Modeling Philosophy and Selection of Pumps for Use in Small Blowdown Experiments

8/6/2019 Modeling Philosophy and Selection of Pumps for Use in Small Blowdown Experiments

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MODELING PHILOSOPHY AND SELECTION OF ./J WVPUMPS FOR USE INSMALL BLOWDOWN EXPERIMENTS

B Y

D.J.OlsonAEROJET NUCLEAR COMPANY

r ABSTRACTIn order to conduct sm al l-s ca le expe rime nts which attempt to duplicate the hy -draulics phenomena oocurring during a loss-of-coolant aooident In apressurized waterreactor (PWB) plant, certain scaling philosophies must be employed to design the smallsy stem appropriately. Scaling considera tions must beapplied toall components ofthesmall system andspecifically tothe primary circulation pump. Operating character-ist ics of small centrifugal pumps are gen era lly quite different from those of PWRtype pumps and thescaling of the sma ll pump may Involve various com pro m ises. Th ispaper describes amethod bywhich the design of asmall pump is specified such thatthe operating characteristics ofthe pump are expected to approach those of alarge pumpwiljhln theoperating gomes of primary interest.

-NOTICE-This report wasprepared as an account of worksponsored by the United Slates Government. Neitherthe Un ited States nor the United States Atom ic EnergyCommiss ion, nor any of their employees, nor any oftheir contractors, subcontractors, or their employees ,makes any warranty, express or implied, or assumes anylegal liability or responsibi l i ty for theaccuracy , com-pleteness orusefulness


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/ i / / f _: "PUMPS FOR USE IN SMALL BLOWDOWN EXPERIMENTS

The op erating c ha rac ter ist ic s of the prim ary loop circulation pumps of a p re s s u r-ized w ater re ac to r (PWB) system are believed to play a significant role in determiningthe hy dra ulic beh avior of the system following a loss -of-c oo lant accident (LOCA},pa rticu larly one due to an inlet pipe rup ture .The acquisition of information leading to the understanding of the hydrau lic b e -ha vio r of a PWB system during the co urs e of an LOCA is the pr im ar y intent of the1-1/2-loop Mod-1 sem isca le pr oj ec t!* ]. This projec t is being conducted to aid indeveloping an und erstan ding of the phenom ena involved in an LOCA, to aid in exp loringthe effects of component simulation as they rela te to thes e phenom ena, and to aid in thedevelopment of a suitable data base for asse ssm en t of system respo nse analyses. TheMod-1 system is designed to re pr es en t, within known scaling limi tatio ns , a PWB systemin te rm s of hydraulic resis tan ce and system time respon se during an LOCA. Sincethe circulation pump is an Important pa rt of the sm all scale syste m , as i t also is in thefull size sys tem ,the scaling or sizing of the sm all pum p, with re spe ct to i ts large counter -part , is l ikewise important.Two con side ration s m ust be included in scaling a sm all pum p: (1) the pump m ustbe capable of op erating at steady st at e, single -pha se (water) fluid flow conditions co m -patible with the r eq uire m en ts of the sm all sca le sys tem , and (2) bec aus e of the lack oftwo-phase fluid flow data, single-phase flow performanc e c ha rac teri st ic s and sing le-phase flow theory must be used as an index for relating the large and small pumps. Sincesi m ila r ope ration during the two-phase fluid conditions of an LOCA cannot be ass ur ed ,the assum ption is made that whe re the homologous c urv es ar e not applicable to thetwo-ph ase condit ions approp riate cor relatio ns can be obtained between two-phasefluid conditions and pump performance.This pa pe r d iscu sse s two methods of modeling the ch ara cte rist ics of a PWB pump,

with em ph asis on the method chosen for the pump to be used in the 1-1/2 loop Mod-1sem iscale syste m . ._SCALING CONSIDERATION AND METHODS

The scaling of a small experimental system to be used to invest igate the hydraul ic"response of a large system involves several compromises because of practical orgeometrical l imitations. Bequirements imposed on scaling the small system includethe following: (1) the core fluid velocity for the small system must be consistent withthe de sired enthalpy ris e for a given core power and core geo m etry, and (2) the h y -draulic resistances must be specified such that the desired magnitude and distributionof pressure drops may be obtained for the given core fluid velo city. The design of thesem iscale system is based on both of these requirements with the result that a sm allpump is required that satisfies a head requirement similar in order of magnitude tothat of the larg e pum p and at the sam e tim e satisfie s ft capacity requirement ord ers ofmagnitude less than that of the large pump.Two procedures, both involving an index of performance and spe cific speed of thepum p, may be co nsidere d for modeling a sm all pump within these requirements: (1)the specific speed of the sm all pump may be maintained similar to the speoiflc speed ofthe large pump by l ine ar sca ling of al l important pump dimensions; and (2) the importantspecific-speed-dependent flow ch ara cte rist ic s of a large m ixed-flowpump m ay be m odeled,as nearly as possible, by implementing the proper constraints on the flow characteristics

of the sm all centrifugal pu m p. In its ba sic form , the spe cific speed of a pump i s & non-dimensional index which is num erically equal to the rotative speed at which a g e o -metrically similar model of that pump would operate In ord er to de live r one unit of


