This document provides technical details on a simplified model for analyzing transient duct flow, including: - A one-dimensional model is developed using a perturbation of duct exit area to account for friction loss and relate transient to quasi-steady duct velocity with a differential equation. - Computer programs are included that calculate duct exit momentum through an iterative momentum balance between inlet and outlet, incorporating engine shock loss and additional duct combustion. - Validation shows the model correlates well with single engine helium and steam test data over a range of chamber pressures. - Application to full-scale conditions indicates maximum air flow is less than actual Space Shuttle levels, suggesting helium flow alone cannot replicate critical conditions.

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
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provided under the Technology utilization Program of the National
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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