DZ-118405-1

POSTFLIG.HT ANALYSIS OF THE APOLLO 14CRYOGENIC OXYGEN SYSTEM

JULY 14, 1971

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MSC-0*ai2Supplement 2

APOLLO lh MISSION REPORT

SUPPLEMENT 2

POSTFLIGHT ANALYSIS OF THE APOLLO lU

CRYOGENIC OXYGEN SYSTEM

PREPARED BY

Propulsion and Power Division

•APPROVED .BY,

r -' /James A.-MeDivitt •.. •Brigadier General, USAF.

... . 'Manager, Apollp Spacecraft :Prp.gram..

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

MANNED SPACECRAFT CENTER

••'•.<-•-•• '•'• •' • : . • • • • • • * • • • • • - , • • : • • • • • ': :••••- HOTJSToK' TEXAS' ''"'•"''

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DOCUMENT NO. D2-118405-1

TITLE POSTFLIGHT ANALYSIS OF THE APOLLO 14 CRYOGENIC OXYGENSYSTEM

CONTRACT NO.

Prepared by:Propulsion and Pov/er Systems

5-2940

Prepared for:National Aeronautics and Space Administration

Manned Spacecraft CenterHouston, Texas

July 14, 1971t ' -

, : •'. _ • . _ • ; . ••., •...- . ..... • • .prepared - by: -. . Q; '.Q. U]Q : ••• •:/•

J. E. Barton'..:.. -••:••.. • . ' • , • . ..r: .,..:'• -..H. . W. PatterS-Ofl.

^• • • / • - — • Approved -.by: ;

Program Manager ' ...

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IHE £5i3ti~g,rJi7£ CCV/.PANY SFACf DIVISION, HOUSTON,' TEXAS

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D2- 11 8405-1

REVISIONS

DESCRIPTION

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DATE

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APPROVED

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D2-1 18405-1 ,

TABLE OF CONTENTS pAGE

PARAGRAPH

and Key Words

Contents .Illustrations viTables ' • vNomenclature *References ^

, 0 introduction I'1

I I Background '•'1.2 Scope 2_}

Summary

Tank Flow Rates 3-bTank Accelerations ^

Preflight Predictions 4-1Nominal Conditions *-«

Analysis5-1

Simulations s_1

5.!.! No^al' Heate^Cycle ^ 5-2

I'll SnlS SS* for EVA Flow Rates J_ , . ,-. .,. \'\'l . Maximum Pressure Decay .- - - 5-7 ..,,;..,,.;,/i, .,,,

,.:,J ., is Sfe1 * ™'H':.'l---:. ;,j;!,. r:;J'SIIS^" ''"'•''O"' " :' "Conclusions . .;...;.. . :;-.^.--.-,

:-. - - v ' -;v: •'" -_^

7 o Recommendations ... . . •. ... ,•••. ....... • • . . - - . . • . • • ••-.-"•

;'r'-.f x* - ™ ^.-•- ••";•:.'.'. '••'.'•. ...Cryogenic Tank -.*>•.-.••.• .; ; ,,-.*.1 ,->xi4 .*'*pV T- ^ ^ ^

- .:>-Apten* ^ """" Appendix C - Heater Temperature Correlations

D2-118405-1

ILLUSTRATIONS

FIGURE

3-1

3-2

3-3

3-4

3-5

3-6

4-1

4-2

4-3

4-4

4-5 -

5-1

5-2

5-3

5-4

-5 -5

5-6

:,::.v .,.,;:..5^7.r...; .,,;.:.,..

; . - ; • • : • • ,-,-.. . --5-8 ;.v.-v.

. . . . . . . ' • - , : .5-9 . / . . , •

::;;-;.;- ;: °;; ;;" - 5-11 • • ; -

5-13

5-14

TITLE

Apollo 14 Oxygen System Flow Schematic

Oxygen Heat Exchanger Restrictor Performance

Oxygen Tank Heat Leak at Zero Expulsion

Tank 3 Pressure and Flow Response During HighFlow Test

Tank 1 Pressure and Flow Response During HighFlow Test

Vehicle Angular Motion During High Flow Test

Potential Pressure Decay Comparisons

Effect of Acceleration on Potential Pressure Decay

Attitude Hold Heater Cycle - 0.95 ft2 Heater Area

Attitude Hold Heater Cycle - 0.475 ft2 Heater Area

Real Time High Flow Test Simulation

PTC Heater Cycle Simulation

PTC Heater Cycle Convergence

Tank 1 Test Simulation - 0.95 ft2 Heater Area

Tank 1 Test Simulation - 0.475 ft2 Heater Area

Tank 1 Transient Pressure and Flow Response

Plumbing System Pressure Response with High Flow..Rates

, ... . lank ..,1. .Jes .t ,S i mula ti .on ,rw.i th. , P res s u.re , Qepen c|e.n,t •, v , .... .Flow Rate ' ' ' • • - • , • • • . . •

. Tank, 1: Test- Convergence with -Pressure .'Dependent • -.

..Tank 1 Potential Pressure. Decay.. During the HighFlow Test . ' \

'• . Cofi verge n-te • o f : M<? xfmum '• Poteri ti al •• P re.s s u re' -De c ay . •• '•.}-. .During, the .Hi.ah.iF.low. Jest .. .. . . , - .,. . . • . . - . . . . . . ' •

Tank: 3 Test Simulation • ' • ;

*'''T an' '' S't''T:Ws:t'fCd>iVeVg'e'ritW!^^^

Simulation of Heater Cycle at AET 5:3.52Potential Pressure Decay, .95 ft Heater Area

PAGE

3-9

3-10

3-11

3-12

3-13

3-14

4-3

4-4

4-5'

4-6

4-7

5-14

5-15

5-16

5-17

5-18

5-19

4®**.^';5-21 '•.;•:.• : •;..••

5 -22V . .

i-23-=.V-:;':::^

5-24 ' ' '•'•'

5-26

5-27

..... .......... > , - . . • ;. ., .'..,. ,, -.- . . . . . . . . .^ • .;.•. ' ' .• '• ,, ...v, .'. . ., .; ....... - . . . • - • .:t: . „ • . . • , ; • : . . . . • •

D2-118405-1

ILLUSTRATIONS (Continued)

FIGURE TITLE PAGE

2 "5-15 Potential Pressure Decay, .475 ft Heater Area 5-28

5-16 Heater Sensor Temperature Simulation, AET 5:15 5-29to 5:44

5-17 Convergence of Maximum Potential Pressure Decay 5-30at AET 5:44

5-18 Convergence of Heater Sensor Temperature at 5-31AET 5:44

5-19 Length of Equilibrium Heater Cycle at 92% Quantity 5-32

5-20 Effect of Acceleration on Hester Cycles, AET 10:30 5-3312:30

5-21 Effect of Acceleration on Heater Sensor Temperature 5-34AET 10:30-12:30

5-22 Simulation of AET 10:30 to 12:00 Using 100 x 10 Grid 5-35

5-23 Effect of Stratification on Length of Heater Cycle 5-36

5-24 Effect of Stratification on Heater Sensor Temperature 5-37

5-25 Convergence of Heater Sensor Temperature at AET 11:50 5-38

5-26 Convergence of Length of Cycle Time at AET 11:45 5-39

5-27 Build-Up of Potential Pressure Decay from AET 10:30 5-40to 12:30

5-28 Convergence.of Maximum Potential Pressure Decay at 5-41AET 12:30

5-29 • ., .Low Density .Heater Cycle S.imtilation . . . . . . 5,-42 ." . . . .

•vS*'3Qv'.i\-•'-=•••••:••-'l;bw-:.Dens-.1ty--'-Hea-ter 'Cyc-le • Convergence ••V*--.:^<:s:v^f.^^ •.'.*•>•-.

5-31 Radiant Heat Transfer During Lew Density Heater Cycle 5-44

. ;$&:V;-s^^^5 - 3 3 " .... ..Empirical. Heater Response,. 97* Quantity • . . . . . . .5-46,

5-34 Empirics! Heater Response. 15'* Quantity 5-47

5-35 • " Empirical Hester Response. 17*'Quantity ' 5-40

'"$-~36''-.- - : ' ' "Friip/1 rica'l -Heater'Response,'"43%'QulritTiy' •:'v "'•';• 'f-<"^:'J.'--i"•-&$$••'•••'.":'v-:- '••••:•

c^e3t^.Resj3pns^;^' " • • ' " • • • - • - • • • • - - • ' - • • • ^ . - - - . . - - . .

D2-118405-1

TABLES

TABLE TITLE - PAGE

5-1 Stratification Model Parameter Surmary 5-11

•.:V;.-i.;.,.;VJ.-.V;: . ..V.;.;-;..- •->•...•,. '..;. .,,/;, ;_.:, ;;v ;..• -..;, . . . - . . : , V. '.^. ....,, • . . - . , • • • . - . - - , . '. . •. . . . - ' . . . ' . ... .

D2-118405-1

Symbols

A

b

C

D

E

F

F

g

GM

h

I

K

L

' M

MC

N

P

Q: -R • • •= .

V

v

W

a

NOMENCLATURE

Area •

Tank wall thickness

Constant in heater temperature sensor lag equation

Specific heat at constant pressure

Stefan Boltzman constant •

Constant in Rayleigh heat transfer equation (equal 0.525)

Diameter

Young's modulus

Impulse Function or Thrust

Thrust vector

Acceleration in Earth gravity units

Product of gravitational constant and attracting body mass

Enthalpy

Vehicle inertia matrix . •

Thermal conductivity

Length

Mass .

Heater thermal mass

Polytropic exponent

'Pressure " '. . ...... ^ . . . . . . . .'. ..Quantity of heat

Gas constant.. .'

.,

; ";'RayTeigh' riumb'er '• '-• '• -: '•'

Tank radius, . .._... -/''.

t •_" 'Time ' " . "•"" ; ..... ' • ' " ' • • '-:' : ' . . ' ; ' • ' " '•' ..; ""•"?*; ••;tj^:v^^>"^^ •"•••'inite'rnaT^e'ner '~'f---^*&!±K~'?-f: :- ~^:7-^-'^:ff. •^•^•^v:--;^ -^- '•-•-:.

Volume

Velocity

Weight flow ,rate . .

Vehicle angular acceleration vector

• ? . . . - . . - .. • •Co.effi>ci.ent of : thermal expansion. . . . . . . . . - . - / . - • . - . - - • :. ..•

D2-118405-1

Symbols

Ye

P

NOMENCLATURE (Continued)

Ratio of specific heatsHeater emissivity (0.2 assumed)Density

Thermodynamic property,— r -

o

V

to

Thermodynamic property, -pr-op

Poisson 's ratioViscosityVehic le angu la r velocity vector

Subscripts

b . B u l k f l u i deg Center of gravity

d Demandf Thrust

g . At t rac t ing body (earth or moon)h HeaterL . .•• •;• Lines • • ' , ' . - . , . , '.- •-. ,

•''^^-^•^•^•-ftefgfef,^

. t . . ..... Tank . . . . . . . . . . . . . _ - . . . . . . . ; . . . .'&S*;''?-?-' $?-*?:*&

».•;•-• . • Condition or state at infinite expansion

D2-118405-1

NOMHNCLATURE (Continued)

Acronyms

AET Apollo Elapsed Time

CSM Command Service Module

DAP Digital Auto-PilotDTO Detailed Test Objectives

EVA Extra-Vehicular Activity

GET Ground Elapsed Time

LM Lunar ModuleMSC Manned Spacecraft Center

PTC Passive Thermal ControlRCS Reaction Control System

SRU Sperry Rand Univac

'vT1-'--' ^

D2-118405-1

REFERENCES

1. C. K. Forester, Pressurized Expulsion of Non-Isothermal SinglePhase Cryogen, paper at the NASA-MSC Cryogenic Symposium,May 20 and 21, 1971.

