NASA Technical Reports Server (NTRS) 20060028188: Blunt Body Aerodynamics for Hypersonic Low Density Flows

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Blunt Body Aerodynamics for
Hypersonic Low Density Flows
(cid:0) (cid:0) (cid:0)
James N(cid:2) Moss (cid:3) Christopher E(cid:2) Glass (cid:3) and Francis A(cid:2) Greene
(cid:0)
NASA Langley Research Center(cid:2) MS (cid:3)(cid:4)(cid:5)A(cid:2) Hampton(cid:2) VA (cid:6)(cid:7)(cid:8)(cid:5)(cid:9)(cid:10)(cid:6)(cid:9)(cid:11)(cid:11)
Abstract(cid:2) Numerical simulations are performed for the Apollo capsule from the hypersonic rare(cid:2)ed to
the continuum regimes(cid:3) The focus is on (cid:4)ow conditions similar to those experienced by the Apollo (cid:5)
Command Module during the high altitude portion of its reentry(cid:3) The present focus is to highlight some
of the current activities that serve as a precursor for computational tool assessments that will be used to
support the development of aerodynamic data bases for future capsule (cid:4)ight environments(cid:6) particularly
those for theCrew Exploration Vehicle (cid:7)CEV(cid:8)(cid:3)Results for aerodynamic forces and momentsare presented
that demonstrate their sensitivity to rarefaction(cid:9) that is(cid:6) free molecular to continuum conditions(cid:3) Also(cid:6)
aerodynamic data are presented that shows their sensitivity to a range of reentry velocities(cid:6) encompassing
conditions that include reentry from low Earth orbit(cid:6) lunar return(cid:6) and Mars return velocities (cid:7)(cid:10)(cid:3)(cid:10) to (cid:11)(cid:12)
km(cid:13)s(cid:8)(cid:3) The rare(cid:2)ed results obtained with direct simulation Monte Carlo (cid:7)DSMC(cid:8) codes are anchored in
the continuumregime with data fromNavier(cid:14)Stokes simulations(cid:3)
INTRODUCTION
Blunt(cid:2)body space capsules form much of the legacy of the international manned space programs(cid:3) With
NASA(cid:4)s recently announced Constellation Program for exploring the moon(cid:5) Mars and beyond(cid:5) once again a
blunt(cid:2)body con(cid:6)guration has been selected as the capsule for the Crew ExplorationVehicle (cid:7)CEV(cid:8)(cid:3) The CEV
includes a capsule much like Apollo(cid:5) but larger(cid:5) and like Apollo will be attached to a service module for life
supportandpropulsion(cid:3) MissionapplicationsoftheCEVincludethatofalow(cid:2)Earth(cid:2)orbit(cid:7)LEO(cid:8)versionwith
a crew of six to the International Space Station(cid:5) a lunar version that would carry a crew of four(cid:5) and a Mars
version that would carry a crew of six(cid:3)
With commitments to evolve the CEV design(cid:7)s(cid:8) for LEO(cid:5) lunar(cid:5) and Mars missions(cid:5) aerothermodynamic
databaseswillbegeneratedutilizingcomputationalandexperimental(cid:7)bothground(cid:2)basedand(cid:9)ight(cid:8)resources(cid:3)
These new data bases along with an extensive capsule heritage(cid:5) particularly that from Apollo (cid:7)Refs(cid:3) (cid:10)(cid:11)(cid:12)(cid:13)(cid:14)(cid:5) for
example(cid:8)(cid:5)willprovidethebasisforoptimizingtheCEV(cid:4)sdesign(cid:5)withparticularemphasisonsafety(cid:5)(cid:9)exibility(cid:5)
and a(cid:15)ordability(cid:3) The current study expands on the results presented in Ref(cid:3) (cid:10)(cid:16)(cid:14) where the focus was on the
aerodynamicsoftheApolloCommandModuleduringthetransitionalportionofitsreentry(cid:5)fromfreemolecular
to continuum conditions(cid:3) New results included in the present study are solutions obtained with a di(cid:15)erent
DSMC code (cid:10)(cid:17)(cid:14) and comparisons of the numerical simulations with (cid:9)ight and ground(cid:2)based measurements(cid:3)
The primaryfocusis on(cid:9)owconditionssimilar tothoseexperienced bythe Apollo(cid:17)(cid:9)ight test(cid:5) with areentry
(cid:0)
velocity of (cid:18)(cid:3)(cid:17) km(cid:19)s at (cid:2)(cid:20)(cid:16) angle of attack(cid:3) Numerical simulations for the transitional (cid:9)ow regime are made
