NASA-TM- 107072

NASA Technical Memorandum 107072 I_ q_00 0_/00

Static Flow Characteristics of aMass Flow InjectingValve

Duane MattemNYMA Inc.Brook Park, Ohio

and

Dan PaxsonLewis Research CenterCleveland, Ohio

November 1995

i JA;'.I O 1_3I 'NationalAeronauticsand [ :SpaceAdministration //"w't r:,, r'-.qct r'r:'] _.:.: I c.,

LIP_R/',il'I';5"_S,",,tb',;,_pTo;],vIP,Gl_ltr_.......... --

NASA Technical

3 1176014235817

Static Flow Characteristics of aMass Flow Injecting Valve

Duane Mattern Dan PaxsonNYMA, Inc. Systems Dynamics Branch

NASA Lewis Group NASA Lewis Research CenterBrookpark, OH 44142 USA Cleveland, OH 44135 USA

(mattern@lerc.nasa.gov) (dpaxson@lerc.nasa.gov)

Abstract

A sleeve valve is under development for ground-based forced response testing of aircompression systems. This valve will be used to inject air and to impart momentum to theflow inside the first stage of a multi-stage compressor. The valve was designed to deliver amaximum mass flow of 0.22 lbm/s (0.1 kg/s) with a maximum valve throat area of 0.12 in2(80 mm2), a 100 psid (689 KPA) pressure difference across the valve and a 68°F, (20°C) airsupply. It was assumed that the valve mass flow rate would be proportional to the valveorifice area. A static flow calibration revealed a nonlinear valve orifice area to mass flow

relationship which limits themaximum flow rate that the valve can deliver. This nonlinearitywas found to be caused by multiple choking points in the flow path. A simple model was usedto explain this nonlinearity and the model was compared to the static flow calibration data.Only steady flow data is presented here. In this report, the static flow characteristics of aproportionally controlled sleeve valve are modelled and validated against experimental data.

IntroductionCompression systems for jet engines have long been vexed by a region of flow

uncertainty as shown on a typical compressor map in Figure 1. To gain an understanding ofthe fluid dynamics in this region of the compressor map, different models have been developed.These models need to be validated against experimental data to gain confidence in thepredictions made by these computer codes. An experimental study of the fluid dynamics ina compression system requires a means by which to perturb the flow. In low speedcompressors, (those with a rotational speed of less than about 6000 rpm) variable inlet guidevanes, bleed ports, the exhaust nozzle, and fuel flow have been used to excite the system.These actuation methods have bandwidths which are insufficient to excite some of the fasterdynamics in high speed compression systems, (those with a rotational speed greater than about6000 rpm). For example it has been shown that rotating stall fluid dynamics can haverotational speeds of 20-50 percent of the compressor shaft speed [1]. In order to excite thefirst three modes in a circumferential modal model of rotating stall [1], a bandwidth of 3 timesthe rotating stall speed would be required. For example, a compressor with a design speed of18000 rpm, (300 rps), and a rotating stall at 50 percent of the shaft speed, an actuator with aminimum bandwidth of 450 Hz would be required to stimulate the first 3 modes representedby a modal model. Thus, the development of a high speed valve for injecting air into the firststage of a multi-stage compression system was undertaken to provide the enabling technologyfor compressor research.

A high speed prototype valve has been developed under the assumption that the valveexit air mass flow would be proportional to a variable choking orifice area within the valve.Static calibration of the prototype valve uncovered a nonlinear relationship between the valveorifice area and the exit mass flow, caused by multiple choking points in the flow. A simplestatic flow model of the valve was developed to understand the causes of this nonlinearity. Inthe following report, the static flow model is presented and the results predicted by this modelare compared to the valve flow static calibration data.

