NASA Technical Reports Server (NTRS) 20160004986: Inviscid and Viscous CFD Analysis of Booster Separation for the Space Launch System Vehicle

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by  NASA Technical Reports Server (NTRS)

Inviscid and Viscous CFD Analysis of Booster Separation for
the Space Launch System Vehicle
DerekJ.Dalle∗,
ScienceandTechnologyCorp.,MoffettField,CA94035
StuartE.Rogers†,WilliamM.Chan‡,
NASAAmesResearchCenter,MoffettField,CA94035
HenryC.Lee§
ScienceandTechnologyCorp.,MoffettField,CA94035
This paper presents details of Computational Fluid Dynamic (CFD) simulations of the
SpaceLaunchSystemduringsolid-rocketboosterseparationusingtheCart3Dinviscidand
OverflowviscousCFDcodes. Thediscussionaddressestheuseofmultipledatasourcesof
computational aerodynamics, experimental aerodynamics, and trajectory simulations for
this critical phase of flight. Comparisons are shown between Cart3D simulations and a
windtunneltestperformedatNASALangleyResearchCenter’sUnitaryPlanWindTun-
nel, and further comparisons are shown between Cart3D and viscous Overflow solutions
for the flight vehicle. The Space Launch System (SLS) is a new exploration-class launch
vehiclecurrentlyindevelopmentthatincludestwoSolidRocketBoosters(SRBs)modified
fromSpaceShuttlehardware.TheseSRBsmustseparatefromtheSLScoreduringaphase
offlightwhereaerodynamicloadsarenontrivial. Themainchallengesforcreatingasep-
aration aerodynamic database are the large number of independent variables (including
orientationofthecore,relativepositionandorientationoftheboosters,androcketthrust
levels) and the complex flow caused by exhaust plumes of the booster separation motors
(BSMs),whicharesmallrocketsdesignedtopushtheboostersawayfromthecorebyfir-
ingpartiallyinthedirectionoppositetothemotionofthevehicle.
Nomenclature
C = CA,Axialforcecoefficient,bodyaxis t = Timesinceseparation
A
C = CLL,Rollingmomentcoefficient w = Linearcombinationweightforoutputfunction
LL
C = CLM,Pitchingmomentcoefficient x = Positionvector
LM
C = CLN,Yawingmomentcoefficient α = alpha,Angleofattackofthecore
LN
C = CN,Normalforcecoefficient,bodyaxis β = beta,Angleofsideslipofthecore
N
C = Thrustcoefficient ∆φ = dphi,RollangleofSRBrelativetocore
T
C = CY,Sideforcecoefficient,bodyaxis ∆ψ = dpsi,YawangleofSRBrelativetocore
Y
L = Residualbasedonsumofabsolutevalues ∆θ = dtheta,PitchangleofSRBrelativetocore
1
M = FreestreamMachnumber ∆x = dx,Axialdisplacementofboosternose
p = Staticpressure ∆y = dy,Lateraldisplacementofboosternose
q = Freestreamdynamicpressure ∆z = dz,Verticaldisplacementofboosternose
r = Radiusfromcenterofcore σ = Standarddeviation
∗ResearchScientist/Eng.,ComputationalAerosciencesBranch,MemberAIAA,[email protected]
†AerospaceEng.,ComputationalAerosciencesBranch,AssociateFellowAIAA,[email protected]
‡ComputerScientist,ComputationalAerosciencesBranch,SeniorMemberAIAA,[email protected]
§ResearchScientist/Eng.,ComputationalAerosciencesBranch,MemberAIAA,[email protected]
Abbreviations
BSM = BoosterSeparationMotor RSRB = RightSolidRocketBooster
CFD = ComputationalFluidDynamics SLS = SpaceLaunchSystem
CSE = CoreStageEngine SRB = SolidRocketBooster
LSRB = LeftSolidRocketBooster UPWT = UnitaryPlanWindTunnel(NASALangley)
I. Introduction
The Space Launch System (SLS) is a new exploration-class launch vehicle currently in development by
NASA and a team of contractors and will be the first exploration-class launch vehicle since Saturn V. To
achieveitsmission,SLSwilluseSolidRocketBoosters(SRBs)thatareslightlymodifiedhardwarefromthe
SpaceShuttleLaunchVehicle. TheseSRBsexpendtheirfuellongbeforetheSLScorefirststage,andthus
thereisaseparationeventthatmustoccurduringaphaseofflightwhereaerodynamicloadsarenontrivial.
