Contents lists available at ScienceDirect

Acta Astronautica

Acta Astronautica 69 (2011) 975–986

0094-57

doi:10.1

n Corr

E-m

antonio

journal homepage: www.elsevier.com/locate/actaastro

Aerodynamic analysis of a Mars exploration manned capsule

Giuseppe Pezzella a,n, Antonio Viviani b

a Fluid Dynamics Laboratory, Aerothermodynamics division, Centro Italiano Ricerche Aerospaziali—CIRA, via Maiorise, 81043 Capua, Italyb Dipartimento di Ingegneria Aerospaziale e Meccanica (DIAM), Seconda Universit �a di Napoli—SUN, via Roma 29, 81031 Aversa, Italy

a r t i c l e i n f o

Article history:

Received 18 February 2011

Received in revised form

16 June 2011

Accepted 17 June 2011Available online 25 August 2011

Keywords:

Atmospheric planetary entry

Non-equilibrium hypersonic flow

Capsule-type vehicle aerodynamics

Planetary exploration

65/$ - see front matter & 2011 Elsevier Ltd. A

016/j.actaastro.2011.06.020

esponding author.

ail addresses: g.pezzella@cira.it (G. Pezzella),

.viviani@unina2.it (A. Viviani).

a b s t r a c t

The paper deals with the aerodynamic analysis of a manned braking system entering

the Mars atmosphere, with the aim to support planetary entry system design studies.

The capsule configuration is an axisymmetric blunt body close to the Apollo capsule.

Several fully three-dimensional Computational Fluid Dynamics analyses have been

performed to assess the flowfield environment around the vehicle to address the

aerodynamic performance of the entry capsule within mission exploration to Mars.

To this end, a wide range of flow conditions including reacting and non-reacting flow,

different angles of attack, and Mach numbers have been investigated and compared.

Moreover, non-equilibrium effects on the flowfield around the capsule have been also

investigated. Results show that real-gas effects, for all the angles of attach considered,

increase both the aerodynamic drag and pitching moment, whereas the lift is only

slighted affected. Finally, comparison of the results highlights that experimental and

CFD aerodynamic findings available for the Apollo capsule in air adequately represent

the static coefficients of the capsule in the Mars atmosphere.

& 2011 Elsevier Ltd. All rights reserved.

1. Introduction

The paper deals with the aerodynamic analysis of aManned braking system (MBS) entering the Mars atmo-sphere, with the aim to support planetary entry systemdesign studies.

The human exploration of Mars will be a complexundertaking. It is an enterprise that will confirm thepotential for humans to leave our home planet and makeour way outward into the cosmos. Although just a smallstep on a cosmic scale, it will be a significant one forhumans, because it will require leaving Earth with verylimited return capability. The commitment to launch is acommitment to several years away from Earth, and thereis a very narrow window within which return is possible.

ll rights reserved.

This is the most radical difference between Mars explora-tion and previous lunar explorations [1].

The paper reports on some aerodynamic analysis of anApollo shaped vehicle performed for flight conditionscompatible for a manned mission entering the Marsatmosphere. With this in mind, those results may be usedto provide numerical data for understanding the require-ments for human exploration of Mars. To this, end aero-dynamic analysis has been made at several levels. Indeed,vehicle aerodynamic assessment has been extensivelyaddressed through engineering-based design approach ashypersonic panel methods. Then, a number of Computa-tional Fluid Dynamics (CFD) simulations of the hypersonicflowfield past the entry capsule have been performed andresults provided in the paper.