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capacity against one unit of head. Since pump rotative speed, capacity, and head allenter into the basic definition of specific speed, aspecific speed can be calculated forany given operating condition of a centrifugal pump. However, the operating specificspeed that gives maximum efficiency for a particular pump identifies the pump typeand intimately relates thephysical characteristics tothe general imp eller design .This specific speed, som etimes referred to as"type specific speed", is that specificspeed which is used iu basic pump design. Relationships between type specific speed andimpeller design are shown inFigure 1.The method of scaling the specific speed of the

8in

8 ooo*

Centerof

Values of Specif ic Speed N s head'

p- f Center ofRotation Centrifugal M lx flo Propeller Rotat ion

F I G . 1 VARIATIONS IN THE! APPROXIMATE RELATIVE IMPELLER SHAPES WITH SPECIFIC SPEED.

small pump tothat of the large pump (linear scaling) was considered unsatisfactory foruse insizing the semiscale pump because itresults in extremely high rotative speeds;thus, this method is described only briefly inthis paper. The method of modeling flowcha rac teristics , which was used for the sem iscale pump, is described in greater d e-tai l .METHOD OF LINEAR SCALING

The method of scaling specific speeds (linear scaling), ifstrictly implemented,results in a pump dynamically similar to the large pump with sim ilar performancecharacteristics. This similarity incharacteristics between a small pump and a largepump is termed" "homologous* and resu lts from the two pumps having sim ilar spec ificspeeds.Based on thehomologous theory, a linearly scaled sm all pump having a headrating, which remains esse ntia lly the same asthat of a large pump, but a flow rating

several orders ofmagnitude lass than that ofthe large pump, requ ires an imp racticalhigh rotative speed toachieve the necessary specific speed. For asmall experimentalsystem such asthe l- l/ 2 -l o o p Mod-1 semiscale system , this method of scaling resultsin the specification of a model pump with extrem ely high rotative speeds (15,000 to20,000 rpm ). Prim arily for th is r easo n, this method was not chosen for modeling thepump to be used in the l- l/ 2 -l o o p Mod-1 sem iscale s ystem .METHOD OF FLOW CHARACTERISTICS MODELING

The method of flow cha ract eristics modeling u se d fo r specification of the sem i-*scale pump is based on the premise that the homologoua head-flow curves, which aregenerated from single-p hase flow tests, and theory, a re applicable not only to tK Tsingle-phase region of the model pump perform ance, but al3o to that portion of the two-phasereg ion where the pump affinity laws are applicable. An example of the homologous head


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h - H/H rV= O/O ra = N/Nr

ANC-A-943-H

P I G . 2 TYPICAL. HOMOLOGOUS HEAD CURVES.

is shown inFigure 2. Hie homologous head curves are dimensionless extensionscommon four-quadrant pump char acte ristics curv es in whioh the param eters(head ), Q (capaoity), and N (imp eller speed) are made dim ension less through divisiontheappropriate rated (point of maximum efficiency) param eter . Hie homologousoffour dimensionless characteristic curves which are allon thesame set ofcoordinates. Inone case the dimensionless head ratio (h =as a function of the dimensionless flow (v *Q/Qr) Is plotted versus the dimen-(a N /N r) which also is a function of dim ension less flow; that is , h /v 8a function ofot/v. In the second case, the dimensionless head ratio as afunction ofis plotted versus the dimensionless flow as afunction ofdimen-nle ss speed; that i s , h /a 2 is a function ofv / c -^ this manner, the complete pumpall zones of operation can aerepresented by an intersecting


