Effect of Air Pockets on Pressure Surge Burrows Et Al (1)

8/11/2019 Effect of Air Pockets on Pressure Surge Burrows Et Al (1)

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Effect of air pockets on pipelinesurge pressureR. Burrows, BEng, PhD, CEng, MICE, MCIWEM3nd D. Q . Qiu, BEng, MPhil

Through a series o f analytical examples, itis demonstrated h o w t h e resence of airp o c k e t s can s e v e r e l y e x a c e r b a t e urgep e a k s during pump s h u t d o w n in singlew a t e r p i p e l i n e s y s t e m s w h e nperatingu n p r o t e c t e d against transient p r e s s u r e s .Single air p o c k e t s of small size and the

to be especially problematic. I t is sug-m u l t i p l epresence of air p o c k e t s are s h o w n

gested t h a t such behaviour m a y triggerpipe f a i l u r e s in circumstances w h e r enormal surge a n a l y s i s m a y ot p r e d i c t

s u c h c o l l a p s e .

Air pockets can developn a pipeline by bubbleIntroduction

entrainm ent through the action f pum p suctionand by air releaserom solution as the waterpressure reduces. The former can arise frompoor suction (wet)well design and throughoperation cycling which permits excessivedrawdown before pump switching or shut-

depen ds on the press ure reduc tion and otherdown. The amountof air release rom solution

factors , but water a t s tandard condi t ions maycontain about2 dissolved air byvolume (Fox,

entrapped air will collect t high points along1977, l and Twor t t al. 1994). It is obvious that

the pipe profile in the form of pockets and thereis also alwaysa likelihood of air collecting a t achange of gradie nt in the pipeline,as shown inFig. 1 (after Twortet al . 1994). It iscommonpract ice in water supply systems to provideautomatic venting to prevent excessive accumu-

sewerage, however, the maintenance problemlation and consequential flow constriction. In

ha s led to frequent omission of air valve s infavour of the provisionof sluicing facilityonly.

sure s experienced bya pipeline can be eitherbeneficial or detrimental froman operationalperformance perspective, depending on theamount , the two phase regimef the mixture(whether homogeneous or slug) and he nat ureand causeof the transient. Itis generally heldtha t when free (undissolved) air,r gas, i spresent in a hydraulic system, i t can greatlyreduce the surge pressure levels because freeair in a hom ogeneous m ixture greatly increasesthe elasticityof the fluid,so reducing the pres-sure wave speed and enhancing surge damping

(Wylie and Streeter, 197 8,3 Ew ing, 19803.

(1993), however, that spati al a nd time varia-3. It ha s recently been demonstrated by Lee

2. The effect of e ntrappe d air on su rge pres-

tion in the degreeof entrainm ent, and hence

can amplify the posit ive peak pressure. Thesewave speed, during the transient processtself

results were obtained froma numerical,variable wave speed,model which sim ulates

pressures change.Lee cites, in support of hisinstantaneous gas release or absorptions

findings, the ex perimen tal obs ervations fhigher first pressure peaks (than those pre-dicted by normal, constant w ave speed, w aterhammer theory) dur ing pump shut-downreported by Whiteman and Pearsall( l959,

1962),6,7 Dawson and Fox1983) and Jonsson(1985).9 Heemphasizes, however, that aspec tsof the physical modellingare unresolved andThorley 1991)lO suggests that the re-absorption process may beo slow th at it canbe ignored. Dawson and Fox attr ibuted theobserved increase in peak pressure to the cumu-lative effectof minor flow changes during thetransient, while Jiinsson proposed compressionof an isolated air cushion adjacento the check(reflux) valve after losure. Th is wa s ustifiedby application of a numerical model using con .stan t wave speed and elastic theory. e con-cluded that: one could only expect tha t thesmaller the air volume is the larger the pressurepeaks. On the other hand theres certainly alower limit on he amou nt of air that could bedescribed as behaving a s a cushion. It wouldappear that both the air releaseodel and thevaporous cavity model are capableof simulat-ing observed pressure amplification. oth Lee

research. Reality probably involves aom-and Jiinsson expre ss theneed for further

can be satisfactorily verified without theorebination of both processes, neitherof which

comprehensive field data .

