Aerodynamic analysis of a Mars exploration manned capsule

Acta Astronautica 69 (2011) 975–986

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Aerodynamic analysis of a Mars exploration manned capsule Giuseppe Pezzella a,n, Antonio Viviani b a b

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

a r t i c l e i n f o

abstract

Article history: Received 18 February 2011 Received in revised form 16 June 2011 Accepted 17 June 2011 Available online 25 August 2011

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.

Keywords: Atmospheric planetary entry Non-equilibrium hypersonic flow Capsule-type vehicle aerodynamics Planetary exploration

1. Introduction The paper deals with the aerodynamic analysis of a Manned braking system (MBS) entering the Mars atmosphere, with the aim to support planetary entry system design studies. The human exploration of Mars will be a complex undertaking. It is an enterprise that will confirm the potential for humans to leave our home planet and make our way outward into the cosmos. Although just a small step on a cosmic scale, it will be a significant one for humans, because it will require leaving Earth with very limited return capability. The commitment to launch is a commitment to several years away from Earth, and there is a very narrow window within which return is possible.

n

Corresponding author. E-mail addresses: [email protected] (G. Pezzella), [email protected] (A. Viviani). 0094-5765/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.actaastro.2011.06.020

This is the most radical difference between Mars exploration and previous lunar explorations [1]. The paper reports on some aerodynamic analysis of an Apollo shaped vehicle performed for flight conditions compatible for a manned mission entering the Mars atmosphere. With this in mind, those results may be used to provide numerical data for understanding the requirements for human exploration of Mars. To this, end aerodynamic analysis has been made at several levels. Indeed, vehicle aerodynamic assessment has been extensively addressed through engineering-based design approach as hypersonic panel methods. Then, a number of Computational Fluid Dynamics (CFD) simulations of the hypersonic flowfield past the entry capsule have been performed and results provided in the paper. Several are the reasons that suggest to get ready Mars manned exploration. Mars is the most accessible planet beyond the Earth–Moon system where sustained human presence is believed to be possible. The technical objectives of Mars exploration should be to understand what would be required to sustain a permanent human

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presence beyond Earth. Moreover, the scientific objectives of Mars exploration should be to understand the planet and its history, and therefore to better understand Earth. The human exploration of Mars currently lies at the ragged edge of achievability. The necessary technical capabilities are either just available or on the horizon. Commitment to the program will both effectively exploit previous investments and contribute to advances in technology. Finally, the goals of Mars exploration are grand; they will motivate our youth, benefit technical education goals, and excite the people and nations of the world. The crew will travel to and from Mars on relatively fast transits (4–6 months) and with long periods of time (18–20 months: days nominal) on the surface, rather than alternative approaches which require longer in space and reduced time on the surface [1]. Fig. 1 illustrates a typical trajectory designed to the worst-case mission opportunity (2007–2009) of the next two decades; the transit legs are less than 180 days both directions. For easier Mars mission opportunities (for example, 2016–2018), the transit legs are on the order of 130 days. Shorter transit time reduces the time spent by crew in zero g to the length of typical of duty for the International Space Station [1]. In the paper, however, neither mission architecture needed to reach Mars from Earth or neighbor Earth space, nor surface exploration have been addressed. Only capsule aerodynamic in Mars atmosphere has been focused in this work as key technology needed to get the real manned descent through the Mars atmosphere. To this end, fully three-dimensional CFD analyses, both Euler and Navier–Stokes, have been performed in order to

address the aerodynamic performance of an Apollo-like capsule for mission exploration to Mars, considering an entry approach scenario to red planet compliant with the spacecraft released from circular orbit [2,3]. Today the need for research activities on Mars entry are ever more apparent, and among the available technologies; capsule option is still the safest and cheapest way to get the exploration vehicle on Mars [4,5]. This paper presents an aerodynamic analysis of a capsule vehicle entering the Mars atmosphere, aimed to support future Mars manned exploration mission studies. The capsule configuration is an axisymmetric blunt body shown in Fig. 2. The Martian atmosphere has been considered as a mixture of 95.7% carbon dioxide, 1.6% argon, and 2.7% nitrogen. The flow has been modeled as a reacting gas mixture 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 thermochemical non-equilibrium, has been used for these computations with a non-equilibrium chemical model suitable for Martian atmosphere. Several numerical computations have been performed in order to obtain pressure distributions and other several flowfield features both over and around the entry vehicle for the aerodynamic system design analyses scopes. For this purpose, a wide range of flow conditions including reacting and non-reacting flow, different angles of attack, and Mach number have been investigated and compared. Moreover, 3-D numerical simulations have been carried out to investigate the effects of chemical non-equilibrium on the vehicle aerodynamics. For code validation purpose, the available numerical and experimental data of Mars Pathfinder probe at the entry peak heating

MISSION TIMES Earth Launch 2/1/2014 Depart Mars 3/11/2016

OUTBOUND

150 days

STAY

619 days

RETURN

110 days

TOTAL MISSION

879 days

γ

Nominal Departure 3/11/2016

Earth Return 6/29/2016

Arrive Mars 7/1/2014 Fig. 1. Typical fast-transit interplanetary trajectory [1].

