One-Dimensional Simplified Compressible Flow Mode NASA Iterative Solution

Published on: **Mar 3, 2016**

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- 1. John F. Kennedy Space Center Kennedy Space Center, Florida 32899 Technical Support Package Simplified Model of Duct Flow NASA Tech Briefs KSC-11495 NIS/ National Aeronautics and Space Administration
- 2. Technical Support Package For SIMPLIFIED MODEL OF DUCT FLOW KSC-11495 NASA Tech Briefs The information in this Technical Support Package comprises the documentation referenced in KSC-11495 of NASA Tech Briefs. It is provided under the Technology utilization Program of the National Aeronautics and Space Administration to make available the results of aerospace-related developments considered to have wider technological, scientific, or commercial applications. Additional information regarding research and technology in this general area may be found in Scientific and Technical Aerospace Reports (STAR) which is a comprehensive abstracting and indexing journal covering worldwide report literature on the science and technology of space and aeronautics. STAR is available to the public on subscription from the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402. NOTICE: This document was prepared under the sponsorship of the National Aeronautics and Space Administration. Neither the United States Government nor any person acting on behalf of the united States Government assumes any liability resulting from the use of the information contained in this document or warrants that such use will be free from privately owned rights.
- 3. SIMPLIFIED MODEL OF DUCT FLOW INTRODUCTION Analysis of the safety of hydrogen disposal in the Space Shuttle Main Engine exhaust duet at Vandenberg was made difficult by the complexity of the transient fluid flow through the duct at critical times. Finite element analysis gave information on overall trends and on local flow, but did not match test data very well, and was much too expensive to u~e for adjusting input to match data. A simple one-dimensional program was developed, using a perturbation of duct exit area to account for duct friction loss, which could be used to iterate aspiration until inlet and exit momentum are balanced. The transient flow can then be calculated as a perturbation of the quasi-steady (equilibrium) flow computed by iteration. Only after the total transient airflow through the duct is known, can local conditions for combustion or explosion be evaluated. '- DESCRIPTION ~ ~ A description of the analysis and listings of the computer programs is given in ~, MCR-81-536, No. 084859, Vol. 1, 1/1-Scale VLS Duct Steam Inerting System, Phase III ~ Tests, Appendix C, which is attached. Also attached is a copy of Section 1.5 - Task V { Duct Transient Tests, from the same report, which~hows the application of this ~ analysis to the actual problem. ~ The first novel feature of this analysis is the inclusion of duct friction loss in an effective duct exit arca, so that the inviscid conservation of inlet momentum can .~ be used to make the solution iteration very simple. The second novel feature is ~ relating the transient duct velocity to the quasi-steady state (equilibrium) velocity ~ with'a simple differential equation. This separation of transient and equilibrium ~ velocity enormously simplifies the converg~nce problem. ~ However, the most important aspect of this work is to again demonstrate that the J~simplest analysis that captures the important features of a problem is the best analysis. ,APPLICATIONS This technique is applicable to any situation in which the knowledge of the transient behavior of average fluid parameters is important, and for situations in which finite element analysis is impractical beca~se of time or cost. The same technique c.an be extended to any' situation in which 'the average properties of a solution to sets of partial differential equations is required, and in which finite difference solutions ar~ impractical. In practice, this usually means solutions in at least three dimensions. KSC-11495 -1
- 4. MCR-87-536, No. 084859, Vol. Duct Stream Inerting System, 1, 1/7-Scale VLS Phase III Tests APPENDIX C AIR ENTRAINMENT ANALYSIS The a~entrainmen[ analysis requires establishment of a uasi-stead flowrate driven by the SSME and steam nozzle flows. A momentum balance iterauon between ~t inlet and exit. incorporating the engine and SIS flows and including aerodynamic shock loss of engine momentum, provides the quasi-steady velocities through the operational envelop~_ O~ce the quasi-steady velocities are calculated, ttansient velocities can be calculated_ An iteratIon to match transient velocity is used to determine the total duct airflow. Acceptable results are provided by a conscious effon to keep the analysis as simple as possible, emphasizing fIrst-order effects and one-dimensional flow_ Data from the Martin Marietta In-scale test series suppons the analysis. The equation for the ll-nnsient duct ,oelocit)· can be simply exp,·cssed in terms of the equilibrium duct ,,-elocity in the follolin<g marlnero If the duct velocity is defined to be the duct exil velocity, Dnd it tho . entrance lbss and the friction loss within the ducl arc expressed in terms of the duct exit dynamic pressure, then pll~ -- = exit dynamic pressure = exit loss 2g .K(p;:2}.....tmtrancelOss~..·friction·lOss pv 2 (1+K)-2< - ·tota.! duct loss. g . < If 'the flow is in equilibrium, the duct equilibrium velocity will be that velocity which results in a duct loss which results in a duct exit static pressure which is just equal to the ambient. pressure. The force available to accelerate or . decelerate the fluid in the duct is just "the difference between the equilibrium duct. loss and t.he transient duct loss times the exit area, or .i Lp . • m = - = mass Within the duct g The rate-ot-change of the duct velocity is just the acceleration of the mass in the duct, which in t.urn is just the ratio of the force to the mass. dV . {l+K)F-=a=-= (V2 _V2) dt m' 2L It KSC-i149~f'