with the (cid:21)D DSMC codes of Bird (cid:10)(cid:22)(cid:14) and LeBeau(cid:10)(cid:17)(cid:14) and for the continuum regimewith the (cid:21)D Navier(cid:2)Stokes
(cid:7)NS(cid:8) codeof Gno(cid:15)o(cid:10)(cid:23)(cid:14)(cid:3) Results arepresentedthat showthe sensitivity ofthe capsuleaerodynamicsto a wide
range of altitude or rarefaction conditions and the sensitivity of the aerodynamics to velocity and angle(cid:2)of(cid:2)
attack variations at an altitude of (cid:11)(cid:24)(cid:16) km(cid:3) Also(cid:5) results from the DSMC and NS simulations show that the
calculated aerodynamics are reasonably consistent near the (cid:18)(cid:16) km altitude conditions(cid:3) Lessons learned from
this study can be applied to simulating other capsule con(cid:6)gurations(cid:5) such as the proposed CEV(cid:3)
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NUMERICAL PROGRAMS AND MODEL PARAMETERS
DSMC Analyses
For the more rare(cid:6)ed (cid:9)ow conditions(cid:5) two DSMC codes(cid:5) DS(cid:21)V and DAC (cid:7)DSMC Analysis Code(cid:8)(cid:5) were
used to both generate the data and provide a check on the consistency of the results(cid:3) The majority of these
calculationsweremadewiththeDS(cid:21)VprogramofBird(cid:10)(cid:22)(cid:14)(cid:5)ageneral(cid:21)Dcodethatprovidesbothtime(cid:2)accurate
unsteady(cid:9)owandtime(cid:2)averagedsteady(cid:9)owsimulations(cid:3) Inthecurrentstudy(cid:5)ascalarversionofthisprogram
wasusedandallthepresentsimulationsweremadebyusinga(cid:21)(cid:3)(cid:20)GHzpersonalcomputerwithamemoryof(cid:20)(cid:3)(cid:24)
GB(cid:3) The DAC programofLeBeau(cid:10)(cid:17)(cid:14) providesboth scalarand parallelprocessingoptions(cid:3) Parallelprocessing
isaccomplishedbydomaindecompositionandtheparallelversionofDACisemployedinthecurrentstudy(cid:3) For
both DSMC programs(cid:5) the molecular collisions are simulated with the variable hard sphere molecular model(cid:3)
The Larsen(cid:2)Borgnakkestatistical model (cid:10)(cid:18)(cid:14) controls the energy exchange between kinetic and internal modes(cid:3)
All simulationsareperformedby usinga(cid:6)ve(cid:2)speciesreactingair gasmodel while consideringenergyexchange
between translation(cid:5)rotational(cid:5)andvibrationalmodes(cid:3) Also(cid:5) thesurfaceisassumedtobe noncatalyticandat
a speci(cid:6)ed wall temperature(cid:3) As for gas(cid:2)surface interactions(cid:5) they are assumed to be di(cid:15)use(cid:5) with full energy
accommodation(cid:3)
An indicator of the resolution achieved in a DS(cid:21)V simulation is given by the ratio of the mean collision
separation between collision partners to the local mean free path (cid:7)mcs(cid:2)mfp(cid:8)(cid:3) As demonstratedin Ref(cid:3) (cid:10)(cid:16)(cid:14)(cid:5) the
averagevalue for this parameteroverthe computational domain should be approximately (cid:24)(cid:3)(cid:11)or lessto obtain
grid resolved aerodynamics(cid:3) The total number of simulated molecules used in the current DS(cid:21)V simulations
rangedfrom approximately(cid:11) to (cid:11)(cid:17) million(cid:5) and the grid adaption produced nominally (cid:20)(cid:24) simulated molecules
per collision cell(cid:3)
For the DAC code(cid:5) the user can implement a sequence of grid re(cid:6)nements of the two(cid:2)level Cartesian grid
such that the cell size is small in relation to the local mean free path(cid:3) The current DAC simulations used
between (cid:23) to (cid:13)(cid:17)(cid:24) million molecules(cid:5) depending on the altitude(cid:5) with the cell dimension equal to or less than
the localmeanfreepath(cid:3) BothDSMC codesused the samede(cid:6)nition forthe Apollo surfacegeometry(cid:25) that is(cid:5)
an unstructured grid consisting of (cid:11)(cid:18)(cid:11)(cid:20) points and (cid:21)(cid:22)(cid:11)(cid:23) triangles while making use of the problem symmetry