Valve Static Flow Model

Figure 2 is a schematic diagram of the prototype valve, with a cutaway section to revealthe valve interior and the flow path. Air enters the manifold through the supply line inlet area,Ao. Aois sized so that the air manifold pressure is maintain near the supply line pressure. Theair then passes through the controlled orifice area, A_. AI is proportional to the linear positionof a sliding sleeve that cover a set of ports in the "arm" of the "sleeve" valve, as shownpictorially in Figure 3. The sleeve motion has a range of + 1 millimeter. Once the air passesthrough AI, it continues through a nearly constant area tube to the ejector exit area A2. Theimportant item to note in Figure 2 is the relative size of flow areas A ! and A2.The points ofinterest in the flow are: "1", which denotes the upstream supply conditions; "2", which denotesthe lumped volume between the supply and the sink (exit); and "3", which denotes thedownstream exit conditions. Figure 4 shows a schematic diagram of the valve model geometrywith points "1", "2", and "3" indicated. The following assumptions are made:

1) A o is large enough to provide suffice mass flow to the largest orifice area, Aj.2) The kinetic energy of the flow is lost after passing through the orifice area, A1.3) The system is adiabatic, (no heat exchange) and isentropic.4) The working fluid, air, is calorically perfect, (ideal gas with constant specific heats).5) No reverse flow will be encountered. .

In Figure 4, T, P, p, and w indicate the temperature, pressure, density, and mass flow raterespectively. The mathematical model of the valve depicted in Figure 4 is relatively simpleand is shown in Figure 5 as a block diagram. The calculation of the mass flow through Al,(w0, and the mass flow through A2, (wz), are represented by two of the blocks in Figure 5.The third block equalizes the mass flow through Al and A2 using continuity and the energyequation. The mass flow calculations for area_A_are:

1

Lt,P,J t,P,J J (1)

tRT,) t(y-1))with

PRF_ = Pressure Ratio Function (nondimensional)

2

w, = mass flow through orifice A,, (Ibm/see)A, = orifice area, (ft2)P, = upstream supply pressure, (psfg)T1 = upstream supply temperature, (deg R)P2 = pressure downstream of orifice, (psfg)R = ideal gas constant for air = 53.3 Ibf f/(Ibm deg R)gc = English units conversion constant = 32.17 lbf f/(Ibm s_)y = specific heat ratio for air = 1.4

Equation (1) and (2) originate from reference [2] and are derived in the Appendix. In the massflow rate calculation, the pressure ratio P2/P_is first checked for choked flow conditions. Ifthe flow is not choked then the actual pressure ratio across the orifice is used in equation (1).If the flow is choked, then the choked flow pressure ratio, equal to 0.5282, is used. Note thatthe mass flow calculation is idealized and no discharge coefficient is assumed. Using equations(1) and (2) with the appropriate substitution of "3" for "2" and "2" for "1" yields the mass flowrate equations for area A2:

__ _ (3)

w2 =A2P2(gc/½((y_l)).PRF2 (4)_RT2)

The steady mass flow through Axand A 2 is balanced by varying the conditions in the lumpedvolume, "2" and recalculating the two mass flows until equalization is obtained. This isachieved by using a lumped volume at point "2" and allowing continuity and the energyequation to provide balancing of the mass flow rates. Continuity at point "2" yields:

dP2 (wl - w2)- (5)dt V2

where

dp2/dt = the time rate of change of the air density in the lumped volume, (lbm/ft3)V = the volume of the lumped system, (fts)

An energy balance of the lumped volume yields:

dP2d-T = YR [T1wl- T2w2] (6)

whereT_ andT2 aretotaltemperaturesandCpisthespecificheatatconstantpressure.Equations(5)and(6)arederivedintheAppendix.SinceTlandT2aretotaltemperatures,andthereisnoheataddition,thenT2=TI.Itcanbeobservedfromequations(5)and(6)thatsteadyflowrequireswl--w2.Eqs.(5)and(6)representsimplifiedvolumedynamicsforsection"2".Currently,theseequationsareonlyusedtobalancethemassflowsforthisstaticvalvemodel.