- 5. The duct pressure loss coefficien[~ K, is determined using steam-air and helium-air test data. Values of K are selected for the computation of velocities arising from a known system flow and the resulting entrained air flow. . . dv V<t+~t) = V(t)+~t· dt where dv =(1+K)<Y2 _y2) dt 2L 'f and .K =Duct Resistance Coefficient L =Duct Length V.. = Duct Quasi-Steady Velocity V =Duct Velocity These resulting velocities are compared against velocities computed from pitot pressure measurements for discrete locations in Plane D (Figures 7-13, -14, -15). Once K is known for the duct geometry, it is independent ofvariatio'1 in gas mixture concentrations or scale factor and can be used for full size prediction. The quasi-steady duct flow and velocity obtained for each time step of the launch abon sequence (shutdown from RPL), shown in Figure C-1, are calculated using a momentum balance between the planes of the duct inlet and exiL Duct friction losses are incorporated when calculating exit momentum. The total duct resistance loss is the sum of friction loss, as ratioed to the duct exit dynamic head, pvi 2 ' and the dumping loss, which is the duct exit dynamic head. The total resistance is then PV2 (I+K)--t. KSC-11495 -2A
- 6. Scenario: Three Engines at RPL I Engine... -E 160 ::5 -4l c:: 'c;,-... 140 c::::t: w ...~ 0 c:: 120 ....4l at i90 c:: at ~ 100 C;;> c::::t: ...':I 80 0 v .:J :CI); I...lit 60(!I Shutdown Sequence-No.1, No.2. No.3 Eu.. 139 :;/, Max Detrimental ., o Unburned GH~ Flow Rate E ... - ~~--~-------------------- E u.. , ...... .......... C(H11bined Detrimental -0 Unburned GHl - 1 ............... / all ". w ..~ •••••/ "t2 ........, ..... .....-:-~-....... / ..... ......, 4l 40c:: :; /' fQ.., :~>/ ....··B .(.:" ',.....'l-.......-J.....- ............... ..................... .Q c:: / ._..."" '. .... "filii'" -_. ......0 ..... - , ::l 20 . L Engine 1 Engine 2 Engine 3 ........, '.'0. , Profile Profile Profile ., '. ,0 o 1 2 3 4 6 7 Time. I Figure C..l. FRF Shutdown Sequencefrom RPL (Case 2) Now, suppose the actual exit area is divided by the factor (l+K)1IZ so that the exit velocity is increased by the same factor. The exit dynamic head will be increased by the factor (1 + K) so that the dumping loss with the adjusted exi ~ area is exacdy equal to the acmal total duct resistance. Thus a simple equality ofinlet and exit momenmm can be used to iterate a solution to determine the aspirated air flow•. The Manin Marietta steamaair tests are used to evaluate the effective inlet momentum of the steamjets, using the same adjusted exit area and thus accounting for duct friction loss in that evalu~tion. rilvOUT =(rilAIJI +1i1.m:.w+m".o)vour Iilvour(l + K.)1IZ =thvlN' where IilvlN' = mvlla0+mvAIII. with vAlR =0 Once steam momentum is known, the momenmm of propellants at full scale or helium at In-scale injected through the SSME nozzles can be added. Evaluation of the nozzle flow momentum entering the duct is uncenain because of the variation in shock train losses as the -engine chamber pressure drops. A simple, conservative (approximately 6% greater loss than calculating multiple shocks) procedure is used (Ref 1). The ratio ofentrained air to engine propellant flow is 6.28 with a shock versus a ratio of9.72 without the shock. This is consistent with previous results of 6.0 obtained at MSFC. The nozzle exit flow passes through a single, normal shock to get[IhC appro:riatc ]IOSS in total pressure, * (M-2)'''' Pc =Pc • (.!tM2_!:!}T-. 1+ I 1+1 KSc-11495 -3A '.
- 7. where and Pc =engine chamber pressure p. = ambient pressure. The flow is then expanded back to a static pressure equal to ambient to get an adjusted Mach number M* is a dimensionless velocity ratio (Ref 2) fonned with the speed of sound at sonic conditions (M = 1) -so that for a given chamber temperature, M* is proportional to velocity. Thus the ratio is just the effect of shock loss on flow velocity, where , Since momentum is mass flow times velocity, the M* ratio is also the effect of the shock loss on momentum. .'Momentum· = Momentum x M M· The components of an energy balance, Figure C-2, are evaluated at static equilibrium at the exit, establishing exit momentum. The In-scale test results limit additional combustion of unburned hydrogen and air to 20% of the air available. Iteration convergence of momentum between inlet ) and outlet is accomplished by adjusting entrained air flow. .' KSC-11495 -4A
- 8. ---Hl HlOVapor (:to' H: Air ------- HlOVapor H20Liquid 183°F -..... ---- N, 10% H2 0 Oropou, Figure C-2. Complex Duct Flow Chemistry which Quickly [nerts Unburned Hydrogen Once the quasi-steady exit velocity for the abott condition is calculated, the transient air flow and velocity can be determined. The duct loss coefficient dc;tenmnes the aspiration decay rate for the entrained air. The resulting transient velocity curve is used to determine total air flow through the dUCl A duct velocity balance is used to detennine conditions in the duct matching the transient velocity. This calculated transient air flow is compared to the quasi-steady airflow at me time of interest to detennine the air flow ratio. . Figure e-3 displays validation of the momentum balance-calculation of quasi-steady velocities 900 800 700 600 ~ ;;. 1 500 ~ 8... a I 400 11 300 200 '00 0 ('1'bousandl) Helium Chamber Pressure. psig 0 Turbine Data 0 RPLDuctvet 6 Design PI Figure C-3. Correlation between Analysis and Data/or S;ngleEng;ne Helium and Steam Tests with K = 1 KSC-11495 -5A, , • '00 2 ..