(1978)3and Safwatet al. (1986) also refer to4. Martin (1976), Wylie and Streeter

the occurrence of serious pressure levels f theair is trapp ed either etween two liquidcolumn s (i.e. air occupies the entire pipeross-section) or neara closed valve during the rapidaccelera tion of the adja cen t column of liquid.Larsen and Burrows1992) report attempts toverify a numerical model against experimentalobservations from several pipeline systemsduring pump shut-down conditions and subject

of air pock ets at hig h points could s atisfacto ryto risk of cavitation: only by the incorporation

calibration to the recorded peak pressurese

achieved.5. Computerized waterhammer analysesar e completed routinely for pumped pipeline

R o c . Instn Civ.Engrs Wat.,Marit.

Energy, 1995.112, Dec., 349-361

Water BoardWater PanelPaper 10859

Written discussioncloses 15 February 1996

R. Burrows,Reader,Department of CivilEngineering.

LiverpoolUniversityof

D. Q. Qiu,Postgraduate Student,Department of Civil

Engineering,

LiverpoolUniversityof

349


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EFFEC T OF AIRPOCK ETS ONSURGE PRESSURE

points plus atmospheric pressurehead(10.0 m water). Of necessity, no cavitationcan occur at nodes wh ere air pockets ffinite size exist.The actual pipe diameter and cross-sectionarea are used in the application of themethod of chara cterist ics at n odal points

containing air pockets (see Fig.b). Noinflu ence of the pocket on local pipe fric-tion is considered, therefore, andno com-putation is m ade of its longitud inal ex tent.Output from the calculations does,however, include the maximum v olume tricexcursion s of the air pocket during theanalysis.Pipe friction is ncluded in the model andpumping station losses ( inlet , valves,bends, manifolds and expansions) are allcharacterized through a singlehead losscoefficient c)applied to the kinetic ead inthe pipeline. Presenc e of check valve pro-tection downstream of the pumpis builtinto the modelling procedu re, but addi-t ional bypass provision (with heck valve)can be specified to p rotec t a deliv eryinecontrol valve against cavitation.Pump dynamics are pecif ied through itslift/flow ( H P - Q ) characterist ic, speedofrotation N ) and overall moment of inertiaI). In modelling pump run-down, a quadra-

tic characterist icis assumed

H p = b l + B Z Q + 839and as the rotation speed changes, thepump characterist ics satisfy the similari tyrelationships for homologous pumps, a sdescribed in Ame ndix 1r ~ ~

10. For compu tational convenience, theposition of air pocketsis restricted to nodepoints, representing junctions etween adjacentpipe reaches, into which the pipe length isbroken dow n. Neglecting v elocity head, whichis small , the total ead above the datum at junc-tion [ , N ( j )+ l ] can be determined from thefollowing com patibility equations for the fluidtransients defined at theend of each computa-tional t ime stepAt

c + : P ~ ~ , N U + ~ I = C P ~ ~ , N U ] - ~ ~ Q P ~ , N ~ + ~ I1)C-: ~ ~ + l , ~ ) = C r n ( j + l , 2 ) + B j + l Q P U + ~ , 1 ) 2)

where

NU ] = Hti,NU ] -l- Bj Qu. NU ]

1

Air Docket pl... .. .. .... ......~~........~..

Datum

a)

Air pocket

Fig. 2. Definition

sketch

in which the subscriptP indicates an unknownvar iable a t the endf the t ime step under con-sidera tion, Le. at timet + At, while a variablewithout the subscriptP refers to i ts nownvalue at the beginningf the time st ep, i.e. attime t ; or the junction j , ), he f i r s t subscr ip t j

j = 1, 2, . . /A efers to the pipe sectionbetween input topographical coordinates, andassumes a l inear grade. Theecond su bscript ii = 1, 2, . N ( j ) + 1) denotes further sub-

division intoN ( j ) eaches, of thejth pipe

section; Q is the disch arge; is the w ave eler-i ty ; Ax is the reach length;g i s gravi ta t ionalacceleration;f is the Darcy-Weisbach frictionfactor; D is pipe diameter andA is pipe cross-sect ion area;B C, and C, are cons tants of thecomp atibility equa tions. If the los ses at th ejunction a re neglected, then

HpLi.No)+l) = H P t i l , 1 = HP 3)

11. For stabili ty of the numerical schem e, itis necessary to satisfy the ourant condition(Chaudhry, 198519), i.e.

C, = c A t / h 1 O

Most accurate results are obtained withC, = 1(Wylie and Streeter,19783 and Chaudhry,198519) and this condition h c d t )has beentaken here.