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set of eight cu rve s. These eight curves are indicated in the example of Figure 2 inwhich a three letter acronym Is used to designate the curve type. H ref ers to head ratio,A indicates division by a \ N indicates the normal pump zone, V ind ica tes division byv 2 ( D i s the zone of energy dissipation , R is the zone of rev ers e flow pump operation,and T is the zone of turbine operation.In order to design and specify a pump by modeling flow ch ara cter istics, three majordesign requirem ents must be con sidered to ensu re, as nearly as po ssib le, that the

performance of the sm all -sc ale pump will be representative of that of the PWR pumpduring an LOCA initiated by an inlet pipe break. These requirements are related tothe general shape of the homologous head flow curves and are as follows:(1) The nondimensional flow c ha ra cte ris tics of the sm all pump duringsteady state design operation a s w ell as during blowdown and refloodshould be sim ilar to that of the large pump._ _._. ^ g r a t i O of rated head to shutoff head and the ratio of rated flow toflow at zer o head for the sm all pump should be sim ilar to those of thelarge pump.(3) The maximum value of stopped rotor forward flow resis tan ce r elative

to the sm all system should be the sam e as that relativ e to the largesystem.The following paragraphs explain in more detail the significance of these requirements.Nondimensional Flow Characteristics

During the cou rse of an LOCA, the capability of a pump to rem ain functioning asa pump is a comp lex function of the sp eed and flow ratio s (N /N r and Q/Qr) of thepump. Flow rat ios for a sm all pump, such as that employed in the sem isca le sys tem ,represe ntative of those in a PWR, are con sidered to result from the design cr iter ia of theexper imen tal sy ste m . Since PWR pumps are designed and rate d, not for blowdown orabnormal cond itions, but for normal operating conditions, the ratio of operating torated conditions i s approximately equal to one. Likew ise, for a sm all model pump therequirement i s , therefo re, that the steady state operating flow and the rated flow r e -lationships be equal to one. Th is requirement i s represented by Point A in Figure 2.Ratio of Rated to Maximum Conditions

The r atio of rated head to shutoff head (H r /H m i i x ) has been determined to be approx-imately equal to 0.6 for a re feren ce PVvfi. Sim ilarly, the ratio of rated flow to flow atzero head (Qr/QmaJ h a B b e e n determ ined to be approximately equal to 0.67 for therefere nce PWR. In Tlg ure 2, the curve s designated HAN and HVN represen t the normalforward flow ch ara cter istics of a pump, and Point B rep rese nts the point of maximumhead for ze ro flow (shutoff head ). Point C repr ese nts the point of maximum forward flowfor zero head.

As previou sly imp lied, pumps of different spec ific spee ds have differently shapedhomologous cur ves; however, specification of the same rated to maximum cha rac teris ticsrat ios in the normal operating quadrant (represented for exa m ple, by Points B and Cin Figure 2) w ill ensu re that those operating lim its will , at le as t, be Approached in themodel pump in a manner representative of the way in which they are approached in aPWR.Maximum Forward Flow Resistance

The point during a pump transient at which the volum etric flow through a pump b e-co m es sufficiently great , because of external press ure grad ients, such that the pumplo se s the capability of generating head and becom es a hydraulic resis tan ce i s re p re -sented by Point C in Figure 2. The m aximum value of stopped rotor forward flowresis tan ce is represented by Point D in Figure 2 where pump rotation changes frompos itive to negative. The representation of this value i s indirect and re su lts from thefollowing derivation:


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Da rcy's equation for head los s is

whereH = static head, ftf = Darcy friction factor, dim ension less

T"~ f5 s length-to-diam eter ratio, dim ension lessV a fluid velocity, ft/secg = gravitational constant.

By substituting an assumed ove rall dimonsionless resista nce coefficient,K * - f , (2>

which inco rpora tes all of the complex hydraulic lo ss es within the pump volute togetherwith entrance and e xit lo ss e s, into Equation (1) the following exp ressio n i s obtainedelating head lo ss to resistan ce coefficient:v 2H " K* 2 i

Since the volumetric flow, Q (ft s /s ec )^ is the product of the fluid velocity, V (ft /sec ),nd the flow ar ea ; A (ft2), substitution QVA 2 into Equation (3) for V 2 results in42gA2r

Substitution of the homologous definitions, h H/H r and = Q/ Q r, Into Equation (5)oduces __K * ' h - < -

OrA resistanc e coefficient, R 1 , in common usage by experimentalists, which relates

m


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whereR ' = resistanc e coefficient, Ib f.s ec 2 / lb m - in .2-ft3AP = pressuredrop, lbf/in.2

:" p f lu id fluid density , lb m / f t 3w = flow arate, lb m / s e o .

Since w w.p~Q and E = (144) &P/p, Equation (7) can be re' . " ' ; . i: : H = 1 4 4 Q 2 R ' .