- 9. using data from the steam/one-engine helium flow tests aU::lifferent helium chamber pressures. The chamber pressure can be increased to at least 10,000 psig without exceeding a duct exit Mach number of .44. Figure 7-18 presents airflow versus chamber pressure for the same conditions.' Figure C..4 illustrates perfonnance of a series of simulated full-scale helium-steam tests. Maximum entrained air flow occurs at 3900 psig and 16,1481bm/s, which is 83% of the 19,383 Ibm/s obtained during RPL. Engine momentum equal to RPL is reached at a helium pressure of 2474 psig, which supplies an airflow of 80% of RPL. These results indicate that helium is not capable of pumping the volume of air obtained in the combustion process. The significance of this result is that helium flow simulation of RPL conditions is not appropriate for study of splash-back, since the appropriate air entrainment cannot be achieved. 20 o 18 16 14 12 ~ ....Qi ~i 10 u.. .c: ~t:::. 8 6 . 2 0 0 c RPt o Max AJI Flow Figure C4. Full-Scale Helium-Stiam Air Flow Less Than RPL The duct exit Mach number is calculated at RPL conditions in response to concern that the total flow is beginning to experience restriction due to velocity effects. The molecular weight of all the gases is calculated for an exit temperature of 1830 F and yof 1.2 and 1.4. The resulting average Mach numbers are 0.417 and 0.386, respectively. This reflects conventional duct design philosophy and confinns that the duct is not too resaictive. 10 (Thousands) Chamber Plessure. psig 4 Equal Momen"m KSC-11495
- 10. The program listing ·':"-lO!'vlVEQ.FOR" contains the analYsis for the momentum balance between ducl inlet and exit. Nain engine shoclt loss and additional duct combustion are included. C MOMVEQ.FOR C C CALCULATES DUCT EXIT NOMENTUM A.~D ITERATES TO 1'-tATCH INLET C MOMENTUM. GIVES FULL SCALE EQUILIBRIUM VELOCITY WRT TIiwlE C TOM LISEC 7-14-87 C PROGRAN MOMVEQ $ DEBUG S STORAGE:2 OPEN(3,FILE='MOi'11.DAT',STATUS='OLD') OPEN(4,FILE='INP.DAT',STATUS='OLD') OPEN(5,FILE='MOf'-1.OUT',STATUS='NEi') OPEN(6,FILE='MOM2.DAT',STATUS='OLD') . OPEN(7,FILE='MON3.DAT',STATUS='OLD') READ(4,*)XK,AIRFLO.TIS,TOS,AE,SMVIN,HWIN,X,RHOL,CPA,CPW,HYK,CPH, + N,DELT,TA,PA WRITE(5,620) 620 FORMAT(IX,'TIlIE EQVEL XX AIRFLO BRAr XMVIN XNV XN + UH2 XMACHl') 650 FORl'otAT(F4.2,1X,F6.1,2X,F2.0,2X,F7.1,2X,F4.2,2X,F9.0,F9.0,F4.0, + 2X,F9.0,2X,F4.0) DO 700 I =1,N READ(3,*) T,XME1,VEl,XME2,VE2,XME3,VE3,~IVE1 READ(6,*) XMVE2,XMVE3,EMV,XME,UH2l,UH22,UH23,UH2 READ(7,*) TEEl,TEE2,TEE3,PCl,PC2,PC3 C LOSS MODIFIED EFFECTIVE DUCT FLOW AREA (FT2) AEFF = AE /«1 + XK) **..5) C ENGINE 1 MOMENTUM REDUCED DUE TO SHOCK XNACHI = «2/(HYK-l»)*«pel/PA)** «HYK-l )/HYK)-l) )**.5 IF (XMACH1 .LT. 1.) COTO 160 STARM1 =( « (HYK+1)/2)* (XMACHl)**2)/( 1+( (HYK-l )/2)*XMACHl**2) )**.5 PCPRIM1 = PCl*(STARM1**2)**(HYK/(HYK-ll)/ + «2*HYK/(HYI{+1»*(XlrIACH1)**2-(HYI{-1)/(HYK+1) )** + (l/(HYK-l) ~ x..~IPRIMl = «2/(HYK-l))*CCPCPRIMl/PA)**«HYK-l)/2)-l)U*.5 KSC-11495 -7A
- 11. ·,1, SRNPRl"ll = C«HYK+ 1)/2)" (Xl'-IPRIl'Il) *J 2/( 1+(( HYI-l )/2) *(XNPRI!'-Il) **2» + **.5 X:VIVEI = XMVEI * SR.~PIDrI1/5TARl'rIl GOTO 210 160 CONTINt!E C ENGINE 2 NONENTUM REDUCED DUE TO SHOCK .210 XMACH2 = ((2/CHYI{-1))'((PC2/PA)**((HYK-1)/HYK)-1))**.5 IF{XMACH2 .LT. 1.) COTO 170 STARM2 = C«(HYK+l)/2)*(XMACH2)**2)/( 1+( CHYK-l)/2)*~1'-IACH2'*2) )**.5 . PCPRIM2 =PC2*CSTARr-I2**2)**CHYK/CHYK-l»/ + C.(2*HYK/(HYK+1) )*CDolACH2) **2-~HYK-1 )/uriK+1»** (1/fH'A-1» X!'1PRIM2 = C(2/(HYK-1J)*C(PCPRIN2/PA)~«HYK-l)/2)-1»"*.5 SR..~PRM2 = «(HYK+l)/2)"'(X.~PRI!'-12)**2/(1+«HYK-l)/2)*(XNPRn-I2)**2» + **.5 XMVE2 = X."'IVE2 * SRMPRM2/STARN2 GOTO 220 1;0 CONTINUE , " C ENGINE 3 -·MOMENTUM REDUCED DUE TO SHOCK 220 XMA.cH3 = «2/(HYK-l»*«PC3/PA)**((HYK-l)/HYK)-I))**.5 IF(XMACH3 .LT. 1.) <iOTO 180 STARM3 =« (CHYK+1)/2)*(XMACH3)**2)/(1+( (HYK-l )/2) *DotACH3'-2) )**.5 PCPRIM3 =PC3*(STARM3**2)**CHYK/(HYK-l»/ + (2*HYK/(HYK+l »*fXNACH3)**2-CHYK-l)/(HYK+l') + **(l/CHYK-l» XNPRIN3 =((2/(HYK-1»*((PCPRI~3/PA)**((HYK-l J/2)-1 n**.5 SR."'1PRM3 = CCUIYK+1)/2)*'XMPRIM3)**2/( 1+( (HYl{-1)/2)* (X~IPRI:'-13)**2) J + **.5 XNVE3 = XNVE3 • SR:-JPRN3/5TAR~t3 COTO 230 180 CONTINl:E C ENTRANCE NO~tENTt:M (LB~I FT/SEC2) 230 X~I~I~ =SNV]~ + X~VEI + X:"I"E2 + X:'IVE3 KSC-11495 8A
