NASA Technical Reports Server (NTRS) 19980236002: Results of a 24-inch Hybrid Motor Performance Uncertainty Analysis

14 Pages·0.97 MB·English

by  NASA Technical Reports Server (NTRS)

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AIAA-98-4021
RESULTS OF A 24-INCH HYBRID MOTOR
PERFORMANCE UNCERTAINTYANALYSIS
Josep h D. Sims
Lockheed Martin Astronautics
Huntsville, Alabama
Hugh W. COleman
Propulsion Research Center -.
Department of Mechanical and Aerospace Engineering
University ofAlabama in Huntsville
Huntsville, Alabama
34th A!AA/ASME/SAE/ASEE
Joint Propulsion Conference andExhibit
I
July 12-15, 1998 / Cleveland, Ohio
Forpermissiontocopyorrepublish,contacttheAmericanInstituteofAeronauticsand Astr_utlcs (A_AA)
1801Alexander BellDrive,Suite600, Reston,VA 22091
"_ -_]UN _S "-38 L5:_.7 Fg:311LSS_.C3 P_O] OFC TO WEEm5 PAGE, 003.'015
RESULTS OF A 24-_CH HYBRID MOTOR
UNCERTAINTY ANALYSIS
JosephD,Skns'
LockheedMarth istronauScs - Huntsville Operations
Huntsville,AL35806 ,
HughW. ColEman*
PropulsionReseemh Center
DepartmentofMechardcal and Aerospace Engineering
UnivemffyofAhbtma inHuntsv/lle
Hunt_vi.Ile,AL35899 "
Abstract A'; Nozzle throaatrea (i_n)
•b: Fittincgonstanftorerosiomnodel
The subscsle(II-and24.inch)hybrid B: BiasuacertaMty
motorsattheMamhallSpaceFlightCenter(MSFC). Bi: Biernumber
havebeenused asversatileand costeffective testbeds C*: _ter_tic velodty (R/see)
.for developMg new technology, .Compar_ons c,: Dischargecoefficient' .
between motor configursdons, ignition iystema, feed D: Diamet_ (in)
systems, fuel formulations, andnozzlematerials have DILl/: Datareduc_onequatio"n
beencarried outwithout dotted coneider_bn u to OOX: Ga_e4_oxygen
how "good"themotorperformancdea,mwere.For GUI: Graphicaulserinterface
the250,000Ibrthrumsottordevelopebdy±e Hybrid h: Perturbation magnitude
PrOl_Ision Demonstration Program¢oneortium, h,: Hot gu-side convective heattnmfer
shortcoming is: particularly risky because motor coefficient
performanoe will likely be used as partof a set of I-IPDP: Hybrid Pro_Islon Demomtn_.'0n Prugram
downseleftoriteria tO choosebetween competing Is: Sea.level _e¢_o fml_se (lbf-lef,/Ibat)
ignitionandfeed systemsunderdevelolnnent. Iv=: Vacuumspecific _tmpuhe'Obf..-sec/]bm)
This analysisdirectly ad_es _hat. JIRAD: Jointhdegcadent Researchend
shortcoming by applying UnCErtJttnty analysis DevelopmEnt
techniques to.the experimental determination of the k Thermaldonducti,d(tByTU/In-seo-*R)
characteristic velocity, theoreti6al oharacterhtie LOX: Liquidoxygen
velocity, and characteristicvelocity ef_ciency for a LSSRC$:LL_geSubsoalSeolidRocketMotor
24-inchmotor firing, With the adoptionoffuel-lined CombustioSnimulator
headends, flow restrictors,end _ mixing chamben, M: Mess(Ibm)
state of the art24-i_oh hybrid motom havebecome
MassflowrateOhm/see)
very efficient However, impossiblyhighoombustlon
Nud • Nmselt numberbescd upon diameter
efficiencies(soraecompmedaShighas 108%)have
ODE: One-dimensioneaqluilibrium•
been measured in SOmEtestswith ll-inch motors.
O/F: Oxidizer-tx>r.aftuicol
Thisanalysihsasgivennew insighinttoexplaining
P: PresmreObtYin_)
how theSEeffcie_ies were meatmred tobeso high,
Prandtnlumber
and intowhich experimental measurementscontribute I',: Precisionuncerte_n,ty
themosttothe Overalluncert_ty.
F. _ental result
R%: Reynoldsz/umbebrasedupondiameter.