Several are the reasons that suggest to get ready Marsmanned exploration. Mars is the most accessible planetbeyond the Earth–Moon system where sustained humanpresence is believed to be possible. The technical objec-tives of Mars exploration should be to understandwhat would be required to sustain a permanent human

G. Pezzella, A. Viviani / Acta Astronautica 69 (2011) 975–986976

presence beyond Earth. Moreover, the scientific objectivesof Mars exploration should be to understand the planetand its history, and therefore to better understand Earth.The human exploration of Mars currently lies at theragged edge of achievability. The necessary technicalcapabilities are either just available or on the horizon.Commitment to the program will both effectively exploitprevious investments and contribute to advances intechnology. Finally, the goals of Mars exploration aregrand; they will motivate our youth, benefit technicaleducation goals, and excite the people and nations ofthe world.

The crew will travel to and from Mars on relativelyfast transits (4–6 months) and with long periods of time(18–20 months: days nominal) on the surface, rather thanalternative approaches which require longer in space andreduced time on the surface [1]. Fig. 1 illustrates a typicaltrajectory designed to the worst-case mission opportunity(2007–2009) of the next two decades; the transit legs areless than 180 days both directions. For easier Marsmission opportunities (for example, 2016–2018), thetransit legs are on the order of 130 days. Shorter transittime reduces the time spent by crew in zero g tothe length of typical of duty for the International SpaceStation [1].

In the paper, however, neither mission architectureneeded to reach Mars from Earth or neighbor Earth space,nor surface exploration have been addressed. Only cap-sule aerodynamic in Mars atmosphere has been focusedin this work as key technology needed to get the realmanned descent through the Mars atmosphere.

To this end, fully three-dimensional CFD analyses, bothEuler and Navier–Stokes, have been performed in order to

Arrive Mars7/1/2014

NominalDeparture3/11/2016

Depart Mars3/11/2016

Earth Launch2/1/2014

Fig. 1. Typical fast-transit inte

address the aerodynamic performance of an Apollo-likecapsule for mission exploration to Mars, considering anentry approach scenario to red planet compliant with thespacecraft released from circular orbit [2,3]. Today theneed for research activities on Mars entry are ever moreapparent, and among the available technologies; capsuleoption is still the safest and cheapest way to get theexploration vehicle on Mars [4,5].

This paper presents an aerodynamic analysis of acapsule vehicle entering the Mars atmosphere, aimed tosupport future Mars manned exploration mission studies.The capsule configuration is an axisymmetric blunt bodyshown in Fig. 2.

The Martian atmosphere has been considered as amixture of 95.7% carbon dioxide, 1.6% argon, and 2.7%nitrogen. The flow has been modeled as a reacting gasmixture of 9 species (Ar, CO2, N2, O2, CO, NO, N, O, and C).The Fluent code together with user defined functions,developed in order to simulate mixtures of gas in thermo-chemical non-equilibrium, has been used for these compu-tations with a non-equilibrium chemical model suitable forMartian atmosphere. Several numerical computations havebeen performed in order to obtain pressure distributionsand other several flowfield features both over and aroundthe entry vehicle for the aerodynamic system designanalyses scopes. For this purpose, a wide range of flowconditions including reacting and non-reacting flow, differ-ent angles of attack, and Mach number have been investi-gated and compared. Moreover, 3-D numerical simulationshave been carried out to investigate the effects of chemicalnon-equilibrium on the vehicle aerodynamics. For codevalidation purpose, the available numerical and experimen-tal data of Mars Pathfinder probe at the entry peak heating

MISSION TIMES

OUTBOUNDSTAYRETURN

150 days619 days110 days

TOTAL MISSION 879 days

γ

Earth Return6/29/2016

rplanetary trajectory [1].

Table 1Freestream conditions of CFD computations.

Mach (dimensionless) Pressure (Pa) Temperature (K) AoA (deg.)

5 1400 560 10

10 1400 560 10

20 1400 560 20

20 1400 560 28

Fig. 2. The manned braking system.

G. Pezzella, A. Viviani / Acta Astronautica 69 (2011) 975–986 977

conditions have been used. The comparison has shown agood agreement between numerical and experimental data.