12. In a pipeline broken into several sec-tions j , o accommodate changes in structure orperhaps topographical detail, adecision isneeded in respect of the discretizationof eachsection intoN ( j ) eaches of equal lengthh jSince At is f ixed and the reach lengthsh j illdiffer at least margina lly, slight adjustm ent fthe ' target ' wave speed is necessaryf theequa lity limit is taken for the Courant condi-t ion. This approach hasbeen taken herein, andan illustration of the effect can be seen in the


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BURROWS AND QIU

Table 1. Influence of t ime step selection for calculations of transients in pipeline profileb fFig. 3

Time step: S At = 0.2t = 0.1t = 0.05t = 0.02t = 0.01

Number ofN Z= 4Z = 82 = 16Z = 41, = 82eachesN , = 6, = 12, = 24I = 62, = 124

N , = 102N4 = 84 = 174 = 354 = 894 = 178N , = 5, = 10, = 20, = 51

AdjustedC, = 310.0= 310.02 = 310.0= 302.4, = 302.4ave speedc l = 311.7l = 311.7l = 311.7l = 301.6l = 301.6

m l s C = 308.0= 308.0= 308.0= 302.0, = 302.0c 4 = 320.2 c 4 = 356.24 = 335.34 = 325.74 = 320.2

CPU time 1.63 3.17 817.76UNIX: S

CPU time PC: 9.77 17.03 39.6069.1892.39S

A t p u mp ex i t 44.7245.4715.652 45.3555.358H m a x I H m i n 113.01113.06713.067 113.07113,071

At junction 1 44.002 43.7593.610 43.6143HmaxIHmin 113.22013.10213.06212.938 112.895

A t junction 2 42.392 41.2890.2320.237H m a x I H m i n 115.092 115.0615.065

At junction 3 36.6435.8515.744 35.4975.501HrnaxIHrnin 116.206 116,38

Target wave speed: c , = 300.0; c, = 300.0; c, = 300.0; C.+ = 320.0Steady-state airpocket volume = 0.05 m

f igures in Table . The alternative is to retainfixed wave speed, thereby tolerating differen-tial valu es of C , (but < 1) or each pipelinesection.

13. In the analysis of the air pocket actinga s a simple accum ulator, shown schematicallyin Fig. 2(a), the pressurea t any ins t an t i sassumed to be the sam e throughout thevolume.The gas i s assumed toollow the reversiblepolytropic relation

H A P = CO 4)

in which the absolute pressure headA =H p + fi, where H is barometric pressurehea d; is the elevationof pipe axi s above theda tum; V is the gas olume in the pocket; thepolytropic exponentn varies in the range1 - 1.4, n average valueof n = 1.2 generallybeing taken in calculations (Wylie and Streeter,19783); O is a constant determined from theinit ial steady-state condition for the airocket.Since equation 4) ay apply at any instant , i tis written for junction[ , N ( j )+ l] t the endof the time incrementAt, a s

( H P R V. N U ) + l])X Vu.N U ) +11 + AVu, ~ ( j ) +1 = CO 5)

In this equation,V is the airvolume at thebeginning of the time stepAt ; AV is the air

volume change during theAt t ime interval. Thecontinuity equation for the unction becomes

14. Substituting Equations 1) hrough (3)and 6) into equation 5) and eliminatingQpU. N u ) + and Q p U andeplacingH P V. N ( j ) + l ] and H P ( j + 1 , 1 by H P yields

At(Bj+ Bj 1) H p ] 2 ( B j B j + )

( H P + H 2u, N U ) + 11) = CO 7 )H p is the only unknown in equation 7), hichis a non-linear equation an d theNewton methodis employed for solution.

15. Given that CO is a positive coefficientevaluated when an airpocket size is specifiedunde r stead y flow conditions and thatH A sconstrained to p ositive values, it is lear that


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EFFECT OFAIRPOCKETS ONSURGE PRESSURE

of the evidence presented in Fig s4 and 5, itappears that the working statef pipeline a isconsiderab ly improved by the presence of thislarge airpocket.