Nomenclature
SHOE: SoftwarfeorHybrid Unceminty Fatimatlon
SLOC: SourceHnesofcode
English
tm: Motor bum time "
TEA/TEB: Pyrophoricmixture of
a: Initialthroatdiameterforerosion model
triethylalumMum and_-iethylborj'de
'PropulsioEnngineerA,dvancedSpaceSystemsM,emberAIAA
*EminentScholairnPropulsioanndProfessoAr.,ss_hte FallowAIAA
fLi'l 2S "98 1_=:27 "--'_I! I_EEF,Z3 Fc3] CFC TO I.tlEEJ\3 PAGE.CC4 015
UPC: Uncertaintpyercencton_ributlon linedwithfuelorsilicpahenolica,ndintheIfinch
Ut: Experimentatlmccrtainty GOX motor,asilicpahenolibcaffliesalsoinserted)
Primitivmeeasuredvariable toenhancecombustioenffici_acy andstabilitTyh.is
pro-and po_-charnbecronfiguratihoansalso carried
Or_k symbols •overinttohe250Kmotor, "
,Anothercommon theme among allthe
a: Coefficient of tbermalexpansion(t/_) programs,includinIg-IPDP,is tlmtno detailed
AT: Temperaturdeifference (°R) analysihsasbeen done to addressmeasurement
¢: Sum ofO,O:massfractioinnsexhaust uncertaintiesT.he fundamentalquestionthat
species uncertainty aitaIDiasttemptsto answeris, "How
'IC. Ratioofspecifhieca_ •good are the data andtheresults calculated from
them?"Theactuaplrocesissstraightforwbaurtdt,l_
_c,: Combustionefficiency
final productrequires care to be sure all the sources
_t: Viscosit(yIbm/in-see)
ofuncertainty have beenaccounted for.
p: Density (Ibm/R')
Inthiseffort, a FORTRAN 90 computer
code wM writtetno cs.lculate tmcer_nties for 28
SubscripatnsdSuperscripts
different experimental reralts for .the four hybrid
motors.The codeuses standaradnalyslts_chniqucs
*" Nozzle Throat
toestimatepartialderivstive_ andto l_agate those
Vap: V_por
derivatives,alongwiththeiLruociated meammmnent
0: Chambercondition
bias andpr_ision limits, into anoverall expertmentz.l
unccr_inty. This overall process ij demousttated
introduction
_tng hot-fire data fromarecent HPDP 24-1nchmotor
test,
Lockheed MartinAstronautics('u the
Additionally, somerecent 1finch motor test
formerGeneralI>#amics,thenMartinMarietta,
rcsultashowImposm'blyhigh combustion e_ciencies. •
beforemergingto form thecurrenCtorporation)
It is asserted in this paper that these impmsible
involvemenwtithhybridpropukiondevelopmenatt
measurementrsemit from con¢,ept(muaoldeling)
theMarshallSpaceFlighCtenterdate, tractko1990,
bimmsinthe calculationt_x_. "
withtheformulatioanndexecutioonf the gRAD
program.
Uncertain W An_dyslS
- The successfuHlRAD programefforwtas
foUowedin1992bytheLSSRC$ programa,concept Onlya brleofverviewofthemethodolo_tro
thatusedsubscalehybridmotorsto simulamthe
obtaiunncertainetsytimateasndhow they pmp_ga_
combustionprocessandexhaustspecieosfa solid
througha givenDRE isgiven here. The readerf_
rocketmotor.Numerouste,tseriewserecompleted
referredto Coleman trod Steele'_ for-a detailed
thatvalldatethdis COSteffective evaluatipornoce*s.
discussioofnuncertainatmytlysistechniqucs.
LMA alsosupportetdheHPTLVB program_which
The word accuracy is generally tme_t,to
starteidn1993.
indicatetherelativeclo#enesosfagreementbetween
Severalhybridpropalsiondevelopmmt
anexperimentally dctcrmincvdalueof a quantityand
programs were i.ntegratcd in 1994m form a single, itstruevalue.Errori_thedifferencbeetweenthe
focused effortto develop and testa seriesof 250,000- experimentallYdetermined value _:l. the troth;
poundthrushtybridmotors(250Kconfiguration),
therefore, as error decreases, accuracy is said to
Common to allll_e programsarethree increase.Only inmrs instances is the truevalue of a
subscalemotorsatthe NASA MarshalSlpace Flight
quantity known. Thin, it is neces_y to estimate
CenterMSFC). Two eleven-incdhiametermotor
_m-or,andthatosttnmteis called an uncertainty, U.
configurati(oInIs"caseO,D.)areused,oneforOOX
Uncertainctaytimateasremade at some _nfldence
andthe otherforLOX. A twentyfour-inch
level - a 95% confidencees_mate, for example,
configuration (24" case O.D,i that exclusively _e_
means that the truevkl_of the quantity b expected
LOX is alsoavailable.The subscalemotor
-to bewithinthe -.*iUntervaablout the experimentally
configuratihoanvsematuredthroughoutthedifferent dotcmined value95time#outof 100.
