Numerical Simulations of Acoustic Resonance of Solid Rocket Motor

172 Pages·2011·14.06 MB·English

umerical imulations
N S
of coustic esonance
A R
of olid ocket otor
S R M
andidate
C
iviana erretti
V F
utors
T
rof aurizio i iacinto
P . M D G
rof ernardo avini
P . B F
epartmentof echanicaland erospace ngineering
D M A E
apienza niversityof ome
S ,U R
iclo
XXIIIC
ottoratodiricercain ecnologia eronauticae paziale
D “T A S ”
epartmentof echanicaland erospace ngineering
D M A E
apienza niversityof ome
S ,U R

I
L’uomoattraversailpresentecon
gliocchibendati. Puòalmassimo
immaginareetentaredi
indovinareciòchestavivendo.
Solopiùtardiglivienetoltoil
fazzolettodagliocchielui,
gettatounosguardoalpassato,si
accorgedichecosaharealmente
vissutoenecapisceilsenso.
M.Kundera,Gliamoriridicoli
II
bstract
A
Theoperativelifeofmanylargesolidrocketmotors(e.g. USSpaceShuttleSRM,Ariane
5 P230 SRM, Titan SRM, P80 SRM, the five-segment test motor ETM-3) is characterized
bythepresenceofsustainedlongitudinalpressure(PO,pressureoscillations)andthrust
oscillations. Their frequency is close to the first, but sometimes also second or third,
acousticmodefrequencyofthecombustionchamber. Althoughtheydonotcompromise
themotorlife,suchoscillationsrepresentapointofinterest. Incaseofcouplingwiththe
launcherstructuralmodes,theycaninvolvestructuralfailures,interferencesandpayload
damages. Further, thrust oscillations can result in guidance and thrust vector control
ff
complicationsandtheycana ectthemotorperformance.
The combustion chamber of an SRM can exhibit a vorticity generation in correspon-
dence of propellant corner, obstacle or boundary layer at propellant surface. Once de-
tached,thisvorticityisconvectedbytheflowanditimpactswithdownstreamobstacles.
Thisinteractiongeneratesacousticsignalthatperturbsthevortexsheddingprocess. The
resonantcouplingoccursifacombustionchamberacousticmodeissynchronizedwiththe
vortexsheddingfrequency. Thisconditioncorrespondstothegenerationofself-sustained
pressure, then thrust, oscillations. These oscillations result from the complex feedback
mechanismfedbyvortexsheddingandacousticwaves,andtheyareduetothecoupling
betweenfluid-dynamicsinstabilitiesandacousticresonantmodes.
Other forms of instabilities can occur in a solid rocket motor, such as combustion
ff
instabilities. An aspect that can a ect the acoustic coupling is represented by two phase
ff
flowe ects. Inthiscontext,purelyacousticcouplingisconsidered,andthesephenomena
areneglected.
Theacousticcouplingsimulationrequiresmodelscapabletodescribeboththeacoustic
and the vortical waves, including their interactions. To achieve a complete characteriza-
tion of motor instability risk, it is important to obtain an accurate reconstruction of both
oscillation amplitude and frequency. A complete description can be obtained by full
numerical simulations, but CFD analysis require high computational costs and times,
ffi
andpresentdi cultiesconcerningthemodeldefinition. Usableforparticularcasesand
documented situations, the obtained results are not so accurate. The fundamental char-
III
IV
acteristicsthatmakeareduced-ordermodelausefultool,arethereducedcomputational
requirementandthepossibleimprovementofrelevantprocessunderstanding.
Rossiter [90, 91] developed a model that describes the aeroacoustic coupling as a
feedback loop. Current calculations of SRM stability are based on a simple first-order
perturbation solution. The classical approaches used in this context are the acoustic
balancemethod,giveninpracticalformbyCulick[27],andthemostcompleteFlandro’s
method [45]. Such methods, capable to predict the motor tendency to become unstable,
donotprovideinformationsontheinstabilitylevelandonthesystemtriggering. Other
ff
simplified models have been proposed by Howe [55], Hirshberg and Hulsho [53] that
analyzedthevortexsoundproduction.
Aparticularattentionhastobeturnedtotheone-dimensionalreducedordermodels
derived by Matveev [78] and Jou & Menon [63, 81]. Matveev’s model is based on a
ODE system and it describes the acoustic modes excitation, accounting for the acoustic
feedback on the vortex shedding. Jou and Menon developed a model for the evaluation
ofthecoupled-modeoscillationfrequency.
Themainideafollowedinthisresearchisproposedbyprof. B.FaviniandF.Serraglia;
theirideaistheuseaquasi-onedimensionalmodel,fortheflowfieldevolutioninasolid
rocketmotor,wherethevorticitydynamicsisalsodescribedbyaQ-1-Dmodel. Asfaras
weknow,thisisthefirsttimethiskindofmodelinghasbeenadoptedinordertosimulate
aero-acoustical phenomenon. Several exploratory studies have been performed in the
lastfewyearsontheirapproach,butthemodelreachedacompletedefinitiononlyinthis
doctoralthesis.
In the present work, the quasi-1D reduced order model AGAR (Aerodynamically
GeneratedAcousticResonance)isdevelopedintheaimofsimulatingSRMinternalflows,
andconsequentlypressureandthrustoscillations.