pipeline b (Fig .3), this t ime for various airpocket volumes at the high oint( x / L = 0.41).Flow conditions and importan t pipeline andpump characterist ics are summarizedn Fig. 6 .I t can be observed that, du ring the transientfollowing pump shut-down, ult imateminimumhead along the pipeline shows uplif t s the airpocket volume is enlarged, except for theupstream sectionof the pipeline n the caseofthe smallest air ocket volume. Close inspectionshows that wi th no ai rocket ( V = O.OOO ,cavi-tation occurs along the approacho the highpoint, and rapid pressure f luctuations result onthe time trace (Fig.7). Th e influence of air pres-ence on the ultim ate maximum head is less con-

sisten t. For m uch of the pipeline profile, largerair pocket sizes are seen ( in F ig.) generally toproduce lower pressure peaks thanwhen air isabse nt. The confused behaviour in the sectionof the pipeline ups trea m of the air pocket iscaused by the superpositionof the m otion ofpressure waves between the air pocket and thepump/check valve system and the mass oscil-lations introduced by the air void. The signi-ficance of these inconsistenc eis in trend is,nevertheless, only marginal.More serious,however, is the substantial increase n peakpressures associated with a sm all air volume( V = 0.025 m3), the occurrence is seen clearlynthe time series plotted n Fig. 7.

27. Stab ility chec ks on the compu tation pro-cedure were made in response to th ese findings,and Table 1 presents some results.A ran ge oft ime step sAt, varying from 0.2 S (adoptedasthe standard for all investigations herein) to0.01 S , were considered for application to pipe-line b. The smaller ime steps were con-sidered to introduceeven greater accuracy intothe finite difference calculations. Standardapplication of the Cou rant cond ition was made ,and discretization of the pipeline, into equa llength reaches withineach s ection, forced

slight ad justment to w ave speeds. ood stabil-i ty is shown over the entire rangef timesstep s, in terms of both the head excursionslisted in Tab le 1 and the t ime variations,sample of which is sho wn in F ig.. The alterna-tive discretization approach, discussed earlier,which fixes w ave s peed n each pipe s ection b yvarying the Courant number, was foundQiu,19951~)o have some influence on the predic-tions u nder cavitation, but th is is ot of signi-ficance to the com parative beha viour unde rinvestigation here.

28. Th e influence of air pocket volume isinvestigated systematically n Fig. 9, whereultimate maximum peak pressures are normal-ized in term s of the stead y-sta te d ynam ic d uty

26. Figures 6 and 7 show sim ilar results for

-. - - - V = 0 0 with surge suppressionv = 0 00

6or V = 0.3550

-

40-

Eij 30

-mw --; 0I

10 -

0 -

I I l 1 I I I

500000500 2000 2500000Distance along pipeline: m

Fig. 4 . Comparison of maxim um and minimum head envelopes alongp ip el ine a F ig .3) o l lo win g p u m p sh u t - d o wn , w i th a n d w i th o u turgesuppression and also with a single air pocket located atlL = 0.53(Conditions: single pump with heck valve, init ial steady f low8.9 11s;pump iner t ia moment0.3 kgm2; pump character ist icsp1 = 60.0, ll =- 1 72.3, l3 = -537.7); pump speedN , 2900 rpm; sump evel 6.02 m ;surge suppression at pum p delive ry-air ch ambe r star t air vol ume.4m3;p ipe l ine o f pvc ; s ta t ion ead loss coefficient l , 10.5)

pressures at the corresponding section.n thelower range, volume incrementation a s small a s0.005 m3 was onsidered in the computations.For thi s pipeline, a sm all air pocket volume ofapproximately 0.025 m3is seen to cause on-

siderable enhancementof positive peak pres-sures at all four sectionshown. Beyond acertain cri t ical volume and downstreamof theair pocket, the pressure head duty decreaseswith the increaseof air pocket volume untiloptim um status is atta ined here init ial steady-state (dyna mic ) pr essu res are ot exceeded. Forupstream sectionsof the pipeline, the picture ismore confused; here, optimal airpocket volume

6V = 0 0 with surge suppression

=o.oo

10 20 30 40 50 60 70 80Ti m e : S

Fig. 5. Var ia t ion o f su rge p ressure a t pump ex i t in p ipe l ine a(Fig.3), under condit ions detailed in Fig.