2. C. !(. Forester, D. D. Rule, and H. W. Patterson, Apollo OxygenTank Stratification Analysis, The Boeing Company, D2-118357-1,November 30, 1970.

3. Apollo 14 Flight Data for Tank Accelerations and MiscellaneousCryogenic System Variables.

4. A. H. Shapiro, The Dynamics and Thermodynamics of CompressibleFluid Flew, Volume 1, The Konald Press Company, 1953.

5. Task Summary, Apollo 14 Oxygen Tank Tests (DTO) Predictions,The Boeing Company, January 29, 1971.

6. Apollo Fuel Cell and Cryogenic Gas Storage System Flight SupportHandbook, NASA-MSC Document, February 18, 1970.

7. hi. W. Patterson, Correlation of Apollo Oxygen Tank Thermo dynamicPerformance Predictions, paper at the NASA-MSC 'Cryogenic Symposium,May 20 and 21, 1971.

D2-118W;

1.0 INTRODUCTION

The Apollo 13 incident resulted in the removal of in': niixinrj fensfrom the oxygon tanks for the Apollo 14 and subsequent spacecraft..Since the performance of such tanks in the IGV/-C; fVirht environmentcannot be duplicate! on the ground, flight performance could not isfirmly established frctf fjround test date?. Thus, the Apollo 14mission provided the first flight data on the performance of theoxygen tanks. . . • '

ti I I o I j ~? 1 O V-' I u I I'_, / i f ' v' I ' W I * O jJ '-• V' v. v. I WN . v- \' i'. t t c\ *-* •- I I v./ I I' •.' ( i:— *.- 1' v' ,.• \- i^ i i •-. i,( v- .

not only to establish the adequacy of the tanks for these futureflights, but to determine if the existing stratification Rioclel for1ow~9 oxygen thorr.iodynair.ic behavior wa-s adequate to predict flightperformance for Apollo 15 and subsequent.'flights.

1.1 Background . .

Cc.ffiprc-hc-nsivG stratified performance analyses of th? Apollo oxygont.d-i.ks vvore not conducted prior to t!<•-'• Apollo 13 ir.cic'cnl: since nixlr-gfens v/ere available to reduce the effects of stratification on rankoperation. After the Apollo 13 incident, an oxyqen stratification-model was developed (References 1 and 2) and verified by analysis ofdata obtained for one period of the Apollo 12 mission. This analysisverified the model ability to predict pressure collapses which could.occur as -a-result of stratification. The ability to-predict heater.-temperatures...cou.l.cJ .not. ,be,.yerif ied; s;ince.the_Apol.l.o.,'1.2, tanks did. not,'coiftain 'hf^ter"temperature sensors'.

The. resulting strati fixation, inod.el was .used .to. produce pre-f.li.giit..;.'^f)redic'i'icin's;'for':-tHb': Apol 'id K1 ''bkyo'e'iV t?n'ks"pc?rforir:ance';->:' These' pre-':-'-'''''.:d.Ktio.rij,,..,however^, would:.not-vbeyadeoua.te-vf;o^v/oiil-'l include 'tan!; conditions (flo'./ rates, qui'ivLi ties/and accelcra-•tions}' for., which .'che. modal, had not.-be. en verified...:-;...-..:/=••;'..

•Th2vApollo'.-l/i: post--fl-ight-:arialysis xonsisted-;:.o.f- stratif-Jcaiion;incH!el •'"•si!:!(•!a'(.ions of tank•'porforr^nee for six c-ifforonf conditions of flowrate; ta.nk (i-jantity. ai'id accelerati(:n. The six coriciit'ions. se'iocledv.'ith the: concurrence of the Technical (-'ior.itor> inr.lufied two periodsof passive thevnr.i'! control, two periods of-attitude hold, and tin.1 two

. Iri.tjh f|ov/l\'A s illicit ion tests .(.OTO). -.Q;ianti ti-^V: frq;r: lf>"io 9/S and

D2-118405-1

1.2 Scope (Continued)

flow rates from approximately 1.5 Ibs/hour to more than 4.5 Ibs/hourwere included in these simulations. The results (tank pressures,heater temperatures, and heater cycles) of the simulations based onactual accelerations and flow rates are compared with the bestavailable flight data. The comparisons of flight data with simulationresults are discussed and the flight stratified performance of theredesigned tanks evaluated. The simulation accuracies obtained fromvaried model parameters are evaluated and model parameters are selectedfor the best prediction capabilities. Simulations of heater tempera-tures based on empirical .heat transfer equations are also comparedwith flight data, and parametric temperature predictions are presented.The ability of the redesigned tanks to satisfy future mission require-ments is assessed based on the combined stratification model andempirical heat transfer equation data.

D2-118405-1

2.0 SUMMARY

The Apollo oxygen tanks were redesigned and the mixing fans removed afterthe Apollo 13 incident. The ability of the redesigned tanks to provideall mission flow requirements was not demonstrated in a flight environ-ment prior to the Apollo 14 mission. Pre-flight predictions of tankperformance for the Apollo 14 mission were made with a stratificationmath model validated by analysis of one Apollo 12 condition. Thesepredictions provided confidence that the Apollo 14 mission could besuccessfully performed, but did not adequately evaluate tank performancefor conditions .such as EVA expected during later missions.

The post-flight analysis of the Apollo 14 mission was performed to betterevaluate the redesigned tank performance in the flight environment, andthe ability of the stratification math model to predict flight performance.The math model was evaluated by simulating tank pressures and heatertemperatures with the model and comparing the results with flight data forsix different conditions. The ability to satisfy future mission requi.re-ments was evaluated on the basis of potential pressure decay data resultingfrom the simulations. The heater temperature data from the simulations wassupplemented with data generated from empirical heat transfer relationshipsto evaluate heater performance for the full range of flight conditions.

The simulations included nominal attitude hold and passive thermal control(PTC) tank acceleration conditions, as well as abnormally high (5 x 10-6 g)acceleration conditions caused by the planned oxygen venting during the-high flow DTO tests. Tank quantities from 15% to 97% and flow rates tomore than 4.5 Ibs/hour during these conditions were included in theseevaluations.

The simulated maximum heater temperatures were in excellent agreement withfl.ight data .for. .the attitude hold and PTC. periods as .shown below.

.sv-./.i-^.^.v^-^w, .-..••.*••,. y^/-.<--./s :;••,.-,•; -iASSUMED-,...•-..•,-:,••TEMPERATURE-..-.-•-> •:•.--•-.->,> f/--:-^"--.QUANTITY, CONDITION ' HEATER AREA ' ERROR ' ' ' • • • • • • • - "

-•i;-i-w: 7fc.di''.-;*;::

7 0 % ; ( D T O ) " ^ ' ''' ''"' " ' '"''OS Ft2 '"'"'•'"'•••'•'••"•^''^vv' •*•• '•••••"• • — --:".,::•:,•.••

";:' 54%,;.PTC'": •.• "'v;—'• ;••'•>.'. -'0.475 Ft2'.-': •' '• •/ "*• 9df ••- -•;..- ''•::-. - - ' ; ••;.'.'

' 0.475 Ft2 +60°F^ ^ :' ;H,;

The best accuracies were obtained by using the larger heater area forhigh quantities. The heater area for best accuracy did not depend on

•;• ' . • • - • • • the.flight condition.'- The..reduced • accuracy., of the DTO--siaujlato.d - ..-. . . . . . .temperatures may have been caused by abnormal accelerations which were

D2-118405-1

2.0 SUMMARY (Continued)

not perpendicular to the heater as assumed by the model. Heater tempera-tures simulated with empirical heat transfer relationships were within50°F of flight for all conditions investigated except the 20% DTO condi-tion. These results, which agreed favorably with the stratificationmodel results, were used to generate parametric heater temperature dataand to evaluate mission capabilities.

The only significant pressure decay resulting from stratification duringthe Apollo 14 mission occurred at 97% tank quantity. The math modelestimated decay of 86 psi was in agreement with flight data. The actualflight decay was between 59 and 100 psi. No other pressure decay occurredduring the flight. The evaluation of the model decay simulation capabilitywas severely limited by the lack of flight decays and resulting data.Since pressure decays and heater temperatures are closely and fundamentallyrelated by the model, the demonstrated accurate heater temperature simula-tions adequately validated the model for predictions of pressure decays.

It was concluded from the Apollo 14 preflight and postflight analyses thatthe redesigned oxygen tanks could supply the known required flow rates forthe Apollo missions. The worst case pressure decay during a three hourEVA period wi l l be less than 230 psi. The stratif ication model was foundto be adequate for predictions of the most important tank performancevariables (pressure decays and heater temperatures).

02-118405-1

3.0 METHODS OF ANALYSIS

3.1 Stratification and Heat Transfer

The constant grid stratification rnath model (References 1 and 2) wasused to simulate the overall oxygen tank stratified performance(pressure, pressure decay, heater temperature, etc). A brief descrip-tion of the model equations and assumptions is included in AppendicesA and B. Heater, temperature sensor response was calculated by anempirical method developed to model heat transfer in supercriticaloxygen. This method uses a Rayleigh number convection correlation withthe fluid properties treated by averaging as described in Appendix C.

3.2 Tank Flow Rates

The oxygen flow distribution system is shown by Figure 3-1. The systemincludes check valves which are intended to prevent flow into the tanksduring normal operation. The isolatioivvalve between tanks 2 and 3 isnormally open and for the Apollo 14 mission was closed only during thehigh flow test. The flow restrictors are capillary tubes with flowpressure drop characteristics as shown by Figure 3-2. The restrictorsare the only significant source of pressure drop in the system.

The .data avai lable from the system include fluid quantity and pressure,and heater temperature for each of the three cryogenic tanks. Thesurge tank is instrumented to provide pressure data only. The flowrate to the environmental control system is measured downstream ofthe surge tank and, therefore, includes contributions from all fourof the tanks. The flow rate to the fuel cells is also measured, butcan be more accurately determined from the electrical current.

The total, flow, from the three, tanks .during the Apollo 14 mission, was ..- . .determined from the fuel cell usage and the pressure drop across the.restrictors. to .the environmental control system (ECS:). The;flow rate tothe fuel cells was computed using the fuel cell current, because thismethod is more accurate thsn the use of the fuel ce.ll flew meters. The;;f;l:owrtr£te'-a:crb£s^.the restrictor pressure drop calibrations. -^During low-flow'periods-, theaverage restrictor flows were obtained from the ECS flow rate (measured •dowriStrecim of the. restrictors) and the net Changs 'of mass in the surge .

-taY>ik-:.'dor1-ng-"tha-''pen"o'd.'--.-TH'e:netV-change-bf-'^iias-s/'iri- the '--surge,-.tank-y-ics-.-'---:--',rC.a.l.cu,l.ated..from., pnl.y..-.the...s;ur.ge...tank- pressure.;,.thus.,..;di.f,fe.'Ce.flces.. in.;,..-.:-...- :-.calibration' of. the' surge':tank..-.'arid oxygen tank'pressure transducers' .^'did .

.not affect the results. . . . . . . . .... . . . .. ..... = . . . . . . - , . ...V^.i;-->Vr\^

The flow rates from the individual cryogenic tanks were not measured;therefore, it was necessary to divide the total system flow among thethree tanks. The individual tank flov.! rates were determined from thetotal system flow on the basis of equilibrium tank thermodynamics. The

.pressure, differences between- tanks-ware used, to deterjr.ine.--the.ch.2ck.valve conficjuration and to constrain the thermodynamic calculations.