such that the (cid:9)ow is computed about only half of the vehicle(cid:3) This surface resolution was deemed adequate
after a calculation was made for a case with a much (cid:6)ner surface grid resoultion (cid:7)(cid:16)(cid:18)(cid:13)(cid:17) and (cid:11)(cid:11)(cid:5)(cid:11)(cid:22)(cid:23) points and
triangles(cid:5) respectively(cid:8) and with a negligible change in results(cid:3)
Navier(cid:2)Stokes Analyses
Navier(cid:2)Stokesanalysesareperformedby usingthe LAURA computational(cid:9)uid dynamicscode (cid:10)(cid:23)(cid:14)(cid:3) LAURA
is an upwind(cid:2)bias(cid:5) point(cid:2) or line(cid:2)implicit relaxation algorithm for obtaining the numerical solution to the
Navier(cid:2)Stokes equations for three(cid:2)dimensional(cid:5) viscous(cid:5) hypersonic (cid:9)ows in thermochemical nonequilibrium(cid:3)
LAURA hasboth thethin layerandfull NS options(cid:5)andboth options wereexercisedin the currentstudy(cid:3) All
oftheLAURAsimulationsassumedthe(cid:9)owtobeareactinggasmixturewiththesurfaceboundaryconditions
consistingofaconstantwalltemperature(cid:5)anoncatalyticsurface(cid:5)andnosliportemperaturejump(cid:3) Thevolume
grid consists of (cid:20)(cid:13) blocks with a total of (cid:11)(cid:18)(cid:17)(cid:17)(cid:24)(cid:24)(cid:24) cells(cid:5) and in the direction normal to the wall(cid:5) there are (cid:23)(cid:24)
cells(cid:5)whichcovertheregionfromthewalltotheouterboundary(cid:3) GridadaptionassuredthatthecellReynolds
numbers adjacent to the wall were at a nominal value no greater than (cid:24)(cid:3)(cid:16) for the highest altitude (cid:7)(cid:18)(cid:16) km(cid:8)
and (cid:16)(cid:3)(cid:24) for the lowest altitude (cid:7)(cid:17)(cid:16) km(cid:8)(cid:3) The structured surface grid consisted of (cid:20)(cid:13)(cid:16)(cid:22)(cid:17) cells(cid:3) To balance the
computationalload(cid:5)calculationswereperformedon(cid:11)(cid:20)dualprocessor(cid:20)(cid:3)(cid:23)GHz Opteronworkstationswith one
block assigned to each of the (cid:20)(cid:13) processors(cid:3) Solutions were considered converged when the surface properties
became steady and changed little after additional integration cycles(cid:3)
Free Molecular and Newtonian Analyses
The free molecular (cid:7)FM(cid:8) and modi(cid:6)ed Newtonian (cid:7)MN(cid:8) results were obtained with the DACFREE code of
R(cid:3) G(cid:3) Wilmoth (cid:7)private communication(cid:5) July (cid:20)(cid:24)(cid:24)(cid:16)(cid:8)(cid:3) DACFREE computes aerodynamic forces and moments
on arbitrary bodies using standard free molecular and modi(cid:6)ed Newtonian methods(cid:3) This code can handle
arbitrarygeometriesspeci(cid:6)ed as an unstructured collection of triangles(cid:5) and for the present study(cid:5) the surface
grid was the same as that used in the DSMC simulations(cid:3)
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CONDITIONS AND RESULTS
Conditions
Considerable resources were devoted to quantifying the impact of the aerothermodynamic environment on
the Apollo Command Module during reentry(cid:5) particularly the thermal protection system(cid:3) Reference (cid:10)(cid:11)(cid:14) lists
some of the reentryparametersfor the (cid:13) unmanned Apollo heat(cid:2)shield(cid:2)quali(cid:6)cation(cid:9)ight tests(cid:5) two at orbital
entry velocities and two at superorbital entry velocities(cid:3) The current study focuses on an altitude range from
(cid:0)
(cid:20)(cid:24)(cid:24) to (cid:17)(cid:16) km at (cid:18)(cid:3)(cid:17) km(cid:19)s (cid:7)corresponding to the Apollo (cid:17) reentry condition(cid:8) and (cid:2)(cid:20)(cid:16) angle of attack(cid:5) for a
range of incidence angles at an altitude of (cid:11)(cid:24)(cid:16) km(cid:5) and for a range of reentry velocities (cid:7)(cid:22)(cid:3)(cid:17)(cid:23) to (cid:11)(cid:16) km(cid:19)s(cid:8) at
(cid:11)(cid:24)(cid:16) km altitude(cid:3)