programs,but all currentlyme a _. Totalerror can be considered tobe
vaporizaticohnamber(linedwitheithefreelorsilica
compo_d oftwocomponentsa:precl,io(nrandom..)
phenolica)ndanaftend mixingchamber(similarly ..
compone_n,ta,ndabi_(systematciocm)ponent_,. andwhere8:,t,he 95% confidenceestimatoefthe
An errorisclassifiaesdprecisioinfitcontributteos covariancaeppropriaftoerthe bias errorsinX_and
thescatteor£thedatao;therwisiet,isabiaserrotA_s X_,isdeterminefdrom
anestimatoorf6,a systematiucncertainotrybias
limitB,,/sdefined.A 95% conPdenceestimaties (B),.(B),. (7)
interpreted as the expvrlment_ being 95%COtLfidcnt
thatthetruevalueofthebiaserrori,fknown,would
fallWithin4-]3,A usefulapproachtoestimatitnhge wherevariableXs_ andXk shareL identicaeln'ror
magnitudeofabiaserroristoassumethatthebias
sourcesT.heseterms_count for correlatiboentween
error for a given case is a single realization drawn
bi_ errorsind_fferentmeasurements.
from some statistical parent distributionof possible
For theanalysis summari_d in thispaper,it
biaser_o_, As anestimatoorfthemagnitudzofthe was assumed that bias uncertainties dominated the
precisioernrors,aprecisiounncertainotryprecision
overall measurement unc_'taJniy, making precision
llmitP,,fora singlereadingisdefined,A 95%
uncertaintineesgligibleT.he onlymeasurements
confidenceestimatoefP isintsrpretteodmeanthat wherepr_isionuncer_ntie_ amimportant are for
the"-PintervaalboutthesinglreeadinogfX_should nozzle throatdiameter measurements and the fuel
cowr the (biased) parent population mean,g, 95
weights,As willbe cliscusso.S.ig_nificant ndn.
times out of 100.
syn_m_'i¢ e_osion typically oceu_. at the throat
In nearly all experiments, the mvasurcd region. These nmdom (from a pro-tint prediction "
values of different variables m ¢_mbln_l using a standpoinvta).danceisnthe _oa_ dt_me_ m
D1LE to form come desh'cgt result A general trea_d mah_ma_cally as precision uncertainty
representatoifoanDRE is sourcesb,ut in mdity,area unique chus ofb'm_
uncertainstoyurcestermedfossiltzb.i_ases,This
r=r(X,,Xz,.,,,X,) (1) ma_omadcal treatment can befoundin.anysta_tica
-_¢xtb,ut the 95%confidence large sampb p_tsion
whereristheexperimenrtea_ltdetermlned'fJr"om limitises_a_d as
measuredvariableYs_, Each of themeasua'od
variablecsontainbsiaserrorsandprecisioenrrors.
These errors in the measured values _en propagate
through the DILE, thereby gen¢rating th.¢ bias and . (s)
precisionsrrors inthe expvrimentalresult,r.
If the 'qarge sample assumption" is made_,
then the 95% cor_dence expreuion forU,b_comcs 1tape, ion of equation (3) shows a
significant effectt_ correlatedbias unccrtaintie_can
u;=s; +P: (2) have,, Because of the cova.danceexpression of the
laity"haLfoftheright hand aide,andmost especially
becausteheh_Mdualpartidaelrlwtiwamu_ (as
where the systematic uncertai_ (bias limit) of the
result isdefined as oppoaed to _6irsquares)th,ecormhted bias terms
e.,aenither_e theoveredluncertain(tiyfthe
paxtia_ am of thesame Sign)or clecm_e:I_ ovmdl
2' J-I
B,_=_o:_: +2E_e,e,n, (3) uncer_inty(ifthepmhlsa_eofopp0si_sign).Tl_
i=l I-I k,_l factplaysadistinct role inthisanalysis, ' '
i
withthebias limit es"timateforeachX_variable asthe .P_r_prmance Calculations
rootsum square combination of its elemental
systen_tic.uneerta_ntics _suggg£2
C*igonemcas_'eoftheenergycontenitna
(4) chemicaplrc;pellcaonmtbinationI.tisdefined
c" =P°f-- "(9)
m
zl_r 25 '38 L5;2.-9 F_,,:,il LSSKC3 V_C_G CFC TO :UEEi',,5 IZAGE.OO6,.OL5
However, instantaneous fuel flow rates in inlet pressRre and temperature. The flow rate was
hybrid rocket motors are currently dimeult, if n_t initiallyeadculatcdusing:
impossible, tomeasure with anyre.enable certainty,
Thereforef,uelusageismeasuredby weighingthe m_o# g =
..Tz).c,.4p(P,. (t2)
fuelgrain(sfortheIfinch)ortheloadedmotorcase
(forthe24-incahnd250K motorsb)othprea-ndpost-" ' " i ":
testa,ndCalculatianngaveragefuelfl0wrate,The
However,sventuri foruse inLOX_rvic¢ is
resulitsthatC* measurementmsustbebasedupon
typically calibrated in a room-temperat_ water
expendedvaluesforfueli,gnitoarndinerptropellant
facility_. TI_ meansthatdue tothecryogenic
andLOX weigIitasv,eragenozzlethroaatrea,anda
temperature duringmotor firing, the actual vmturi
total pressure integral. In effect, aUthe variables are
throat diameteris somewhat smaller - inmx_ing a
integrated over the motor bum time, r_alting in a bias into the LOX flow ram meas_ements. One
modifiedfromof(9):
involved methodfor calculating the actual throat area
wouldrequirtheeuseofafiniteelementmodel.An
easier method,however, is to dmply_ the
0dr
coc_cientofthermal expansion and the teml_'ature.