D2-118405-1

3.2 Tank Flow Rates (Continued)

The flow distribution is affected by the heat input to the separate tanks.Individual tank heat leaks were estimated from flight data. The tank 1and tank 3 heat leaks were found to be nominal at zero flow rate at 90%and 10% quantities, respectively (Figure 3-3). The tank 2 heat leak wasnot verified, but is believed to have been slightly greater than nominallyexpected. The tank 2 heat leak could not be determined for a zero flowcondition because the check valve provided to isolate the tank was foundto be leaking, thus causing abnormal pressure rise rates within the tankwith the heaters off. The check valve also permitted warm fluid to flowback into the tank causing warming of the insulation and increasing theheat leak.

The flow rate distributions were obtained by simultaneous solution ofthe pressure change equations (see Appendix A) for the tanks supplyingthe system flow. The calculations included the effects of tank elas-ticity, a factor strongly affecting the relative pressure change rateswithin the tanks. The simultaneous solution of the pressure changeequations for the tanks supplying the system demand related the individualtank flow to the total flow. The total flow used for this calculationincluded the flow rate required to pressurize the external line volumes.These calculations are simplified if the pressure change rate is knownand used with the nominal heat leak to determine the individual tankflows. The flow rates from this method are in the sama ratio as thoseprovided by simultaneous solution of the equations.

The tank 2 check valve leak required special consideration to determine• the flow into the tank which caused the tank 2 pressurization rate with

heaters off to be the same as the tank 3 rate with heaters on. The flowrate into the tank was determined from the volume change required toproduce the observed pressure change.• Using equation A-13 from Appendix A

.....-and considering.the volume-change .due .to. a hot-bubble .as-well as tank. . , ..... / elasticity, ..the .pressure, change is;: . . . . . . . . . , ...... , ,. . . . . .. : . - . . . . . ' . - . . . - . - . .

^«^/A\\

, ; ; • where.. H-rj ;is,. the., volume, change d.ue.. to. a. bubble of. fluid at the line ... . ., . . - . . " . .L ' • - • - • • • • - . . • • . ' » • - • ,

3-2

02-118405-1

3.2 Tank Flow Rat.es (Continued)dMdDuring pressurization, the demand flow -pr— is zero. Substituting

- — jr- for (^£\ and solving for ^results in

dM PL V

This method of determining tank 2 inflow during the tank 3 heater cycleat 26 hours AET showed the check valve leakage rates to be approximately0.05 Ibs/hour which is believed to be realistic.' The tank 2 inflow isan additional demand flow for tank 3 when the check valve is presumablyclosed, but the small additional flow is within the accuracy of the dataand was neglected in subsequent analyses.

The flow rate distribution calculations were accomplished in a sub-routine of the stratification math model for simulation of periods withseveral heater cycles. The surge tank pressure in the model was calcu-lated from the initial pressure and the net mass inflow.determinedfrom the restrictor and ECS flow rates. The restrictor flow rate wasdetermined from an equation approximating the restrictor pressure dropcalibration data/(figure 3-2). The surge tank pressure change equationwas switched from an isothermal approximation to an adiabatic approxi- 'mation when the pressure change rate exceeded 4 psi/minute.

The flow rate subroutine treated the inactive tanks with equilibriumthermodynamics. The inactive tanks did not share the system flow whenthe active (stratified) tank pressure was above the inactive tanks

' •• pressure. 'When the active tank"pressure'was-not greater than the"- •-........• ••-.•^inactive tanks,/the total;flow, was distributed -among •.'•all. -tanks..;'..-. Switch--'

' ' ing between these two flow configurations resulted in some instability; •as, for example, when the active tank(s) was (were) capable of pressur-

;.'. :,?:;-j.<^; ''-." '.'/,'.tank(s) .was ..('were;)"'.f 1 ov/i ng./.' This'inst'abi 1 j ty persi'ste'd for'"a''ffey.' ti;me/"'.'' . . : . - : steps- and caused erratic pressure change rates, .but. did not. a f fec t . . . ' . . . ..

heater temperatures. The instability was most significant when the.;• •;:;.•,•';. •..v.in.actrye. tanks.were -capable- p.f: .-supplying.;the...total .flow -.wi tb,-l^t^le./:;. -..-^ .. . . . . . . . press.ure/. change. . The instability .affected, th'e pressure rise rate f q'r"' \ " " ' " • _•- : ' '-•;•'"•'th'e' sVmulatVon: o-f-the ^^^

time for this simulation was manually corrected during the period of " • ' . .^^'^••^•ns tabi^

of other simulations.

3-3

D2-118405-1

3.2 Tank Flow Rates (Continued)

.Thermodynamic analyses were not required to distribute the flows duringthe high flow tests, since the isolation valve was closed and the systemflow logic determined each of the tank flow rates. The tank 3 flowrates during the tests were determined from the restricto'r pressuredrop while the surge tank valve was open (Figure 3-4). Flo/; rateswere assumed constant while the surge tank valve was closed. Thetank 1 flow rates (Figure 3-5) were also determined from the restrictorpressure drop, but included the fuel cell flow rate when the tank 1pressure was greater than the tank 2 pressure. The flow rates fromboth tanks 1 and 3 increased by approximately 0.35 Ibs/hour at AET168:40 when the urine dump valve was opened. The tank 2 pressure riseafter 168:40 was apparently caused by a leak of 0.08 Ibs/hour throughboth the fuel cell valve module check valve and the tank 2 check valve.This estimated leak rate is small compared to the total tank flow andwas neglected.

f;^''5-^:AV.^f-^'^i^^v ; !.

D2 •• 118405-

3.3 Tank Accelerations

The sources of accelerations in a space vehicle in drifting -flight includevehicle rotations, thrusts caused by fluid venting, gravity gradients andsolar pressure. The solar pressure is approximately 10-7 ibs/ft? andproduces an acceleration of less than 5 x 10~9 '"g" for the Apollo vehicle.The acceleration due to solar pressure was an order of magnitude smallerthan the accelerations produced by vehicle rotations during typicalattitude hold periods and was, therefore, neglected.

The procedure for the analysis of accelerations during attitude holdconditions used rotation rates from guidance data directly for the centri-petal acceleration. The rotation rates were numerically differentiatedfor the angular acceleration term. The total acceleration due to rotationis:

32.174 g= u x u x(R t-Rcg) + a x(R t-Rcg) (3)

Telemetry data from the digital auto pilot used for the analysis includesthe three components of the rotation vector and the calculation is, inprinciple, straightforward. Some difficulty does, however, arise due tothe angular acceleration, The angular acceleration terms tend to dominatethe centripetal terms, because the centripetal acceleration depends on the . .....square of the rotation area. The acceleration term also introducesquestions of signi ficance due to the short durations of application.Typically, the reaction control system jet firings cause angular accelera-tions greater than 2 x 10 "^ radians/second2, but the duration is of theorder of 10 milliseconds. This acceleration results in a movement of theoxygen tank of about 10-7 inches during the time the acceleration isapplied. This small displacement would appear to be negligible; however,

.the angular accel.erat.ipris. should certainly, not be. entirely ..ignored,. The .approach used Was to distribute 'the angular acceleration' over tinie '

.intervals of 10 seconds or greater by numerical : different! ati on of the •: • •:observed angular rates at the end points of the tirna interval. The timeintervals, were "selected on the basis', of 'engineering Judgelr,2ht':to 'adequatelyc¥aV&c-te^ ' ' 'arbitrary y the- results- appear/to be. -satisfactory -arid a bettcr 'method h-a:. .

•not -'presented itself ..--••. •; • ' • • ' : " • • • / • : . -.• ••"•..: - • • - • • - • . • . . . • • . - . • • • . . . . . . • . . - . , ,• ._-.••.•.• ._>:;.., •. • : . . - . _ . . .

• The'-.ta-hK- ecce.ler.ations^tfiO"irig'>s table' periods ;of ••passive'.' tlier-Rta-1 ;'controT-,": •• • ••••••• "••(PTC) v;ere calculated v/ithoi-t consulsrction of engulcr accelerations'.'

..During. .PTC flight ...modes., ..the. reaction, control system is deactivated/and :.,.,.,,,,the .yehi Qle ,is. essenti ally .spi.n stabi.li zed. ...For .this. qon.d.i..tip:n , an.gular,:: ... .^

?'a'cc'elVr'a%'rdhs'iV;:g're''r-g'elrier2lT •"a"tceWratvo'fi''-:'-":"''r'''v':'5V

only is significant.

02-118405-1

3.3 Tank Accelerations (Continued)

When the vehicle is in attitude hold in the near vicinity of the earthor moon, the gravity gradient acceleration is significant. This terjn5which must bo added to the rotational accelerations, is:

2 GM (R^ •£,).£ • /,\32.174?- ,9 l 9 (4 )

V'V . . ,The gravity gradient term is of -the order of I0"7 "g" for a 100 milealtitude earth orbU. Since the magnitude of the gravity gradient isproportional to 1/|RQ{3 , the term becomes negligible at distances of2 to 3 earth radii. The radius vector to the attracting body in the vehiclecoordinate system is necessary to the gravity gradient calculation. Thisvector can only be determined from the vehicle trajectory and inertialplatform data. A computer program for the calculation of the accelerationincluding the gravity gradient term derived from trajectory data wasdeveloped by NASA-MSC for the Apollo 14 mission. The tank accelerationsfrom this program (Reference 3) were used for nominal attitude hold andpassive thermal control (PTC) periods analyzed.

The high flow oxygen tank tests during the Apollo 14 mission were not innominal flight "g" conditions due to overboard dumping of oxygen. Theoxygen dumped overboard through & convergent nozzle in the command moduleentry hatch produced a significant thrust and vehicle acceleration. Apreflight estimate of the tank accelerations during the high flow testwas made by analyzing the vent nozzle thrust and vehicle dynamics.

The thrust from the oxygen vent was calculated as 'the thrust from aconvergent nozzle exhausting to vacuum. The choked nozzle thrust is

wh'ore'' \F^/.^. :is';':th:'eV?a;£i.;6'pressure .to .the, Impulse furict'ion; a't . 'the. son i.c -throaty "•••Th.s impulse'. . ., . . . . •. .function ratio is '1.4289 at zero pressure' from the isentropi.c -'tables • • • • ' " • , • ' .(Reference 4)>..-.v/:j th .a. specific, heat, ratio of 1.4 for, oxygen. The thrustresulting f ronv expansion - to " zero ''pressure'- 'is'.:-' '• •••' ' - . ' _ • : '* :<. •• ' • • • • • ' • . ' • • • • • ' : -. >• - • ' •

• ^ • • • • • • . ' - - • ^ . - . - ^ . v >.- • • • . - . • - • • •v- - : . | j | • • . - • • • ; . - - - - - . : v ,..:..:.-.•.;.,.., = ,..,,,.:.,.....,,. _...,,. ...

^^and for a perfect gas

3-6

: D2-118405-1

3.3 Tank Accelerations (Continued)

Therefore:

F = ~ U ' '

The nozzle thrust is then:

FN = H

The vent flow at 0.00172 Ibs/sec or 6.2 Ibs/hour resulted in a thrust of0.091 pounds. The calculated thrust of 0.091 pounds is a lower limitsince no expansion downstream of the throat or plume effects wereconsidered.

The 0.091 pounds thrust produced a linear "g" of 3.65 x 10"6 for the24,985 pounds vehicle weight at the time of the test. The thrust vector

was not through the vehicle center of mass, therefore, rotationalaccelerations were also produced. The equation for the angular accelera-tions is:

If xT = la (10).

and solving

a = I"1 (Rf x F") (11)

The'mo'me'rits of 'inertia obtained from'prefTight-mass' properties data were •'•: ' - : ' •,.v used -with-equati on (11) ,;tp predi ct .angular acceleration rates. -The rotation.-.•.,.•. •-•

rates were then calculated from the time required to rotate the .vehicle' •'• through the 5°-dead band. : FinalTyi rotational tank- accelerations" were . •• • ' ' : ":(:;; ca'l cuToted.-f rpm:,:eflu^tiQn;:;(3^

. •/. l6-6"and for trink: 1 .a "tj" of .4/7 x 10".V was' obtained.'. /'These'' Vccele'rati6ns/' : '/ :

••-. .neglected the. effects/of reaction'coiitrol.. system .firings as .well.as. .plume y-. ......;• effects and should be somewhat lower than actually experienced.