- 12. C NOZZLE STEAM (LBM/SEC) ST~tIN = X * HvIN C ENGISE ~ASS FLOW COOLING HEAT REJECTION TO WATER (BTU/SEC) HREI = XME1 * CPW * (TEE1 - TOS) HRE2 = XNE2 * CPW * (TEE2 - TOS) HRE3 = XME3 * CPv * (TEE3 - TOS) C COOLING ENGINE EXHAUST TO !"IAKE STEA!'-l (LBM/SEC) EECS = (HREI + HRE2 + HRE3) / 970 DO 99 Kli = 1,100 C HEATING INLET AIR BY CONDENSING STEAM TO l"IAKE NEW H20 (LBN/SEC) HRAIR =AIRFLO * CPA * (TOS - TA) HRAIR =HRAIR/970 C 02 BURNED AS F(H2) (LBM/SEC) 02 = 8. * UH2 C BURSED AIRFLO RATIO, IS IT 20% OR LESS OF AIRFLO BRAT = 02*4.3l25/AIRFLO IF( BRAT ~GT••20 ) THEN 02 = 0.2*AIRFLO / 4.3125 BRAT = .2 ENDIF C CREATED EXCESS N2 (LBM/SEC) XSN2 =3.3125 * 02 C NEWLY BURNED UH2 BH2 =02 / 8 C NEW STEAM (LBM/SEC) XNS = 02 + BH2 C REMAINING UNBURNED H2 RUH2 = UH2 - BH2 C CORRECTION TO LOGIC FOR NO H2 FLOW IF( UH2 .EQ. 0.0) UH2 = .0001 . C COOLING REMAINING UNBURNED H2 TO MAKE STEAN HRU21 = RUH2/UH2 * UH2l * CPH * (TEEI - TOS) HRU22 = RUH2/UH2 * UH22 * CPH * (TEE2 - TOS) HRU23 = RUH2/UH2 * UH23 * CPH * (TEE3 - TOS) C COOLING SU~INATION CRUH2 = (HRU21 + HRU22 + HRU23) / 970 KSC-11495 ·-9A
- 13. C CONBt;STIOS AND COOLING OF AIR + UH2 (LBM/SEC) C LOWER HEATING VALUE OF H2 =51571 BTU/LBN HRCC =51571 * XNS/4.032 * 1/970 C SEW STEAM GENERATED (LBM/SEC) XNNS = EECS + HRCC + CRUH2 C EXIT ~ASS FLOlv OF STEAM CONPONENTS (LBN/SEC) STMOUT =STfvllN + XNNS + XNS - HRAIR C i'ATER DROPLETS AT EXIT (LB!'vl/SEC) HWOUT = .9 * HwiN" - STt-IIN - XNNS + HRAIR C UNBURNED AIR (LBM/SEC) AIROUT =AIRFLO - 02 - XSN2 C l'rlOLES OF MIXTURE ETAH20 = STMOUT/18.02 ETAN2 = XSN2/2S.02 ETAAIR = AIROUT/2S.97 ETAH2 = RUH2 / 2.016 ETAT = ETAH20 + ETAN2 + ETAAIR + ETAH2 C MOLE FRACTION XH20 = ETAH20/ETAT XN2 = ETAN2/ETAT XAIR =ETAAIR/ETAT XH2 =ETAH2/ETAT C flIXTURE MOLECULAR WEIGHT XM = (STMOUT + XN2 + AIROUT + RUH2)/ ETAT C AVERAGE GAS MIXTURE DENSITY (LBM/FT3) RHOM = PA * 144 * XM/( 1545 * TOS) C TOTAL DENSITY (LBM/FT3) RHOT =RHOM * (STMOUT + HWOUT + XSN2 + AIROUT + Rt:H2)/ +(STMOUT + XSN2 + AIROUT + RUH2) VEFF = (STNOUT + HlvOUT + XSN2 + AIROUT + RU'H2)/(RHOT * AEFF) VEQ = VEFF / «1+XK) ** .5) XMV = (ST~JOUT + HWOUT + XSN2 + AIROUT + RUH2) * VEFF DELMV = XMVIN - x."'1V IF(ABS{DELMV) .LE. (.OOOOOOl*XMVIN» GO TO 600 AIRFLO = (XNVIS/XMV)*AIRFLO 99 IF(AIRFLO .LE. 0.) GOTO sao KSC-11495 ~lO1-
- 14. WRITE(*,'(A)') 'CO~VERGENCE DID NOT OCCUR IN 100 PASSES' 600 CONTINUE WRITE (5,650) T,VEQtXKtAIRFLO,BRAT,XMVINt~"'MV,X!vI,UH2,XMACH1 700 CONTINUE GOTO 900 800 CONTINUE WRITE(5,670) 670 FORMAT(lX,'BACKFLOW INMINENT - COVER THE DUCT!') 900 CONTINUE STOP END .- KSC-ll4·.9S .-llA-:
- 15. The program listing "Dl"CTA.FOR" uses the quasi-steady duct ,·elocity and duct loss characteristics to generate the transient duct velocity. C DUCTA.FOR C C COMPARES TRANSIENT AND EQUILIBRIUM VELOCITIES DURING .-~ SS~IE C PART SCALE OR FULL SCALE STARTUP-SHUTDOlvN EVE!'!T. C TOM LISEC 1-27-87 C PROGRAN DUCTA S STORAGE:2 OPEN(3,FILE= 'DUCT.DAT',STATUS:'OLD') OPEN(4 ,FILE='DUCT.OUT',STATUS='NEW') PI =3.141593 A = 0 F =0 C C SCREEN INTERACTIVE PROMPTS ---------------------------------------- WRITE(*,'(A)')' DUCT DIAMETER,FT ' READ(*,*) DEFF WRITE(*,'(A)')' DUCT LENGTH,FT READ(*,*) Xi.. WRITE(*,'(A)')' DUCT FRICTION DISSIPATION CONSTANT, FL/D-DLESS ' READ(*,*) XK ' WRITE(*,'(A)')' KINEMATIC VISCOSITY,FTA 2,SEC ' READ(*, *) XNU WRITE(*,'(A)')' INITIAL TIME,SEC ' READ(*,*) TI vRITE(*,'(A)')' FINAL TIME, SEC (ENTER O.IF VEL. FREQ. DEP.) , READ(*,*) TF WRITE(*,'(A)')' TINE STEP, SEC (ENTER 0 IF VEL. FREQ. DEP.) , READ(*,*) DELT WRITE(*,'(A)')' INLET VELOCITY, FT/SEC ' READ(*.*) VIN WRITE(*,'(A)')' VELOCITY TRANSIENT AMPLITUDE, FT/SEC ' READ(*,*) A WRITE(*,'(A)')' FREQUENCY, HZ ' READ(*,*) F C C PRINT FORMAT ------------------------------------------------------ WRITE(4,570) DEFF 570 FORMAT(/'DUCT DIAMETER: ',FIO.2,' FT') WRITE(4,575) XL 5i5 FORMATe/'DUCT LENGTH:',FIO.2,' FT') WRITE(4,578) XNU 578 FORMAT(/'KINENATIC VISCOSITY :',F10.8,' FT"2/SEC') WRITE(4,579) A 579 FORi"lATC/'VELOCITY TRANSIENT AfvlPLITUDE =',FIO.2,' FT/SEC') WRITE(4,580) F 580 FORNATC/'OSCILLATION FREQL1ENCY =',FIO.2,' HZ'//) KSC-11495
