Heidmann, Marcus F

Priem, Richard J

English

NASA Technical Reports Server

-J
4z
“I
v
NATIONALDVISORYCOMMIIM’EE
FORAERONAUTICS
TECHNICALNOTE4219
PROPELUNT VAPORIZATION AS A CRITERION FOR ROCKET ENGINE
DESIGN;RELATION BETWEEN PERCENTAGE OF PROPELLANT
VAPORIZED AND ENGINE PERFORMANCE
Washington
March 1958
By Marcus F.HeidmannandRichardJ.Priem
LewisFlightPropulsionLaboratory
Cleveland,Ohio
=6I?.3 fi.-+q
*.*&__,L“.-.:I
https://ntrs.nasa.gov/search.jsp?R=19930085136 2020-06-17T15:46:40+00:00Z
TECHLIBRARYKAFB,NM
NATIONALADVISORYCOMMITTEE
TECBIUCALNOTE4219
I:llllllllllllllllil:lll‘
FORAERONAUTIC UClbLNO+
PROPEIUIWVAPORIZATIONAS A CRIXTRIONFORR~ EKGIKEDESIGN;
KEIATIONBETWEENPERCENTAGEOFPROPEliI.zMTVAPORIZED
ANDENGINEPEEU?0RMANC31
ByMarcusF.HeidmannandRichardJ.Priem
STJMMAKY
y An analysisispresentedon thequantitativeeffectof inco~lete
5 propellantvaporizationrocket-engineperformance.A relationbetweencharacteristicexhaustvelocityc* andthepercentagesofoxidantand
fuelvaporizedandburnedisgiven.Theanalysishowsthat C* effi-
cienciesof 70to90percentcanbe realizedwhenonlyhalfthefuelis
vaporized,whereasC* efficienciesofabout60percent can be realized
whenhalftheoxidantisvaporized.Thespecificrelationsbetweenc*
andpropellantvaporizedarepresentedgraphicallyforthehydrogen-h fluorine,hydrogen-oxygen,amonia-fluorine,andJP-4- oxygenpropellant
combinations.Theanalysisisappliedtoexperimentaldataforthese
l
propellantcmibinations.
INTRODUCTION
Characteristicehust velocityiscommonlyusedas an experimental
measureof thecompletenessof combustioninrocketengines.Thisparam-
etermayindicateinefficienciesinthecombustionprocessthatmaybe
dueto incompleter action,mixing,propellantvaporization,andother
causes.Reportedhereinisan analysisrelatingthecharacteristicex-
haustvelocityto thepercentageofpropellantvaporized.
Propellantvaporizationisconsideredinthisreportas thefactor
thatlimitstherateatwhichthecombustionprocessproceedswithina
rocketengine.Theimportanceofpropellantvaporizationisalsoem-
phazisedinreferences1 to3. Theanalyticalstudiesofreferences4
and5 arebasedonthehypothesisthatthecombustionrateiscompletely
governedby therateofpropellantvaporization.Qualitatively,these
analysesareinagreementwithexperimentalresults.Exactcomparisons
ofexperimentalndanalyticalresults,however,requirefurtherefine-
mentsintheinterpretationofdata.Forthispurpose,a methodof data
2 NACATN 4219
analysishasbeendevisedtorelateexperimentalC* datato theper-. 4
centageofpropellantvaporized.
Thetreatmentof experimentaldatareportedhereinisconsistentwith ‘
theanalyticalcombustionmodelusedindrojlet-vaporizationcalculations
reportedinreferences4 and5. Applicationfthemethodofanalysisto
thehydrogen-fluorine,hydrogen-oxygen,ammonia-fluorine,andJ2?-4- oxygen
propellantcouibinationsisdescribed. —
P
SYMBOIS E
At nozzlethroatdiameter,sq tn.