The basic guidance data from the Digital Auto Pilot (DAP) was uso'd'for the.ppstflight analysis, to determine,.if the .prefli.ght acceleration predictionwas.: valid./.The vehicle attitude errors for a 1.4 minute'period analyzed%re;;-shb^hubyv'-Fi:gUire'VJ-B^'-'th^e data 'hidi e'ate: that':tKe/ veh;i c;1e"•'w'-S<f-v"'- ': :^:/oscil lating primarily Ebo:.!t the; y ex i s ^ end tha oscillation ainpli tucia was-less than 0.3 degrees. The oscillations result from the steady torque ofthe vented oxygen increasing the attitude error to the deadband limit(approximately ± 5°) and the RCS correction firings driving the vehicle

..backyi.nsi.de .the. desd. band.-. . . . . . . . . . . . . . . .

D2-118405-1

3.3 Tank Accelerations (Continued)

Rotational accelerations were calculated from the angular error amplitudesand time between RCS firings assuming the accelerations were constant .between the RCS firings. The torque caused by the vented oxygen wasinferred from the rotational accelerations :and the vehicle mom-ants ofinertia. The thrusts were in turn calculated from the torques and thelocations of the vent and the center of gravity.

The average vent thrust calculated from these data were approximately 0.06pounds, but variations of more than a factor of 2 occurred between succes-sive vehicle oscillations. Since; a vent thrust of .09 pound was used forthe preflight acceleration estimate, it was concluded that the 4.9 x 10"°"g" used for the simulations could net be significantly improved. The 0.09pound thrust calculated for a choked nozzle is believed to be more accuratethan the 0.06 pound estimated from the guidance data. A thrust lower than.09 pound could only be obtained if the flow was significantly less than 6pounds per hour.

The guidance data indicates RCS firings about once per minute. Each of thefirings causes a high acceleration of very brief duration. This accelera-tion contribution was neglected in the estimated acceleration. Includingan average value- for this term would raise the "g" level by less then 30%-resulting in less than 10°F change in heater ternperatura. It was concludedthat the 4.9 x 10-6 "g" estimate was sufficiently accurate for use 1n allpostflight analyses of the high flow test.

3-8

D2-11840,5-1

TO ENVIRONMENTAL CONTROL SYSTEM

SURGE TANK

e ? FLOW RESTRICTOU

TO FUEL CELLSTANK HO. 3

f ISOLATION VALVE

-afl>

' "• "TANK NO TANK N O . 2 '

FIGURE 3-1 - APOLLO M OXYGS'.N SYSTEM FLOW SCIIhHATIC

D2-118405-1

3.0

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2.0

W = .176

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20

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02-118405-1

***

NOMINAL HEATLEAK (REF 1).

TIME - AETi i

O 19:00 '26:0037:00 .

m 205:00.© 206:00.O 215:00 "

TANK 3

0 10 20 30 40 50 60 70 80 90 100QUANTITY

• "FIGURE v.V-'J.-=- OiWCEW^NK -HEAT ;LEA;K-AI ZfiRO 'EXPULSION • • • ; • < • - • • ' • ' - ' •'-.

D2-118405-1

20 30 40 50 60 10 20 30 40 50 60 10 20 30

167: 168: 169:

AEt - MRS:MIN

FIGURE 3-4 - TANK 3 PRESSURE'AND FLOH RESPONSE DURING HIGH FLO'/TEST

,/,;.v^..-*"- ':r';-"/-'-';-:'-';/:-:-,.">L':-' '^'-^ :;<;Vr.;oO;-'.>^v::^ ^ v; •--:^vcy^; ••':VV:' ••v-;: „-: .-<V'-.v

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D2-118405-1

, •..•. v>•A-VS'i.' 'ii'ft'.'V.'-

167: 1G8:

ALT - HRS:MIN

; ' - ' 4 0 ' "50'"'60 "' 10" T20 ' 30

169:

' • • • FIGURE'3-5-- 'TONK'-'i 'Pfl£sSLllJE'"AHb"-FL'bW'RE§p6H§i: 'DURING VfrGH 'PLOV/ TEST "

0-13

D2-118405-1

8:23 24 25 26 27 28 29 30 '31 32 33 34 35 36

AET - H R S : M I N

, .- . .;.-.,., ..;v... .,. .FJ.GURt. .3-6.-.-.. VEHiaE ./lMGyUfi-NOTI-ON :-.DURLtiG-.}JJGM:.-^OW. JEST--. • • • , . . i,- -. . , •• •• *

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D2-11840S-1

4.0 PREFLIGHT PREDICTIONS

4.1 " Nominal Conditions

The analysis of nominal flight conditions was primarily directed towardspredicting pressure decays which could occur during normal system opera-tion with relatively low tank flow rates. These analyses indicated thatno pressure decays in excess of 100 psi would occur as a result of normalsystem operation (Figure 4-1). The high flow rates required for theCommand Module purge early in the mission were not included in the analyses,since this condition was previously analyzed (Reference 2) for Apollo 12.The maximum pressure decay resulting from stratification during the Apollo14 mission was less than 100 psi and occurred at an Apollo Elapsed Time(AET) of 5 hours 45 minutes. No other significant pressure decays occurredduring the mission.

4.2 DTO Tests .

Test predictions (Reference 5) were made to determine the tanks ability toprovide the high flow rates required for the EVA simulation, and thenominal flows required for emergency return with low tank quantity. Thehigh flow EVA simulation test included overboard oxygen venting whichproduced significant vehicle and tank accelerations. The vent configura-tion was not firmly established when the analyses were initiated, there-fore, two accelerations were used for the tank 1 pressure decay predictions(Figure 4-2). The accelerations estimated from the vent configuration aridflow were 4.7 x 10-6 -g" for tank 1 and 4.9 x 10~6 "g" for tank 3. The'predicted pressure decay due to the fluid properties at the 20% quantitycondition was predicted for tank 3. No decay was observed for either tank

'1 or 3 because the test was prematurely terminated, and a maneuver to stirthe fluid did not occur for a considerable time until after the end of thetest. . ...

... The emergency return test condition, tank.3 depletion from 20% to 5%.... ;..•'•quantity, pre-flight prediction determined that the heater temperature

;• .would approach, but not exceed'-500°F-for three•'heater 'element operation;- - '•:;•-k. .peiheate^'•"'•'"only"two he:?tier elements:were' used during 'ihe;'teSt''pen6d?:'''F'ftghi'''fi£&&r''''''"' '''""•

• v. t .tftpperat.ure data,.ar.e,.• therefore, -not availabje -.for. .-the.. con.d:i,ti.ons -anaJyfed.-..;.,;>;. 'and'meaningful'comparisons c a n no t 'be-macJe . ' . . ' • • • . " • • "<• / • . " ' ' ; - • - • •

' 4 ^ 3 ' ' V 'Real Time 'Flight 'Analysis " ' " • " "' • ' ' ":" • '

.."' ..The tank 3 high flow test..'at .,20%. .quantity was 'conductedI with two .heater' '.''".' •":*r-eiemenW:which'-'iiiva'Ti&^

tion model was also modified prior to the mission to "include the heaterthermal mass which was neglected in the first predictions. Analyses wereperformed during the mission to verify the modified model heater tempera-ture predictions and to provide realistic predictions of the tank 3 test

. . _ b e f o r e the test v as. starte.d. An.3lysis.:of the. h.eater cycle at AET 78:20.

•M.-.V..

D2-118405-1

4.3 Real Time Flight Analysis (Continued)

2verified that a heater area of 0.95 ft predicted the peak heater tempera-ture within 30°F (Figure 4-3) while the heater area of 0.475 ft? providedless accurate results (Figure 4-4). Revised predictions for the tank 3high flow test were, therefore, made with 0.95 ft? effective heater area(Figure 4-5). The predicted peak heater temperature for the first heatercycle was in excellent agreement with flight data. The predicted heatertemperatures and tank pressures remained in .good agreement with flightdata until the test was terminated at GET 169:38:57. Deviations betweenpredicted temperatures and flight data immediately after the start of theheater cycle were caused by the temperature sensor lag which was notincluded in the model used for these analyses.

D2-118405-1

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D2-118405-1

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D2-118405-1

5.0 POSTFLIGHT ANALYSIS

-5 .1 . Stratification Model Simulations

Flight periods for simulation v/ere selected with the concurrence of thetechnical monitor in order to demonstrate prediction capabilities forimportant tank performance parameters. The selected periods included themost critical flight conditions, flow rates and tank quantities. Thebases for selecting the six flight periods analyzed are summarized by thetable below.

BASIS FOR FLIGHT TANKPERIOD SELECTION . CONDITION QUANTITY AET

Nomina l Heater Cycle PTC 54% 26:00Maximum Quantity for EVA DTO 72% 167:00Flow Rates

Minimum Quantity for EVA DTO 20% 167:00Flow Rates

Maximum Pressure Decay Attitude Hold 97% . 5:00

Short Heater Cycles Attitude Hold 92% 11:00

Heater Temperature at Low PTC 15% 186:00Quantity

These flight periods were simulated on the NASA-MSC SRU-1108 computersusing the stratification math model. As discussed in Section 3, thesimulations used input parameters either measured or computed from flightdata. These included acceleration levels, initial tank pressures, initialheater temperatures, percent quantity of fluid, and fluid flow rates. The

. simulations resulted in heater cycles, potential pressure decay andheater temperature; these were-then compared to.actual values of these....

'•"parameters demonstrated'in f Tight'." 'the comparison'showed that 'the ApolTo•i ,14 cryogenic oxygen system operated satisfactorily. :. In addition, this ; . . • • • • ,

effort showed that the stratification math model .could .accurately predict . . . . . . . .*'- system •performance with"•certain •Trinitations'.' ''TKe''ires'u.lts o'f. the;

:s"iinuTatidn "'..;.>a.nd:.:; <J f s.c;,uss or^" • "pa rag raphs . ' ' • ' ' " • ' " " " ' " - " : ' " " ' • ' • • ' '

5.1.1 _. Nominal Heater. Cy.c'lc . . . . . . . , . -V -.'.' .: . . . . . , • ,.-.; ; .. . . - . . . '

A'-'PTC heater cycle at A E T 2 6 : 0 0 w a s " s i mutated to verify nominal system.operation. ,The results of this analysis established a baseline for •' • •, (;Selectinj,model...,par.ameters..fp r;,p.th•:'%'«fnaly£i ^ YabTeT a"n"dv; '":"'' ; "''"'"

an acceleration of 3.0 x 10~° "g" was estimated from available data forguidance rotation rates. The flight acceleration data (Reference 3)confirmed that the average acceleration was within about 10% of theestinifite. The average tank flow rate during the pressurization cycle

.. .vyas, 2,67, Ibs.-.pe.r hour, inc-ludi-ag-b'CS.-a-p.d-fuel -cell-.-- fl-'ow.--ra-tes-- of .9-1--afid- '•'•'" -- -1.45 Ibs/hour, respectively, f,no .?«j Ibs/hour into the surcc tanh.

. .5-0,- ....: • - • ' . • . :,.-.'. - .' -. . . ' , -.'•/-'• '.