- 16. WRITE(4,590) 590 FORMAT(7X,'TIME',7X,' K ' ,8X,'REYNOLDS',6X,'VEL.',4X,'EQ.VEL.', +5X,'V/VEQ') WRITE(4,592) 592 FORNAT(8X,'SEC' ,21X,'~O. ',4X,'FT/SEC' .3X' FT/SEC' /) C C i'rIAIN COMPUTATIONS OMEG =2*PI*F T =TI ------------------------------------------------- V =VIN C SELECTS DELT AND RUN Dt:RATION BASED ON FREQ. IF( F .GT.O) THEN TF =S/F DELT =.1*F ENDIF 620 RE = V*DEFF/XNU C SELECTS FREQUENCY DEPENDENT TEST VELOCITY RELATIONSHIPS IF(F .EQ. 0) GO TO 615 CALL SCA~VEQ(VIN,A,OMEG,T,VEQ) 615 CONTINUE READ(3,*) N DO 630 I=I,N 617 CONTINUE READ(3,*) T,VEQ DVDT = (I+XK)/C2*XL)*(VEQ**2-V*ABS(V» IF(VEQ .LE. 0.0) THEN VEQ =VEQ + 0.001 ENDIF VRAT = V/VEQ WRITE(4,600) T,XK,RE,V,VEQ,VRAT 600 FOR.NAT(2X,2(F10.2),F15.2,3(F10.2)) v = V +DELT*DVDT 630 CONTINUE END c C FREQUENCY DEPENDENT EQUILBRIUN VELOCITY PROFILE C SUBROUTINE SCALVEQ(VIN,A,OMEG,T.VEQ) VEQ = VIN + A*SIN(OMEG*T) RETURN END C KSC-1149S -13A
- 17. C FREQUENCY INDEPENDENT EQUILIBRIUM VELOCITY PROFILE C SUBROUTINE FULLVEQ(T,VEQ) IF (T .LE. 0.15) THE!iJ VEQ = 94.5 * (T/.15) ELSEIF (T .GT. 0.15 .AND. T .LE. 0.25) THE!' VEQ = 94.5 + 17.7 * «T-.15)/.10) ELSEIF(T .GT. 0.25 .AND. T .LE. 2.) THEN VEQ = 112.2 + 8.8 * «T-.25)/1.75) ELSEIF (T .GT. 2••AND. T .Lh:. 2.15) THEN VEQ = 121.0 - 121.0 * (T - 2.)/.15 ELSEr!"' (T .GT. 2.15) THEN VEQ = O. ENDIF RETURN END KSC-11495 -14A
- 18. /~ The program listing "TVBAL.FOR" uses the transient duct ,·elocit~· for a "elocity balance to determine total sirno,;. C TVBAL.FOR C C CALCULATES DUCT EXIT VELOCITY AND ITERATES TO NAT.CH TRA!'>JSIEKT C EXIT VELOCITY. GIVES FULL SCALE TRA~SIENT AIRFLOi ~RT TINE C TOM LISEC, 8-20-87 C PROGRA.~ TVBAL $ DEBUG $ Sl'ORAGE:2 OPEN(3,FILE:'MOM1.DAT'.STATUS:'OLD') OPEN( 4,FILE:'INP.DAT',STATUS:'OLD') OPEN(5,FILE:'TVBAL.OUT',STATUS:'NEW') OPEN(6,FILE:'MOM2.DAT',STATUS:'OLD') . OPEN(7,FILE:'MON3.DAT'.STATUS:'OLD') READ(4,*) XK,AIRFLO,TIS,TOS.AE,SMVIN,HWIN,X,RHOL,CPA,Cpw,HYK,CPH, + N,DELT,TA,PA WRITE(5,620) 620 FORl"tAT(IX,'TI~1E EQVEL XX AIRFLO BRAT XMVI~ ~"IV X!"I + UH2 XMACHl') 650 FORl"1AT(F4.2,lX,F6.l,2X-,F2.0,2X,F7.l~2X,F4.2,2X,F9.0,F9.O,F4.0, + 2X,F9.0,2X,F4.0) '"'; DO 700 I = l,N READ(3,*) T,XMEI,VEl,XME2,VE2,DrIE3,VE3,X.1YIVEl READ(6,*) XMVE2,XMVE3,EMV,XME,UH21,UH22,UH23,UH2 READ(7,*) TEEl,TEE2,TEE3,PCI,PC2,PC3,TVEL C LOSS MODIFIED EFFECTIVE DUCT FLOW AREA (FT2) AEFF : AE /t( 1 + XK) ** .5) C ENGINE 1 MOMENTUM REDUCED DUE TO SHOCK XMACHl : «(2/(HYK-I) )*( (PCl/PA)**( (HYK-l )/HYK)-l) )**.5 IF(XMACHI .LT. 1.) GOTO 160 STARMl = ««HYK+I)/2)*(X.~ACHl)**2)/(1+((HYK-l)/2)*XMACHI**2))**.5 PCPRIMI =PC1*(STARMl**2)**(HYK/(HYK-l»/ + ((2*HYK/(HYI{+1) )*(L~CHl) '**2-(HYK-l )/ (HYK+1) ) ** ... (l/(HYK-l)) XMPRI!wll =«2/(HYK-l»*( (PCPRIMl/PA)**«HYK-1 )/2)-1) )**.5 SRMPRMI =«(HYK+1)/2)*(XMPRIMI )**2/(1+( (HYK-l )/2) *(XMPRIM1 )**2») + **.5 X!tIVEl : Xl"'IVEl * SRNPRMI/STARNI GOTO 210 KSC-l149S' -15A
- 19. 160 CONTINUE C ENGI!'JE 2 MONENTUM REDUCED DUE TO SHOCK 210 XMACH2 =«2/(HYK-l))*((PC2/PA)**CCHYK-I)/HYK)-l))**.5 IFCX~IACH2 .LT. 1.) GOTO 170 STARM2 = (C «HYK+l )/2)* (XMACH2) **2)/( 1+( (HYK-1 )/2)iXNACH2**2) l**.5 PCPRIM2 = PC2t(STARM2**2)**CHYK/CHYK-1»/ + «2*HYK/(HYK+l »*(XNACH2)**2-CHYK-1 )/(HYK+l) )i*( 1/(HYI-1)) XMPRIM2 = (C2/(HYK-1) )*( (PCPRIN2/PA)**C (HYK-1 )/2)-1 »**.5 SR!vIPRl'-'12 = ( (HYIi+l )/2)* (XMPRli"12 )**2/( 1+( (HYK-l )/2)* (XNPRIN2) **2)) + **.5 Xl"IVE2 =XNVE2 * SRMPRN2/STARM2 GOTO 220 1iO CONTINUE C ENGINE 3 NOfwlENTUM REDUCED DUE TO SHOCK 220 XMACH3 = «2/(HYK-l»*«PC3/PA)**((HYI{-1)/HYK)-1»**.5 IF(XMACH3 .LT. I.' GOTO 180 STARM3 = ««BYK+ll/2)*(XMACB3)**2)/( l+«HYK-l)/2)*XiIACH3**2) )**.5 PCPRIM3 =PC3*(STARM3**2)**(HYK/(HYK-ff)/ + «2*HYK/(HYK+l»*(XMACH3)**2-(HYI{-1)/(HYK+l» + **(l/(HYK-l» XMPRIM3 = « 2/(HYK-l» *((PCPRIM3/PA)** «HYK-1)/2 )-1»**.5 SRMPRM3 =« (HYK+1)/2)*(XMPRIM3)**2/(1+( (HYK-l)/2)*(XMPRIM3)**2)' + **.5 X.