Lt--0t, .J diffez_zoe betweenthe ¢_bration facility and the
c_ogenio feedl_ to reduc_ the throat diameter an
-- m_ . dt+ jm_ dt
appropriate mount, rcsultlng in a slightly modified
[=l. la t. Ip formof(19)
(10)
The denominator of (10)t_sults from
accountinfogr allfluids thatare_ated andexpcUed (13)
throughthe motor nozzle. This includ¢_, of cou_'se,
Equation (D) has two tem_ tluit ate
themain LOX and fuel, but also includes the
dcpend,entupontheinlettemperature;.namely, p
TEMTEB ignitionfluidandni_'og_purge mass_.
It should benotedthat the limeintervalused P,_.Thesetwo.q,_mdriaer_ecalculatue_dingGAS#
andaWagnerian cm'v_t', r_pco_vely." . . '
Iocalculaetaechavengefactorsoutofequation (10).
Two typ¢_ofignitiosnource!am u_edfor
Additionally, the integr_:lsin(10) s_ecalculated using
thesubs:almeotors.TheIl-incOhOX motorus_ a
a trapezoidMael approximationex-ceptfor thefuel
smallGOX-hydrogentorch,and all_ LOX
totamlass,whichisCalculatbeyddirecftuelweights
mot6rtuse_B, apyrophorifclui& Following
pro-andpost-test. Theappendixcon_ti_ the gram'el
DRE usedtocalculamtoetorC*. apre-scltengtohftime over which the 1etch islit or
TEA/T_B is flowing, a gaseott_ nitrogen purge.b
Nearly allthe termsinthe DRE showninthe
sta_d to keep combustionproductsfromflov_g
append/xcan be broken down into constituent
backintothe Ignition feed system. There2ore,(12) h
components.For example, A* isthesimpleaverage
used to calculateTEA/T]_ flow ra_, with the
of the pre-md post-fire throat arras. But, to
dcmltymodeledasafire.on of mmpemtureonly(a
complicate thingsfurther, bothof thediametersused
con_eptuMbiss), and with the'vaporpressure
inthe average area calculationam themselves dmple
assumedtobe zzro',
averages Of four (each) pre- and post-fire
measurements (see the equationbelow). Nitmgm ismetered using the sameorifice as
forthe T_A/_B (or th_OOX-hydrog_ torch). The
equationfor sonic gas flow through a dmrp-edged
=D O+DA,+D. +D,..
D-'_ (11) orificeiS
4
1"'
ramificatioofnequatio(nI1), exploz_cl
in gream-dc.m.illater in this paper,is that the throat
ar_a isassumed to changeLinearly- i.e., the average
throat diameterchanges asa second-order function Of
rB,¥,---- ._
time.