AdrawingofSLSwiththetwoSRBsattachedontheleftandrightsidesisshowninFig.1.
Since gravity is not acting in a way that pulls the expended boosters away from the core, and aerody-
namic loads also do not act in a way to substantially encourage separation, small rockets called Booster
SeparationMotors(BSMs)areusedtoactivelypushtheboostersawayfromthecore. Thereare16ofthese
BSMs—four forward BSMs and four aft BSMs on each booster. The forward BSMs fire in a partially for-
ward (upstream-facing) direction, which results in complex plumes and interactions of those plumes with
the high-speed freestream flow. In addition, the low dynamic pressure during the separation event com-
Figure1. ArtistrenditionoftheSLSBlock1configuration
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a) Topview b) Sideview
Figure2. ComparisonofattachedboosterpositionsforSLS(grey)andSpaceShuttleLaunchVehicle(orangeoutline)
binedwiththerelativelyhigh-thrustseparationmotorsmeansthattheplumeaffectsaverylargevolumeof
flow—onthescaleoftheSLSvehicleitself.
The SRBs are similar to Space Shuttle hardware, which have a rich history of successful flights. How-
ever, separating from the SLS core is more challenging than separating from the Space Shuttle External
Tank Figure 2 shows an overlay of the two vehicles. The reason for this is simple: whereas the External
Tank essentially ended at the point where the SRBs were attached, SLS has a substantial amount of hard-
ware, including its main engines, directly aft of the SRB attachment point. As a result of the change in
configuration with no corresponding design change in the separation mechanism, clearances between the
aft portion of the SRB and the aft portion of the SLS core stage can be small. Furthermore, the closer
proximityoftheboosterandcorestageenginesresultsinmoreplumeinteractionsthatmaketheflowmore
challengingtosimulate. Tohavesufficientconfidencethatnorecontactwilloccurduringflight,achievinga
smallaerodynamicuncertaintyis essential. Furthermore, determininga defensibleuncertaintybecomesan
importantpartoftheaerodynamicdatabase.
AnotheraspectthatmakesCFD forthisportionofflightchallengingisthevastnumber oforientations
andconditionsthatmustbesimulated. Theseparationoccurswithinafinitewindowoftimewithinarange
of temperatures and altitudes, and the rest of the vehicle has its own uncertainties during ascent that make
the separation environment even less concrete. Assuming symmetry between the left and right boosters,
there are six degrees of freedom for the position and orientation of the boosters, two degrees of freedom
fortheorientationofthecore,twomoredegreesoffreedomforMachnumberanddynamicpressure,anda
range of possible thrust conditions. After further simplifications, the database produced for this effort was
8-dimensionalandrequiredmorethan20,000CFDsimulations. Therunmatrixandthedecisionsthatwent
intoitarediscussedinSec.II.
Due to the immense size of this run matrix, the decision was made to utilize Cart3D both for its speed
and ease of setup. Cart3D [1,2] is a solver developed at NASA Ames with exactly these capabilities and
usesancut-cellCartesiangridapproachthatmakesvolumemeshgenerationautomatic. Thesolveralsohas
a history of use with powered rocket boundary conditions, including nozzles that are small relative to the
scale of the vehicle, from its use in support of the Orion program [3,4]. The run methodology developed
forCart3DinthistaskishighlightedinSec.III.ThisworkbuildsonpreviouseffortsforthesimilarAres-V
vehicle [5], design and analysis cycle 2 for SLS [6], and critical design review for SLS [7]. Some lessons
forthelesssimilarAres-Iconfiguration[8,9]werealsoappliedtothepresenteffort.
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Comparedtotheintermediatedatabasediscussedin[7],thisworkaddressesimprovedrunstrategiesfor
Cart3DandOverflow,completionofthedatabasetocovertheentireseparationmaneuver,concentrationof
CFD simulations around the nominal trajectory, inclusion of a separate database to model the case that a
coreenginefails,anddeliveryormoredetailedinformationforuncertaintyquantification.