355


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BURROWS AND 8 I U

50 -

4 0

E

-

I - -

30--m

20 -

-

22 -

E

m

2 1 8 -

:-m --

14 -

-.-

I

0 200 400 600 800 1000 1200400 1600Dis tance a long p ipe l ine : m

Fig. 6 . Comparison of maximu m and minimum head envelopes alongpipeline b with different air pocket volumes ( located at/ L = 0 .4 1 )(Conditions: single pump with heck valve, init ial steady f low 54.11s;pump iner t ia moment 0.3 kgm2; pump chara c te r i s t ics p , = 60.0 =- 5 1 6 . 9 , p 3 = - 4 8 3 8 .9 ) ; p u m p sp e e dN , 2900 rpm; sump leve l 13 .11m ; pipeline of pvc; s ta t ionhead loss coefficient c,1 0 . 5 )

10 20 30 40 50 60 70 80Time: S

Fig. 7, Var ia t ion o f su rge p ressure a t pump ex i t wi th and wi thou t a i r

pocket (atx / L = 0 . 4 1 ) in pipeline b ', under condit ions detailed inFig. 6

56

(that minimizing ultimate maximum pressure)is finite. f pocket size is increased furth er,some growth in transient pressures is caused,albeit to valuesclosest to the figuresproducedwhen air is absent V = 0.000). The validityofthe modelling becomes questiona ble for largeair volumes since such accumulationswould

have frictional implications, and , in extrem ecases, thecomputed volumes may extendacross adjacent reach boun daries, whence modi-fied compu tation should be made at theaffectednodes. Neither of these aspects is currentlyincorporated.

29. On the bas is of the evidence collected,the following hypothes isis offered for theeffect of ai r voids. Following sudd en chan ge inoperation, such as pump shut-down, pressurewaves propagate back and forth along the ipe-line, being reflected from the upstream anddown stream bounda ries while being damp ed bypipe friction. Intermed iate air pockets introducean energy source to theluid flow system, andan internal boundary rom which the pres surewaves will be modulated and partially reflec-ted. Moreover, by virtue of the cushioningeffect of their volume change under pressurevariations, they are able to bring ab out aoregrad ual deceleration of the flow by conv ertingpar t of the rapid fluid transien t into amorecontrolled m ass oscillation. T his actionis com-parable to thatf an air chamber but withoutthe additional friction damp ing rovided by anoutflow/inflow constriction.Small air pocketsproduce a mas s oscillation period longer than

the transient pressure waverequencies, whichare typic ally four imes the travel time betweenrelative boundaries. Thisperiod increases andthe pressure amplitudes educe as the airpocket size is enlarged.

30. Detailed scrutiny of Fig.7, aided byother output datanot included here, show s, forV = 0.025 m3, a ma ss oscillation of appr ox -imately 24 S period, w ith a first cycle amplitud eof about 16 m head. Superimposed on this is asmaller oscillation characteristic of the tran -sient oscillation between the pump/valve andthe air pocket. Time series, at the sectionson-sidered in Fig.9, confirm the time sync hro-niza tion of the ma ss oscillations (Q iu, 1995 ).Th e wave form arisin g from the behaviou r ofthe air pocket is illustrated in Fig.8, but herefor the slight ly larger olume ofV = 0.05 m3.T hi s form, w ith narrow peak a nd elongatedtrough, is characteristicof experime ntalobse rvatio ns of air accum ulations Jonsson,1985'). For the larger airvolume, V = 1.000 m3a ma ss oscillation of much smaller amplitud e,about 4 m head and 55 S period, arises. Thispocket, however, now reflects a much stro ngertransient wave than the small airocket suchthat the trace n Fig.7 is dominated by th is

componen t. Downstream of the airpocket,stron ger evidence of the transi ent press ure


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waves is seen for the small airolumes, demon-st rat ing lessefficiency in the energ y c onve rsionto massoscillation and the weaker reflectivecapa bility of the sm allpocket.

31. The findings in respect of the massoscillation element of the beh aviour are consis-tent with the onclusion of Jonsson (1985)9 from

his f ield observations and numerical analysisfair cush ion form ation n front of a pum p checkvalve. In fact, Jonsson show ed that the sim plerinelastic, rigid column, ana lys is of the oscil-lating waterbetween the upstream reservoirand the air ocket gave reasonable predictions.For sm all air volumes, with more rap id oscil-lations, Jonsson demonstrate d the need for theelastic properties of the wate rcolumn to beincluded by application of the w aterham meranalysis, as considered here. W ith t he airpocket at thecheck valve, the whole pipeline issubjected to the m ass oscil lation nly, a sdemonstrated by Jonsson's results.When theai r pocket is at an in ternalhigh point, theupstream sectionof the pipeline is still subje ctto the transient pressure cycles, as seenn Fig.7, which now trave l back and forth between thepum p/check valve and the air ocket. In thecase of large a ir pocke ts, the result ing p ressurevariations will be dominated by these transientfluctuations since the amplitudef mass oscil-lation will be small . This accordswell with th efield obser vatio ns of delivery main pres suresreported by Jonsson (1994)14and Larsen andBurrow s (1992)13.This tendency for large airpockets to approach the actionf a reservoir(constant head) boundary condition reduces theeffective length of the pipeline and cansocreate larger transient peaks,as evident fromthe results inFig. 9.