D2-118405-1

5.1.1 Nominal Ivo.jtv: Cycle (Continued)

Simulation lesuits for heater sensor temperature and tank pressure fortwo different heater areas bracketed fl I'yht -data (Figure 5-1). Thesmall area simulation was made with a heater -rea of 0.475 ft^, which isthe flat plate area equivalent to the 0.59 ftL outer surface of thecylindrical heater tube. Since the heater tube is perforated, flowthrough the Lube could provide a flat plate area equal to the areas ofthe inner and outer tube surfaces, a total of 0.95 ft^. Analyses wereconducted for both heater arear, to determine -which provided the mostaccurate simulation of sensor temperature and pressurization time. Thelarge heater area reduced the heater sensor temperature, and the timerequired to pressurize was also reduced; because the small heater athigher temperature stored more thermal energy. Simulated pressure resultslag behind f l i g h t data i:arly in the stroke due to averaging the flow intothe surge tank over the cycle. The actual flow rates increase as the differ-ence in pressure between the oxygen and surge tanks increases. Therefore,an average surge tank flow over-estimates the flow immediately after theheater turns on and and causes the simulation pressure to rise more slowly.

The asymptotic limit for the heater temperature with the 0.475 ft2 areais within 9CF of the flight data, while the heater on time for the samearea Is within 40 seconds of the flight data (Figure 5-2). These resultsare within 'ihe accuracy of the data itself. The asymptotic sensortemperature anci heater on time with the larger heater area are not ingood agreement with flight dfcta, which implies that the inside of theheater tube was not an effective heat transfer surface. The effect onconvergence of the number of cells in the Y-direction was als,o investi-gated by repeating simulations with a heater area of 0.95 ft^ and gridsizes of 40 x 10 and 40 x 15. These simulations produced essentiallyidentical results with pressurization times of sixteen minutes and a

.sensor .temperature. of. 46°F* • These- results- imply that a- 1. -lower-' -quantities •-•

.nominal .-tank pe.rfQni)ance, ca:n. be closely simulated wi.th -^..heater, area, of .. ./.. . •„0/475 fl/. Satisfactory convergence 'in" this quantity range can be,.Oi>,tai.n2d..wi'th..!!iaxiauj!Ji grid, sizes .of .60. .x.-. 10. with- convergence/ .pot •.:•-'•.,•/.•>•.<:, --,';. d&p'e'nden.t .upon the. .number-'oi .-.cells ..in the. .Y-d.ireeti on i ;•••'• .. ..-'..*•. . .-i,.-, •«. /o. '- ;•"•;••':;;i:;-Vv:v;Kiv-

.5.1.2, -. Maximum. Quantity for EVA -.Flow Rates -. . .-

•,i:.: : ; •%-.,. -;a^-s" 'catcuTa'te'ci fV6V:F.C'S''erid' fuel cell 'de:nands :.: • '-' "• ''.".'•• ''•' •'•'•••

. . . .'••""Wtivvt 'line ':iieperidortt''fl-ow- ra

'i.h-j tank accelerot ion was calculated from the oxygen vent thrust• (Paragraphs 3.2 and 3.3) . Abrupt changes in; tank flow rates (Figure 5-3) ..^oteu^ed-^ur^ag^heX^st" supplied" f uel cell flow rates (Paragraph 3'!2)/ -The heater cycles simulated

v.( it.ii 40 x 1C grids and heater areas of 0.95 ft^ and 0.475 ft^ are in pooragreement v>'ith flight data early in the simulation (Figures 5-3 and 5-4).

. The tank flow rates were investigated to determine if they could differthe f i x e d demands

the- l-rrar-.'iii 'h'es'ter cycs used to perfonri the simulation enough to cause ..ycle's.-' ' R o w 'rate's' c'aTc'ulatecl froni. th:e actual tank ' • • •

D2-118405-1

5.1.2 Maximum Quantity for tVA Flow.Rates (Continued)

. pressure change rates by equilibrium thermodynamics indicated negativeflow rates (flow into the tank) during part of the period (Figure 5-5).The large differences between flow rates based on demands and flow ratesbased on tank pressures indicated that flow rote errors caused thesimulation inaccuracy.

The plumbing system thermodynamic behavior was investigated as a possiblesource of flow rate errors. When the demand flow rapidly increases, acold, dense slug-of fluid is drawn from the tank into the warm tubing.The density of the fluid inside the tank is approximately ten times thedensity of the fluid at the ambient temperature in the system plumbing.If no heat transfer is assumed between the hot and cold fluid, then tomaintain pressure in ti.e lines an equal volume of cold fluid must replacethe volume of hot fluid. The tank flow rates will exceed the averagesystem demand for some period of time to fill the lines with cryogenic

.fluid after the demand increases. This phenomena was investigated byusing the existing math model to simulate the plumbing response to suddenhigh flow demands. The simulation outflow rate was 2.5 Ibs/hour at 60°Fand the inflow rate was 25 Ibs/hour at the tank temperature of -195°F.

The simulated line pressure decreased for the first 15 seconds eventhough the -inflow was an order to magnitude higher than the outflow(Figure 5-6J. The pressure decrease with the high flow into the lineconfirms that the plumbing system could cause gross variations in tank

. outflow. After the lines were initially filled with cold cryogenicfluid the thermal capacitance of the system could cause sufficientpressure rise in the line to cause flow back into the tank. No attemptwa's made to analyze this effect for the duration of the high flow test,because computer time requirements are prohibitive with the existing model.The simulation of the line response for 18 seconds required more than one

, • ; - . hour, of -computer-time.-•• It was' con-eluded "that Targe variations' in the'"""" " '"" '":. ,, . - tank. 1 flow rates, occurred during -the first few heater cycles of the high • ,;.: .•--

flow test as a result of plumbing system thermodynamics.

.... ^^y;v.'The .tank.;fiGw.^ate^/yc.Quld.ba/^^ .s,ima?-S1t-ibnsV fo f "•••• fl-£#i•:<•'••'•'• "'•-..• "'6hTy" the ::fes't''heater cycl'e: duri'ng the high 'flow'tesV when the plumbing' ' ' ' •"

was near thermal equilibrium.- Simulations of the last heater cycle weremade with the model flow rate adjusted on.the basis of pressure to properly .

...,,.;.-:.;-,...:',;:':;--•;;,:,•:!n:c.lude .-the--:fuelvc.el.l ::f)-ow-.-demands..••;...Under/these; •cpridi.-t-Y.pnsv.'f^i'-r;-agreement >;•• • XV .-.'• • ' ' . - . . ' • " • : • . '•'•". "'was 'obtains:! wit!V the flight pressure-response for'the BO x 10 qr'id w i th 'a ' '

heater area of 0.95.ft? (Figure. 5-7). . The. heater sensor temperature , _. ,:... . . . . ,: " ' '''asymptpti c es'.tl mate was 30°F above' f 1 i ght data j[ F;i gure. '5-Q). ; ...The heater-onl ... ; _

vfe ;, ^was not adequately resolved. The resolution obtained was adequate forasymptotic extrapolation of the heater temperature which was in sat isfactoryagreement with flight data.

D2-118405-1

5.1.2 Maximum Quantity for EVA Flow Rates (Continued)

-Potential pressure decay is a function of total heater-on time only and •simulations of this variable were valid for the duration of high flow test.The potential pressure decay as a function of time is shown in Figure 5-9.When the oxygen vent was closed at AET 169:GL, the acceleration decreasedby an order of magnitude. This change in "g" level caused some modelinstability and the potential decay was not valid for later times. Themaximum potential pressure decay during the heater cycle immediatelypreceeding termination of the high flow test-was 32.3 psi (Figure 5-10).A pressure decay was not. observed in flight because the tank 1 heater wasturned off at 169:34 and no significant vehicle maneuver occurred toabruptly mix the fluid before the potential pressure decay had dissipated.Extrapolation of the potential pressure decay history, shown by Figure 5-9indicates that the potential pressure decay dropped to less than 10 psiaapproximately 30 minutes after the heater was turned off.

5.1.3 Minimum Quantity for EVA plow Ra,tes

Detailed simulations of the tank 3 high flow tests at AET 167:00 were per-formed with hester areas of 0.95 and 0.475 ft^. Expulsion rates were basedupon ECS and fuel cell demands and the acceleration level was calculated fromthe thrust produced by the oxygen being vented overboard during the test(Paragraph 3.2 and 3.3) . The DTO was terminated at the end of one andone-half hours instead of the planned three hours. When the cabin orificewas closed, terminating high flow, the vehicle acceleration dropped fromapproximately 4.9 x 10-6 "g" to 7.2 x 10-8 "g». p0$t flight analysisindicated that the estimate of 4.9 x 10-6 "g" cannot be significantlyimproved, but the acceleration level after the termination of the highflow test may have been as much as an order of magnitude higher than7.2 x 10"B "g". The saturated heater temperature at either accelerationis much higher' than the' observed heater temperature- (Figures 5-37c'and - • • •-.••••<•'-•'5 ^37d) . . 'Hea t transfer-rates at temperatures far below saturation are low .-. .:,..and most of the energy is being stored in the heater thermal mass. Thetemperature; rise rate at this quantity is dominated by the heater tuba thermal

'$?-fP'° $*$?$$£ ?£:f?' ';.j;^

The heater power was manually changed from 70 watts (2 elements) to 110 ,. . . . - .-watts; (.3 .elements) near AET 169:09. The stratif ication math modelsimulates the.effects of the h igh ' f low, the decrease' in "g" level, andi'h"e' th3ri(j&/'in'1'ie'3ter--.pov/er'.'' ''F.i'cjure'SVil". comperes '-the- .resuVts-.-.of -.a:"simi!lav •:>••'• v,tipn w,i th a heater area of Q.95.._ft2. and a grid of 40 x 10 with flight data..Since, the surge tank flow; rate was treated as a time averaged value over ' • ' • ' " vtfie^-cyfci Or-vasVprevltius-ly -:i<lvs cu's-s-edi' the^tmulatetf::^ ress:ure:: l-6gs;*f l daia^%^<;;early in the upstroke. Furthermore,-tank ? pressure was init ial ized'at 8 7 6 'psia because the heater had already been activated by the pressure switchat 868 psia prior to the initiation of high flow. This particular combina-tion of grid size and heater area predicted e heater sensor temperature 23°F

5-4

D2-118405-1

5.1.3 Minimum Quanuty for L'VA Flow Rates (Continued)

above the observed temperature at end of the first high flow cycle.During the second pressurization cycle, the test was terminated and thesimulation tank acceleration dropped almost two orders of magnitude.Instead of saturating at a temperature comparable to the first cycle, theheater sensor continued to rise. When the heater power was stepped upfrom 70 to 110 watts, the temperature rise rate increased even more. Thesensor continued to rise to 310°F showing no tendency to saturate, whenthe heater was turned off by the pressure switch at 169:34.

When a convergence study of heater sensor temperature and heater-on timewas performed (Figure 5-12), the results for either heater area werenot in as good agreement with flight data as the 40 x 10 grid with thelarge heater. By comparing the results of combinations of grid and heaterarea with flight data (Figure 5-12), the 40 x 10 grid and larger heatersimulates the high flow test pressure and temperature response better thanany other combination. However, the asymptotic heater temperature with the0.95 ft2 heater area converged 45°F below flight data while the temperaturewith 0.475 ft^ area converged 60°F above flight data. Convergence of timeto pressurize also span flight data. Previous analyses of a PTC heater .cycle at GET 26:00 indicated that a low quantity, a heater tube area of0.475 ft^ produced better agreement with flight data when the externalvariables of "g" level and flow rate were accurately defined. This impliesthat these variables may not be as well defined during the high flow testsas they were during the nominal PTC cycle.