TheinviscidassumptionistentativelyacceptableduetothehighsupersonicMachnumber(greaterthan
4.0)atseparationandlowdynamicpressure. However,complexflowandlargeboundarylayersimplythat
viscous effects merit consideration, and full Reynolds-Averaged Navier-Stokes Overflow [10] simulations
have been used to evaluate this assumption and provide an increment to the flight database uncertainty
quantificationthataccountsforviscouseffects. OverflowisasolverdevelopedatbothNASALangleyand
NASAAmesusingoversetstructuredgridtechnology. SectionIVcoverstherunstrategyusedforOverflow
inthisworkincludingadiscussionofmeshadaptionappliedtothiscomplexconfiguration.
In order to increase confidence in the booster separation database, a wind tunnel test was conducted
at NASA Langley Research Center’s Unitary Plan Wind Tunnel [11]. Different from many high-profile
aerodynamic databases, resources were not available to conduct a wind tunnel test that could be used to
constructaflightdatabase. Instead,theCart3Dresultsdiscussedinthispaperaretheunderlyingdatasource
fortheboosterseparationaerodynamicdatabasewhiletheOverflowandwindtunneltestresultscontribute
totheuncertaintyanalysis. TheresultspresentedinSec.VfocusondirectcomparisonsbetweenCart3Dand
the wind tunnel test and between Cart3D and Overflow results. In combination, these results demonstrate
thecapabilitytoconstructanextremelylargeaerodynamicdatabasewithcomplexflowfieldsandadetailed
vehiclegeometry. Evenincludingtheconservatismnecessarilyattachedtohuman-ratedrockets,theresults
demonstrate high enough quality throughout the database that uncertainty bounds need not be excessively
large.
II. IndependentVariablesandRunMatrix
Theaerodynamicdatabaseisafunctionofeightvariables,whicharedescribedinTable1. Atext-onlyname
for each variable is provided to make references to them a little simpler; a more traditional mathematical
symbolisalsoprovidedinTable1. Thesevariablescanbedividedintofourgroups: boostertranslations,dx,
dy, dz; booster rotations, dpsi and dtheta; core orientations, alpha and beta; and booster separation motor
thrust, CTBSM. Furthermore, most of these are grouped into three pairs: dy and dz, dpsi and dtheta, and
alphaandbeta.
Table1. Inputvariablesforseparationaerodynamicdatabase
Variable Symbol Description
dx ∆x Boosteraxialtranslation[ft]
dy ∆y Boosterlateraltranslation,awayfromcore[ft]
dz ∆z Boostertranslationin+z-direction[ft]
dpsi ∆ψ Boosteryawanglerelativetocorebodyaxes[deg]
dtheta ∆θ Boosterpitchanglerelativetocorebodyaxes[deg]
alpha α Angleofattackofthecore[deg]
beta β Angleofsideslipofthecore[deg]
CTBSM C Boosterseparationmotorthrustcoefficient
T,BSM
Axial booster translation, dx, is a special variable that is used to schedule each of the other variables.
For example, let dx be a particular value of dx, such as 8 ft. The aerodynamic database includes CFD
i
solutionsatthreevaluesofdy: dy ,dy ,anddy . Theseminimum,nominal,andmaximumvalues
i,min i,nom i,max
come from a full six-degree-of-freedom simulation by the guidance, navigation, & control group using a
lower-fidelity aerodynamic database with large uncertainties. In addition, these minimum, nominal, and
maximum translations have different values at each dx. The same description also holds for the remaining
sixvariables,althoughsomevaluesofCTBSM areomittedathigherdxwhenthethrustisverylow.
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Δy
Δx
Δz
Figure3. Sketchofrunmatrixconcept;circlesrepresentpointsandtranslucentshapesarecrosssectionsatonedxvalue
To prevent requiring roughly 38=6561 CFD simulations at each dx to cover three values of eight vari-
i
ables, variables are grouped into three pairs. For each pair, the only simulations included are the nominal-
nominalpairpluseachofthefourmin-max,min-min,etc.corners. Theminimum,nominal,andmaximum
valuesforeachvariablechangeasafunctionofdx,resultinginacurvedpyramidshapefortherunmatrix.