2. Mars entry braking vehicle

The MBS configuration, under investigation in thiswork, is shown in Fig. 2. It consists of a blunt body closeto an Apollo shaped capsule measuring about 5 m indiameter, with a nose radius of 6.05 m, a sidewall angleof 331, and an overall height of 3.8 m.

Such a system design choice has been addressed inorder to reduce overall development cost, and design risk.In fact, capsule technology is still the safest and thecheapest way to get an exploration crew into orbit andthen its entry to planetary atmosphere as in the case ofMars. Moreover, even if the configuration is essentiallyballistic, the vehicle is able to exhibit lifting capabilitiesby offsetting the Center of Gravity (CoG). Note that, theaerodynamic lift capability is fundamental for rangeextension and maneuverability in the descent and landingphases since lift permits the correction of errors occurringin the guidance, navigation, and control systems, thusattaining the desired landing site in spite of such errors. Inaddition, aerodynamic lift gives desirable advantages inthe form of operational flexibility in the positioning of theline of nodes of the parking orbit and in maximizing thetime available for performing the de-orbit manoeuvre.

3. The Mars manned entry scenario

Generally speaking the MBS design depends on mis-sion flight scenario requirements, which define capsuleentry corridor. Indeed, the entry corridor envelopes all theflyable/admissible entry trajectories whose loading envir-onment is tolerable by the capsule. It is bounded from oneside by the heat flux peak and the maximum deceleration,from the other by the ablator thermal limitations (totalheat load), if present, and the skip angle. The dispersion ofthe trajectory within the entry corridor depends on twomain design parameters that are the entry flight pathangle, and velocity, which are characterized by the

selected planetary approach trajectory. Indeed, the angleand the velocity at entry interface determine the time ofpermanence in the Martian atmosphere. The shallowerthe entry angle, the bigger the flight time and thedispersion due to the atmospheric model error, and hence,the worse the landing accuracy. From the point of view ofapproach strategies, the different values of velocity atentry interface (given the entry angle) will characterizethe MBS design by means of mechanical loads (i.e.pressure and acceleration), thermal loads (i.e. heat fluxpeak and integrated heat load), and landing dispersion.These parameters counterbalance with each other, in thesense that the higher the entry velocity (or the steeper theentry angle), the larger the deceleration during the des-cent path (higher structure solicitations), and the higherthe heat flux peak (higher TPS solicitations). Moreover,the lower the entry velocity (or the shallower the entryangle), the bigger the total heat flux (thicker ablativematerials layer), the longer the atmospheric flight time,hence the higher the landing dispersion (bigger atmo-spheric model errors).

In this paper the flight scenario refers to entry conditionscompatible to a capsule released from Mars Parking Orbitthat the overall expedition system to Mars achieves after thered planet capture through aerobraking maneuvers.

With this in mind, fully three-dimensional CFD simula-tions both for perfect and chemically reacting gas approx-imation have been computed at the freestream conditionslisted in Table 1, and for laminar flow conditions only.Several Mach number and different angles of attack a, havebeen investigated and compared. Note that, for the perfect

G. Pezzella, A. Viviani / Acta Astronautica 69 (2011) 975–986978

gas case, the Mars atmosphere is characterized by a specificheats ratio g (e.g. 1.3755) very close to that of Earth(e.g. g¼1.4). Therefore, it follows that force coefficient arenearly independent of CO2 concentration and are essentiallythe same as those obtained using air.

As shown, also non-equilibrium computation have beenperformed since, as it is well known, one of the mostchallenging problem facing the design of atmospheric entryvehicle is the phenomenon of ‘‘real gas behavior’’.

Indeed, the shock wave produced ahead of the vehicle,when travelling at hypersonic speeds, suddenly elevatesthe temperature of the gas surrounding the vehicle,so that the thermal energy of the gas may be compar-able with the energy associated with a whole range of gasphase chemical processes such as the excitation ofmolecular modes of vibration, the dissociation of atmo-spheric molecules into their atomic forms, the formationof other chemical species through recombination reac-tions, and the ionization of both molecular and atomicspecies [6].