(14) ":
TheLOX mass flow rateis metred" _in$ a
cavitativnegnturwi,hich requires the measureme_ of
4
ThenitrogeTnisalsocalculateudsingGASP. investigahtoewd measurementuncer_nt/es affected
Thefuelintegraisl asimple weight change themodelingoftheSSMEpowcrb_Imc_. A Similar
calculat/on based upon average pre- and post-ffn_ procestsothatusedinColemanandSternwasused
weighing: •for theworkrepo_d intltisp@er, thoughno attempt
was made to esfima_ the uncertaintiiensthe
theoreticcaallculatiotnhsemselvesT.he u_:ertainty
in the _oredca] C*, then, results directly from
t_ un_n_e_ in_ in_¢ data
Historicatlllzyo,micacl' was cdcula_l
+M,,+,,M,,).-, )]('>
by int_poiatitnagbuia_dvaluesthat"resultferdom
thermochc-misr_u'nysoomplet_by a consortium
member.ThevaluesweretabulatemdsRm_Jonof
D_f_dation of(15)showsclearl_y the
ON andchamberpressure. How_v_, tl_v_lu_did
pre- andpost-Rr_grainweightmeasweme_tshaw
notaccountfortheTEA/_B, theOOX.hydrogen
derivativetshatareof o_ositosign.Thisfact,
torch 8n_es,the silica phenolic from the aft mixing
highlighted in apreviou_sectiohne,lps toroducethe
chamberandthebaffle (inthe.It-inOchOX motor)
overall measurement uncertainty, Thepro-andpo6t.
or thenilrogenpurge. It was felt _11these fluids
fire mea_ements have con'elatedbiasuncertainties
conuibut_to _ measwed C* pressure iinegnd and
because the same load cell (or scale, for thelight_
totheth_orsticdcslctdations,sndthatnotaccounting
motor pieces) is usod for both sets ofweights, Since forthem in_'odu_ _ldldonal blasm into tim
abiasuncertainitsysys_mtic,themagnim& of the
experimentraelsultTsh.ereforteh,isanalysuissedthe
uncertainty does not clmnge from pre- to post-t_,t latestreleaseof tl_classiNcASA-Lawls ODE
Wdgh_gs. In effect, the bias is "calibra_ out,"
module writtebnyGordonandMd_& called CF-,A.',
re_sult_g in a more ccfmtn wdght difference
•longwitha completeinput ofallthe prol_llant_
me_sremcnt than either individual pre- or post-fire
expendedduringatest
weights.
AR _esmm meam_ements. W"m',e.,I.o
One additionalpointthat shouldbe noted is
forinput to CEA.. Other_um inclu&motor
that the chamber pressure integral (and re6ulting
propelhnt fOnnul_on - cs[c_latedduring
average)w,as originally ba_I uponmeasummenm andcu_xg olx_ions.-md O/i_--c_l_l
takerintheheadendofthemotor.A well.known
.total .e._ueadedpro_ll_ts via direct weight
phenomenonexists insoliadndhybrid rocketmotor_,
measurements orintegrated mass flow rates.
however,suchthatthere canbe adgn_cantpressure
$incea computer cock h now m_
drop down the lengthofthemotorthatiSa oomp!ex calcul_ the theoretical C*, closed form solutionfor
function of chamber conditions andflow rn_e. With
partialdedvatNes isrendered impo.iblo. Tncrcfore,
theaddkionofamixingchamberaftofthef_el grain
•they, too, w_e estimatendumerlo_llbyy pertarblng
in hybrid motors (whic,hptomo_$ combustion individual measur_entswhichaffected the CEA
product _mgnation due to a diffuser-like effect and
inputdata
amplifietshepressure drop), itwas.fel.tthautsing
ho_nd pres_rmm'eeasur_vnenb contn_mted another.
conceptualbias tothe p_-formancecalculations.
•Overall, the DRE for measured C'*becomes
C* efficienicsyameuum ofhow much
acomplicateadmalgamofexpressio(n_se al_endix)
energyismkas_lbycombustio-n-u gaugedbyee
that.&ties closed formpartial derivativecalculations.
pmuttm g_era_ - com_u'odto th_ th_or_de_
chemicaplotentieanlergy,totedinthe_t(s),
A simpleequatiofnorcombustlone_cie_yis
Estimating the uncertainties as_cia_d with
a theoretical model isa relativelynew additionto
=.C;o, .
uncertaintyanalysiasrena. ColemanandSternt'rove
Inv_t/ga_eudsinguncertaintetcyhniquestovalidatae
CFD code in whichthe vslidation level is set by the
Sinceboth the,de_omina_r and the
combinatioonfthe uncertah_ies'ia the experimental nume_or arethemselvesfun_ons of numerous
dataandthe portioonfthe uncerU_ntlienstheco&
thatcanbe estimated,BrownandColeman'also
r.
primitive variables and inputs, equation (16) is meant
only to convey the notion of combustion efficiency.