An example visualization of this approach is shown in Fig. 3. The example pair used in the figure is the
boostertranslationpairofdyanddz. Twovaluesofdx—onelower(orangerectangle)andonehigher(green
rectangle)—are shown. The filled circles (five in each of the two dx slices shown) are the points included
in the run matrix. The nominal reference trajectory is shown as the thick black curve through the middle
oftheslices. Thebluecurvesrepresentthecornertrajectoriesthatfolloweithertheminimumormaximum
value of both dy and dz. Using this approach reduces the number of points at each slice from 9 (if each
combination of minimum, nominal, or maximum were included) to 5, which seems like a small reduction.
However, this process is repeated for the other pairs of dpsi-dtheta and alpha-beta. Combining these 5/9
reductionsforthreepairsresultsinan83%reductioninthenumberofsimulations.
Finally, thereareseveralmoreinputvariablesthatplayarolebutdonotincreasethedimensionalityof
the database. These include variables such as Mach number and dynamic pressure that change during the
booster separation but do not vary enough or have a significant effect on overall aerodynamics. Another
important value is the thrust from the core’s main engines, which is programmed to increase in time from
the moment the boosters separate. Since there is very little expected dispersion of the core-main engine
thrustfromtheprogrammedvalues, nominalvaluesareusedinthesimulationsandthereisnoneedtoadd
more simulations to the run matrix. On the other hand, the SRB thrust has a wider dispersion during the
separationevent,buthasonlyasmalleffectonaerodynamics. Thefulllistofsuchvariablesisdescribedin
Table2.
This entire run matrix was simulated three times; once for the nominal case where all core engines
operate properly and two more times for the situation that one of the core engines fails. There are four
engines,andsymmetrywasappliedtoeliminatetheneedtoanalyzeafailureofeitherleftengine. Analysis
of the failure of a single booster separation motor (BSM) was also requested, but an initial investigation
showed that BSM failure could be covered by the nominal database. Thus there were three run matrices:
oneforthenominalascent,oneforafailureofthetoprightcoreengine,andoneforafailureofthebottom
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Table2. Variablesscheduledasafunctionofdx
Variable Symbol Description
t t Timesinceseparation[s]
dphi ∆φ Boosterrollanglerelativetocorebodyaxes[deg]
mach M CoreMachnumber
q q Coredynamicpressure[psf]
CTCSE C Corestageenginethrustcoefficient
T,CSE
CTSRB C Solidrocketboosterthrustcoefficient
T,SRB
rightcoreengine. Enginefailurescanoccuratanytime,andthevehiclemakesadjustmentstothetrajectory
tocompensateforthefailure. Asaresultofthesetwofactors,therunmatrixforcoreenginefailurescenarios
isdifferentfromandhasamuchwiderdispersionthanthenominalrunmatrix.
III. Cart3DRunStrategy
The primary advantages of using Cart3D for this type of database are its speed, efficient handling of ge-
ometric complexity, and adaptive meshing capability. Even so, this particular configuration has enough
complexitythatspecialcareshouldbetakentodeveloparunstrategythatutilizestheseCart3Dadvantages
efficiently. The approach used here takes advantage of Cart3D’s output-based mesh adaptation. Starting
fromarelativelycoarseinitialmeshwithabout150,000volumecells,fiveadaptationcyclesareused,which
growsthemeshsizetoabout16millioncells.