Derivation of Nonlinear Flow Relationship

During the design of this prototypevalve, it was assumed that there would be onechoking point in the flow, that this point would be at the controlledvalve orifice area,point"1", and that it would always be choked for sufficientsupply pressures. For choked flow anda fixed supply pressure, PRFl from equation(1) would then be a constant, (P2/P1=0.5282forchoked flow). Plugging this constantPRF! into equation(2) yields an equationfor the massflow rate,w_ that is only a functionof controlledorifice area, AI and this functionis linear forconstantvalues of Pt,T_,and P2. As it turnsout, P2is not constant.Undercertainconditions,the flow can choke at point "2" and unchoke at point "1". Once the flow has unchoked atpoint "1", PRFI is no longerconstantand w_becomes a functionof A: and a nonlinear functionof P2. The resulting nonlinear relationshipcan be shown in a nondimensional format bymanipulatingequations(1)-(4). During steady flow, wg--w2 and equation(1) can be equatedto equation (3) as shown below:

W 1 =W 2

[RT=) [(¥-1))

The upstream supply conditions, P_, TI, and downstream sink condition, P3,T3, and exit area,A2, are all known. The orifice area A_ is the only variable to manipulate and the lumpedvolume conditions, P2, T2, and P2are the only unknowns. Noting that T2=Tl as previouslystated and cancelling like terms results in the following:

AlP1 PRFx = A2P2 PRF 2

[[Pt) kPx) J [kP2) [P2) J

Dividing through by the fixed, nonzero values A2and Pt yields the following nondimensionalmass flow function:

A_ [(P2/2 - (P2/!_x]½ _ P2 [(P3/3 - (P3/!_-x]½ (9)MFF[!,Pi) _PI) J P1 L_P2) _P2) J

This mass flow function can be used to examine the static flow trends as a function of the arearatio, for fixed Pt, TI, P3, and A2,without regard to units. The model was run to steady flowstate for several different controlled orifice areas, A_, for fixed values of Pt, Tt, Ps, and A2.Figure 6 is a plot of the mass flow function, MFF, defined in equation (9), versus the arearatio, A1/A2,with Pt=100 and P3=14.7psig, T1=68 deg F, and At=0.07 square inches). Also

plotted in Figure 6 are logical indications corresponding to choked flow for orifices A1and A2.For instances, in Figure 6, with an area ratio of 0.4, MFF=0.03 and both Aland A2 are chokedand for AI/A2=0.8,Az is choked and AI is unchoked. The choking at Az causes P2to be largerthan P3. A varying P2and equations (1) and (3) lead to the nonlinear relationship from A_tomass flow.

Comparison to Experimental Data

The valve was calibrated in the Flow Calibration Lab at NASA Lewis Research Center.The mass flow was measured using a calibrated orifice upstream of the valve at severaldifferent supply pressures. Figure 7 is a schematic diagram of the flow calibration setup. Thesupply pressure was measured just upstream of the valve inlet area Ao. The mass flow wasmeasured with the value in it full closed position to get a bypass or leakage mass flow rate.This leakage mass flow was used to estimate a leakage flow area in order to properly comparethe calibration data to the model generated data which does not include a leakage model.When the valve is fully closed, it is assumed that P2=P3 and equation (2) is used to estimatea leakage area, AU_k. AU_k and wu_ are used as the origin for the model estimated data.Thus the model area ratio and the model predicted mass flow are offset by A_ and w_I_respectively. Figure 8 compares the actual flow calibration data to the model predicted datafor supply pressures of 40, 60, and 80 psig, with atmospheric exit conditions and a fixed exitarea of 0.07 inches2, (diameter = 0.3 inches). The model predicted mass flows do not matchperfectly because the model is idealized, but the nonlinear trend observed in the data isrepresented by the model. It is clear that in order to maintain a single choking point at A_overthe entire range of operation of A_,that the exit area A2must be properly sized relative to thelargest controlled orifice area, A_, if linearity is to be maintained. Figure 9 is a plot of themass flow to orifice area for the prototype valve with three different exit diameters, ( 0.3,0.344, 0.375 inches), at one supply pressure, 100 psig. Note that the maximum possible massflow increases with the increase in the exit diameter and the linear range of the valve operationis extended.