Computer Code
Ktt,dam£_
Due to the rcc_ent to integrate mass
flow rates and the fact that closed form tolutio_ for
partial derivatives were rendered impossible, a
computer program was written forthis analysis. It is
a Windows'-based, FORTRAN 90 routine that
incorporates GASP and CEA. A Vimufl FORTRAN"
GUI' was written remake the code assimple touse as
possible. Figure 1 shows the opening _ereen for Fig. 2: Typical SHIRE dialog box.
SHUE.
Once allof the requiredinformationis
provided,theuaetis!otisany Oralloftheanalyses
that _e required to be performed, This h selected
throughthe drop-down m_ms at the top of the"
program window, an example of which is shown in
Figure 3. "
Fig. 1: SI-tUEopening screen.
SHUE will be capable of performing 28
s_ar_:.cuncertainty m_lyse_, ran_n_ from mass
flowram andtotalimpulseuncertaintiteosC*,I_and
Iv= (measured, theoreticaland eff_¢iot_y)
uncertainties. Currently, all but the It, and I_. Fig. 3: Selection of an unc_ty tmaID_.
analyses are complete and validated. To date, the_e
are approximately 25,000 SLOC, of which 8,000 are After selecting which mmlyac_ to Imrform,
from GASP and CEA, Once Completed,it is the user then opens the data file for the motor test and
estimated SHUE. willcontainmore than 30,000 select_ "Got" under tl_ "Ells" menu. Depending
SLOC.
upon the analysis, the use_ may be required to It@at
The userisrequired to inputwhichmotoris Start- and stop-times for the limits of. int,_do_
being anaiyzed, whichfuelformulation wasused, and Run-timesvary_roma few second_to threehotrod.
a test name, as well as pre- and post-test AnalFds results am etm-_tlyout'putto an ASCII text
measurements for fuel grain weightsand nozzle file.
dimensions. Additional input includes fluid meter
parametei's, elemental biaslimit e,tims_, and tim AlaorltSm De_.rintlon
data-sampling ram. A typical input dialog appears ii_
Figure 2. Ttm repetitive algorithm used for Sh'UE is
atraightforward, but because ofth_du:ar number of
calculstlontsh,ealgorithm/squ/tcintricateA.Rc¢ the
u3erinpuutherequire&d_ andtimest,hecodel¢op_ Resultsand Discussion
throughoverymeasuremem@ressures_,mpe:amr_s,
et cetera) to calculate a nominal value of the
experimental result. Calculadom for nozzle and
weight measurements are completed during user _n order initiate valida_ion of $__, data
input, and the integrals are calculated using the
fi'om a 24-incthest (I-IP24-503w0e)s used for this
trapezoidal rule. Other, more sophisticated schemes analysisa,sthattestwes a closeanalog tothe
fornumericalintegratiwoenreini_a_yconsidered,
upcoming250KmotortestsO.nce$.HL_iscomplete
but were abandonedbcceuse results for the
andvalidated) theHP24-5030 testdata will be scaled
tr_t)ezoidalrule•were nearly identical and requited
-m match expectecdonditiofnosrthe2_0Ktest t_Lng.
less CPUtime.
The scalinwgillbedone in orderto geta pre-te_t
Once the nominalresult iscalculatetdh,e,
uncertainptryedictiosno,thatm Understandicnagn
partial deriv_ive_ are estimated bysinglyperturbing be derived _ to whichmeasuremems"ate most
every measurement used in the nominal calculation
importanftorreducintgheuncertainitnythefulslcale
by0.5%--hence the name'°jitter '' routine-szzulsing motortests.
equatio(n3).Itshouldbe notedthatperturbinag Thereeye23 varisbles ormeasurementtshat
single variablienanintegral meansthatacomplete arerequiredto c_culat_C* (mea_ed, theoretical,
integral isreded with eachpass through the loop. md ef_cimcy), Factoryspedfi_afiownesrereed for
otherwords, if thereare5000pressurdeata poMts, " e_timafing bias limits for pressure transducers;
a singlepoint is pert_ed and a new integral with, thermocoupleasn,dload cells. _timates for. tim
that shigle perturbed va_tble (along withthe other
venmri and orifice cah'brationbiases .were assumed
4999 nombaal &ta points) iJ calculated. This fact
basedUpon.ther_ults of an anl_ltshed cal_mtion
requiredthatthe codebe writ_-n ruing REAL*8
enalysis for the 2_0K motorventudcompletedby
variableg in order to calc:_lattheed"erivatives with
•engineerastMSFC. LOX p _d nitroge7nbiases
•sufficient accuracy.Thisjitterproce_ was _peated
were takenfromthe GASP user's mamml,ass_ed in
for every variablethat affected th'e experimental
[2]. TheLOX vapor pressurebias estimate was taken '
mmlt. For example, there are 25 typesof as the largest i'eporteerrdoresfimete in[4]. Finally,
measuremmtswhich affect motorC*effidencyO,f
•weight percentbias estimates for each constituentin
those25 types, 9 involve recalcuIa_ng integndfsor •the fuel formulatiwoansbasedupona conservz_ve
each of the multiplmeeasurements takenin that
e_t/mate (i.e,, larger than is probable) of the bias in
(venmri/nlet pressuref,or example)r,esultinign
thescaleusedattheoast_ngfadUtydividebdyeach.
approximately 12,300partialderlwtivefosratypical const/tu.etnott'awsleightl_rmix.."