A. Cart3DVolumeMeshing
Theoutputfunctionusedtodrivethismeshadaptationis
J =C +C +0.5C +0.5C +0.5C +0.5C
Y,LSRB Y,RSRB N,LSRB N,RSRB A,LSRB A,RSRB
(cid:88)13 p(x)− p
+0.5C +C +0.5C + w i ∞ (1)
A,CORE Y,CORE N,CORE i
p
i=1 ∞
In output-based mesh adaptation, an adjoint solution is computed after the flow solution using the same
(or similar) mesh. The adjoint measures how sensitive a user-defined output function, like that defined in
Eq. (1), is to residuals in each cell. That information is used to determine how much a refinement of each
cell(i.e. splittingonevolumecellintoeightsmalleroneswithhalfthesidelengthoftheoriginalcell),which
leadstoarankingofwhichvolumecellswouldbebesttorefine. Theoutputfunctionusedhereincludesall
threeforcecoefficients(C ,C ,andC )onallthreebodies(LSRB,RSRB,andCORE)withroughlyequal
A Y N
weights. Aslightemphasisisplacedonthelateralforces, whichhavethebiggestimpactonthesuccessor
failure of the separation maneuver. This output function also utilizes 13 point sensors at selected locations
toward the front of the vehicle. Each point sensor measures static pressure at a point x minus freestream
i
pressure, nondimensionalized by freestream pressure [12]. These point sensors all have weights between
0.001 and 0.005 and focus on points in the volume solution that affect the integrated forces and moments
butaredifficulttoresolveontheearlycoarsermeshes. ThedetailsarepresentedinTable3whereclocking
angleθgivesangularlocationviaz=rcosθandy=−rsinθ. Theoriginis1009.1inchesinfrontofthenose
ofthecore,whichwaschosentorepresentapointintheVehicleAssemblyBuilding.
Fortunately,theresultsarenotsensitivetothedetailsofthelocationsofthesepointsensors,butincluding
afewofthemhadabeneficialimpactontheconsistencyofthefinalflowsolutions. Intotal,thesumofthe
pressuresensorsisabout10%to30%ofthetotalvalueofthecombinedfunctional. Thedecisiontousepoint
sensorstoaugmenttheoutputfunctionwasbasedonanextensiveinputsensitivitystudy,whichshowedthat
theyaddedrobustnesstothesystem.
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Table3. Outputfunctionpointsensorlocationsandweights
i Axiallocation(x) Radius(r) Clockingangle(θ) Weight(w)
i i i i
1 2000in 200in 0◦ 0.005
2 2000in 300in 90◦ 0.005
3 2000in 300in 270◦ 0.005
4 2400in 200in 180◦ 0.002
5 2600in 800in 0◦ 0.002
6 3000in 300in 30◦ 0.001
7 2000in 300in 60◦ 0.001
8 2000in 300in 120◦ 0.001
9 3000in 300in 150◦ 0.001
10 3000in 300in 210◦ 0.001
11 2000in 300in 240◦ 0.001
12 2000in 300in 300◦ 0.001
13 3000in 300in 330◦ 0.001
Inadditiontogeometriccomplexity,theSLSboosterseparationproblemalsowassubjecttoawiderange
ofscales. TheBSMboundaryconditionplanesarejustafewinchesindiameterwhilethefullvehicleiswell
over300ftinlength. TheBSMsareextremelyimportantfortheoverallaerodynamicsoftheconfiguration,
andsomeetingthechallengetoresolvethemontheinitialmeshiscriticallyimportant. Fortunately,Cart3D
has two features that enable tailored initial meshes appropriate for this task. First, the Cart3D volume
meshing program called cubes creates a mesh that has finer cells closer to the surface of the vehicle. With
the settings used here, this first pass at the volume mesh has its finest cells with sides of about 100 in.
Next, inputs are prescribed using Cart3D’s XLev setting to request five additional levels of refinement for
any volume cell containing a part of any BSM boundary condition plane or nozzle interior surface, which
is fine enough to put a few cells inside each BSM. Finally, several of Cart3D’s BBox specifications are
defined to create a finer mesh in certain volumes. These boxes are defined as a minimum and maximum
coordinate for x, y, and z along with a minimum number of refinements for cells within that box. For the
SLSboosterseparationconfiguration,tworegionsofthevolumewererefinedinthismanner: thecoreengine
plumesandtheforwardregionofthecorewheretheforwardBSMexhaustplumeshavecomplexbehavior.
Theseforwardvolumesbenefitfromhigherresolutionontheinitialmeshessothattheinteractionbetween
upstream vorticity (due to both curved shocks and losses near the abort motor nozzles) and BSM exhaust
can be captured earlier in the mesh adaptation sequence. The details of these initial mesh considerations,
alongwithadiscussionoftheconsequencesofmissingthiseffect,canbefoundin[7].