~VE3 =XMVE3 * SRMPRM3/STARM3 GOTO 230 180 CONTINUE C ENTRk~CE MOMENTUM (LBM FT/SEC2) 230 XMVIN = SMVIN + D-IVE1 + X!'1VE2 + XMVE3 C NOZZLE STEAM (LBM/SEC) STMIN = X * HWIN C ENGINE MASS FLOW COOLING HEAT REJECTION TO 'vATER (BTtT/SEC) HREl = XMEl * cp,,, * (TEEl - TOS) HRE2 = XNE2 * CP1" * (TEE2 - TOS) HRE3 = XME3 * CPW * (TEE3 - TOS) C COOLING ENGINE EXliAt!ST TO MAKE STEA~ (LBN/SEC' EECS =(HREI + HRE2 + HRE3) / 9;0 KSC-11495DO 99 I:I = 1,50 - ~ ':'16A
- 20. C HEATING INLET AIR BY CONDENSING STEA!'-l TO NAIE NEW H20 (LBM/SEC) HRAIR = AIRFLO * CPA i (TOS - TA) HRAIR = HRAIR/970 C 02 BURNED AS F(H2) (LBN/SEC) 02 =8. * UH2 C BURNED AIRFLO RATIO, IS IT 20% OR LESS OF AIRFLO BRAT = 02*4.3125/AIRFLO IF( BRAT .GT••20 ) THEN .02 = 0.2*AIRFLO / 4.3125 BRAT = .2 ENDIF C CREATED EXCESS N2 (LBM/SEC) XSN2 = 3.3125 * 02 C NEWLY BURNED'UH2 BH2 = 02 / 8 C NEli STEAM (LBM/SEC) XNS =02 + BH2 C REMAINING 'UNBURNED H2 RUH2 = UH2 - BH2 C CORRECTION TO LOGIC FOR NO H2 FLOW I IF(UH2 .EQ. 0.0) UH2 =.0001 C COOLING REMAINING UNBURNED H2 TO MAl.E STE»I HRU21 =RUH2/UH2 * UH21 * CPH * ('ItEE1 - TOS' HRU22 = RUH2/UH2 * UH22 * CPH * (TEE2 - TOS) • HRU23 =RUH2/UH2 * UH23 * CPH * (~EE3 - TOS) C COOLING SUMf.'lATION I CRUH2 = {HRU21 + HRU22 + HRU23) / ~70 C COMBUSTION AND COOLING OF AIR + UH2 ~LBM/SEC) C LOWER HEATING VALUE OF H2 =51571 BT'lf/LBM HRCC =515i1 * XNS/4.032 * 1/970 C NEli STEAM GENERATED (LBM/SEC) XNNS =EEes + HRCC + CRUH2 C EXIT MASS FLOW OF STEAM COMPONENTS CLBM/SEC) STMOUT =STMIN + XNNS + XNS - HRAIR C WATER DROPLETS AT EXIT (LBM/SEC) HWOUT =.9 * HWIN - STMIN - X~NS + iHRAIR C UNBURNED AIR (LBM/SEC) AIROUT = AIRFLO - 02 - XSN2 -17A
- 21. C MOLES OF MIXTURE ETAH20 = STNOUT118.02 ETAN2 = XSN2/28.02 ETAAIR =AIROUT/28;97 ETAH2 = RUH2 1 2.016 ETAT = ETAH20 + ETAN2 + ETAAIR + ETAH2 C MOLE FRACTION XH20 = ETAH20/ETAT XN2 = ETAN2/ETAT XAIR =ETAAJR/ETAT XH2 =ETAH2/ETAT C MIXTURE MOLECULAR WEIGHT XM = (STMOUT + XN2 + AIROUT + RUH2)/ ETAT C AVERAGE GAS MIXTURE DENSITY (LBM/FT3) RHOM = PA * 144 * Xl'tU(1545 * TOS) C TOTAL DENSITY (LBM/FT3) RHOT = RHOM * (STMOUT + HWOUT + XSN2 + AIROUT + RUH2i/ +(STMOUT + XSN2 + AIROUT + RUH2) VEFF = (STMOUT + HWOUT + XSN2 + AIROUT + RUH2)/(RHOT * AEFF) VEQ = VEFF / «1+XK) ** .5) DELV = TVEL - VEQ IF(ABS(DELV) .LE. (.OOOl*TVEL» GO TO 60~ AIRFLO = (TVEL/vEQ)*AIRFLO 99 IF(AIRFLO .LE. 0.) GOTO 800 WRITE(*,'(A)') 'CONVERGENCE DID NOT OCCUR IN 50 PASSES' ,600 CONTINUE . WRITE(5,650) T,VEQ,XK,AIRFLO,BRAT,XMVIN,XMV,XM,UH2,XMACHI 700 CONTINUE GOTO 900 800 CONTINUE lvRITE(5,670) 670 FORMAT(lX,'BACKFLOlv IM~tINENT - COVER THE Dt!CT!') 900 CONTINUE STOP END KSC-11495: -18A
- 22. REFERENCES 1) Shapiro, A. H. uThe Dynamics and Thennodynamics of Compressible Fluid Flow," Vol 1, pp 135·137~ The Ronald Press Company, New York, 1953. ,I e,.. 2) Shapiro, A. H. "The Dynamics and Thennodynamics of Compressible Fluid Flow," Vol I. P 81. The Ronald Press Company, New York, 1953. KSC-ll4~5 -19A-· ~
- 23. 7.5 TASK V-DUCT TRANSIENT TESTS 7.5..1 Approach The purpose of these teSlS was (0 determine whether duct transient flow had a significant effect on the lesl condilions that should be simulated for SIS demOnSlr1uion and 10 pro vide sufficient data to calculate those condilions. A series 0; KSC-11495 -20A-:
- 24. leSIS was planned using helium at selected steady flow rates. with the helium then to be shut off as rapidly as possible. This I71S cxpected to give the opponunity to measure both the steady now as a function of helium flQw rale and 10 give a series of transient measurements with (he steam system operating continuously. It v.-as realized that such sudden shutoffs would excite organ pipe response oscillations in the duct. but calculations indicated that the lowest organ pipe frequency would be about 11 Hz. which would not interfere with the measurements. Unfonunately, the first tests showed that the duct organ pipe frequency was much lower than expected. about 1 Hz. Fur ther. the magnitude of the oscillations was so large that only a qualitllive evaluation of the transient flow could be ob tained. The wave speed in a duct. and consequently the organ pipe frequency, is a function of the compressibility of the fluid and extendabilil)' of the duct walls. Examination of the duct revealed flat regions where a tow force of a few pounds could move the duct wall an inch or so. Thus, an unexpected result of the duct construction technique invali dated the intended procedure for measurement of transient flow. This made necessary the use of a different measurement technique. A hot-wire anemometer bad been installed at the cnttance ofthe duct in the hope that it could be correlated 10 the lOW air flow. Results showed that it was completely insensitive to the pumping of the helium jet. The measure... ment could be correlated with the air flow pumped by the steam jers. but could not be correlated wilh lOW air flow. A turbine anemometer placed in the duct showed a good mea sure of steady velocities. but its time conslant made impos sibl~ the measurement of ttansient ~clocitics. A new test was then added 10 the series. A hot-wire anemometer was placed in the duct, near the turbine anemometer. Obviously. steam flow could not be used. so the test us...--d helium only. The bot wire was calibrated using the no-flow condition and the s&Cady-state reading of the turbine anemometer. The hot wire shows some fluctuation because of the organ pipe ef fect. but the effect is minor compared to the effcct on the measured duct impact pressures (which arc referenced 10 external ambient pressure). 7.5.2 Duct Loss Coefficient Figure 7-12 presentS the measured duct velocity transient using a hot-wire anemomelCr at Zone O. Superimposed are the equilibrium (quasi-steady-state) velocil)' caused by the helium jet and a calculation of the transient velocity using a duct loss coefficient of 1.0. The duct loss coefficient 'is defined to be the friction loss in the duct divided by the duct dynamic pressure. NOle that it does not include the duct exit dumping loss. The agreement between measured and calcu lated duct velocity is c!:-tceUent for both buildup and decay of 150 If!,,.,nf1 ' • • • • E........b'....n Vt!luCII" " / ~ - , Mr..."u't!d V~lo,.IV120 ............j';.i;J,.r· _..-:. - - - T...." ...nl V..luC"" :., ",. I ' . : to. 1(. , : 1/ : - 90 II :. I • : ~ i I' : ~ ~ 60 ; ~ ;~30 rO~--------------~---------------- o 2 Figure 7-12 Duct Transient Flow (Helium Only, Run JJ) flow through the duct. Thus. at least for the flow wilhout steam. the existence of transient flow is clearly demon strated, and a duct loss coefficient of 1.0 characterizes the flow through the duct. The duct loss coefficient should be a characteristic of the duct geometry and YOuld not be ex pected to change with the fluid in the duct. To confirm this invariance. pressure data from the transient run with the . least organ pipe effect. Test 34, was compared with tran sient calCulations. Figures 7·13 through 7-15 compare ve locities computed from measured impact pressure at several Zone 0 locations with transient velocities computed for duct loss coefficients of 0.0, 1.0, and 3.0. Although the results arc distorted by the organ pipe effect, a value of 1..0 is consistent with the measured pressures. 7.5.3 Transient Effect The evaluation of the transient effect for shutdown from RPL is made diflicult by the fact that a good deal of uncer tainEy exists concerning the eqUilibrium flow conditions at RPL. and even more uncertainEy existS concerning the quasi-steady tlow during the shutdown.. A program has been written that evaluates duct inlet momentum from the SSMEs. including shock losses. and from the steam jets. Empirical equations from lCStS calculate the hydrogen com bustion in the dUCI inlet. A heat balance determines the water evaporated in the duct. A duct pressure loss is ap plied. and the dUcl air aspiration is iterated until the exit and inlet momentum are balanced. This makes possible a con sistent calculation ofquasi-steady ducl velocity during shut down from RPL. Then the transient duct velocity and the additional aspirated air due to the transient flow can be calculated. Figure 7·16 shows the results of these calcula tions during shutdown from RPL. Appendix C conr.ains program listings and a discussion of the theory used. KSC-11495 -21A