A linear function for orifice area to exit mass flow makes the valve easier to implement.Also, the increase in useable range allows the valve to deliver more mass flow, increasing theeffectiveness of the valve for perturbing the fluid dynamics in a compressor. While only thestatic flow properties of the valve are being discussed here, it is important to note that toachieve this increase in mass flow an increase in the stroke of the sleeve is required. This willreduce the achievable bandwidth of the valve, for a fixed orifice geometry. The orificegeometry can be modified to obtain this increase mass flow range without changing the sleevestroke if necessary to maintain the valve design bandwidth.

Summary

A static flow model is used to predict the characteristics of a prototype air valve. Themodel predicted static mass flow as a function of controlled orifice area compare favorablywith the prototype valve static calibration data. The nonlinear relationship between controlledorifice area and valve mass flow is properly represented by the static flow model. The modelcan be used to properly size the valve exit area to provide for a linear relationship between thecontrolled orifice area and the valve mass flow. This linear relationship also result_in a largermaximum mass flow rate capability of the valve.

Acknowledgements

The authors would like to thank J.D. St. Clair and Andrea Clary in the NASA Flow Calibrationlab for providing the flow calibration of the prototype valve.

References

1) Gamier V.H., Epstein A.H., Greitzer E.M., "Rotating Waves as a Stall InceptionIndication in Axial Compressors", Journal of Turbomachinery, April 1991, Vol. 113.

2) Paxson Daniel E., "A Model for the Space Shuttle Main Engine High Pressure OxidizerTurbopump Shaft Seal System", NASA TM 103697, Nov., 1990.

3) Fox R.W., McDonald A.T., Introduction to Fluid Mechanics, John Wiley & Sons, 1978,ISBN 0-471-01909-7, p x.

6

Appendix

Derivationof Equations(1) and (2): The following analysis of seal leakage flow wasoriginal done for reference [2] and is applicable here. The flow consists of two sections, anozzle region and a constant area duct region. Assume that the flow is isentropic andadiabatic. Continuity yields:

w= pAu(A1)

w = _ PoAMaIO

wherew = mass flow rate through the nozzle, (Ibm/s),p = density of the gas at the nozzle, (Ibm/f3),po = density of the gas upstream of the nozzle, (lbmilS)m

( )o = denotes upstream conditions,A = duct area, (sq. ft),u = gas velocity, (fps),M = gas Mach number, (nondimensional),a = sqrt( yRTgc) = speed of sound at the nozzle, (fps),_, = specific heat ratio, (nondimensional),R = ideal gas constant (lbr f / Ibm deg R),T = local gas temperature, (deg R),g¢ = English units conversion constant = 32.17 Ibff/(Ibm s2).

For a calorically perfect gas (isentropic):

Po

Substituting for "a" in equation (A1), and using equation (A2) to replace "T" and P/Poyields:

w = ,t PoAM y_-'ff_(A3)

w = _o v PoAM y_/y'_o (PoJ

Using the definition of "total" enthalpy yields an equation for the square of the velocity:Noting that u2=(Ma)2 and using equation (A4) yields:

U 2ho =h + --2

u2 (A4)cpTo = CpT + --2

U2 = 2Cp(To - T)

a 2M2 = 2c P(To_i-)

M2 _ 2Cp (To-T)¥R T

M2-2y-I (_-I), using Cp- YRY_I (A5)

M2 - 2 using P -fT/_-I3'-1 P'o /'Too)

Equation (A3) can be simplified using (A5) and the ideal gas law, (po=Po/RTo),yielding:

w = (P/IA Pogc 2y_l [(P/2- _ [(P/-_3-__ 1] ]½_Po) R_ff_og_ _Po) _Po)

w = APo I_--_ogc (2--_Y1)½[1-(_oo)'_1] ½(_oo)¼ (A6)

w 4"which is the same as equations (1) and (2) in the body of this report.