Ateachlevelofmeshadaptation,theflowisrunfor500iterations,whichresultsin3000totaliterations
(adapt00 through adapt05). Each adaptation cycle increases the number of volume cells in the mesh
byauser-specifiedratio,andthemeshgrowthratiosusedforthisworkwere1.5,2.0,3.0,4.0,and3.5. For
simulations in which the BSMs are on, which tend to be unsteady, an additional 3000 or more steady-state
iterationsarecompletedonthefinalmeshinordertocalculatemeanvaluesforeachoftheforceandmoment
coefficients.
B. Steady-StateandTime-AccurateComparisons
Solutions for the nominal separation trajectory using time-accurate inputs to Cart3D were simulated in
order to quantify the differences in forces and moments between steady-state and time-accurate solutions.
Thetime-accuratesolutionsusedtensubiterationsateachtimestepandanondimensionaltimestepof0.1,
meaning that a particle traveling the freestream speed of sound moves 0.1 grid units (in this case, inches)
each time step. The results, shown in Fig. 4, show consistent results between the two solution approaches,
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RSRB (±1.0 ) RSRB (±1.0 )
Steady-State RSRB Steady-State RSRB
LSRB (±1.0 ) LSRB (±1.0 )
Steady-State LSRB Steady-State LSRB
CA CLL
0.00
0.0
0 5 10 15 20 25 0 5 10 15 20 25
dx [ft] dx [ft]
a) Axialforce,CA b) Rollingmoment,CLL
RSRB (±1.0 ) RSRB (±1.0 )
Steady-State RSRB Steady-State RSRB
LSRB (±1.0 ) LSRB (±1.0 )
Steady-State LSRB Steady-State LSRB
CY CLN
0.0 0.0
0 5 10 15 20 25 0 5 10 15 20 25
dx [ft] dx [ft]
c) Axialforce,CA d) Yawingmoment,CLN
RSRB (±1.0 ) RSRB (±1.0 )
Steady-State RSRB Steady-State RSRB
LSRB (±1.0 ) LSRB (±1.0 )
Steady-State LSRB Steady-State LSRB
0.00
N M
C CL
0.0
0 5 10 15 20 25 0 5 10 15 20 25
dx [ft] dx [ft]
e) Axialforce,CA f) Pitchingmoment,CLM
Figure4. Comparisonoftime-accurate(black)andsteady-state(red)Cart3DresultsandmomentsfornominalBSM-on
trajectory.Standarddeviationoftime-accuratehistoryshowninblue.
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109 109
108 108
107 107
al106 al
du du106
esi105 esi
L1 R104 L1 R105
103 104
102 103
101 102
0 500 1000 1500 2000 2500 0 2000 4000 6000 8000
Iteration Number Iteration Number
a) dx=150ft,BSM-off b) dx=8ft,BSM-on
109
108
107
al
du106
si
e
1 R105
L
104
103
102
0 1000 2000 3000 4000 5000 6000
Iteration Number
c) dx=8ft,BSM-on,time-accurate;bluelineisresid-
ualbeforesubiterationsateachtimestep
Figure5. HistoryofCart3DL densityresidualsforselectedcases
1
and thus steady-state inputs were used to construct the database. This constitutes significant savings since
thesteady-statesolutionsrequiredaboutseventimesmoreCPU-hours.
Figure5showsresidualhistoriesforthethreemaincategoriesofCart3Dsolutionsrelevanttothiswork.
When the BSMs are not firing, convergence is consistently good, which is shown by example in Fig. 5a.
However, when the BSMs are firing at full strength in the first second or so of the separation, convergence
on the final mesh is usually poor or nonexistent, as shown in Fig. 5b. This result, while discomfiting, is
typical when using a steady-state solution method for an unsteady problem. When using time-accurate
inputs for the same conditions as Fig. 5b, convergence can be obtained, as shown in Fig. 5c. The blue line
between iteration 3000 and iteration 6000 shows the residual before any subiterations at each time step,
and the black curve over this same period shows the residual after subiterations; the difference between
these two shows the amount of convergence obtained at each time step. The combination of time-accurate
convergenceasshowninFig.5candgoodcomparisonbetweentime-accurateandsteady-stateresultsshown
in Fig. 4 serves as the justification to use steady-state solutions for the bulk of the database. However, this
weakconvergenceistakenintoconsiderationwhendevelopinganuncertaintymodelatalaterstep.