32. Figure 9 also investigates the influenceof the polytropic exponentn , describing thebehaviou r of the gas n the pocket (see equation4)). he e xponent depends n the thermodyna-

mic process followed by the gas n the pocket.If a perfect gas is assu me d: at ne extrem e, theprocess may be isothermal,n = 1.0; or at theother limit, it may e isentropic (reversible,adiabatic), n = 1.4. For smal l chambers or accu-

mulators with fast response t imes, the processmay be taken as isentropic (Wylie and S treeter,19783).In larger systems wi th a larger watervolume and sm all air mass, the transformationmay approach an isothermalprocess. In orderto examine the ffect of polytropic exponentson surge p ressure predictions, wo extremecases and one average casewere considered inthe fore going analyses. it is lear from Fig. 9tha t the value of the polytropic exponen tisonly of seconda ry im portance in these studie s.If not stated otherwise, a valueof 1.2 ha s beenassumed elsewhere herein.

transients when the pipeline' b ' syst em i ssubject to delayed pump tr ip-out is shownn

33. Th e effect of a ir pockets on the pressu re

51

41

E..m

31

EFFECT OF AIRPOCKETS ONSURGE PRESSURE

4 t = 0.02A t = 0.10

- d t = 0 . 2 0xlL = 0.41 air pocket location)

1 1 ~ ' ~ ' ~0 10 20 300 50 6 70 80

Time: S

Distance alongpipeline: m

Figs 10 and 11. The second pump run-down is Fig. 8. Stabil i ty estdelayed by 25 S relativ e o hat of the irst o n computationalpump.Theair pocket isagain located at the routines;maximumhigh point and the behaviour is sim ilar to that and minimum headfor the uddenpump hut-down, here now envelopes nd headbeing nhancedultimatepressureduty long profilesassociatedtheentire pipelinewhen the air pocketsize is withresults invery sma ll (0.025 m3). For theotherair pocket Table lvolumes considered inFig. 10, little changeisseen in the maximum head envelopes. Th e

delayed trip of the second pum p assis ts surgesuppression and maximum pressure experi-enced during a transient w ith no a ir present isthe normal dynamic duty, represented yP(maximum)/P(steady sta te)= 1.0 in Fig. 11.This is seen also toe the case for air p ocketsof size grea ter than .5 m 3 at ach section of thepipeline considered in Fig.11

34. The expa nded scale of Fig.11, againstFig. 9, mak es clear the obse rvation that differ-ent points along the ipeline will the suscep-tible to maximum peak pressu re enhancementby air pockets of differing (small) ize and also,altho ugh not illustrated here (Qiu, 199515),odiffering airpocket location.

35. For pipelines constructed over undu -


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EFFEC T OF AIRPOCKETS ONSURGE PRESSURE

appears to cause amore general and greaterrisk to the pipeline system.

Conclusions38. The examp les presented in this paper

have i l lustrated the varying influence that airpockets can have on the surge experienced in

pipeline systems operated without the protec-tion of surge suppression devices. n extremecases, the high peak pressures arising mighteexpected to have a potentially catastrophiceffect: peak pressure enhancements a s high as1.6 or even 2 times the normal steady-flow dutypressures have been predicted.

39. While a larg e air cavity acts as an effec-t ive accumulator and suppresses the maximumpressure excursions-following pump sh ut-down , for example-it seem s that suchvolumesplit between multiple pockets can subs tan-tially exacerbate the peak pressures experi-

enced. In either situa tion, the presenceof only asmall air volume (in these exam ples< 0 5 m3)isthe ca use of significant peak pressure enhance-ment.

40. The degree of peak pressure enhance -ment has been shown to dependon both theposition of the air p ocket n the pipeline and thelocation along the pipelinewhich is under scru-tiny. The quantitative data presented herein arespecific to the pipeline configurations investi-gated and no attempt at transposal to othersi tuat ions is justified.

41. Th e potential impact of air entrain men tin pipeline systems has een widely understoodfor some time by researchers in the field, andthe topic is covered extensively in the liter-ature, only a s mall samp le rom which ha s beencited here. Field evidenc e of peak pres sureenhancements have been reported by Jonsson(1985)9 and Larsen and Burrows1992),13among others, and both ffer mathematicaltreatment in the m anner outlined here s themeans for satisfactory synthesisf the pipelinetransients. Lee (1993),' however, advocates thesimulation of gas release and re-absorption, ina variable wave speedmodel, in order sim ilarlyto reproduce the observed high pressure peaks.