The average acceleration level during the DTO is apparently not significantlydifferent than that used for the simulation;'(Reference Section 3 .4 ) , however,the effect of the high "g", low time duration, RCS acceleration spikes maynot be accurately modeled by averaging over time. As shown previously byFigure 3-6 these firings occur at a rate of about one per minute during

"the 'DTD'" and' these spikes-could significantly af feet' Heater 'temperatures '"arVd ' ;•pressurization -times. The two dimensional model assumes an acceleration...... •"perpendicular to the heater; which is not valid during the high flow test,.when the linear, acceleration due to the venting oxygen caused the accelera-

-vti bn:-ye'ctor^ vto;^phenomena" could significantly affect the results''of the high flow testsimulation. No satisfactory method of modeling these'effects is avai lable. '

.5-5 • • : '

D2-118405-1

5.1.4 Maximum Pressure Decay

The only significant pressure drop during the flight of Apollo 14 due"to stratification occurred during LM/CSM separation at AET 5:47. Thetank 1 pressure dropped to 804 psia from an initial pressure in thecontrol band of 868 to 905 psia. Prior to tuis at AET 4:57, dockingcaused the oxygen tanks to assume an equilibrium state which was main-tained until the beginning of the next heater cycle at AET 5:14. Thepurpose of the simulation of this period is to predict the build-upof potential decay during- this heater cycle.

The only available data for oxygen tank pressure and temperature duringthis period was that taken by hand during the Apollo 14 flight. Thus,it was difficult to determine the exact starting conditions of theperiod to be simulated, the exact length of the heater on cycles,and the pressure in the tanks at LM/CSM separation.

This difficulty led to the use of different initial conditions for eachof the two sets of simulations performed to analyze the pressure drop.The first simulation, which was run with a heater area of .95 ft^, usedan initial pressure in tank 1 of 872 psia, while a second simulation(which was run with a heater area of .475 ft2) was initiated with tankpressure at 864 psia. This caused a difference Of approximately oneminute in the heater-on times for the two simulations. Although the"potential decay and heater temperature depend directly upon the heateron time, this difference in the two simulations does not lead tosignificant error in predicting the potential decay or maximum heatertemperature.

Another difference between the two simulations was the surge tankvolume used. Due to the repressuri/ation of the LM/CSM beginning at

•-AET--5:14 >the-surge tank-:pressure-dropped to- 414 psia.-- -The first'simula^ ••••.-..•••••.•••-•• •••.-•-.• •-•t.ion. used tank. flow, rates .-derived from the assumption that only .the..: . ' . . . ; - . . . - . . .- ..:.••.-,-;surge tank volume and LM/CSM were being repressurized. .Later, it wasfound that the repress bottles were also depleted at the beginning of

Jth.e..:;pj=ra'ia'h'k Volume'of' tvnce''"that'ofvthc"fTrstcs:imuTp;t:ion.- vFVbw"rates -used'•'"'' " '••• '••- '" ":••-•:"..*.•:••••••••?.•?.':• •:in both, simulations , hoy/ever, were lower than those experienced in ... • .. . .- ... . --_flight '(See Figure 5-13)".. Since both the potential decay and the. . . .-heater temperature arc independent of tank outflow, this discrepancyis;-no.fc. importsrit .for-rthe.--:an3lysi$;;.-of/tii.a'S;e':par&!r!eters';;;.. '•: •:•.-• •'•'•• '••.•:.'•":•'• :•••-•>\:'^'-f"'''^--•-'-'•;•>-.'•• •''

Some difficulty with the stratification model stability was encountered.'. ' ' • ' . ' . ' . . - . . ' . " . •du r i-ng.: h e^s.ti'mu.l a t i^o n o f; ithis xh e ate. ^caused by a step dpv.'n in accelorntion level that occurred during thsupstroke of tits heater cycle (See Figure 5-13). Because of a lack ofsufficient computer core in the MSC 1108, a fine enough grid couldnot be utilized to avoid oscillation in the predicted potential decayafter the step down in "g" level. The simulation Instability caused _.

5-6

D2-118405-1

5.1.4 Maximum Pressure Decay (Continued)

the rise 1n the potential decay to be invalid after the accelerationchange:. The residual flows from the high "g" period during the firstpart of the period should cause the growth in potential pressure decayto be constant through the low "g" period. Therefore, since potentialdecay is a linear function of heater on time, the decay just beforethe "g" change was extrapolated to predict the later potential decayfor each grid size (Figures 5-14 and-5-15). These predictions alongwith predictions for maximum heater temperature (Figure 5-16) were•then extrapolated to an asymptotic value (Figures 5-17 and 5-18).

The simulation using a heater area of .95 ft is in very good agreementwith the flight values for maximum heater temperature and potentialpressure decay. The maximum heater temperature for this cycle was-115°F at AET 5:44 while the extrapolated simulation temperature for anequal heater-on time was -113°F (Figure 5-18). The pressure drop inflight can not be exactly determined due to the limitations of theavailable data, but is is estimated to be between 59 and 100 psi.The maximum potential decay predicted by the simulation using thelarger heater size was 86 psia which again agrees well with the flightdata (Figure 5-17).

While the pressure response of the tank during this period was not ofprimary interest to this analysis, the initial pressure rise rate oftanks 1 and 2 was investigated. An equilibrium calculation indicatesthat pressure can not be maintained in tank 1, but must decrease atleast -1.06 psi/min because of the high flow rate of 3 Ibs/hour duringthis period. However, flight data indicates that the tank pressurerose at 1.1 psi/min during the initial portion of the heater cycle(Figure 5-13). At AET 5:25, the pressure leveled off for a period of20 minutes after which the pressure rose to a peak of 906 psia and

' - the' heater" shut off. '"The effect "of stratifrcatioh of the'Tlmd doe's" " '":':'• .not explain .,this initial sharp pressure rise and subsequent leveling ;. •/ •-'/..•

off. Nor does the stratification model indicate a rise in pressure

ight'pressure' rise rate' computed'-eb'oye' could be significantlyin error because of. inaccuracies..in. the determination..of the .pres.su.re- • . ;

time response. Other possible explanations -for- this-unusual pressure. -. •response are discussed further .in Section 5.2.2. .. .,,..... ' ... - .- , . - - .

. : 5.1.5 ,. .-'.Short..Heater. Cycles, . ,. ............ .....,, ..-....:.. .. -... ..,,, .-.,.-• .... -....

;^cycling .in the automatic mode in attitude hold. At the start of thisperiod, the total cycle time was approximately ten minutes, but by AET11:30 the cycle time had shortened to six minutes. The minimum cycletime derived from equilibrium thermodynamics, however, is 12.3 minutes.(.F,igur..e 5--19.). ... Because. -these ...unus.ually .short .-cycle..times, were., felt... ••_.. „ ..,..„tb be 'due to the effects of stratification, this period'was' chosen'for ' •analysis.

'5-7-

D2-118405-1

5.1.5 Short Heater Cycles (Continued)

An examination of "g" data for this period indicated that an average •acceleration level for this time period was. 3 x 10"' "g". Since thisvalue is higher than was expected; and because noise in the "g" datacould have caused the average to be high, an 80 x 10 simulation runwas made for this "g" level to compare it to an earlier 80 x 10 runat 7 x.10'8 "g". The results, which are presented in Figure 5-20 and5-21, did not indicate that the higher "g" level was valid. Therefore,the simulation was performed at an acceleration of. 7 x 10"° "g".

It was initially felt that the math model would stabilize into thesteady state cycles in one hour of simulation .time. Using the initialconditions for tank 1 at AET 11:30, the simulation was run for a rangeof grid sizes. The heater cycles did not in fact stabilize fastenough for an accurate simulation of the short heater cycles due to theinclusion in the present math model of the effects of thermal mass.In the previous analysis of Apollo 12 flight data, a math model whichneglected thermal mass was used. , Tha simulations conducted at highquantity heater cycles using the previous model stabilized into veryshort cycles in much less time than is evident with the present mode.

To enable the one hour simulation to be extrapolated to the steadyshort cycli? state, a 100 x 10 grid simulation .was run to simulate one-and one-half hours of flight time (Figure 5-22). Using this simulationas a guideline, the values for the pressure fall time, pressure risetime, maximum heater sensor temperature, and minimum heater sensortemperature for the one hour simulation runs were extrapolated tovalues that would have been observed for one and one-half hour simula-tions (Figures 5-23 and 5-24).

.• -It -was- realized., that the, .initial, conditions, used, for .the ..one. hour..,. ..,,.-....-.... . «..„. ',.. .,...simulation. runs did not produce the proper average flow rates to simulate

•'exactly the full one and' one-half hour period! An examination of the ' ""• :i ' . • • • - • • - .relationship between total cycle time and average.- - f low rate, however,

.ft-.-Aoxl-icstedi tpal-s^ajl ..-variations, in ..fjpw .^ate^djd. not.. s,ign.^ficant..]y. • . - , • - . .. . . ,;.. . ......... . ..|jf>i* !the^

.and a. tank quantity of 92% (Figure 5-19). Since the average flow ; . . . . ...rate during 'this period w?.s -approximately 1.2 lb/hour, the one hour ' . . ' • '

'simulation ' 'was extrapolated to one and one-half hours! • ' • '• •

The results of 'the 'extrapolation indicate good agreement with flight • ' • " • • ' • " ': •" 'data from AET 11 :30 to 12:30 for the minimum and maximum heater tempera- , - •••

^ tures:.;: ^were quite close 'to those predicted by ths 'TOO- x ' lO'cjr id 'run, an extra- '; '•"*'•'polation to an infinite grid asymptote was made (Figure 5 -25) . Thepredicted minimum heater temperature was thus found to be within 1°Fof the flight data. Further , assuming a linear extrapolation of themaximum heater temperature (Figure 5--2S) > the asymptotic value for the

"'•• temperature' -after-' one- and -ono-hs-lf' hours- • was • W-i th i f>- 12 p.f • of :; the .-f 1 .1 gii-t..- ••• .-. .-. • • .

D2-118405-1

5.1.5 Short Heater Cycles (Continued)

value. This last figure, however, could be significantly in-errorbecause of the coarseness of the extrapolation for the maximum heatertemperature.

The results of the simulation of total cycle time was not in goodagreement with flight data. The extrapolated values for pressure risetime shown in Figures 5-20 and 5-23, for instance, did not converge.The trend of these extrapolations, however, indicate that if sufficientcore were available on the MSC 1108 to adequately resolve the boundarylayer, an asymptotic value near flight data would be observed.

The asymptote for the pressure fall tirns, on the other hand, convergesto a value significantly higher than observed in flight (Figure 5-26).Since the 80 x 10 grid fall time is quite close to the 100 x 10 gridtime, the asymptote of 5.5 minutes is felt to be accurate. The dis-crepancy between the simulation and flight is due to the flow ratepredicted for tank 1 by the math model being too low during the heatercycle down stroke. Tank 3 bogins to flow along with tanks 1 and 2when the pressure in tank 3 becomes equal to that in tanks 1 and 2.Ths point in the down stroke where thase pressures become equal isdetermined by the pressure rise in tank 3 due to heat leak. The heatleak-into tank 3 used in the math mods! was equal to the zero flow rateheat leak given in Figure 3.4.5 .of Reference 6. The heat leak valuelisted in this reference is now felt to be too high. Further, the zero •flov.' rate heat leak into tank 3 should not have been used for the shortheater cycles because of the retention of cold fluid in the vapor cooledshield during the short up strokes. Before this fluid is allowed toheat up enough to allow the heat leak to be equal to that listed in

. Reference 6, another downstroke occurs allowing more cold .fluid to enter.- ..the .vapor, cooled'shield.. ...Thus,, a much, smaller he.at....leak,.should..have..... . , - . . . . . . -

been used in the analysis; ... . . . • . . , . ' . ... ... . . . • • , . . , . . ' ; . : , .

Because of the assumption of too larf>e a value for the heat leak, tank 3.v pressurised.-.faster .i;i the s.ii'nula.ti.qri..than, actualJy;.occurred.-.. ..T;l;ie.r.e,fore.,.,-... •,..••.-.,.,......

. dowristrok.es -than it.actually would. ' This caused.?, discrepancy in the . ' . ... . .flow from tank 1 since the quantity in tank 3 was-nearer tho'minimumdO'/dM level and thus provided more of ths required'flow than &'ither

.~.ytar.ks- ..Ho.iT'.j2;....:-::' 5-A..-.re_su.].t;,. ;thev;:downstro[;es-.Gf...ti'i.^^ r">?--;-• _ • • lengthened significantly! ' ' ' " • ' . " ' .