Since the ratio between the specific heats (g) dependson the number of active degrees of freedom of the species,it is evident that as the temperature increases, the valueof g cannot be considered as a constant (perfect gashypothesis). Therefore, the gas mixture has to be consid-ered in thermal and chemical non-equilibrium.

Further, the ‘‘real gas effects’’ play a relevant role inthe thermodynamics of the flow around the vehicle. Forexample, thermodynamic equilibrium is not establishedinstantaneously in the moving gas, but requires a finitetime known as relaxation time. Departure from thermo-dynamic equilibrium can have significant effects onshock wave structure, thus affecting the flowfieldaround the vehicle [7].

Table 2Reactions mechanism and rate parameters.

Reaction Third body (M) A

CO2þM-COþOþM CO2, CO, N2, O2, NO 6

Ar 6

C, N, O 1

COþM-CþOþM CO2, CO, N2, O2, NO 2

Ar 2

C, N, O 3

N2þM-NþNþM CO2, CO, N2, O2, NO 7

Ar 7

C, N, O 3

O2þM-OþOþM CO2, CO, N2, O2, NO 2

Ar 3

C, N, O 3

NOþM-NþOþM CO2, CO, N2, O2, NO 1

Ar 5

C, N, O 5

C2þM-CþCþM All 2

NCOþM-COþNþM All 6

NOþO-NþO2 8

N2þO-NOþN 6

COþO-CþO2 3

CO2þO-COþO2 2

The chemical dissociation of the flow in the shock layercan result in a large density ratio e across the strong bowshock compared with a flow of the same gas where nodissociation take place [6]. Under conditions where dis-sociation exists, the aerodynamics of capsules dependsprimarily on shock density ratio. In fact, the change ofaerodynamic characteristics is the result of change insurface pressure acting on the vehicle forebody [8].

Further, both the shock shape and stand-off distanceare markedly influenced by e. The surface pressures areaffected by a change in shock density ratio, because of thelevel of pressure at the stagnation point (e.g., Cpmax) ischanged:

Cpmax ¼ Cpt2 ¼Pt2�P1

q1¼

Pt2

P1�1

� �2

gM21

ffi2�e ð1Þ

instead of the classical newtonian value of Cpmax¼2,where the density ratio across the bow shock wave, e, inthe hypersonic limit reads

e¼ limM1-1

r1

r2

¼g�1

gþ1ð2Þ

Moreover, the non-dimensional distribution of surfacepressure relative to stagnation point pressure is changedas highlighted by numerical results collected hereinafter.

The sonic line position shifts because of the change in g[8]. Therefore, as static aerodynamic instability is asso-ciated with changing sonic line location, high temperatureeffects result in modifying vehicle hypersonic aerody-namics and aerothermodynamics by means of a veryabrupt change in the trim angle of the capsule [9].

Body stability is a critical requirement for reentry vehicle,because of static instability could lead to catastrophic failure

r (cm3 mol�1 s�1) br Td (K)

.9�1021�1.5 63,275

.9�1020

.4�1022

.3�1020�1.0 1,29,000

.3�1019

.4�1020

.0�1021�1.6 1,13,200

.0�1021

.0�1022

.0�1021�1.5 59,750

.0�1021

.0�1022

.1�1017 0.0 75,500

.0�1015

.0�1015

.0�1021�1.5 59,750

.3�1016�0.5 24,000

.4�1012 0.0 19,450

.4�1017�1.0 38,370

.9�1013�0.18 69,200

.1�1013 0.0 27,800

Fig. 3. The MBS panel mesh.

Fig. 4. Pressure coefficient contours for on MBS surface at a¼01 (left), and at a¼251 (right) for MN¼20.

SIM

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

130

AoA (deg)

Lift

Drag

L/D

140 150 160 170 180

Fig. 5. Lift, drag, and L/D ratio coefficients versus a. Panel methods results.