The axisymmetric geometry for the Apollo Command Module used in the present study is shown in Fig(cid:3) (cid:11)(cid:3)
The Apollo capsule was (cid:9)own at an angle of attack while using an o(cid:15)set center of gravity (cid:7)cg(cid:8)(cid:5) where the cg
coordinates used in the current study are listed in Fig(cid:3) (cid:11)(cid:3)
When the pressuresandshearstressesareintegratedoverthe surface(cid:5)the resultantforceactsatthe capsule
center(cid:2)of(cid:2)pressure(cid:7)cp(cid:8)(cid:3) Thetotalforcevectorcanberesolvedintocomponents(cid:5)andthenomenclatureusedfor
the body (cid:7)axial(cid:5) CA(cid:5) and normal(cid:5)CN(cid:8) andvelocity(cid:7)drag(cid:5)CD(cid:5) and lift(cid:5) CL(cid:8) oriented coordinatesareasshown
in Fig(cid:3) (cid:20)(cid:3) Y
CL
3.4306 y CN
2 3Rs x
1
33 CD
Rb Cm, cg
Rn + cg + CA X
4 Ra Cm, 0 cp
cg
CL 5
Location x y s Db = 3.9116
1 0.3743 1.8368 1.8872 Rb = 1.9558 V∞
2 0.5543 1.9558 2.1158 Rn = 4.6939
3 0.6608 1.9242 2.2284 Rs = 0.1956
4 3.3254 0.1938 5.4056 Ra = 0.2311
5 3.3406 0.0000 5.6355
cg 1.1455 0.1600 - Dimensions in m Xcp
Fig(cid:3) (cid:11)(cid:3) Apollo outer mold line(cid:3) Fig(cid:3) (cid:20)(cid:3) Nomenclature for aerodynamic forces(cid:3)
Free(cid:2)stream atmospheric conditions (cid:7)details given in Ref(cid:3) (cid:10)(cid:16)(cid:14)(cid:8) are based on the data of Jacchia (cid:10)(cid:11)(cid:24)(cid:14) (cid:7)an
exospheric temperature of (cid:11)(cid:20)(cid:24)(cid:24) K(cid:8) for altitudes of (cid:18)(cid:24) km and above and on that of Ref(cid:3) (cid:10)(cid:11)(cid:11)(cid:14) for altitudes
less than (cid:18)(cid:24) km(cid:3) The surface temperatures are assumed to be uniformly distributed at constant values based
on stagnation point heating conditions as discussed in Ref(cid:3) (cid:10)(cid:16)(cid:14)(cid:3) The free(cid:2)stream Knudsen numbers listed in
the (cid:6)gures are based on the free(cid:2)stream number density(cid:5) a characteristiclength of (cid:21)(cid:3)(cid:18)(cid:11)(cid:20)m (cid:7)maximum capsule
(cid:2)(cid:0)(cid:2)
diameter(cid:8)(cid:5) and a constant molecular diameter of (cid:21)(cid:3)(cid:22)(cid:23) x (cid:11)(cid:24) m(cid:3)
E(cid:3)ects of Rarefaction
Results presented in Fig(cid:3) (cid:21) provide an overall summary of the Apollo aerodynamics as obtained with the
DSMC and NS programs(cid:3) Results are presented in terms of a hard sphere free(cid:2)stream Knudsen number with
a coverage of approximately six orders of magnitude(cid:3) As shown previously (cid:10)(cid:11)(cid:20)(cid:14) for a related blunt body
con(cid:6)guration(cid:5) the pressure contribution is fairly constant(cid:5) but the shear contribution increases with altitude
such that the drag coe(cid:26)cient increases and the lift coe(cid:26)cient decreases(cid:3) As detailed in Ref(cid:3) (cid:10)(cid:16)(cid:14)(cid:5) the DS(cid:21)V
results included in this (cid:6)gure are those that are grid resolved to an accuracy of probably (cid:21) percent or better(cid:3)
Examinationofthe gridsensitivityresults(cid:10)(cid:16)(cid:14)providequalitativeinformationastothe e(cid:15)ect ofgridresolution
on simulated aerodynamics(cid:25) that is(cid:5) poor volume grid resolution for the Apollo capsule resulted in an over
prediction of the drag(cid:5) axial(cid:5) and normal force coe(cid:26)cients and an under prediction of the lift and lift(cid:2)to(cid:2)drag
coe(cid:26)cients(cid:3)
Sensitivity studies conducted with the NS calculations (cid:10)(cid:16)(cid:14) indicated that the aerodynamics were insensitive
to ionization e(cid:15)ects(cid:25) that is(cid:5) the use of a (cid:16)(cid:2)species neutral gas model as used in all the DSMC simulations or
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one that accounted for neutrals(cid:5) ions(cid:5) and electrons with a (cid:11)(cid:11)(cid:2)species gas model did not signi(cid:26)cantly a(cid:15)ect