Equating Equations (4) and (S) results in. K *

Substitution of Equation (8) into Equation (9) gives

R - 2. ' A ' V i V 1 4 4 Q x

The quantity in paren theses is constant for a givenrpunip. 3Tie maximum value oft h f d d th i b l t e b f h / (th i t t i P i t_ q y g p pR ', therefore, depend* on the magimum absolute, vabie of h/ye (the inters ection PointD in the exam ple of [Figure 2) . The value of h /o * has toeec determined to be affunctionof specif ic | speed, with, the maximum absolute value decreasing with [decreasing specificspe ed. Thus, a mutually dependent relationsh ip ex is ts between the maximum possib lestopped rotor forward flow resista nce and the rated head-flow chara cterist ics of a givenpump. Figure 3 depicts the relationship for sev era l valu es of spec lflo speed within the range of consideration. Th is relationship must be considered when a pump i s specified'a n d may result in a comprom ise between the jfesired rated conditions and the desire dpump resistan oe. . ' . . . '

APPLICATION OF FLOW CHARACTERISTICS SCALING TO SEMISCALE PUMPthe requirements of the semiscale system design, attempts to simultaneouslysatisfy the three requ irem ents listed by an appropriate modification of an exis ting se m i-sca le pump resulted in these requirements beiag ranked in relative Importance. Becausethe main emphasis of the semiscale program is on th.e Inlet break situation, the majorityof the te st s wi ll result in forward flow through the pump. The pump transient path forforward flow w ill , therefore , be from Point A to Point C to Point D along the HVN curveas shown in Figure 2 . Since the magnitude and distribution of system resist an ces in -fluenoes the flow split in the operating loop and ultimately the core flow during an LOCA,the point at which the pump becom es a res ista nce (Point C) and the maximum value ofthat resis tan ce (Poiu: O) were considered most important in specifying the cha rac ter-is ti cs of the s m all pump. The initial operatlngpoiat (Point A) of tbe sm all pump was con -sidered next in importance because of the requirement on the sm all pump during thetransient to tra verse the path from the operating point to the point of maximum flowfor positive head (Point C) i* relatively the sane time as for the large pump. The pointof rated to shutoff head (Point B) is of least importance to current semiscale require-m ents, because operation on the HAN curve i s not anticipated. Table I giv es the e x -


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000 2000 3000 4000Specific Speed,Ns 5000 6000ANC-A-944-HF I G . 3 RELATIONSHIP BETWEEN HOMOLOGOUS HEAD PARAMETER AND SPECIFIC SPEED.

TABLE ICOMPARISON OF SIGNIFICANT PUMP PARAMETERS

Ratio ofrated to maximumconditions~H/Hr maxVS.ax

Ratio ofoperating to ratedflowMaximum forward flow resis-tance (R')l

ai(lb_-sec2/lb-in.2-ft3)r m

Specific speed \Rotative speed (rpm)

Semiscale

0.780 7 6 6 "

1.1

3.310002600"

[a] R1PUR (scaling factor relating semiscale to PVR)R'

Typical PWR

"'0.600767

1.0

4.65200~1200~

semiscale'


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pected values of the parameters for the semiscale pump and, for comparison, those ofa reference PWR. Figure 4 presents theestima ted homologous head curv es for thesemiscale pump based on the modeling philosophies outlined in this paper.

h =H / H rv - Q /Q ra =N / N rNormal PumpEnergyDissipationNormalTurbineReverse Pump

HATHV THARHVR

ANC-A-949-H

F I G . 4 ESTIMATED HOMOLOGOUS HEAD CURVES FOR THE 1 1/2LOOP MOO1 SEM I SCALE SYSTEM.

SUMMARYA method formodeling small pumps based on the single-phase homologous char-acteristics of large pumps has been chosen foruse in specifying the design of the1-1/2-loo p Mod-1 sem iscale pump. The suc cess of this method ofspecifying asmallpump depends on several factors, themost important being the applicability of thesingle-phase homologous theory to a pump within a system undergoing arapid two -phase fluid transien t. Currently many two-pha se pump test progra ms are underway orbeing planned inwhich pumps of variou s spec ific speeds' are to be tested through allzones of pump operation. Results of these test programs are expected to provide,if not a direct indication of theapplicability of the-sing le-pha se homologous theory,at least a data base onwhich todevelop an em pirica l or analytical cor relation betweenthe two-phase fluid conditions and pump perform ance.

REFERENCE1. J,O. Zane, "Separate Effects Testing," Annual Report of the Nuclear Safety D ev el-opment Branch, January 1 - December 31,1970, K. A. Dletz (ed.), ANCR-1089(November 1972) p155.

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Modeling Philosophy and Selection of Pumps for Use in Small Blowdown Experiments