G. Pezzella, A. Viviani / Acta Astronautica 69 (2011) 975–986 979

Fig. 6. Mars Pathfinder. Mach number contours at trajectory peak

heating conditions. Comparison among perfect gas (upper side) and

equilibrium flow. Axisymmetric computation.

Fig. 7. Mars Pathfinder. Temperature contours at trajectory peak heating

conditions. Comparison among perfect gas (upper side) and equilibrium

flow. Axisymmetric computation.

Fig. 8. Mars Pathfinder. Contours of CO2 and N2 mass fractions at tr

G. Pezzella, A. Viviani / Acta Astronautica 69 (2011) 975–986980

if the thermal shield is not protecting the vehicle any-more. This is the explanation of the relation that existsbetween pitching moment coefficient (CMY), and sonicline location. For instance, the change of CMY is associatedto the motion of the sonic line location on vehicle leeside.

In order to address the real gas effects, the Martianatmosphere has been considered as a reacting gas mixtureof nine species (Ar, CO2, N2, O2, CO, NO, N, O, and C)involved in 49 forward, and backward chemical reactions[10–12]. The reaction mechanism and the related chemicalkinetics, taken into account in the present non-equilibriumCFD computations, are summarized in Table 2, where M isthe reacting partner (third body) that can be any of the ninereacting species. Both reaction mechanism and kinetics aredue to Park et al. [10].

4. Numerical analysis

The aerodynamic analysis of MBS is shown in term oflift (CL), drag (CD), and pitching moment (CMY) coefficients,

ajectory. peak heating conditions. Axisymmetric computation.

Fig. 9. Mars Pathfinder. Comparison of surface pressure to stagnation

pressure ratio between present computation and results of Ref. [13].

G. Pezzella, A. Viviani / Acta Astronautica 69 (2011) 975–986 981

which are calculated according to Eqs. (3) and (4),respectively:

Ci ¼Fi

ð1=2Þr1v21Sref

i¼ L,D ð3Þ

CMj ¼Mj

ð1=2Þr1v21Lref Sref

j¼ Y ð4Þ

The reference parameters that have been chosen for thedefinition of the aerodynamic forces and moment non-dimensional coefficients are the longitudinal referencelength (Lref ¼D¼2Rb), equal to the capsule diameter (e.g.5.0 m), and the reference surface (Sref¼pR2

b¼19.6 m2),that is the maximum cross-section area of the MBS. The

Fig. 10. The computa

Fig. 11. Mach number (left), and static pres

pitching moment is computed from the nose of the capsulevehicle.

The evaluations of the vehicle aerodynamic database(AEDB) have been mainly performed by means of engi-neering tools, while a limited number of accurate CFDcomputations have been carried out in order to verify theattained accuracy, and to focus on some critical designaspects not predictable with simplified tools as, forexample, the real gas effects.

4.1. Engineering-based results

Engineering based aerodynamic and aerothermody-namic analyses have been extensively performed using a

tional domain.

sure contours for MN¼5 and a¼101.

Fig. 13. Static temperature contours for MN¼20 and a¼201. Perfect gas

computation.

G. Pezzella, A. Viviani / Acta Astronautica 69 (2011) 975–986982

3D Panel Methods code developed by CIRA (SIM, SurfaceImpact Method) in the frame of its research activities onpreliminary design of reentry vehicles.

This tool, at high supersonic and hypersonic speeds, isable to accomplish the aerodynamic and aerothermody-namic analyses of a complex reentry vehicle configurationusing simplified approaches as local surface inclinationmethods, and approximate boundary-layer methods,respectively. The SIM typical of hypersonics are New-tonian, Modified Newtonian, and Tangent Cone theories.

In Fig. 3 a typical mesh surface of the MBS, used for theengineering level computations is shown.