C* characteristicexhaustvelocity,ft/sec
~- fuelvaporized,percent
g gravitationalconstant,32.2ft/sec2
o oxidantvaporized,percent
Pc totalchamberpressure,lb/sqin.abs
‘f fuelweightflow,lb/see
‘o oxidantweightflow,lb/see
T; characteristic-velocityefficiency,percentoftheoretical
Subscripts:
exp experimental
0/’ ratio,ofvaporizedoxidantovaporizedfuelweightflow,
l
—
b
Ow+%-wf
@/f ratioofvaporizedoxidantofuel
0/s ratioofoxidanto
o/f oxidant-fuelweight
th theoretical
vaporizedfuel
ratio,wo/wf
weightflow,@wo/w’f
/weightflow,W. ~wf
I?ACATN 4219 3
TEEORY
4 A mixtureof oxidantandfueldropsvaporizinginan atmosphereof
theircombustionproductsisassumedforthecombustionmodelinthis
analysis.Forincompleteconibustion,therocketexhaustcoqprisesa
mixtureof oxidantdrops,fueldrops,andgaseouscombustionproducts.
Thegaseouscombustionproductsareassumedtobe at thermodynamicequil-
ibriumconcentrations.Ifthevolumeandkineticenergyoftheliquid3a dropsareneglected,thecharacteristicvelocityC* thatcanbe theo-+ reticallyrealizedmaybe computedfromthethermodynamicpropertiesof
thecombustionproductsandrelatedtocouibustion-chauiberpm~eters by
thefollowingequationfromreference6:
PcAtg (1)(c;h)@/,= @Wo +-fa
8Q
4 The~erimental c* intermsofmeasuredengineparametersis
~
expressed
pcA#3 (2)(c&Jo/f = ~
.
Combiningequations(1)and(2)gives
Owo +-Swf
(c&)o/f = (c?h)6’/s W. +
The c* efficiency~c* is‘sually‘*en
(4)gives
Wf
to be
Combiningequations(3)and
‘nC*’o/f‘%%% (“% :2)
(3)
(4)
(5)
Equation(5)relatesc* efficienciesto
oxidantvaporizedandmaybe used forthe
data.
thepercentagesof fueland
interpretationofexperimental
Thepercentagesoffuelandoxidantvaporizedareparametersthat
cannotbe readilyevaluatedfofmostrocketenginetests.A simplifying
.
assumptionthatmaysatisfymanyoperationalconditions,however,isto
considereithertheoxidantorthefuelcompletelyvaporizedat the
—
4 NACATN 4219
exhaust nozzle. Sucha combustionmodelwasassumedfordroplet-
vaporizationcomputationsreportedinreferences4 and5. Withthis
assumptionequation(5)maybe usedtoconverta measuredc* efficiency
intothepercentageofthepropellantvaporized.Theexpressionsfor
theseconditionsfollow.
Withthefuelcompletelyvaporized,the c* efficiencyisrelated
tothefractionofoxidantvaporizedby
@wo ~ ~()* ‘f(?lc*lo/f= (C;h)o,f “o—+1“f (6)
Withtheoxidantcompletelyvaporized,the c* efficiencyisrelatedto
thefractionoffuelvaporizedby
(7)
Suchcomputationsrequirea knowledgeofthevariationintheoretical .
c* overan extendedrangeofmixtureratios.Thesevariationsfor
severalpropellantcouibinationsareshowninfigure1. Theoreticalvalues
reportedinreferences7 to9 wereextrapolatedovertheregionshown.
Theextrapolationswerebasedontheassum@ionsthat: (1)forlow
percentagesof oxidantandfuel,thecombustiontemperaturevariesdirectly
—
as thepercentageoffuelor oxidantinthemixtureand(2)c* ispro-
portionaltothesquarerootofthecombustiontemperature.