the results(cid:3) Furthermore(cid:5) it was shown that the NS results were insensitive to whether the thin(cid:2)layer or full
NS equations were used at the lower altitude conditions (cid:7)(cid:23)(cid:16) km(cid:8)(cid:5) but other studies (cid:10)(cid:11)(cid:21)(cid:14) have shown that the
full NS solutions provide higher (cid:6)delity results for the more rare(cid:6)ed conditions(cid:3)
Also included in Fig(cid:3) (cid:21) are the new DAC results that provide grid resolved solutions to an altitude of (cid:18)(cid:16)
km(cid:5) overlapping the NS results(cid:3) Di(cid:15)erences in the two DSMC sets of solutions are larger than expected(cid:5) and
currentlyitisnotknownwhattheymightbeattributedto(cid:3) Perhapstheyarebecauseofsimulationorphysical
modeldi(cid:15)erences(cid:5) orpossiblyuserimplementation(cid:3) Speci(cid:6)cally(cid:5) di(cid:15)erences inthetwosimulationsforcommon
altitudes between (cid:11)(cid:11)(cid:24) to (cid:11)(cid:24)(cid:24) km are less than (cid:13) percent for drag(cid:5) lift(cid:5) axial(cid:5) and moment (cid:7)about the nose(cid:8)
coe(cid:26)cients(cid:5) but (cid:22) percent for L(cid:19)D and as much as (cid:11)(cid:20) percent for the normal force coe(cid:26)cient(cid:3) However(cid:5) the
DSMC and NS results (cid:7)overlap for DAC and extrapolated for DS(cid:21)V(cid:8) show generally consistent agreement in
thevicinityof(cid:18)(cid:16)km(cid:5)orahardsphereKnudsennumberof(cid:24)(cid:3)(cid:24)(cid:11)(cid:13)(cid:3) Notethatrarefactione(cid:15)ectsarepresentat(cid:18)(cid:16)
km and lower altitudes(cid:25) however(cid:5)the integrated e(cid:15)ect on the aerodynamics is apparently not that signi(cid:6)cant(cid:3)
2.0 0.5 5 0.05
65km 85 100 120 150 200
C
L Alt.=65km 85 100 115 125 200
1.8 0.4 4 Cm,cg 0.00
L/D
x
CP
1.6 0.3 D 3 -0.05
CD DDLASAUC3VRA andL/ x,mCP Cm,cg
1.4 FM 0.2 CL 2 -0.10
x =1.1455m
ycg=0.1600m
1.2 CD 0.1 1 cg -0.15
DS3V
DAC
LAURA
1.0 0 0 -0.20
10-5 10-4 10-3 10-2 10-1 100 101 102 10-5 10-4 10-3 10-2 10-1 100 101 102
Kn∞,D,HS Kn∞,D,HS
Fig(cid:3) (cid:21)a(cid:3) Drag(cid:5) lift and L(cid:19)D coe(cid:26)cients(cid:3) Fig(cid:3) (cid:21)b(cid:3) Center of pressure and moment coe(cid:26)cients(cid:3)
FIGURE (cid:3)(cid:2) E(cid:15)ect of rarefaction onaerodynamics as calculated with DSMC andNScodes(cid:3)
Figure (cid:21)b details the movement of the center of pressure and the corresponding moment coe(cid:26)cient about
the centerof gravityas afunction of Knudsennumber(cid:3) As the capsuledescends from (cid:20)(cid:24)(cid:24)to (cid:17)(cid:16)km(cid:5) the center
ofpressureexperiencesasubstantial translationasit movesfrom aposition forwardof thecenter of gravityto
one well aft(cid:3) The corresponding change in the moment coe(cid:26)cient is from a negative value to a small positive
value(cid:3)
E(cid:3)ects of Angle of Attack
Figure (cid:13) presents results of the DS(cid:21)V simulations that show the dependence of the Apollo capsule aerody(cid:2)
namics to variations in angle of attack at (cid:11)(cid:24)(cid:16) km altitude conditions and (cid:18)(cid:3)(cid:17) km(cid:19)s(cid:3) Figure (cid:13)a highlights the
dependence of L(cid:19)D on incidence angle and also demonstrates its sensitivity to rarefaction by including the
free molecular (cid:7)FM(cid:8) and modi(cid:6)ed Newtonian (cid:7)MN(cid:8) results(cid:3) The FM and MN results were generated with the
DACFREE code at the (cid:20)(cid:24)(cid:24) km and (cid:23)(cid:16) km conditions (cid:7)free(cid:2)stream gas composition changes with altitude(cid:8)(cid:5)
respectively(cid:3)
Results for the center of pressure location and the moment coe(cid:26)cient about the o(cid:15)set center of gravity are
presented in Fig(cid:3) (cid:13)b(cid:3) These simulations show that the stable trim point for the Apollo capsule at (cid:11)(cid:24)(cid:16) km