20-_cond test.
•It shouldbenbted thatthere areonly three
Onceeachpartialderivative isc_ou_ed the meau_.,_ents thath_ve the potential for siprLflca_
code pa_sesc,ontrol to the uncertaintypropagation uncertaintiesimrodu_edfi'ompre¢isi0n sourcest:he
subroutinew,here the Iz_d d_ivativesare
nozzle throatdiameter measurements, the_el
combined with the uncertainty estimatesA.nother
weights, md theheadendwei_t_; Thenozzle throat
pm_'neter is alsocalculateidnthisportionofthe m_ements willbe discussedseperateiy, but
code: the UPC,
typicalluyy,mmordc erosiooncc_ duringthemotor
Most simply, the UPC allows therankingof
f_g. These,e,_nnmerle_ are treatedlike precision
themost significant uncertaintcyontn'butorb(ys) erron and combinedwith the biaslimit for the
tabulating what percent of the overall uncertainty-
calipen reed, by us[ug a root-_m-square method.
squaredeach type of measurement con_ibute_. Shni1_procedures areused forLhegrain andh_d
Equst/on (17) showshow theUPC i_calculatfeodr
weights, thoughtheprecision contn'_utlonissmall in
eachvariable:
bothcases. Table 1summarl_e_ eachmeuamment
alongwithitnsominalvah_andbiesllnlit.
(17)
v;
:Li" -5 "-_ L!: !Z ='?'7!! L_-F'_-_--, -':':_-G :3F'7 FAGE. OlO/OIS
ParRmctor NominalVslu_ BiasLimit cornponcnts reported for all three c_'perimcnt_l
Pet=a-. 380 pgla 5l_si results,Note thalsixmeasurements (F_ v_ P_
7l_i ,.,., T_,_. _,, LOX Venmri _ y._=,.p_, and N,
3_F
OrificCe_)donot_pearinthefollowin_g
P_ 15o_mia spsi tables.They each contrt_te le_sthan 0.01% tothe
7L_ 3"F
me_urcmcnt uncertaintyforthe three experimental
results.
44Ibm/R' I0% R_d_
1.4447 o.s% R_Kii_ Regt.ilmm
Lo×vi_ c, 0.9622 M_memt
LOX Venmd 9.6x10_/_ t/PC
LOX Ventu_ $1.04%
_112%
N,Om'lee'c,
N,Otiflce D_am_er 19.0a%
Wei_l_ .Lms 322Ibm'!...... 25Ibm' 0.86%
HeadendWdght 28.4Ibm 0,005Ibml
Loss
D* 4.6In. O.OLO_ ....
Zr,,o_: I_.,# N/A Ixl0_% 5.45%
Z.-4Sm. % N/A
6xlO_%
N/A lxlO_% . 0.20%
Agm'it_White w_% NIA lx!O"_%
,=
CnrbdnBlsok _% N/A " 3xi0"%
o.u%
Ttble 11Biaslimit, forcttohsl_l imtmet_.
In general, the C* meamr.ementa art fairly
good- C* efficiency had _ :1:9.% uncertainty brad.
Table 2 summarizes the results Of the malysb, and
compares the old calculation method results with the
new method proposed in this paper. The comparison
shows that the ctmpges in procedure affeot_ the re¢_It_ 20,82%
at a magnitude lower than the overalluncertainty-
i.a., the ctmnges, to: all practical purposes, oannot be
seen for lack of measurement resolution. However,
the "lessons learned" in tl_$ process have more
significantrami_cadons fortheIl-inchOOX motor,
Old'Value.,, New Vxtue Unccdah_
C*...... 5753"R/ice _,7.7__t_s._C 113PJs_
C*__ 5769 R/s_ _772tt/_¢¢ •l,!9/t_m 0.00%
1%. 99,7% 100% .. _A
Tabb _:Overaluluc=tl_W _mtlyslr_multt.