IV. OverflowRunStrategy
TheOverflowsolutionswerecomputedusingthestandardreleaseversion2.2koftheOverflowcode,using
theMessage-PassingInterface(MPI)parallelversion. ThecomputationswereperformedontheSGIAltix-
IcesystemknownasPleiadesattheNASAAdvanceSupercomputing(NAS)center. Alloftherunsused25
Haswellnodeswith24coreseach,foratotalof600coresperrun.
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a) BSMon,dx=10feet b) BSMoff,dx=8feet
Figure6. ConvergencehistoriesofforcesandmomentsontherightboosterfortwoOverflowsimulations.
The third-order HLLC upwind differencing scheme was used in Overflow. The SSOR implicit scheme
was used as it was found to retain numerical stability in nozzle flow regions. Local time-stepping with a
constant CFL number was used, and all viscous terms, including cross terms, were enabled in the code. A
slowstartoverthefirst500iterationswasusedforthenozzleinflowboundaryconditions.
The overset grid system contained 469 body-fitted zones with over 160 million grid points. Together
with the off-body grid adaptation, a total of 250 million grid points were used for each run. The final
adapted meshes contained about 5000 to 6000 off-body zones. The grids in the BSM nozzles, the core-
stage-engine nozzles, and the booster nozzles all included a short plenum upstream of the nozzle throat.
Theplenumendedinaplanarboundarywhereuniformnozzleboundaryconditionsareapplied. Boundary-
conditionsweregeneratedforeachnozzlewhichspecifiedthethedesiredtotalpressureandtotaltemperature
conditions. These were generated using isentropic relations and the area ratio between the throat area and
the boundary-condition surface area to compute the static flow conditions on the nozzle inflow boundary.
Thespecifiedvelocityvectorwasmadenormaltotheboundary-conditionface;carewastakentoensurethis
was done properly for the booster main nozzles and BSM nozzles to account for the pitch and yaw of the
booster. Differentgasspecieswereusedforeachofthethreetypesofnozzles,andOverflowwasrunusing
a variable gamma formulation. Calibration cases were run to provide the ratio between the total pressure
andtheresultingthrust,allowingtheproperthrusttobeachievedinallsubsequentproductioncases.
TheSpalart-Allmarasturbulencemodelwasusedandtheflowwasassumedtobeturbulenteverywhere.
Eachsimulationwasinitializedwithfreestreamflow,andstartedexecutionusingfull-multigridsequencing
for4000steps. Thecodecontinuedwithsteady-stateiterationsusinglocally-varyingtimestepsizesuntila
totalof20,000iterationswererun,thenthecasewascontinuedwithtime-accurateintegration. Thisuseda
dual time step approach with 2 Newton subiterations per time step. They were run until the time-averaged
meanofthevehicleforceswereconverged, andthefinalsolutionwasextractedfromatimeaverageofthe
last 2000 time steps. A nondimensional time step of 1.0 was used, meaning that a particle moving at the
freestream speed of sound moves one inch in each time step. The force and moment histories of multiple
componentsweremonitoredtodeterminewhenacaseconverged,includingthecore,andtherightandleft
boosters. Atotalof8millioncorehourswereusedtoperformthe390Overflowsimulations,withanaverage
timepercaseofjustunder21,000corehours.
Someexampleconvergencehistoriesoftheforceandmomentcoefficientsontherightboosterareplotted
in the following figures. Figure 6a shows the history of the force and moment coefficients for the nominal
casewithBSMsfiringatdx = 10feet. Figure6bshowsthehistoryoftheforceandmomentcoefficientsfor
thenominalcasewithBSMsoffatdx = 8feet.
Overflow’s grid adaption capability [13] was utilized to help improve the accuracy of the solution in
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