Thetheoreticalc* values howninfigure1 wereusedtoobtain
graphicalrepresentationsf therelationbetweenc* andpercentageof
propellantvaporized.Thesegraphicalrepresentationsi cludethevaria-
tionof c* efficiencywiththepercentageofoxidantvaporizedandthe
percentageoffuelvaporized,asexpressedbyequations(6)and(7),
respectively.Applicationfthesecurvestoestimatingthepercentage
of vaporizedpropellantfromexperimentaldataisdiscussedinthefol-
lowingsection.
l?XSULTSANDDISCUSSION
Effectof IncompleteVaporizationEnginePerformance
Thevariationsof C* withpercentagesoffuelandoxidantvaporized *
areshowninfigures2 to5 forthehydrogen-fluorine,hydrogen-oxygen,
ammonia-fluorine,andJP-4- oxygenpropellantcombinations.Forall d
NACA‘IN4219 5
.
propellantcombinations,a higherc* isobtainedwitha givenpercentage
offuelvaporizedthanwithanequalpercentageofoxidant;forexample,
u withhalfthefuelvaporized,the c* efficiencyisbetween70and90
percent,whereaswithhalftheoxidantvaporized,the c* efficiencyis
about60percent.Thisdifferenceisattributableto severalfactors,
includingtheshapeofthetheoreticalc* curve,thefactthatpeak
theoreticalc* occursinthefuel-richregion,andthefactthatthe
oxidantweightflowaccountsfora largepartofthetotalpropellant
flow.
Figures2 to5 maybe usedto interpretexperimentalc* performance
intermsofthepercentageoffuelor oxidantvaporizedprovidedtheother
propellantcanbe assumedtobe completelyvaporized.Forexample,for
theammonia-fluorinepropellantcombination,a c* efficiencyof 85per-
centatan oxidant-fuelratioof 3.0mayindicatethatonly60percent
oftheammonia(andallthefluorine)or 80percentof thefluorine(and
alltheauraonia)hasvaporized.Thefollowingtablepresentsa similar
comparisonforotherpropellantcombinations:
Propellant
Hydrogen-fluorin~
Hydrogen-oxygen
Ammonia-fluorine
JF-4- oxygen
c*Effi-wo~wfFuel Oxidant
ciency, vapor-vapor-
percent ized, ized,
s, u,
percentpercent
85 4.0 37 82
85 2.0 51 80
85 3.0 60 80
85 2.5 70 79
Theresultsmaybe furtherinterpretedto showthepercentagesof
propellantshatmustactuallybeburnedtoobtainagiven c* efficiency
level.Forexa~le,withhydrogenandfluorine,only37percentofthe
hydrogeneedevaporateandco?qpletelyconsumethefluorineinorderto
obtaina c* efficiencyof 85percentatan oxidant-fuelweightratio
of 4.0.
centis
chamber
This,ineffect,ist~ c* efficiencyobtained~ ~he37per-
completel.yvaporizedandthefluorinecompletely
andtheremaining63percentislostas liquid.
burnedinthe
InterpretationofExperimentalData
Typicalexperimentalvariationof C* efficiencywithchamberlength
(data F&nref.- 10)is showninfigure6 fora single:elementinjector-
withJT-4andoxygen.The c* efficiencydataarealsoevaluatedin
termsofthepercentoxidantvaporizedandthepercentfuelvaporized,L
assumingineachcasethattheotherpropellantiscompletelyvaporized.
J
6 NACATN 4219
.
An explicitevaluationof thepercentageufpropellantvaporizedcannot
be madeifincompletevaporizationfbothoxidantandfuelisassumed;
—
probablyneithertheoxygenorthehydrocarbonvaporizedcompletelyin .
theexperimentsreportedinreference10. Eachvalueof c* efficiency,
however,maybe expressedasa specificrelationbetweenthepercentages
of oxidantandfuelvaporized.Theserelationsareshowninfigure7 for
oxygenwithJP-4andmaybe appliedtotheexperimentaldatashownin
figure6.
-. —
Thesemethodsof dataanalysisprovidea meansof correlatingdroplet- $
evaporationcalculations(e.g.,refs.4 and5)withexperimentalengine %
performance.