MBS aerodynamic results provided by engineering-based analysis cover a ranging from 1301 to 1801. It isworth noting that the AoA is measured from the capsuleapex, as done in the past for Apollo Command Module.

As an example of SIM results, Fig. 4 shows the contoursof pressure coefficient over the capsule surface at a¼01(left) and at a¼251 (right) for MN¼20.

The curves of lift, drag, and aerodynamic efficiency areshown in Fig. 5. It collects MBS aerodynamic coefficients,which represent the preliminary aerodynamics assess-ment of Mars entry capsule.

4.2. Computational fluid dynamics results

Computational fluid dynamics analyses are performedto simulate the flowfield past the entering vehicle toassess MBS aerodynamic performance. Both perfect gas,and reacting gas with finite rate chemistry models (seeTable 2) are used in fully three-dimensional Euler andNavier–Stokes computations.

The CFD analysis of the MBS has been preceded by acode validation phase performed considering the avail-able numerical and experimental data for the MarsPathfinder probe [7,13]. To this end the freestream con-ditions of Mars Pathfinder capsule at trajectory peakheating have been analyzed.

Fig. 12. Mach number (left), and static press

As an example of the results provided by the validationphase, Fig. 6 shows the Mach number contours compar-ison among the perfect gas and the equilibrium flowresults. Fig. 7 reports the same comparison but for thestatic temperature contours. Flowfield streamlines arealso shown in order to highlight the vortex structures,which arise on the capsule leeside.

As one can see, both comparisons between ideal gasand real gas numerical computation underline that realgas effects markedly affects the flowfield around thecapsule, and hence its aerodynamic performance.

The effects of chemical dissociation can be recognizedin Fig. 8.

Finally, Fig. 9 recognizes the comparison of surfacepressure to stagnation pressure ratio between presentcomputation and results of Ref. [13], as evaluated on the

ure contours for MN¼20 and a¼201.

G. Pezzella, A. Viviani / Acta Astronautica 69 (2011) 975–986 983

capsule centerline. As one can see, the comparisonhighlights a good agreement between numerical andexperimental data.

Present CFD computations of MBS have been carriedout on a multiblock structured grid (shown in Fig. 10)generated by means of the commercial tool ICEM-CFD.The grid consists of 62 blocks for an overall number of829,000 cells (half-body) and is tailored for the free-stream conditions summarized in Table 1.

The distribution of surface grid points has been dic-tated by the level of resolution desired in various areas ofthe vehicle such as the stagnation region and the basefillet, according to the computational scopes. A close-upview of the 3-D mesh on the vehicle surface can be seenon the right-hand side of Fig. 10. Grid refinement instrong gradient regions of flowfield has been madethrough a solution adaptive approach.

The preliminary results of CFD simulations performedso far are summarized hereinafter. For example, theflowfield predicted around the MBS at MN¼5, anda¼101 can be appreciated in Fig. 11, where the Mach

Fig. 15. Contours of CO2 and N2 mas

Fig. 14. Static temperature contours for MN¼20 and a¼201. Non-

equilibrium gas computation.

number and static pressure fields are reported both on thecapsule surface, and pitch plane.

The same flowfield features are reported in Fig. 12 forMN¼20, and a¼201 in order to appreciate the effect ofboth the Mach number and the AoA.

As shown, when the MBS flies at MN¼20, and a¼201the bow shock is closer to the capsule and the wake flowregion is wider.

The next comparisons are reported in Figs. 13 and 14where are shown the static temperature contours for bothperfect gas and non-equilibrium gas computations atMN¼20, and a¼201, respectively. Flowfield streamlinesare also reported in order to appreciate the complex flowpattern. The maximum flowfield temperature in the caseof perfect gas is close to about 40,000 K. This means thatthermo-chemical processes occur behind the bow shockas species show vibrational excitation and dissociation.

s fractions on MBS pitch plane.

Fig. 16. The static temperature field on the capsule symmetry plane and

on two flowfield cross. sections at MN¼20 and a¼201. Static pressure

contour on capsule forebody. Perfect gas computation.