Derivation of equation (5): This is simply the conservation of mass for a fixed control volume.M is the total mass in the lumped volume and V is the fixed volume.

Derivation of equation(6): Performing an energy balance on the control volume shown inFigure 4, using reference [3] and assuming no heat transfer and no work done on the controlvolume results in the following equation:

d_(w) =win- Wo.,

_(pV) win Wo._ (AT)Win - Wout

V

L v20 = epdv + (u +pv + m + gz)pu dA (A8)2

wherecv = control volumecs = control surface

e = u + V2/2+ gz, total energy per unit massu = internal energy per mass

Substituting for "e" and assuming the potential terms gz are small yields:

of. (u+ _)pdv =-f (u+pv+_)pu aA (A8)

Using the definitions of total temperature and specific heats and solving the integral for thelumped volume and the surface integral for the two ports yields:

-_(c_pT) = 01+T ) w (AS)

Substituting for pT=P/R and using the specific heat at constant pressure results in equation (5):

cv d

&( P )= [cpT,w,-cpT2w2](AS)

d-_( P ) : ¥R[TlW1 - T2w2]

ShadedRegion= Regionof FlowUncertainty

CorrectedMass Flow

PolePiece

Air MovingManifold Sleeve

MagnetAssembly

Voice Coil Actuated Sleeve Valve

Figure 2 Prototype Valve Schematic

10

PortsOpen Ports

Closed

ValveOpen ValveClosed

Figure3 Descriptionof a "Sleeve"Valve

ra

W2

IPl W1T1 '_

"Lumped"Volume

Figure4 Schematicof ValveModelGeometry

11

*ne*AaA:iupplonof hMa owAconon IwowEquzaoniCalcala_on of 1"2

Exit _ MassFlowConditions ThroughA2

Figure 5 Math Model Block Diagram

I , I r I . _ l ' I a I ,

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

AreaRatio,A 1/ A 2

Figure 6 Nondimensional Mass Flow Function versus Area Ratio

12

CalibratedOrificeforMass Flow

• Measurement,, ....................... o..o,,

0 i --_ ValveSupply

PressureMeasurement

............................... Tap

Figure7 Schematicof StaticFlowCalibrationSetup

Psupply= 40 60 80 pslg.14 =

! i °

; i I _ i i i 80Z i I I _ t i• ! ! ! ' I !

.12 i ! j ! ' : 'i ! E Ii i z , I i! z : . ii I _ i _ i :. 60

ol ti i i i "ii I I _ ..i : i i

.08 " I '

_" , i i I t i 40o I i i: = I

i i i = .

." .06 i ! " l ..................Ii..................! _ i _ i Ii I I' i :' I ! Ii

.o4 i I I , Ii i "

i i i I , I! : i I I

i i i i i........ 'i i ii i I , ,! . I t i I !

00 .01 .02 .03 ,04 .05 .06 .07 .08 .09 .1

Inlet Area (sq. Inch)VelldaUonof StaticValve Model (real data comparison)

Figure8 Comparisonof theModelPredictedMassFlowRatetoExperimentalDatafor3 SupplyPressures

13

ExltDlam=0.3,11/32,3/8Inches

.27 , i t I l ..! ! ! ! ! I/, I I i.......L .........................!...................L................L......_..._i ..............

_4 ...... I ! ! ! ! ..._ I !! ! ! ! ,.i-!'. " !_.. I! I I i _ 1 _ I

"-' ...................F.............;,..................!................__r ...............i ! i .>"1.:i i i i.................'__............•....................t........__! ..................

_..la i i i .J<"_""! i i ii i/=>" i : _,..,._' i it / ,,,_ i..__- i i iI i i i i

'."° i- i _i-_-r ...............i ,1;,-" i i ! ! !