••• "dev'eiope'd'ciuri rig the 'two" hour" peri b'r! 'from'"AET 10:30 to 12:30. ThV "' """"moximuru potential pressure ciecciy begins to build up linearly with timsafter the heater cycles reach a rela'civsly steady stratified state(Figure 5-27). Since the 80 x 10 grid simulation is quite close to the100 x 10 grid prediction, tho extrapolation of the-100 x 10 grid

.:•- press jre • ctecay^•••bui'l d- t!p-.to-7ifT--V?:30 -v-^ff--tak'en vttf-b^^the^aSyi/iptotii-fc-•'-'•• -: •"--• ; ' ••-

02-118405-1

5.1.5 . Short Heater Cycles (Continued)

value (Figure 5-28). This extrapolation indicates that the potentialpressure decay at AET 12:30 when the heaters in tanks 1 and 2 were turnedoff was 94 psi. Over the next hour the magnitude of the potentialdecay decreased until it was negligible when PTC was initiated atAET 13:44.

5.1.6 Heater Temperature at.Low Quantity

A heater cycle at AET 186:00 with 15^ quantity was chosen for analysis toverify satisfactory heater-tank performance end the capability of the modelto simulate performance at very low density. During this period, thevehicle v/as in a very weak PTC_manpuver. F l ight data show the accelera-tion on tank 3 to be 3,3 x 10"' "g". Fuel cell oxygen demands werecalcula ted from post f l i g h t current da ta , w h i l e ECS and surge tankflows were ca lcu la ted du r ing this period wi th the f low d i s t r ibu t ionsubrout ine described in Section 3.2. The total tank 3 expuls ion wasapproximately 2.0 Ibs/hour. Heat input was set at 70 watts to matchthe two heater element configurat ion.

The sensor temperature response for the 40 x 10 and 60 x 1-0 grids(Figures 5-29 and 5-30) arc almost i den t i c a l , i n d i c a t i n g satisfactoryconvergence of the 60 x 10 grid at th is low r qucn t i ty . The heatersensor temperature results for the 0.475 f't^ heater area convergedto w i t h i n 10°F of the observed f l i g h t maximum temperature of 325°F.S i m u l a t i n g the cycle wi th the larger Hester area would have resultedin a sensor prediction s ign i f i can t ly below f l i g h t data, and it wasdecided not. to repeat the s imula t ion for the larger heater. •

Ins t ab i l i t y in the flow d is t r ibu t ion subroutine caused the s imulatedtank pressure to be in s i g n i f i c a n t error dur ing the f i rs t ten minutesof the upstroke. The pressure change rote response was manua l lyconstructed from the output 'and''iritecj'ra'ted to form the pressure response

••.'-- -.presented.-In -Figure :5-29-. f.; A.total pressu'rization time e7ev'er»::m'1nute"s; '• . :"•'.-shorter thon the observed f i f ty- three minu te s was calcula ted. This

.discrepancy is exp la ined by the; manner - . i n which the s t r a t i f i ca t ion^v.^.tTOidgk.'tr'eefy^^..'.. .it .is .assumed, tha t ' the ' t o t a l hsa't -to. th'e fluid. Includes radiation."- .." " •

The heater convects energy in to the f l u i d w h i l e i t ' s i m u l t a n e o u s l y ' ' ' " ' • ' . - ' : ' • ' " "••radiates •ensroy to the tank w a l l . - - This rsdistcKJ energy .raises the • '- .

v. .-.. .wall, temperature,and. is .convqcted. b.a.ck-.intp the. f lu id . A;n. alternate. . . . . . . . . ...••" '•":• way-''bf;ni6*dg'^ ft"'totally !'absor5ed': *'•*;''''••''"•"•"•'".; .. .by; the tank-. .wall and .not ava i lab le to -raise. . the- .f luid-pressure. , for.,, . . . ..." - . . . . . . . . '....,,;..;v a., heater teni[):er,atyre.: .of.;;3tOCI°F,,. r.a.di.a.t,i.q.n; accounts.,,,for..,5.0..BTjU/hpur;.'..ojr,,^', v,,,.. -. .,.-..;.,,-.'""••' : ; ' '21% of the• 1-6t'al' two"ele'meJit' hlea'ter'p'owe'r : '(Figurd 5-31:)?'.'' By^:fe'ducing'^'-'--•'".•"^";'':5;";'.-??-:

the f l u i d hso.t i n p u t by this 50 BTU/hour . t!;s prej :p.uHzation time islengthened to f i f ty minutes (Figure 5--H9) . This result is w i t h i n6% of f l i g h t ciatp. and well w i t h i n the 10% granular i ty of pressure dataover th is range. The results imply that for many problems where radia-

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D2-118405-1

5.1.6 Heater Temperature at Low Quantity (Continued)

is not convected into the fluid for some length of time. The errorin calculating pressurization times can be no greater than the. fractionof radiant energy to total heater power. This discrepancy in thetreatment of radiant energy does not affect the heater temperaturesensor time response, Furthermore, these effects are negligible forthe problems of interest at lower heater .temperatures. For example,for the two element heater cycle during the tank 3 DTO at '20% quantity,the heater sensor reached a maximum of 27°F. Radiation only accountedfor about 8 BTU/hour or 3% of the total heater power (Figure 5-31).This error is even less stgn'ifi'cant during the other simulations.

5.2 Determination of Model Parameters. i

The simulations discussed in Paragraphs 5.1.1 to 5.1.4 correlated tankpressure and heater temperature results from the stratification model withflight data. These correlation? were for a range of quantities from 15% to97%, accelerations from 7 x 10'8 "g" to 4.9 x 10"6 "g", and flow ratesfrom nominal system usage to the maximum of approximately 5 pounds perhour. Good agreement was obtained between simulation results andflight data when the model heater area was properly selected, and thegrids were fine enough for convergence of the solution.

The heater area which resulted in the best hsater temperature predictionswas 0.95 ft2 for tank quantities greater than 60% (Table 5-1). A heaterarea of 0.475 ft2 resulted in better agreement with heater temperaturedata for tank quantities less than 60% with the exception of the Tank3 high flow test at 20% quantity. Simulation of the tank 3 high flowtest with a 0.475 ft2 heater area produced a'temperature of 60°F toohigh while the 0.95 ft2 heater temperature prediction was 45°F too low.Since these inaccuracies are nearly, the seme with the smaller heaterpredicted temperature being conservative, use of the smaller heater areais'recommended for all .quantities less than 60%'.'' ' \' '". .'.'..'

The number of cells or grids required for adequate simulations is affected

quantityconvergence of the solution must be investigated for a range of grids '.to de.termins the prediction sccuracy end parsmoters-of- interestextrapolated to .asymptotic values. . App.rp.xinnately 10 ,ce.'i.l.s..ar.e. adequate..,.,

••'in;'the'-'Y'-'di're^results obtained.with,.10 and. 20 cells, in the Y direction with 4.0 cells ,.,

,in ,the :X. direct ion ..are. ess.en.t1 ally: identical.: _,Jhe>;number4,pf-J;_directi.on,.__..;•ceTls 'mayX direction. The available SRU-110G core storage is not adequate toinvestigate convergence in the Y direction with, greater then 100 cells

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D2-118405-1

5.2 Determination of Model Parameters (Continued)

1n the X direction. The simulations which can be conducted are,therefore! effectively limited to 100 cells 1n the X direction and10 cells 1n the Y direction.

Model parameters used for simulations and verified by correlations oftank pressure and heater temperature include:

Model Dimensions

Height (Y) 2 ft

Width (X) 1 ft

Depth 1.1875 ft

Heater Area .95 ft2 above 60% quantity

.475 ft2 below 60% quantity

Heater Emissivity 0.2

Heater Temperature .26 minutes"'Sensor Lag

.Heater Thermal Mass 0.1 BTU/°F

5.3 Results of Heater Temperature Correlation

An empirical correlation using Rayleigh equation was developed to supple-ment the stratification model predictions for heater temperatures. Thissimplified modal was used to provide predictions over a wide range ofexpected flight "g" levels> tank quantities, and heater powers. Thesepredictions were compared to flight data from 20 .Apollo 14 heater..,cycles . .

'"(Figure 5-32).• The''average''temperature', deviation between, .flight data- .•• :;.•• 'and .prediction was 18.5°F while the standard deviation was 21.9°F.; The ' ":

individual 'predicted temperatures ware within 50°F of flight data except.- for tho data point taken from the tank 3 DTO (see Figure. 5-32). . This....... ...•£'jd;isc;r.§p^'•''"«" vector 'to 'the heater tube during tho DTO. .Typical examples of the .. .-;.-'-heater'cycle's -STmulated are1 sh'own"'1 fV::-F-i[ii!'fes"''5-33 "through"5-'36'.: Tfese ""'.examples, include heater -powers of 70 and 120 w'nttsr» accelerations :.frorn. •'

3.0 x :10"6 "g!" to.7,.5 xJQ"/ ".9".end tank ..quantities^frpra-.li>,6^; tQ::??%...;.v.iv>";-:Iri -eoth-'•c'ase:v'-:-t!'3 agresfnVnt betvveen .pV:edicted 'heater te'nip'erature 'an<i. . ' ' . . . -

flight .data..was wi.thin 50°F for the full length of the heater cycle.. •

correlation for two heater pov.'ars, BO and "120 watts (Figure 5-37).These data provide heater temperaturfi' response as a function of quantityfor PTC (3 x 10-6 "g"), lunar orbit (5 x 10-7 »g''), and altitude hold(7.2 x 10'8 "g") for each heater-power.

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5-47

02-118405-1

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D2-118405-1

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5-50

02-118405-1

600HEATER POWER = 120 WATTS (3 ELEMENTS)ACCELERATION = 5.0 x TO'7 "g"

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D2-118405-1

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D2-118405-1

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FIGURE 5»37f - PARAKETRIC HEATER RESPONSE

5-55

D2-118405-1

6.0 CONCLUSIONS

Conclusions based on analyses of the flight performance of the redesignedApollo 14 oxygen tanks are: .

1. The tank heaters, sensors, and controls 'functioned satisfactorilyand normally during the mission.

2. The tanks supplied the high flow demands during the test simulat-ing EVA requirements without heater temperatures exceeding the350°F maximum limit or pressures dropping below normal operatingranges.

3. The heater temperature is strongly affected by the tank accelera-tion and fluid quantity. Heater power must be reduced byoperating less than three elements at low quantities andaccelerations to avoid exceeding the 350°F heater temperaturelimit during long heater-on cycles.

4. The tank accelerations during the high flow test were approxi-mately 5 x 10"6 "g". This relatively high acceleration wascaused by the oxygen vented overboard. Tank accelerations duringfuture mission EVA periods will be determined by the astronautlocation and suit vent configuration. The average tank accelera-tion during the EVA is not expected to be less than 7 x 10~8 "g"which is the lowest "g" observed for a long time period.

5. The heater temperatures during the Apollo 15 EVA period willi?s higher than the heater temperatures during the Apollo 14high flow test because tank acceleration may be as low as7 x 10" "g". Two heater elements can be used for quantities

• • above 35% without exceeding the 350°F heater temperature limit :... .......; at tln\s.acceleratro.n. .Manual. .control of. .the heaters can. provide. ...._.