G. Pezzella, A. Viviani / Acta Astronautica 69 (2011) 975–986984

This is clearly shown in Fig. 14 since the maximumflowfield temperature reaches only about 8000 K.

The contour fields of carbon dioxide and nitrogendioxide, taking into account for the flow species dissocia-tion, which arises at MN¼20, and a¼201 are shown forthe capsule pitch plane in Fig. 15.

Fig. 16 shows the static temperature contours oncapsule symmetry plane and two flowfield cross sectionstogether with the static pressure contours on capsulesurface at MN¼20, and a¼201, considering the Marsatmosphere as a perfect gas. The MBS bow shock struc-ture around the descent vehicle can be appreciated con-

Fig. 17. Mach number contours for MBS bow shock and on two flowfield cro

forebody. Perfect gas computation.

CL

0.0

0.1

0.2

0.3

0.4

0.5

0.6

130AoA (deg)

SIMCrowder & MooteCFD M = 5 PGCFD M = 20 PGCFD (Air) M = 19 RGCFD M = 10 RGCFD M = 20 RG

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

140 150 160 170 180

Fig. 18. Lift and drag coefficients versus a. Comparison betwe

sidering contour fields of static temperature and Machnumber reported in Figs. 16 and 17, respectively. In thelatter figure the shock wave that envelopes the capsulecan be clearly recognized through the iso-Mach surfacetogether with the Mach number contours reported on adownstream cross plane. Moreover, in Fig. 17 a number ofstreamtraces are also shown in order to highlight therecirculating flowfield region at the capsule leeside. Notethat, at capsule leeward take place two counter rotatingvortices that are clearly shown also in Figs. 13–15. Thecurves of lift, drag, aerodynamic efficiency, and of pitchingmoment coefficients are shown in Figs. 18 and 19.

ss sections at MN¼20 and a¼201. Static pressure contour on capsule

CD

130AoA (deg)

SIMCrowder & MooteCFD M = 5 PGCFD M = 20 PGCFD (Air) M = 19 RGCFD M = 10 RGCFD M = 20 RG

140 150 160 170 180

en panel methods, CFD results and experimental data.

L/D

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

130AoA (deg)

SIMCrowder & MooteCFD M = 5 PGCFD M = 20 PGCFD (Air) M = 19 RGCFD M = 10 RGCFD M = 20 RG

CMy (pole @ nose), Lref = 5 m

0.00

0.02

0.04

0.06

0.08

0.10

0.12

130AoA (deg)

SIM

CFD M=5 PG

CFD M=10 RGCFD M=20 RG

SIMCrowder & MooteCFD M = 5 PGCFD M = 20 PGCFD (Air) M = 19 RGCFD M = 10 RGCFD M = 20 RG

140 150 160 170 180 140 150 160 170 180

Fig. 19. L/D ratio and pitching moment coefficients versus a. Comparison between panel methods, CFD results and experimental data.

AoA = 0 deg

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-1.2s/Rb

Pw/P

t2

Eq.(5)

CFD Perfect gas

Ref. 15

AoA = 10 deg

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-1.2s/Rb

Pw/P

t2

Eq.(5)

CFD Perfect gas

-0.8 -0.4 0.0 0.4 0.8 1.2 -0.8 -0.4 0.0 0.4 0.8 1.2

Fig. 20. Pressure distribution in the capsule pitch plane for two AoAs (i.e. 01 and 101). Comparison among MN, present CFD results and WT data [15].

G. Pezzella, A. Viviani / Acta Astronautica 69 (2011) 975–986 985

In particular the capsule’s thermal shield nose is assumedas pole for pitching moment calculation (i.e. 0,0,0).