A need clearly remains for further controlledhigh quality data, rom field or laboratoryexperimentation, to enable absolute verificationof the modelling approaches.

subject is offered in this paper; i t has een theauthors' aim simply to demonstrate, by system-atic computer synthesis, the potentially adverseimpact of air accumulation on pipeline systemsunprotected against surge, and to bring i t to thenotice of the professio n a t large.

43. From first-hand experience of one post-failure inquiry, it proved impossible to demon-strate through routine applicationf acomputer model, that extreme pressure tran-sients, created at the t ime,f several repeated

42. No new theoretical advance on the

1'301-Polytrophic exponen tn = 1.2

Initial air pocket volume:m3

pipe failure incidentson the sam e pipelinewould exceed normal pipe working stresses.This arose in the circumstance where an airchamb er had been taken out of service and nostep s were taken for surge sup pression b y theoperators. The computer analysisdentified andsimulated the effect of cavitation. The pipelineprofile contained an intermediate high point,but no automatic air venting w as incorporated.In circums tances where air (gas ) ocket forma-tions are possible (a highly likely situationnsewerage systems) and air ventings ineffec-tive, it ha s been demons trated h ere th at pe akpressures can be considerably enhanced overthose arisingfrom cavitation if the pocketvolume is of som e critical dim ension at the timethat the serious transient is generated.

44, It is the authors' view that such impon-

derables as possible air accumulation and,perhaps equally, air entrainment,which canhave a seriouseffect on peak pressures, shouldbe appraised and incorporated in analysis as amat ter of routine w here ris k of surge exis ts.Those charged w ith assess men t of pipeline p ro-tection should ensure that all feasible oper-ational scenarios likely to give rise to severetransients are fully investiga ted and reported tthe design stage.Of special relevance in thisregard is the si tuation where surge suppressiondevices may be temporarily taken out f servicefor emergency repair or replacement while thestation must remain in service.

Fig. l l Vari ation ofu l t imate maximumpressure du ty, a tsections alongpipeline withincrease in air pock ets ize (a t x /L = 0.41),fo r delayed pumptr ip -ou tas detailed inFigure 10

Appendix 145. As the pump slows down after power failure,

i t s head/discharge and torque/discharge character-istics change. Its cus tomary to a ssume tha t , a shepump speed changes, the pump characteristics at anyspeed can be found using the similarity relationshipsfor homologous pumps, s fol lows (Wat ters ,1979' )

N T = constant

HP--N 2 D 2 onstant

T-- N 2 D ~ onstant


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BURROWS AND QIU

1.81

1 o L

where Q , H P, T nd N are discharge, head increase(lift), torque and rotational speed respectively; spump dimension (generally the impeller diameter).For a particular unit , the homologous equations maybe represented by

Q 2 = Q , ( N , / N , )

H P, = H P, ( N l / N , ) 2 (10)

T2 = T, ( N 2 / N J 2

The subs cr ipts efer to two homologous opera t ing

0 2 4 6 8 10246

a)

i '.

1 1 I I I I I I

Total air,pocket volume: m3(c)

Fig. 12. Variation in ult imate maximum pressure duty at differentsections along pipeline c Fig.3) with air pockets at f ive high pointsand volume distr ibuted: (a) equally;b ) linearly increasingdownstream; (c) l inearly decreasing downstream (Conditions singlepump with check value, init ial steady f low53.3 1ls;pump condit ion is

same as Fig .4 ; sump level 6.21 m ; ipeline of pvc; stat ion ead losscoefficient c,10.5

360

si tua t ions.For various speeds, the pump character-i st ics are ca lcula ted from the or iginal curve a to .

found by using the basic equation for torquesfollows

46. The chan ge n speed of pump rotation may be

T = - I (do/dt ) (11)

where I i s themoment of inertia of rotating parts,

including the l iquid within the impeller; and dw/dtsthe angular acceleration. n a finite sm all t ime inter-val At, the torque is represented as the averagef T , ,the kn own torque at begin ning fAt , and T,, theunknown torque at the nd ofAt. Integra t ing equa-tion (11) and replacing angular velocityW by rotationspeed N yields