'the required flow rate (4.5 Ibs/hour) for quantities' between ''^ and 35% without exceeding 350°F heater temperatures.

ac-ce]be less 'than' 230 psiper hour flow for 3. lowest ..anticipated aecG'ier.ation, .(.7.- x UT"-. !'g !!);•:..••

iis tp: tha:..lp.w ac-ce] era.tion. '. Ths..-rim-ximuin ..pressure 'cje-cay .wi.ll :-.- ,.....,......,-.,e less 'than' 230 psi for' the" worst 'case cnndiUo'hs "bf '4'.5 "Ibs"' ' ' •'

per hour flow for 3 hours duration at 70^ quantity and the' "- '

-7. ; The oxygen tank pressure response and flow rates are strongly- •.-.-:;V:S^fected -by vheat;;.1;rsn

hour after the initiation of. high system flow rates (3-4 Ibsper hour per tank).

6-1

02-118405-1

6.0 CONCLUSIONS (Continued)

8. The stratification math model accurately predicts heatertemperature and tank pressure response during driftingflight with tank accelerations from 7 x 10-8 to 5 x IQ'6 "g".The simulation accuracy is primarily limited by the accuracyof the tank flow rates and acceleration levels."

9. Heater temperatures can be predicted within 50°F withsnperical Rayleigh number heat transfer equations for steadyacceleration conditions.

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7.0 RECOMMENDATIONS

.No hardware or operational changes are recommended for the redesignedoxygen tanks which were found to be adequate for known Apollo1miss ionrequirements. Additional analyses recommended to improve predictionaccuracies and capabilities for future missions are:

1. Perform post-flight analyses of the tanks performance duringthe Apollo 15 EVA which will duplicate later mission EVAperiods more closely than the Apollo 14 simulation tests.

2. Modify the stratification math model to calculate tank flowrates from system demands for planned configurations andoperating modes not included in the present model.

3. Determine model parameters required for accurate simulationswhen using the improved math model developed under thiscontract.

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APPENDIX A

THE PRESSURE CHANGE EQUATION FOR ACRYOGENIC TANK .

The pressure changes in a cryogenic tank resulting from heat additionand mass extraction are usually calculated with the assumption that thetank is a constant volume container. This assumption causes large-errors-when the fluid is nearly incompressible and the pressure vesselis highly stressed. An error in the pressure change calculation is alsocaused by flows not usually measured that are required to pressurizeplumbing .system volumes at ambient temperature. In order to eliminatethese errors, the pressure change equation for an equilibrium fluid inan elastic container has been derived and a method for including theexternal volume effects developed.

The thermodynamic system is bounded by the inside surface of thepressure vessel and is closed at the fluid outlet from the pressurevessel. The volume inside the thermodynamic boundary 1s not constantsince the pressure vessel is elastic. The outflow velocity is assumedto be small enough that the kinetic energy and momentum of the outfloware negligible. The conservation equations for mass and energy,therefore, determine the system response to heat and mass flows.

The conservation of mass:

dt = Vdt + pdt (A"1)

The conservation of energy: , .,, : .-.•........••. -..:•.. .... r •..,. . ,/.;.. ..-..-.•.

•:V-'. ----.---.V,.. ,f ril.. l:-.jg,-,i-.*: ,,,,f ,,,,.,

tiding'AVg ntfi .s ng >:A. ':''•• •'f:'-•'•' •";- --:

$(>.•'+ ••QL\ •- '20. + ^H'fn •!• -V P— • (A-3V • • • • • : -dt dt / dt dt \ ' p / • dt

-.Substituting. Arl.-in.A~3 •and/.simpl-ifying • ..-,. •-•.;•.• .•;.; • - . . . ' . . • • • • . - .

^VM^r; ^

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The internal energy is taken as a function of pressure and density

dU 8U dP . aU dp ,. ,Ht " W Ht * ap~ dt (A~5)

Using A-1 and noting that M = pV

dU aU dp , aU /I dM H dV\ . ,. .Ht ' aFHf + ap~ WHt • HtJ (A-6)

Substituting A-6 in A-4

aU dP aU /I dM H dV\l dQ . P dM DdV .. %" + - - = + - -

dPSolving for -rr and rearranging

dQ P dM DdV 3U /dM M dV\Bt p dT " PdT " P3p" Ul " V 7F >/dP = di p dt rdt pap Vdt V Ht/ (A,_8)

^ pVfp-

Rearranging dQ + dM/£._ Hl\ 8JJ M dV _ pdV

Ht ~ ,,aU + . ,,aU

and reducing the last term

dQ . dM / P a•,-..;.. : • / . . . ...dp _.Ht 4,di\p " p"a7A .ut..Vop.. P'

Now. define _ . . . . . . . : . . - . . . . . ,

'-^"^••^-•'•f-'^-:±^• • • • • • • • .Q-p • • . - • • • • : . . - . - . . . •

and

;r:is ; -v4 ;.y£^

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Substituting A-ll and A-12 in A-10

df> « Jt/da + odM\ 1 dVdt " V f a t * *3tr V'3F

.» •

Equation A-13 provides a convenient method for calculating pressureresponse if the volume rate of change is known. The last term iszero for a constant volume system. If the container is elastic sothat the volume change is related to the pressure change, some furtherreduction is possible.

Again solving for

1 dV dP!t ~ ?V3t T °cTf/"

dP

for a spherical tank

1 dV

therefore

_. ..dM

2 b E

Now 'the 'outflow "is 'measured, .at -the end of the distribution lines••'• -which contain :gas at the sams -pressure as the t?;nkv --The flow across '? -

the thermodyncimic boundary must include the flow required to pressurizethe lines. Two assumptions for determining the flow into the lines' '

fhe--t'ari'KsH'hsi-"mainteins its density while compressing gas in the lineseither adisbatically or Isoth&niislly.

... . . . . . - : 2. .'Fluid expelled f.rorn... the. tank..does, not .affect the .tempera-t^.^.."^.vv;,^V<-^^Ur^;,di^ tq .:-,:.,.

••>-•••• "-••• :-• ••-' -.*.• •'' ••••• -^he System'out let, but* the 'density .'in the lines changes1

adiabatically or isothermally.

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The phenomena of assumption 1 can be described by writing thapolytropic relationship for the volume of gas 1n the lines.

oTaking logarithms and differentiating we have:

dVL • 1 dP

The flow rate Into the tank thermodynamlc boundary due to the linesis therefore: "

Where N=l for Isothermal compression and N=1.4 for adlabstlccompression.

Now writ ing A- 14 in terms of the demand and line flow rates.

dP _ &dQ . *od\ . iedMd I d V d P . f l• BT - V dt * r "3T * F BT " V BF df p*e.

dPSubstituting A-20 in A-21 and again solving for - we have;

t .vtThe relationships for assumption 2 are developsd by assuming thst thefluid density In the lines is related to the pressure by the poly-tropic exponent.. . . . . . . . i • •

"""" • • • ' - • ^ • - ' ' • " • ' • v : ^ - - - l ' - A ' ^ : w t

• , : . • • : /^9?i-?::'M'^nS jR9£r1^ '.TV,.'.;- .JJ. -.v'.,\:'

. A-4

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Therefore, the flow rate into the tank from the lines is:

I (A-25)

Substituting A-25 into A-14 and solving for 4^- as before we have:

" " H

dP . . (A_26)

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APPENDIX B '

STRATIFICATION MATH MODEL

The stratification math model used for these analyses is based on theGeneral Elliptic Method (GEM) developed by Mr. C. K. Forester of Boeing-Seattle to solve finite difference approximations to the mass, momentumand energy conservation equations (Reference 1 ). The fundamentalassumption of the method is that the pressure terms in the energy and

.momentum equation are not coupled. This assumption is valid for lowvelocity flows in which acoustic waves do not contribute significantlyto the fluid energy. This assumption permits a much longer time stepthan is otherwise necessary for stability. The uncoupling is accomplishedby using only the global (average) pressure in the energy equation toeliminate the effects of acoustic waves. Other assumptions which havebeen validated by comparing model results with Apollo 12 flight data are:

1. Two dimensional rectangular geometry (Figure B-l)

2. Viscous energy dissipation and kinetic energies are neglected

3. Radiation heat transfer within the fluid is neglected (radiationfrom the heater surface is included).

4. Acceleration body forces are constant through the tank

The difference equations used by the math model are based on the controlvolume concept. The rectangular flow field region is subdivided intoelementary control volumes or cells. The difference equations areformulated with the mass fluxes defined on the cell boundaries, whilethe fluid properties are defined at the centers of the cells. Thisformulation results in conservation of mass for each easily defined cell,

. whereas formulations ..wi.th fluxes and state properties defined at the . ,.same point do not. . .

The difference equations are solved by extrapolating an initial set offield variables by a time increment. Preliminary field pressure are

y-; calculated '..at th.e ^xt.r,app'lat,dd-.:tl.Rie-. inelydi.ng.'the-' effects -of. the •preHmi-'nary.'energy ?.rid tnasE transfers between cells. The pro! i mi nary pressures atthe extrapolated tim<; are used to revise the energy and mass transfer inthe time increment.- The extrapolated pressures are revised to account forthe new energy and mass transfers, and the -extrapolation procedure repeateduntil satisfactory convergence is obtained. The field variables at thepew time are taken as .initial conditions for the next time'. increment.. ... ... . .

. .. Succes^s.iye iterati^•'•" for" the simulated ""time period. ' ' - • " • • • • ••- •• • - :- • . • - - - - • = • -.

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B-2

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The difference equations solved by the program are only approximationsto the partial differential equations describing the processes in the tank.The quality of this approximate solution improves and approaches thesolution of the exact equations as the cell sizes are reduced. The cellsizes required to obtain an adequate approximation can not establisha priori. The effect of cell size on the model results must be investigatedfor each tank condition simulated to assure that the approximate solutionsare convergent. Separate simulations with at least three different cellsizes or grids are required to test the convergence at the solution for eachtank condition. Particular parameters, heater temperature for example, area function of grid size and are extrapolated to "asymptotic" limits. Theasymptotic limit, when obtainable, is the exact solution to the controllingpartial differential equations. The extrapolation procedure used in theseanalyses is based on the parameter differences related to the number of .cells in the X direction of the model as shown below.

No. of Cells Parameter-Temperature Pifference

20 60 4Q40 100 > *60 120 I *°80 130 1U

The successive differences form a geometric series. The ratio betweensuccessive terms is found and the sum of the infinite geometric seriesdetermined. The sum of the series of differences is added to theappropriate parameter to obtain the parameter asymptotic limit.

D-3

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APPENDIX C

HEATER TEMPERATURE CORRELATIONS

Heater temperatures can be determined from the numerical math model,but the computer usage times are excessive for the generation ofparametric data and to conduct routine flight analyses. Empirical heattransfer equations were investigated to develop a more convenient toolfor heater temperature studies.

The corrective heat transfer from a horizontal cylinder is usuallydetermined from a Rayleigh number equation.

The Rayleigh number is determined from:

D3 2 32.174 g p AT C ''R _ P _ P_

a pK

The f l u i d properties used to evaluate the Rayleigh numbers areusually taken at the mean f i l m temperatures. This convention is basedon tests with simple f lu ids under 1 "g" conditions. Since the propertiesof supercri t ical oxygen may vary by an order of magnitude in the boundarylayer, the properties in the Rayleigh number were averaged instead oftaken at the mean f i l m temperature. The viscosity, conduct ivi ty , anddensity were taken as the average of their values for the b u l k temperatureand the heater temperature. The specific heat was evaluated as thedifference in the enthalpy at the heater, and b u l k temperatures d ivided bythe temperature difference. The coefficient of expansion used was,

-1 W

The radiation from the heater is also significant and was included in thecomplete heat transfer equation.

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Heater temperatures were developed as a function of heater--on time bynumerical integration of the equation,

dT -.dg ,lxcfif ~ cit MC'

where MC is the heater thermal mass of 0.1 BTU/°F. The heater temperaturesensor lag was inducted in the integration to provide a means of comparisonwith flight data. The temperature sensor response was determined from:

dTsO. _ p /T T \

dt " Lk ljh '$;

The constant was estimated as 0.26 minutes" .

NASA— MSC

C--2 . .