altitude occurs at an incidence angle of (cid:2)(cid:11)(cid:17)(cid:13) degrees rather than the nominal (cid:2)(cid:20)(cid:16) degrees (cid:9)own by Apollo (cid:17)(cid:25)
that is(cid:5) the capsule is statically unstable for much(cid:5) if not all(cid:5) of the transitional (cid:9)ow regime(cid:5) a result not that
uncommon for capsules in the transitional rare(cid:6)ed regime(cid:3)
4
0.8 FM,Alt=200km 0.15
DS3V,Alt=105km
MN,Alt=85km C 1.40
0.6 m,cg
x ,m
0.10 CP 1.20
0.4
1.00
0.2 Stabletrimpoint
0.05 atα=-164o
L/D 0.0 Cm,cg 0.80x,mCP
-0.2 0.00 0.60
-0.4 0.40
-0.6 AV∞ref==91.62.k0m2/ms2 -0.05 xyccgg==10..11465050mm KAAVn∞lt.∞==,=D9H11S.620=.5k00m2k.0m0/s7m92 0.20
-0.8-180 -120 -60 0 60 120 180 -0.10-180 -120 -60 0 60 ref 120 1800.00
,degrees α,degrees
Fig(cid:3) (cid:13)a(cid:3) L(cid:19)D coe(cid:26)cients(cid:3) Fig(cid:3) (cid:13)b(cid:3) Center of pressure and moment coe(cid:26)cients(cid:3)
FIGURE (cid:4)(cid:2) E(cid:15)ect of angle of attack onaerodynamics as calculated with DS(cid:16)V andDACFREEcodes(cid:3)
E(cid:3)ects of Free(cid:2)Stream Velocity
Toexaminethee(cid:15)ectsoffree(cid:2)streamvelocityvariations(cid:5)DS(cid:21)VsimulationsweremadefortheApollocapsule
at an altitude of (cid:11)(cid:24)(cid:16) km and (cid:2)(cid:20)(cid:16) degrees incidence for (cid:16) free(cid:2)stream velocities ranging from (cid:22)(cid:3)(cid:22) to (cid:11)(cid:16) km(cid:19)s(cid:3)
Four of the velocities correspond to the nominal re(cid:2)entry conditions of the (cid:13) unmanned Apollo quali(cid:6)cation
(cid:9)ight tests (cid:10)(cid:11)(cid:14)(cid:3) The (cid:11)(cid:16) km(cid:19)s velocity is representative of the upper bounds for a Mars return mission(cid:3) Conse(cid:2)
quently(cid:5) this range of entry velocities is inclusive of that for reentry from LEO(cid:5) lunar return(cid:5) and Mars return
missions(cid:3) Results of the simulations for variations in free(cid:2)stream velocity show (cid:7)Fig(cid:3) (cid:16)(cid:8) that the changes in
the aerodynamic coe(cid:26)cients with increasing velocity are similar to those incurred with increasing rarefaction(cid:25)
that is(cid:5) the magnitude of the drag(cid:5) axial(cid:5) and normal force coe(cid:26)cients increases with increasing free(cid:2)stream
velocity while the magnitude of the lift and lift(cid:2)to(cid:2)drag ratio coe(cid:26)cients decreases with increasing velocity(cid:3)
These (cid:6)ndings are consistent with the correlations demonstrated by Wilhite et al(cid:3) (cid:10)(cid:11)(cid:13)(cid:14) (cid:7)Fig(cid:3) (cid:22)(cid:5) p (cid:11)(cid:22)(cid:20)(cid:8) for the
Shuttle Orbiter axial(cid:2)forcecoe(cid:26)cients as a function of a viscous correlation parameter(cid:3)
15
1.8 0.4
C
1.6 D
0.3
D
CL L/
CD1.4 nd
a
CL
L/D 0.2
1.2
DS3V
Alt = 105 km
1 0.1
6 8 10 12 14 16
V, km/s
∞
Fig(cid:3) (cid:16)(cid:3) E(cid:15)ect of velocity on aerodynamics(cid:3) Fig(cid:3) (cid:17)(cid:3) Flight(cid:5) computed(cid:5) and wind tunnel data(cid:3)
5
Comparison with Flight and Wind Tunnel Data
Figure (cid:17) presents the results of the present calculations for the aerodynamic ratio of normal(cid:2)to(cid:2)axial force
coe(cid:26)cients as a function of altitude(cid:3) Also included in this (cid:6)gure are the (cid:9)ight data for the (cid:7)Apollo(cid:2)Saturn(cid:8)
AS(cid:2)(cid:20)(cid:24)(cid:20)unmanned(cid:9)ighttest(cid:7)relativeentryvelocityof(cid:23)(cid:3)(cid:20)(cid:18)km(cid:19)s(cid:8)andwindtunnelmeasurementsmadeatthe
ArnoldEngineeringDevelopmentCenter(cid:7)AEDC(cid:8)(cid:10)(cid:11)(cid:16)(cid:14)(cid:3) Asindicated inFig(cid:3) (cid:22)aofRef(cid:3)(cid:10)(cid:11)(cid:16)(cid:14)(cid:5)theangleofattack
(cid:0)
formostoftheAS(cid:2)(cid:20)(cid:24)(cid:20)reentrywaslessthanthe(cid:2)(cid:20)(cid:16) experiencedbytheApollo(cid:17)mission(cid:3) The(cid:9)ightinferred(cid:10)(cid:13)(cid:14)
(cid:0)