- 25. 200 Me.sured Velocity - -. C.llcula.ed Trlln,;enc Velocity ••••• Equilibrium Velocity 150 V.locity. his 100 50 ......•..•..•..........••.•..•....•.•.• O~-----------------r-----------------T----------------~----~--~------~------ ·0.5 o 0.5 1.0 1.5 Tim•• s Figure 7·13 Duct Transient Flow-Location 20 (Helium and Ste..m. Run 34) 200 M.....red V.'Dcity Calculated Tr.nsient VelDcity ••••• Equilibrium Velocity 150 ~,oo 1...> 50 o ·0.5 o 0.5 1.0 1.5 Figure 7·1-1 DUCI Tralls;t!llt Flow-Locatioll 21 (Helillm i111d Steam. RlIlI 34) KSC-11495 -22A
- 26. 200 Legend: Musured VelocilY Calculated Transienl Velocity •••• - Equilibrium Velocity Velocity. hI. 150 100 50 o ~----------------~-----------------r-----------------r---------------.-- -0.5 o. 0.5 1.0 1.5 Time,. Figure 1·15 Duct Transient Flow-Location 23 (Helium and Steam, Run 34) 22 20 18 L",nd: 16 Qu••i·Ste.dy Transient 14 8 & 4 2 o~--------~.....------~------....~--------~--------~--------~--------~--------- o 2 4 6 Time.s Figllre 7-16 Predicted Duct .-lir Flow Jllri,,! Sblltdo.t.::l1 [rom RPL -23A
- 27. All of these calculations use a dUCI loss coefficient of 1.0. helium pressure on duct flow. Figure 7-18 presenls calcula The 3spiraled air flow 3( RPL is calculated (0 be over lions tor 3ir flow as a funclion of helium pressure. The air 19.000 Ibis, about six limes the mass How of the three .low increases with helium pressure up to a value of 10.000 SSMEs. NOlO that the aspiraled air now does not have the psi. Bcc:ause general duct bacldlow could not occur unlil smooth character associated with lhe decrease ofduct veloc even higher helium pressures were reached. this strongly ity. The air flow also refleclS me changing composition of suggests that the observed backflow must be a consequence me flow. For instance, from time := 0 to :about 0.8 seconds. of local flow conditions. Specifically. the proximity of the air flow increases to compensate for the sudden drop in No. 1 engine to the west wall makes it probable that a engine flow. locally separated flow is the cause of the splashback. Ap pendix C. Figure C-2. presents data correlation with analy The paramecer of interest to me design of the steam inening ses which substantiate the calculation of airflow as a func system is the ratio of the transient air flow to the quasi tion of helium pressure. Slcady-state airflow. Figure 7-17 presents this ratio for the entire shutdown process. The design point for the SIS is the time at which the last engine reaches an oxidizer-to-fuel ratio of one. the condilion for which combustion inside the engine ceases. This design poim is reached at 4.0 seconds. and the air flow ratio at this time is 2.SS. 7.5.4 Observed Splashback During the highest helium pressure test (Run 35), a signifi. cant water backtlow was observed. Concern about the cause ofthis backtlow prompted an analysis of the effect of nozzle 3.5 3 ,..":I •• 2.5 ~•::I 0.... 2 ..C • ...•c ... !i. '; a: 0.5 O~--------r-------~--------T-------~--------~-------r--------r--------r o 2 6 8 Time. I Figure 7-17 Predicted Air FloUJ Ratio duri"g Sh,ltdowIl from RPL KSC~~~49~ -:-24:A-.
- 28. 260 1/7·Sc.l. Entrained Air 240 SingI. Engine Helium and St.am, K-l 220 200 180 110 140 100 10 20 O~----~__----~----~------~----~------~----~------~----~------r-----~----~ o IThCKI..ndU Helium elMm..., Preuure. paig Figure 7-18 Predicted Effect ofHelium Pressure on Duct Air Entrtlinment KSC-11495 -25A