Theshapeofthe c* efficiencycurveinfigure6 istypicalfor
mosttn$ectorsandpropellantcotiinations.Itwillbe usedasa hypo-
theticalcurveforseveralpropellantcombinationsto illustrateheim-
portanceofpropellantvaporization.Thevariationsinthepercentages
offuelandoxidantvaporizedforvariouspropellantsareshowninfigure
8 at theoxidant-fuelratioforpeaktheoreticalperformance.With
oxidantvaporizationcontrollingthereaction,the
-—
C* efficiencyis
slightlygreaterthanthepercentageofoxidantvaporized,regardlessof
thepropellantcombination.Withfuelvaporizationcontrolling,however,
theresultshowthat c* efficiencyissignificantlyhigherthanthe .
percentageoffuelvaportzedandthatthisdifferenceisgreaterfor
kt@rOgeLI thanfor~-4 orammonia.Thevalidityoftheseevaluations
dependsonwhethercompletevaporizationf onepropellantcanjustifiably b
be assumed.Injectordesignfeaturesandpropellantphysicalproperties
arefactorsthatinfluencethisassumption.
SUMMARYOFRESULTS
An analysisispresentedonthequantitativeeffectof incomplete
propellantvaporizationengineperforumnce.An emressionrelating
characteristicexhaustvelocityto thepercentagesoffuelandoxidant
vaporizedandburnedisgiven.A graphicalrepresentationoftherelation
ispresentedforthehydrogen-fluorine,hydrogen-oxygen,ammonia-oxygen,
andJl?-4- oxygenpropellantcombinations.Ifthevaporizationfone
propellantisassumedtocontroltheextentofreaction,thisevaluation
showsthat,atmixtureratiosforpeaktheoreticalperformance,c* effi-
cienciesofabout60percentareobtainedwithhalftheoxidantVaporizedj
and c* efficienciesfrom70to90percentareobtainedwithhalfthe
fuelvaporized.Efficienciesarehighestforthehydrogenfuels.
LewisFlightPropulsionLaboratory
NationalAdvisoryCommitteeforAeronautics
Cleveland,Ohio,Deceuiber10,1957
HACATN 4219 7
l
. 1.
2.
3.
4.
5.
6.
4
7.
8.
9.
REFERENCES
Ross,ChandlerC.: ScalingofLiquidFuelRocketCombustionChambers.
AGARDSelectedCouibustionProblems,II - TransportPhenomena;Igni-
tion,AltitudeBehaviorandScalingofAeroengines.Butterworths
Sci.Pub.,1956,pp.444-456.
Penner,S.S.,andDaiiner,P.P.: CombustioninLiquid-FuelRocket
Engines.FifthSymposium(International)on Combustion,Reinhold
Pub.Corp.,1955,pp.11-29.
Penner,S.S.: OnMaximumEvaporationRatesofLiquidDropletsina
RocketMotor.Jour.Am.RocketSot.,vol.23,no.2,Mar.-Apr.
1953,pp.85-88;98.
Priem,RichardJ.: PropellantVaporizationasa CriterionforRocket
EngineDesign;CalculationsofChamberLengthtoVaporizea Single
~-HeptaneDrop.NACATN 3985,1957.
Priem,RichardJ.: PropellantVaporizationas a CriterionforRocket-
EngineDesign;CalculationsU ingVariousLog-ProbabilityDistribu-
tionsofEeptanehops. NACATN 44)98,1957.
Sutton,GeorgeP.: RocketPropulsion”Elements.Secondcd.,John
Wiley& Sons,Inc.,1956,p. 74.
Gordon,Sanford,andHuff,VearlN.: TheoreticalPerformanceof
LiquidHydrogenandLiquidFluorineasa RocketPropellant.NACA
RME52L11,1953.
Gordon,Sanford,andHuff,VearlN.: TheoreticalPerformanceof
LiquidAmmoniandLiquidFluorineas a RocketPropellant.NACA
RME53A26,1953.
Huff,VearlN.,FortinijAnthony,andGordon,Sanford:Theoretical
PerformanceofJP-4FuelandLiquidOxygenasa RocketPropellant.
n - EquilibriumComposition.NACARME56D23,1956.