anglesofattackforAS(cid:2)(cid:20)(cid:24)(cid:20)werenear(cid:2)(cid:20)(cid:16) foraltitudesof(cid:11)(cid:11)(cid:24)to(cid:11)(cid:24)(cid:24)km(cid:5)andthen decreasedtoapproximately
(cid:0)
(cid:2)(cid:11)(cid:22)(cid:3)(cid:16) at (cid:18)(cid:20) km and remained near this value as the capsule descended through (cid:17)(cid:24) km(cid:3) When the NS results
for the Apollo (cid:17) mission are adjusted to account for the AS(cid:2)(cid:20)(cid:24)(cid:20) (cid:9)ight attitude(cid:5) then good agreement between
(cid:9)ight and computation is obtained(cid:3) An approximate adjustment is made based on the DS(cid:21)V results at the
(cid:0) (cid:0)
(cid:11)(cid:24)(cid:16) km altitude condition in which a reduction in angle of attack from (cid:2)(cid:20)(cid:16) to (cid:2)(cid:11)(cid:22)(cid:3)(cid:16) produces a (cid:21)(cid:11) percent
reductioninthevalueofCN(cid:19)CA(cid:3) When thiscorrectionfactoris applied tothe (cid:13)calculatedvaluesat altitudes
below (cid:18)(cid:20) km(cid:5) the results are displayed by the dashed line in Fig(cid:3) (cid:17)(cid:5) with generally good agreement between
(cid:0) (cid:0)
(cid:9)ight and calculated results for two sets of conditions(cid:27) (cid:11)(cid:11)(cid:24) to (cid:11)(cid:24)(cid:24) km at (cid:2)(cid:20)(cid:16) and (cid:18)(cid:20) to (cid:17)(cid:24) km at (cid:2)(cid:11)(cid:22)(cid:3)(cid:16) (cid:3)
CONCLUSIONS
Signi(cid:6)cant (cid:6)ndings of the present investigation are(cid:27) (cid:7)(cid:11)(cid:8) the current numerical results are shown to be
consistent with (cid:9)ight data for normal(cid:2)to(cid:2)axial force ratios(cid:5) (cid:7)(cid:20)(cid:8) the Apollo Command Module is statically
unstable for much of the rare(cid:6)ed (cid:9)ow regime(cid:5) (cid:7)(cid:21)(cid:8) changes in the aerodynamic coe(cid:26)cients with increasing
velocity have the same trend as that for increasing rarefaction(cid:5) (cid:7)(cid:13)(cid:8) the DSMC simulations are shown to be
reasonably consistent based on the results from two di(cid:15)erent codes(cid:5) and (cid:7)(cid:16)(cid:8) close agreement in aerodynamics
is obtained with DSMC and NS programs for the (cid:18)(cid:16) km altitude condition(cid:25) thereby(cid:5) providing a capability
for calculating hypersonic blunt body aerodynamics for the spectrum of (cid:9)ows that include free molecular(cid:5)
transitional(cid:5) and continuum conditions without relying on bridging functions(cid:3)
REFERENCES
(cid:11)(cid:3) Lee(cid:6) D(cid:3) B(cid:3)(cid:6) (cid:17)Apollo Experience Report(cid:18)AerothermodynamicsEvaluation(cid:6)(cid:19) NASATN D(cid:14)(cid:5)(cid:20)(cid:21)(cid:16)(cid:6) June (cid:11)(cid:22)(cid:10)(cid:23)(cid:3)
(cid:23)(cid:3) Lee(cid:6) D(cid:3)B(cid:3)andGoodrich(cid:6) W(cid:3)D(cid:3)(cid:6)(cid:17)The AerothermodynamicEnvironmentoftheApolloCommandModuleDuring
Superorbital Entry(cid:6)(cid:19)NASATN D(cid:14)(cid:5)(cid:10)(cid:22)(cid:23)(cid:6) April (cid:11)(cid:22)(cid:10)(cid:23)(cid:3)
(cid:16)(cid:3) Lee(cid:6)D(cid:3)B(cid:3)(cid:6) Bertin(cid:6)J(cid:3)J(cid:3)(cid:6) andGoodrich(cid:6) W(cid:3)D(cid:3)(cid:6)(cid:17)Heat(cid:14)TransferRateandPressureMeasurementsObtainedDuring
Apollo Orbital Entries(cid:6)(cid:19) NASATN D(cid:14)(cid:5)(cid:24)(cid:23)(cid:20)(cid:6) April(cid:11)(cid:22)(cid:10)(cid:24)(cid:3)
(cid:21)(cid:3) Hillje(cid:6) E(cid:3) R(cid:3)(cid:6) (cid:17)Entry Flight AerodynamicsfromApollo Mission AS(cid:14)(cid:23)(cid:24)(cid:23)(cid:6)(cid:19) NASATN D(cid:14)(cid:21)(cid:11)(cid:20)(cid:12)(cid:6) October(cid:11)(cid:22)(cid:5)(cid:10)(cid:3)
(cid:12)(cid:3) Moss(cid:6) J(cid:3)N(cid:3)(cid:6)Glass(cid:6) C(cid:3)G(cid:3)(cid:6)andGreene(cid:6)F(cid:3)A(cid:3)(cid:6)(cid:17)DSMCSimulationsofApolloCapsuleAerodynamicsforHypersonic
Rare(cid:2)edConditions(cid:6)(cid:19) AIAAPaper (cid:23)(cid:24)(cid:24)(cid:5)(cid:14)(cid:16)(cid:12)(cid:10)(cid:10)(cid:6) June (cid:23)(cid:24)(cid:24)(cid:5)(cid:3)