Both those figures collect MBS aerodynamic coeffi-cients compared with some experimental data, reportedin order to highlight accuracy of engineering-basedresults. As one can see, experimental and numerical datacompare very well, thus confirming that engineering-based estimations represent a reliable preliminary aero-dynamics of Mars entry capsule. In those figures are alsoreported the CFD results for MN¼20, and a¼201 obtainedfor both perfect and reacting gas approximations. Bycomparing those numerical results it follows that realgas effects increase both the aerodynamic drag andpitching moment coefficient, whereas the lift is onlyslighted influenced.

Note that, Figs. 18 and 19 report the Crowder–Moote andCFD results (CFD air M¼19 RG), respectively, available forthe Apollo capsule in air since, as said before, the staticcoefficients available for the air adequately represent the

static coefficients for an aerodynamic braking vehicle in theMars atmosphere [14].

The next set of comparisons, among experimentaland numerical results, are reported in Figs. 20 and 21,respectively.

It displays the pressure ratio Pw/Pt2 comparison, on thecapsule pitch plane forward thermal shield, among presentCFD results, and wind tunnel (WT) experimental dataprovided in Ref. [15], for four AoA (i.e. 01, 101, 201, and 281).

Experimental data, available only for a¼01 and 201,refers to a test performed in the Tunnel C at ArnoldEngineering and Development center (AEDC) at free-stream Mach number of 10.18, and a Reynolds numberRND of 1.1�106 [15]. As further comparison note that thepressure distribution (Pw) on the capsule centerline canbe evaluated considering that MN theory states that:

Pw

Pt2¼ sin2 yþ

P1Pt2

cos2 y ð5Þ

g

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-1.2s/Rb

Pw/P

t2

Eq.(5) CFD Perfect gas

Ref. 15

AoA = 28 deg

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-1.2s/Rb

Pw/P

t2

Eq.(5)

CFD Perfect gas

-0.8 -0.4 0.0 0.4 0.8 1.2 -0.8 -0.4 0.0 0.4 0.8 1.2

Fig. 21. Pressure distribution in the capsule pitch plane for two AoAs (i.e. 201 and 281). Comparison among MN, present CFD results and WT data [15].

G. Pezzella, A. Viviani / Acta Astronautica 69 (2011) 975–986986

As one can see, numerical, experimental, and theoreticaldata compare well for all the AoAs, thus confirming reliabilityof the CFD simulations. Finally, it is worth noting that thedifferences existing between numerical and MN pressures, atthe capsule corner (i.e. s/Rb¼0.965), are due to the vehicleforebody, which is a truncated spherical cap. This means thatthe streamwise velocity gradients must be relatively large(i.e. above the value needed for a full hemisphere) in order toproduce sonic flow at capsule corner [15].

5. Concluding remarks

The paper deals with the aerodynamic analysis of amanned braking system for Mars exploration mission. Tothis end, a number of fully 3D Navier–Stokes, and EulerCFD computations of the hypersonic flowfield past anApollo-shaped MBS has been performed in the frameworkof a loading environment for Mars entry conditions.

These evaluations have been aimed to carry out only apreliminary AEDB for the MBS configuration, in compliancewith the Phase-A design level. The range between Mach 2,and Mach 20 has been analyzed, with the goal to provideaerodynamic database for the flight mechanics analyses.

The aerodynamic coefficients have been provided as afunction of Mach number and angle of attack (zero sideslipangle) according to the ‘‘space-based’’ design approach.

In the present analysis only continuum regime (hyper-sonic speed ranges) with the flow modeled both as perfectgas and reacting gas mixture has been studied.

Engineering-based analysis based on hypersonic panelmethods have been extensively used in order to rapidlydevelop a very preliminary capsule aerodynamic database.

Finally, numerical results show that real gas effectsincrease both the aerodynamic drag and pitching momentcoefficient, whereas the lift is only slighted influenced.Moreover, several results comparison highlight thatexperimental and CFD aerodynamic findings availablefor the Apollo capsule in air adequately represent thestatic coefficients of the MBS in the Mars atmosphere.

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