10.Heidmann,M.F.,andAuble,C.M.: InjectionPrinciplesfromCom-
bustionStudiesina 200-Pound-ThrustRocketEngineUsingLiquid
OxygenandHeptane.NACARME55C22,1955.
.I I
Fuel Oxlaant Reference
1- FluorllleLo,alo 8 =G Oxygen Or@u&shedEACA 6ata -44
-_l — Exhqd@.ted
8,(33) ~ ~
m“
4
w--
6,0CKI
/ ~
/ /c
YB
.-
~’ /’ ,1
4,CW ,5/ / /
// ‘/‘ ‘
/~
z, ‘/
/
2,Ow /
o .2 .4 .6 .8 1.0
()~.l/2(m-tic-md .16ant In Emu.@, —W. + Wr
I I I
.
I 1 I I I
o .01 .m .1 .2 .5 1 24
Oxlllant-fuel‘mightratio, VJV*
. .
1/2
[)
Vf
W. + W*
~
2
Gxi(lant-fuelweightratio, Wo/wf
Figure1. - VuiatimoftheoreticalCkracta.ieticR.rbauatVEloci@vithdxture ratiofaraf.ti
WQPUt c~~ti~ nt ccabustlm—chaubmWC- & ~ Dur@.6per squareinchabaoluteand
equilibrium~im.
1
w
. CX-2 4649
.
1“1 I ‘AU kxidnt v&&a&,u-mTheo’retlali , I I , I II =M---l_ I I & &A.e4 I
I lx I x I ml I
40
1 1 1 1> I 1 m 1 1
m
o 5. 10 15 200 5 la M 20
Oxiclmt.fielwei@t mtiO, ~o/wf
(a)VnrlntiOnof C* with ml.xtum ratio.
?lglu’e2. - JWf.emtof Inoaqletavnparizutionon d+ and c*efficiencyfor hydro~ an~ fl.uorlne.
-. .-
1.(IQ
- All fuel vaporized, ~= 100 f
80 A
/
60
f’
(
40
[// r
o
All oxidant vaporized, u = 100
I 1
n 20
4
0 20 40 60 80 100 0 20 40 60 80 100
OxidantVaporized, u, percent Fuel vaporized, ~, percent
(b) Variation of C* efficiency with percentage of propellant vaporized.
s
Figure 2. - Conchdied.. Effect of inccarpletevaporization on c* and c* efficiency for s
hydrogen and fluorine.
~
*
N
P
w
.
. v . 6%9? ! +
6-/. * L t CX-2 back 4649
I 1 1 1 1 1 1 I , I I I I
o 2 4 6 a 10
Oxldent-fuelweightratio,v#q
(a)Varlatkm of c’ tithmixtureratio.
Fi6ure3. . Effectof inccmpktevapmlzatlonon c* and c* efficiencyfor t@m3gen and oxygen.
I
.—
1-
N
100 .
— All fuel vaporized,S = 100-
60
60
40 -
20
0 20 40 60 80 100
Oxidantvaporized,(), percent
I I I 1 1 1
All bxidant vaporized, O = 100
(
o 20 40 60 80 100
(b) Variation of c* efficiency with percentage
Figure 3. - Concluded. Effect of incomplete vaporization
hydrogen and oxygen.
‘T ‘
1,. , ,,,
< 9
1
Fuel vaporized, ~, percent
of propellant vaporized.
on C* .gM C* efficiency for
i%
P
W
d.’ ,,
Clm
3
8LX?0~
All fuel vaporized,~. lCKI Oxi!.ant‘
I I vaporl=d,—
Theoretical~ 0,
7cKa percent _
\ /- — —
- 100
/ —
— 90
fccfl
/ - w
,70
Ecca / -
a60
# -
4000
50
/
/ -
40
W30
/ 33
2CXI0 20
10
lm
01 2 5 4
4E4C9
i,
03Mant-fuel veif#3t-mti0, WojWf
(a) Variationof C* with mixtureratio.