(cid:5)(cid:3) LeBeau(cid:6) G(cid:3) J(cid:3)(cid:6) (cid:17)AParallel Implementationof the Direct SimulationMonte Carlo Method(cid:6)(cid:19) Computer Methods in
Applied Mechanics and Engineering(cid:2) Parallel Computational Methods for Flow Simulation and Modeling(cid:6)Vol(cid:3)(cid:11)(cid:10)(cid:21)(cid:6)
(cid:11)(cid:22)(cid:22)(cid:22)(cid:6) pp(cid:3) (cid:16)(cid:11)(cid:22)(cid:14)(cid:16)(cid:16)(cid:10)(cid:3)
(cid:10)(cid:3) Bird(cid:6) G(cid:3) A(cid:3)(cid:6) Visual DSMC Program for Three(cid:10)Dimensional Flows(cid:3) The DS(cid:16)V Program User(cid:25)s Guide(cid:6) Version (cid:11)(cid:3)(cid:23)(cid:6)
March (cid:23)(cid:24)(cid:24)(cid:12)(cid:3)
(cid:20)(cid:3) Cheatwood(cid:6) F(cid:3) M(cid:3)(cid:6) and Gno(cid:15)o(cid:6) P(cid:3) A(cid:3)(cid:6) (cid:17)User(cid:25)s Manual for the Langley Aerothermodynamic Upwind Relaxation
Algorithm (cid:7)LAURA(cid:8)(cid:6)(cid:19)NASATM (cid:21)(cid:5)(cid:10)(cid:21)(cid:6) April(cid:11)(cid:22)(cid:22)(cid:5)(cid:3)
(cid:22)(cid:3) Borgnakke(cid:6) C(cid:3)(cid:6) and Larsen(cid:6) P(cid:3) S(cid:3)(cid:6) (cid:17)Statistical Collision Model for Monte Carlo Simulation of Polyatomic Gas
Mixture(cid:6)(cid:19) Journal of Computational Physics(cid:6) Vol(cid:3) (cid:11)(cid:20)(cid:6) No(cid:3) (cid:21)(cid:6) (cid:11)(cid:22)(cid:10)(cid:12)(cid:6) pp(cid:3) (cid:21)(cid:24)(cid:12)(cid:14)(cid:21)(cid:23)(cid:24)(cid:3)
(cid:11)(cid:24)(cid:3) Jacchia(cid:6)L(cid:3)G(cid:3)(cid:6)(cid:17)ThermosphericTemperature(cid:6)Density(cid:6)andComposition(cid:26) NewModels(cid:6)(cid:19)SmithsonianAstrophysical
Observatory(cid:6)Cambridge(cid:6) MA(cid:6) Special Rept(cid:3)(cid:16)(cid:10)(cid:12)(cid:6) March (cid:11)(cid:22)(cid:10)(cid:10)(cid:3)
(cid:11)(cid:11)(cid:3) Anon(cid:6)(cid:17)U(cid:3) S(cid:3) StandardAtmosphere(cid:6)(cid:11)(cid:22)(cid:5)(cid:23)(cid:6)(cid:19) Dec(cid:3) (cid:11)(cid:22)(cid:5)(cid:23)(cid:3)
(cid:11)(cid:23)(cid:3) Celenligil(cid:6) M(cid:3) C(cid:3)(cid:6) Moss(cid:6) J(cid:3) N(cid:3)(cid:6) and Blanchard(cid:6) R(cid:3) C(cid:3)(cid:6) (cid:17)Three(cid:14)Dimensional Rare(cid:2)ed Flow Simulations for the
Aeroassist Flight ExperimentVehicle(cid:6)(cid:19) AIAA Journal(cid:6) Vol(cid:3) (cid:23)(cid:22)(cid:6) No(cid:3)(cid:11)(cid:6) (cid:11)(cid:22)(cid:22)(cid:11)(cid:6) pp(cid:3) (cid:12)(cid:23)(cid:14)(cid:12)(cid:10)(cid:3)
(cid:11)(cid:16)(cid:3) Moss(cid:6) J(cid:3) N(cid:3)(cid:6) Glass(cid:6) C(cid:3) G(cid:3)(cid:6) Hollis(cid:6) B(cid:3) R(cid:3)(cid:6) and Van Norman(cid:6) J(cid:3) W(cid:3)(cid:6) (cid:17)Low(cid:14)Density Aerothermodynamics of the
In(cid:4)atable Re(cid:14)entryVehicleExperiment(cid:7)IRVE(cid:8)(cid:6)(cid:19) AIAAPaper (cid:23)(cid:24)(cid:24)(cid:5)(cid:14)(cid:11)(cid:11)(cid:20)(cid:22)(cid:6) Jan(cid:3) (cid:23)(cid:24)(cid:24)(cid:5)(cid:3)
(cid:11)(cid:21)(cid:3) Wilhite(cid:6) A(cid:3) W(cid:3)(cid:6) Arrington(cid:6) J(cid:3) P(cid:3)(cid:6) and McCandless(cid:6) R(cid:3) S(cid:3)(cid:6) (cid:17)Performance Aerodynamics of Aeroassisted Orbital
Transfer Vehicles(cid:6)(cid:19) Progress in Astronautics and Aeronautics(cid:6) Vol(cid:3) (cid:22)(cid:5)(cid:6) Thermal Design of Aeroassisted Orbital
Transfer Vehicles(cid:6) edited byH(cid:3)F(cid:3) Nelson(cid:6) AIAA(cid:6)New York(cid:6) (cid:11)(cid:22)(cid:20)(cid:12)(cid:6) pp(cid:3)(cid:11)(cid:5)(cid:12)(cid:14)(cid:11)(cid:20)(cid:12)(cid:3)
(cid:11)(cid:12)(cid:3) Boylan(cid:6)D(cid:3)E(cid:3)andGri(cid:27)th(cid:6)B(cid:3)J(cid:3)(cid:17)SimulationoftheApolloCommandModuleAerodynamicsatRe(cid:14)EntryAltitudes(cid:6)(cid:19)
Proceedings ofthe Third NationalConference onAerospace Meteorology(cid:6) AmericanMeteorological Society(cid:6)Boston(cid:6)
May (cid:5)(cid:14)(cid:22)(cid:6) (cid:11)(cid:22)(cid:5)(cid:20)(cid:6) pp(cid:3)(cid:16)(cid:10)(cid:24)(cid:14)(cid:16)(cid:10)(cid:20)(cid:3)
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