Np = N , - - ( T p T,)15At

IrI

This i s the computa t ional formulaf rotational speedafter power failure. Since there are two unknownva lues i n equa t ion12), the new speed N , cannot bedetermined. According to the homologous relation-ship, equat ion lO) , however, T , = To (N , /N o )2 ,ndel iminat ingT , in equat ion 12) yields a quadraticequa t ion a s

.IN:

in which subscript0 denotes the steady-state condi-t ion; and subscr ipt1 designates the condition atbeg inni ng of At. The new rotational speed can ow bedetermin ed exp licitly using the kno wn v alues ftorque and speed. I t i s then possible to proceed wi ththe calculation for the heads and discharges undertransient conditions. The factors f the p ump charac-teristic curve under ew speed-p,, / l 2 and p,-maybe found by using a regression method.

References1. Fox J. A. Hydraulic analysis of unstead yflow in

pipe networks.MacMillan Press, London,1977.2. TWORT . C. et al. Water supply.Edward Arnold,

London, 1994.3. WYLIE . B. and STREETER. L. Fluid transients.

McGraw -Hill, New York, 1978.4. EWING . J. F. Allowing for free air in water-

hammer analysis.Proc. 3rd Int. Conf. n PressureSurges. British Hydromechanics Research Associ-a t ion, Canterbury,1980, 127-146.

5. LEET. S . Numerical m odelling and com putation offluid pressure transients with air entrainment inpumping insta l la t ions. roc. Int. / . f o r N umerica lmethods in Fluids, 1993, 19,89-103.

6. WHITEMAN . J. and PEARSALL. S. Reflux valveand surge tests at Kingston pumping station.BHRA/National Engineering Laboratory,Glasgow, Joint Report1, 1959.

and surge tests a t a s ta t ion.luid handling, 1962,XIII, 248-250 and 282-286.

suppression techniquesfor a water supplyscheme-a case study. Trans. Inst. meas.Control, 1985, 5, No. 4, 134-142.

9. JONSQN L. Maximum transient pressures in aconduit with check valve and air entrainment.Proc. Int. Conf. on the Hydraulics of Pumping Sta-tions. British Hydromechanics Research Associ-ation, Manchester,1985,55-76.

7. WHITEMAN . J. and PEARSALL. S. Reflux valve

8. DAWSON. A. and F oxJ. A. Surge analysis and


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EFF ECT OF AIRPOCKETS ONSURGE PRESSURE

10. THORLEY . R. D. Fluid transients in pipelinesystems. D. L. Geor ge, 1991.

11. MART IN . S. Entrapped air in ipelines.Proc. 2ndInt. Conf.on Pressure Surges. British Hydro-mechanics Research Association, London1976,F2-15-F2-28.

12. SAFWAT . H., ARASTU A. . and HUSAINI. M.Generalized applicationsof the method of char ac-teristics for the analysisf hydraul ic t ransientsinvolving empty sections. o c . 5 t h nt. Conf. onPressure Surges. British HydromechanicsResearch Association, Hannover,1986, 157-167.

13. LARSEN . andBURROWS. Measurements andcomputations of t ransients in pumped sewerplastic mains.Proc. BHR GroupllAH Rnt. Conf.on Pipeline Systems, Manchester, 1992,117-123.

(eds)). Leak detection in pipelines using hydraulict ransients .Hydraulic engineering software V Vol.I : Water resources and distribution.Computa-tional Mechanics publications,1994, 344-352.

15. Q I UD. Q. Transient analysis and the effect of air

14. JONSSON L.BLAINW. R. and KATSIFARAKIS. L.

pockets in a pipeline.Department of Civil Engineer-ing, Universityof Liverpool, 1995, MPhil thesis.

16. LARSEN. Waterh ammer a tp u mp sh u td o w n( WH PS) .Torben Larsen Hydraulics Aps,Aalborg, 1992, Programme User Guide, version2.13.

hammer.J. H y d rau l . En g n g , A m.oc. Civ. Engrs,17. WYLIE . B. Fundamen tal eq uationsof water-

1984, 110, NO. 4,539-542.18. WYL IE E. . Closure to discussio ns on

' Fundam ental equations of waterhamm er'. 1.Hydraul. Engng,Am. Soc. Civ. Engrs,1985,111,NO.8,1197-1200.

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WHPSDEMO.Torben Larsen Hydraul ics Aps,Aalborg, 1992.

21. LARSEN. escription of the demo program:

Effect of Air Pockets on Pressure Surge Burrows Et Al (1)

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