Figure4. - 2ffect of incompletevaporizationon c* and c* efficiencyfor
-nia and fluortie.
100 1 I I 1 II ..- ,!- 1 I
$‘“l--t--k
iH--t75
o- 20 40 60 80 100
OxidantVaporized,o, percent
I I I I I I AA
All oxidant vaporized, 0= 100
~-
f
20 40 60 80 1
Fuel vaporized,$, percent
)0
(b)Variationof c*efflclency uith percentage Of propellant vaporized.
Figure4. - Concluded. Effect of inccqlete vaporization on c* emil @ efficiency for
anunonia and fluorine.
I
l ’
,,
. *
I ,, Ill 11, ,
d’. . 4 4649
I
*
u
al
-5
*’
.3
c1
I I I I I
All fuelvaporized,$= 103
I oxidant
m eoretlcal-] vaporized,
mm ! 0>/ ~ percent
~ 100-—
/ “ — ~ 90
5000 — —
/ -
~ ~ —
80
—
/ ~ ~70
~ —
40Q0 60
- -
50
— —
Km
40
<m
2000
20
1000 “10
1.5 2.0 2.5 3.0 3.5 1.5 2.0 2.5
OxIdmt-fuel weight ratio, wJvr
(a) Variation of c* with refire ratio.
Figure 5. - Effect of incomplete vaporization on c* and c* efflclency
3.0 5.5
for JP-4and oxygen.
I
P
a
100 I 1 I I ( r
All fuel vaporized, # = lW
c
o 20 40 60 80 100
Oxidantvaporized,U , percent
1 I I I 1 I
All oxidant vaporized, 8 = KCI
o 20 40 Ml 80 100
Fuelvaporized,$, PeX=t
(b) Variation pf c* efficiency with percentage of propellant vaporized. 5
2
Figure 5. - Concluded. Effect of incomplete vaporization on c* and C* effIciency for JP-4 end oxygen.
s
*
N
P
a
<. rQ
,, 679% ,
ma.
80
60 /
/ /
40 /‘
/ i
/11
f
/
d *
20 /f /
/
“o 1
EXp&herital c* (ref.10, fig. 7)
~ ~
— —
—
- —
F
/ ‘ 1
“ ‘oxidant vaporized
/ / (allfuel vaporized) _./
0’
~ / -
/ -
/ ~
/ “ L Fue1 Vaporized (alloxidantvaporIzed)
/{
2
Figure6. - Evaluationof
Propellants,oxygenand
3 4 5 6
Chamberlength,k.
4
—-
--
— -
— -
7 El
typicalperformuce data for pmcenteges of fuel and oxidantvaporized.
JP-4j oxidant-fuel weight ratio, 2.2.
G
18 NACATN 4219
I I I I I I I I
I c* Efficiency,percent
loo20 3040 50 60 70 %; 90 95 100
80
i
60
40
\
20
0 20 40 60.
Fuelvaporized,%,percent
80 100
Figure7.- Percentagesofvaporizedfuelandoxi-
dantrequiredtomaintaina givenc*efficiency.
Propellants,JP-4andoxygen;oxidant-fuelweight
ratio>2.2.
r
—.- —
---—
, 1 I
C* Efficiency dld
80-
al.P
60
Hydrogen-fluorine - ;’!
Hydrogen-oxygen ;~
PO
20
m
w
1 I I L 1 1 1 1 I
Propellants VJT?*
“H “
s
a
JP-4 - oxygen 2.5 *
Ammonia-fluorine 3.0 P
Hytigen-fluorine
w
4,0
Hydrogen-oxygen 3.0
0 2 4 6 8“0 2 4 6 8
Chamber length, in.
Figure 8. - Comparisonof calculatedpercentagesof propellantvaporized for several
propellantcombinations,using a typicalexperimentalvariation of c*’ uith chaniber
length.
I


Propellant vaporization as a criterion for rocket engine design : relation between percentage of propellant vaporized and engine performance

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server