The detailed breakdown of uncertaimy
contributions/s interesting,and _ probably more
informative. Table_ 3 through 5 sunm_trlze UPC
values, with uncorrdated aad correlated UPC
'These biaslimits applytoeach individual pro-aad
0,24%
po_t-_e measurement and not to the overallweight
difference (see Uncerminp_ Analysis for explanation).
.' Due to ITAR restrictions, these nom_ values Tablt 3: Detziled U'PCvahumforC_,..=_,
cannot be reported,
Parar_ttr UPC R_altam pa_ UI)C R_tullant
Cor_onen_s) Motsum_ont Compon*mO) Mtmurement
U_ i v_c
[,,
LOXV_lurl C:' ' 7168% 72.6S°/) LOXV_tu_C, 42.90% 42.90%
LOXVenmriTe_. 3.00% 3,00% LOX vtm_iI'.,... t.84% I._4%
Uncorr_laPt_e._d 0.00% Un_ormlatie,.'.c..l.....
+..
CorrelatedP___. 0,19°/o o.19%
U_correhted 0.00% 0.00%
0.67% 0._7%
Correlated 2.0g% 2.og% :
P_mff,a.,
Uncorrtlated 0.00% 0.00%
_Cnyo_rrelated 5.91% 5.91% Correlatmi 4.93%
Uncorrclat_eadx 0.00% t'ncorr¢lpa,.t_e,d 0.00% lU, i
Correlat0e.d,,_ "0.54% 0.54% Co_Isr_p,, 0.15% • " oAs%...
UncorrelatN¢__Orfflcc 0.:)2% Umorrdtt_ N, Orl_¢ o.1o%
Diam_-r
Cor_lated N, Ortfioo _54% 0.09% Corrolatod N, Ori_o 0.00% o.10%•
Dlameter
U_orr=latcd: Fuel 1.08% r_ond,at_ Fuel 0.02%
mtltuent
Conttlt_
Wright% Co,,,..t.,,,t r.,,i ' o.oo% o.02%
Co_lar_i Fuel 0,22% •1,29%
Constitum-tt _mtitum
Wei_t %
Weltht%
0.24%
Uncorrolatod Pro-F_ 0.00% )_lit_ Pr)-Fim
Hudm-,d._W__ht.
Uncortt_odPo6t-Fir, 0.00% UmmrrelatMPo,t-Flro ._.29%
_d._dw,i#t,
: o:reg "....... -
_l.m_d _re-FimO'
Corr¢l).t_ Pro+Fire • 0.0O%
I-lde_t.dWeight 17,orrel_tePdo+'t-F_D*
Cormhuod Post.Fire 0.00% f:orr_ Pre- 2.77% 24.91%
P_t-FffeD°
H_tdend.Weight ...... ,, ,, =, , --
Correlated Pie- and lJmon_lat_l " Pm-Firt 0.00%
H_dend Weliht •
Port-Fire He.end
Weight _Jmormlatod Pen=Fife 0.00%
Ua.orrelamt,l P_-_" 274.84% "_dMwenWdd_t .....
C(mterSem'rm_Wolght _ I_-F_ 0,00%
Un¢orr_ted Poor-Fire 345.73%
CenterSegm_mtWd_tt rmlatod" _on.F_ 0.00%
Corrolamd Pro-Fire '"_49.68% dWd#t
ton'elatePdro- and -o,oo% 0.00%
CenteSregmentWoilkt
Po_t-Flr_ l_end
_orrelitcd Post-Fire 691.46%
Wev_ht
Cem_ Stgrn_t WoighL_
Umormlat_dIS'm-F_ 7&_0% •'
Coffee,cad Pro- tml -1847.72% I_.9_A
Post.Fire . Ctmtor Center_e_nt Wt_t
Uneo,ffdst_Po_t-FLm 86.43%
Sezmontweight
Cm_t__ Wei_tht
Tt.ble4:DetailedUFC._ valutfaorC*_,_: Corre_d Pi_-Flte I$7.79_
C_nLerSe_J'nenWt el_/s
It shouldbe stressetdhatfor all thr_ cases, Con_lat_l Pelt-Flit 172.86%
the most significant contEoutor to tim overall CareerSet,meritWdtht ...........
experimental unc_ty is tlm LOX venturi C(. In Corrdat_l Pro- md -494.98% "1.00%
addition, the fucl grain and. h©adond weight Poet-Fire. Cert. r
measurements are neglig_lecontE0utor_tothe .Sg._W_4)zht - . -
overall tmcertain_, Some discussion provi&s some Table$:Detailed_ valu_ _orTlo..
insight as to why thoso measurements once aFpeared
•Inspectionof the thr¢,tablesthows a
to contribut, significantly.
sign/ficant sensitiyity totlmoverall result for etther
.