•":' .....................F................f.......................................[..................T.................I....................!...................._" i

_"' Ii"! ! ! ! ! !...................L........_ ....................i i " i ' ' '

..............................i...................i..................i.................i...........I.................1.................06 "Z .......................................................................................................2"ii i i i i i

................_ _..........-i...................'...................'i-...............i............i...................i....................o3 --..7ii_- .............................:................................................................................l i i i '

0 I l f I I I I i I I I I 1 l I t I i I t I t t I I i I i I I0 .02 .04 .06 .08 .I .12 .14 .16

ControlledOrlflceArea(sq.Inches)MassFlowvl OrificeAreafor3differentexltareas

Figure9 ComparisonoftheMassFlowRateversusOrificeAreaforThreeDifferentExltAreas

14

I FormApproredREPORT DOCUMENTATION PAGE OMBNo.0704-0188Publicreportingburdenfor this collectionof Informationis estimatedto average 1 hourper response,includingthe time for reviewinginstructions,searchingexistingdata sours.gathering and maintainingthe data needed and completingand reviewing the collectionof Information. Send commentsr.egatdingthisburdene.stirnaleo_any other as .l:_t.of thiscollectionof Informationincluding suggestionsfor reducingthis ourden, to washingtonHeaoquarters_en/tces. utrestorate roemrormatlonUPeratlonsano Haports, 1215 JenersonDavis H_ghway.Suite 1204, Arlington.VA 222024302. and to the Office of Managementand Budget,Paperwork Reducton Project (0704-0188), WashIngton,DC 20503.

1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE [ 3, REPORT TYPE AND DATES COVERED

November1995 [ TechnicalMemorandum4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

StaticFlowCharacteristicsof a MassFlowInjectingValve4

6. AUTHOR(S) WU-505-62-50

DuaneMattemandDanPaxson

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATIONREPORTNUMBER

NationalAeronauticsandSpaceAdministrationLewisResearchCenter E-9936Cleveland,Ohio 44135-3191

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORINGAGENCY REPORT NUMBER

NationalAeronauticsandSpaceAdministrationWashington,D,C. 20546-0001 NASATM- 107072

11. SUPPLEMENTARY NOTES

DuaneMattern,NYMAInc., 2001AerospaceParkway,BrookPark,Ohio44142(workfundedbyNASAContractNAS3-25266)andDanPaxson,NASALewisResearchCenter.Responsibleperson,DanPaxson,organizationcode2560,(216)433-8334.

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE

Unclassified-UnlimitedSubjectCategory07

This publieatlon is available from the NASA Center for Aerospace Information, (301) 621-0390.13. ABSTRACT (Maximum200 words)

Asleevevalveis underdevelopmentforground-basedforcedresponsetestingofair compressionsystems. Thisvalvewillbe usedto injectair andto impartmomentumto the flowinsidethefirst stageof a multi-stagecompressor.Thevalvewasdesignedto delivera maximummassflowof 0.22lbm/s(0.1kg/s)witha maximumvalvethroatareaof0.12in2 (80mm2),a 100psid (689KPA)pressuredifferenceacrossthe valveanda 68°F,(20°C)air supply.It wasassumedthatthe valvemassflowratewouldbe proportionalto the valveorificearea. Astaticflowcalibrationrevealeda nonlinearvalveorificeareato massflowrelationshipwhichlimitsthemaximumflowratethatthe valvecan deliver.This nonlinearitywasfoundto be causedby multiplechokingpointsin the flowpath. Asimplemodelwasusedtoexplainthisnonlinearityandthemodelwascomparedto thestaticflowcalibrationdata. Onlysteadyflowdataispresentedhere. Inthisreport,thestaticflowcharacteristicsofa proportionallycontrolledsleevevalveammodelledandvalidatedagainstexperimentaldata.

14. SUBJECTTERMS 15. NUMBER OFPAGES16

Staticflow;Valve is. PRICECODEA03

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITYCLASSIFICATION 20. LIMITATION OF ABSTRACTOF REPORT OF THIS PAGE OF ABSTRACT

Unclassified Unclassified Unclassified

NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)Prescribed by ANSI Std. Z39-18298-102