> 24, are all prone tothis problem. Short pipes don't provideenough inter-facial condensation area to giverise to a sufficiently vigorous steam counterflow to force a transition to slug flow. Thismeans that no bubble is trapped and noSBCIWH water hammer occurs.Conservatively, water hammer will occur if,L/D > 24. (5- 1)

The L/D in equation (5-1) is the number ofL/D's of horizontal pipe between components.Bends, in a horizontal plane, don't count as acomponent in this case.A special combination of fluidthermodynamic states, and conditions mustprevail if water hammer is to occur. The mostimportant of these is the sub-cooling must belarge enough. Precisely how large isunacceptable, is not clear at this time, butlooking at a lot of water hammer data,

subcoolings less than 20" C do not often leadto serious steam bubble collapse induced waterhammers. Many subcoolings greater than this

NUREG/CR-6519 28


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The next condition is the subcooling. Itshould be more than 20" C if there is to be awater hammer. As it is proposed to be used,RELAP does not allow vapor and subcooledliquid to coexist in a single control volume.Therefore, where vapor is present, subcooledliquid will not be found. Though thisconditionprecludes a water hammer, this limitation is notthe problem that it appears to be.

The SBCIWH problem only arisesduring transients, usually refilling transients.In these we can easily imagine cold wateradvancing into a horizontal pipe. At some timeduring the transient it is almost certain that onecontrol volume will contain some void while anadjoining control volume will containsubcooled water. It is proposed that aSBCIWH is likely to occur if there issubcooled water in a control volume which isnext to one with void in a horizontal pipe.Though many of the details of the SBCIWHprocess will be missed, the dangerous state andthe approximate time and location whereSBCIWH might occur will have beenidentified.

Next we should examine the velocity orFroude number condition. If the cold water isadvancing such that the Froude number in thecontrol volume containing the subcooled wateris greater than one, the pipe will run full and nowater hammer will occur.The condition that the void fraction beless than 0.8 if water hammer is to occur isharder to apply. My recommendation is topursue the transient a little longer in time, afterwhich the control volume receiving the coldwater will probably show the conditions underwhich a water hammer will occur. In a word, Isuspect failing to meet the void fraction limit onwater hammer will not prevent it if theremaining conditions are met. At some time

during the refilling process, the conditions for awater hammer will be met and failing to meetthe void limit of 0.8 at one moment won'tprevent it from occurring later.

Choosing the pressure below which nodamage from SBCIWH is to be expected is alittle harder. Talking to people who haveoperated plants, doing some order ofmagnitude calculations and surveying thelicensee event reports is probably necessary tochoose a satisfactory cut-off pressure. Ibelieve, however, the system pressure level atwhich a SBCIWH can be tolerated isappreciably more than one atmosphere andidentifying this limit will significantly reducethe amount of screening that needs to be done.It might, for instance turn out that after the 4thstageADS blows, no damaging water hammeris possible. The pressure might well be toolow.By far, the most common consequenceof a water hammer is the damaging of a

snubber or pipe hanger. Some of this may betolerable if the event is rare enough. Thepotential payoff both in terms of ease ofscreening an unbuilt system and in laying outclear instructions for the operators makes itworthwhile to answer the question of whatpressure level is low enough so that waterhammer is not a problem.If the criteria recommended in thisreport are followed, I believe many more waterhammers will be predicted than will ever beobserved in the experiments. Experience may

allow us to relax these criteria. Even then,questions as to what constitutes an acceptablewater hammer remain to be addressed. Toanswer the outstanding questions, people inother areas like stress analysis, licensing andoperations must be involved in setting thecriteria. I believe, however, we now have thetools we need to get a useful answer to theproblem of steam bubble collapse inducedwater hammer in the advanced light waterreactors. If it is a concern, I'm confident thatthe design and operation can be shaped so thatit is not a problem.

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Appendix A

Calculating the allowable system pressure to insure that steam bubblecollapse induced water hammer won't lead to failure.

Introduction: The example calculation givenbelow is provided so that when the failurecriterion which determines the limiting waterhammer pressure (for which water hammer isnot a problem) is identified, it can easily berelated to the acceptable system operatingpressure. As this is only an example, it shouldbe stressed that the failure modes listed inSection 5-10 should be reviewed forcompleteness and worked out for severalspecific systems in order to make sure that themost limiting condition has actually beenidentified.

For simplicity, we shall assume that thelimiting failure mode is yielding of the pipe dueto internal pressure. The yield stress, pipegeometry and initial conditions are as follows:Pipe Steel

OD= 2"ID = 1.8"

zy = 50,000 psi

fw = 0.02Fluid conditions

To = 60' F so P,, = 0Po= 14.7 psia

State of the System:As idealized in Figure (3-1),

L, = Lb = 48" so that,cx = 0.5

We must now find the velocity of theslug. Either the inertia or the wall shear stresson the slug determines this limit. The inertialimit is calculated from equation (3-2). It is,

(3-2)

while the wall shear stress limit is calculatedfrom equation (3-3).