A model opted of simulating internal ballistics requires to be constituted of several
sub-modelsas: a)grainburnbackmodelforthepropellantgrainsurfaceevolutionwith
time (GREG, Grain REGression model) b) flow field evolution model (SPINBALL, Solid
Propellant rocket motor INternal BALListics model) c) aero-acoustic simulation model
(POX,it’snotanacronym).
InordertovalidatetheAGARmodelandtoverifyitscapabilityanditsmaincharac-
teristics,afirsttestcaseconsideredinthisworkisacoldflowinanaxisymmetricramjet
combustor. Thissimplecaseallowsadetailedanalysisoftheinteractionbetweenvortex
dynamicsandacousticwaves.
Thenthemodelhasbeenappliedtoarealcase,representedbytheP80SRM,thefirst
stageofthenewEuropeansmalllauncherVega. Duringitsqualificationanddemonstra-
ff
tionstaticfiringtests,themotorhasexhibitedfourdi erentphasesofpressureoscillations
duringthewholeoperativelife.
V
ThepresentPh.D.dissertationisorganizedasfollows.
Chapter 1 Anoverviewofpressureoscillationphenomenologyinasolidrocketmotor
is highlighted. To understand the origin of pressure oscillations, a presentation of the
basicphenomenacharacterizingtheaeroacousticcouplingisprovided. Theaeroacoustic
resonancecharacterizationiscompletedwiththedescriptionofRossiter’sfeedbackloop
model and its possible interpretation. Some notes about flute mode behavior, lock-in
phenomenonandcombustioninstabilitiesaregiven. Thevorticalstructuredefinitionand
identificationcriteriaarealsopresented.
Chapter2 Thestateoftheartofthemostimportantmethodsforaeroacousticmodeling
arepresented. Afterageneralhistoricalsummary,themethodsaredescribedintermsof
their fundamental features. Generalities are given about the full numerical simulations.
ThenMatveev’sandJouandMenon’sreducedordermodelsareintroducedandanalyzed.
Chapter 3 An overview of SRM aeroacoustic mathematical model is provided, with
special care in the derivation and analysis of the vorticity equation. A description of
AGARquasi-onedimensionalmodelispresented.
Chapter 4 The validation test case here presented is the simulation of cold flow in an
axisymmetric combustor. A comparison with Jou and Menon’s results is provided. The
behavior and main characteristics of AGAR model are described, and an analysis of the
interactionbetweenvortexdynamicsandacousticwavesisobtained.
Chapter 5 The simulation of the aeroacoustic phenomena of P80 solid rocket motor,
first stage of Vega launcher, by AGAR model is considered. The experimental data and
thenumericalresultsaredescribed,analyzedandcompared.
VI
ontents
C
bstract
A III
istof igures
L F XI
omenclature
N XV
cknowledgments
A XXI
ublications
P XXIII
eports
R XXV
olid ocket otor eroacoustics
1 S R M A 1
olidrocketmotors
1.1 S 1
olidrocketmotorpressureoscillations
1.2 S 2
luid dynamicsinstabilitiesandvortexshedding
1.3 F - 3
ortex obstacleinteraction
1.4 V - 5
eroacousticcoupling
1.5 A 7
ossiter smodel
1.6 R ’ 9
lutemodebehaviorandlock in
1.7 F - 11
ossiter smodelinterpretation
1.8 AR ’ 12
ortexdefinitionandidentification
1.9 V 14
ombustioninstabilitiesandstructuraldynamics
1.10 C 15
eroacousticmodeling
2 A 17
tateoftheartoftheaeroacousticmodeling
2.1 S 17
cousticbalancemethod
2.2 A 20
ortexsheddingsourcetermfortheacousticbalancemethod
2.2.1 V 22
ortex soundtheoryandacousticanalogy
2.3 V - 23
ulshoff smodel
2.4 H ’ 25
ydrodynamicstabilityanalysis
2.5 H 26
landro smethod
2.5.1 F ’ 27
nthoine smodelforsubmergenceinteraction
2.6 A ’ 28
nthoine smodelforthe numberatmaximumsoundgeneration
2.7 A ’ M 30
umericalmethod
2.8 N 31
VII
VIII CONTENTS
educedordermodels
2.9 R 31
ouand enon smodel
2.10 J M ’ 32
atveev smodel
2.11 M ’ 36
athematicalmodelsandtheirnumericalimplementation
3 M 39
onservationlawsandconstitutiveequations
3.1 C 39
cousticfield
3.2 A 41
orticityandcirculation
3.3 V 42
orticityequation
3.4 V 43
eroacousticmodel
3.5 A 45
orticityequation
3.5.1 V 46
ortexcreationandgrowth
3.5.2 V 48
ortexdetachmentcriterion
3.5.3 V 49
cousticexcitation
3.5.4 A 50
tructureofthe model
3.6 S AGAR 51
model
3.7 SPINBALL 51
asdynamicmodel
3.7.1 G 52
nitialandboundaryconditions
3.7.2 I 54
avitymodel
3.7.3 C 54
urningratemodel
3.7.4 B 55
eatingandignitionofthepropellantsurface
3.7.5 H 56
umericalintegrationtechnique
3.7.6 N 57
model
3.8 GREG 59
omments
3.9 C 60
umericalsimulationofoscillatorycoldflows
4 N 61
ouand enon stestcase
4.1 J M ’ 61
4.2 AGARsimulation: inletMachnumberM = 0.32 64
in
ortexdetachmentcriterion
4.2.1 V 64
ourcetermsforacousticsexcitationandvorticityequation
4.2.2 S 64
4.2.3 Vorticity(Ω)distribution 65
ressureandvelocitydistribution
4.2.4 P 65
4.2.5 Pressureandvorticity(Ω)fluctuations 67
omments
4.2.6 C 70
nlet achnumbereffect
4.3 I M 70
ortexdetachmentcriterion
4.3.1 V 72
4.3.2 Vorticity(Ω)distribution 73
ressure velocityandspeedofsounddistributions
4.3.3 P , 73
4.3.4 Pressureandvorticity(Ω)fluctuations 73
omments
4.3.5 C 82
onclusions
4.4 C 83