The smallest of these governs the resultingvelocity.Equation 3-2 yields a velocity of 46.7 Wsecwhile equation,3-3 yields a velocity of 95.4ft./sec. So inertia governs. See Figure (3-2).The extinguished velocity is then

AV = 46.7 ft/sec.In order to determine the resultingpressure rise when the slug of water hits thecolumn of water, equation (1-1) must be used.AP =KpfC(AV) (1-1)

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In this equation K = 1 for hitting a shut valveor blind-ended pipe; while for hitting a columnof water, such as here K = 0.5. A velocity ofsound "C" s most conveniently obtained fromFigure (A-1). For liquid water. Figure (A-la)is appropriate. (For two phase mixtures,Figure (A-lb) should be used).

we obtain,AP = 1 167 lb#in2

Either this or the 1256 lbf/in2 is the danswer.In fact, selecting the appropriate soundvelocity is the most dubious part of thiscalculation. Even a tiny void fraction, air orvapor, can greatly reduce "C". In mostexperiments we have found the effectivevelocity of sound in apparently subcooledwater is well below that of Figure (Al),typically about half of that given. Smallbubbles, most likely consisting of non-condensable gases, always appear to bepresent. The elasticity of the pipe contributes

too, further reducing the pressure rise. (SeeReference 1). This reduction is about 10 to20% for a steel pipe. For a best estimitecalculation, I'd recommend using half the valuegiven in Figure (A-la) for subcooled water.For two phases, the sensitivity of the sonicvelocity for a two phase mixture to the voidfraction (or equivalently to the vapor to mixturedensity ratio) is obvious on Figure A-lb.

Returning now to equation 1-1 andusing a sonic velocity of 4000 ft/sec:(46.7)(62.4)(4000)(32 .2) (144)AP = (0.5)

= 1256 lb#in2 (A-2)A usually-conservative, easily-remembered ruleof thumb for calculating the pressure rise in awater hammer for cold, gas-bubble-free waterin a steel pipe with the end closed is,

AP - 5OpsiAV ftlsec--

Alternatively, if we use the rule of thumb tocalculate the peak water hammer pressure,AP = 0.5 (50)(46.7) (A-2)

sir d

NUREG/CR-6519 32


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2000 -v) Saturated water, C fE\-'0a94 1000 -Wc0av) Saturated steam, Cp

0 I II 10 IO0Pressure , tmosphercs

1.0 7C-%0.10 -

t

Figure A-1.The velocity of sound in: (a) saturated water and saturated steam, (b) two-phase mixtures (homogeneous). Reference 2.

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There are some experiments to whichthe above recommendations can be compared.The first comparison was reported in Reference(13). A calculation much like that given aboveis shown along with the data in Figure A-2.This data was taken in a small, low pressuremodel of a PWR. A cartoon showing aschematic of the cold leg in this model whereECC was admitted and the pressure measuredis also provided.

The most important things that welearned from these experiments is that scatter isalways present, that it is very large, and theabove calculation method is generallyconservative. Calculating the pressure rise forthis experiment using the rule of thumb yields,

AP = 2042 psiso it too is slightly conservative for all thepoints measured.

If the study of the most limiting failuremode shows that the motion of a pipe limits,then the time the force acts is important too.The time it acts can be estimated as twice thetransit time of the pressure wave from theimpact front to the other end of the slug andback to the impact front. A rough calculationof this time using a sonic velocity of 4000ft/sec yields,

2LsA t =-C (A-3)

35

To measure such a brief transient requires goodinstrumentation. If a lower sonic velocity isused for the peak pressure calculation, a lowersonic velocity should be used to estimate thetime that the pressure acts.A second set of data is shown in Figure A-3.The scatter here is also considerable. Usingequation ( 1 - 1 ) , the K limit of one, and the ruleof thumb of 50 psi/(ft/sec) of extinguishedvelocity, for the pressure rise (equation A-l),the peak pressure calculated for the apparatus iscalculated to be,

AP = 1723 psi.This is for cold water. This is considerablyhigher than the highest data point shown onFigure (A-3). In retrospect, omitting theeffects of any bubbles due to noncondensiblegases originally in the steam, the reduction inflow velocity due to the contraction at theentrance to the tube, and the variability in theoperator valve opening time probably accountsfor both the scatter and general reduction in themeasured peak pressure from that anticipated.

When extraordinary care is taken todefine the system, reproducible and predictableexperimental results can be obtained (17). Thepractical problem is no one ever has enoughknowledge of the state of a real, full-sizedengineering system to allow one to make aprecise calculation of the severity of the waterhammer.

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400

3 0

300n0u)Q.-- 2502?1Y,u)0 ,& 200Y0aa I50

I O 0

5 0

0 ,

a

a

a0..\e0 '0 0 \e o \

0 @ \\0

* 62S"

-@

a Lo\ @

\

e @ \i\

I I pel- 1Temperoture ("C 1

Figure A-3. Peak steam bubble collapse induced pressure measured in the apparatusshown at the upper right. Reference (16).

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15. Izenson, M.G., Rothe, P.H., Wallis, G.B., "Diagnosisof Condensation-Induced WaterHammer". NUREGKR-5220. Vol. 1, ol . 2, 1988.16. Perkins, G., "Peak Pressures Due to Bubble Collapse-Induced Water Hammer". SBThesis in Mechanical Engineering, M.I.T., May, 1979.17. Easom, B., "The Effect of Noncondensible Gas on Steam Bubble Collapse Induced WaterHammer". Ph.D. Thesis in Mechanical Engineering, M.I.T., June, 1992.

screening reactor for water hammer

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