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Fig. 2. The manned braking system.

conditions have been used. The comparison has shown a good agreement between numerical and experimental data. 2. Mars entry braking vehicle The MBS configuration, under investigation in this work, is shown in Fig. 2. It consists of a blunt body close to an Apollo shaped capsule measuring about 5 m in diameter, with a nose radius of 6.05 m, a sidewall angle of 331, and an overall height of 3.8 m. Such a system design choice has been addressed in order to reduce overall development cost, and design risk. In fact, capsule technology is still the safest and the cheapest way to get an exploration crew into orbit and then its entry to planetary atmosphere as in the case of Mars. Moreover, even if the configuration is essentially ballistic, the vehicle is able to exhibit lifting capabilities by offsetting the Center of Gravity (CoG). Note that, the aerodynamic lift capability is fundamental for range extension and maneuverability in the descent and landing phases since lift permits the correction of errors occurring in the guidance, navigation, and control systems, thus attaining the desired landing site in spite of such errors. In addition, aerodynamic lift gives desirable advantages in the form of operational flexibility in the positioning of the line of nodes of the parking orbit and in maximizing the time available for performing the de-orbit manoeuvre. 3. The Mars manned entry scenario Generally speaking the MBS design depends on mission flight scenario requirements, which define capsule entry corridor. Indeed, the entry corridor envelopes all the flyable/admissible entry trajectories whose loading environment is tolerable by the capsule. It is bounded from one side by the heat flux peak and the maximum deceleration, from the other by the ablator thermal limitations (total heat load), if present, and the skip angle. The dispersion of the trajectory within the entry corridor depends on two main design parameters that are the entry flight path angle, and velocity, which are characterized by the

Table 1 Freestream conditions of CFD computations. Mach (dimensionless) Pressure (Pa) Temperature (K) AoA (deg.) 5 10 20 20

1400 1400 1400 1400

560 560 560 560

10 10 20 28

selected planetary approach trajectory. Indeed, the angle and the velocity at entry interface determine the time of permanence in the Martian atmosphere. The shallower the entry angle, the bigger the flight time and the dispersion due to the atmospheric model error, and hence, the worse the landing accuracy. From the point of view of approach strategies, the different values of velocity at entry interface (given the entry angle) will characterize the MBS design by means of mechanical loads (i.e. pressure and acceleration), thermal loads (i.e. heat flux peak and integrated heat load), and landing dispersion. These parameters counterbalance with each other, in the sense that the higher the entry velocity (or the steeper the entry angle), the larger the deceleration during the descent path (higher structure solicitations), and the higher the heat flux peak (higher TPS solicitations). Moreover, the lower the entry velocity (or the shallower the entry angle), the bigger the total heat flux (thicker ablative materials layer), the longer the atmospheric flight time, hence the higher the landing dispersion (bigger atmospheric model errors). In this paper the flight scenario refers to entry conditions compatible to a capsule released from Mars Parking Orbit that the overall expedition system to Mars achieves after the red planet capture through aerobraking maneuvers. With this in mind, fully three-dimensional CFD simulations both for perfect and chemically reacting gas approximation have been computed at the freestream conditions listed in Table 1, and for laminar flow conditions only. Several Mach number and different angles of attack a, have been investigated and compared. Note that, for the perfect

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gas case, the Mars atmosphere is characterized by a specific heats ratio g (e.g. 1.3755) very close to that of Earth (e.g. g ¼1.4). Therefore, it follows that force coefficient are nearly independent of CO2 concentration and are essentially the same as those obtained using air. As shown, also non-equilibrium computation have been performed since, as it is well known, one of the most challenging problem facing the design of atmospheric entry vehicle is the phenomenon of ‘‘real gas behavior’’. Indeed, the shock wave produced ahead of the vehicle, when travelling at hypersonic speeds, suddenly elevates the temperature of the gas surrounding the vehicle, so that the thermal energy of the gas may be comparable with the energy associated with a whole range of gas phase chemical processes such as the excitation of molecular modes of vibration, the dissociation of atmospheric molecules into their atomic forms, the formation of other chemical species through recombination reactions, and the ionization of both molecular and atomic species [6]. Since the ratio between the specific heats (g) depends on the number of active degrees of freedom of the species, it is evident that as the temperature increases, the value of g cannot be considered as a constant (perfect gas hypothesis). Therefore, the gas mixture has to be considered in thermal and chemical non-equilibrium. Further, the ‘‘real gas effects’’ play a relevant role in the thermodynamics of the flow around the vehicle. For example, thermodynamic equilibrium is not established instantaneously in the moving gas, but requires a finite time known as relaxation time. Departure from thermodynamic equilibrium can have significant effects on shock wave structure, thus affecting the flowfield around the vehicle [7].

The chemical dissociation of the flow in the shock layer can result in a large density ratio e across the strong bow shock compared with a flow of the same gas where no dissociation take place [6]. Under conditions where dissociation exists, the aerodynamics of capsules depends primarily on shock density ratio. In fact, the change of aerodynamic characteristics is the result of change in surface pressure acting on the vehicle forebody [8]. Further, both the shock shape and stand-off distance are markedly influenced by e. The surface pressures are affected by a change in shock density ratio, because of the level of pressure at the stagnation point (e.g., Cpmax) is changed:   Pt2 P1 Pt2 2 Cpmax ¼ Cpt2 ¼ ¼ 1 ffi2e ð1Þ 2 q1 P1 gM1 instead of the classical newtonian value of Cpmax ¼2, where the density ratio across the bow shock wave, e, in the hypersonic limit reads

e ¼ lim

M1 -1

r1 g1 ¼ r2 g þ 1

ð2Þ

Moreover, the non-dimensional distribution of surface pressure relative to stagnation point pressure is changed as highlighted by numerical results collected hereinafter. The sonic line position shifts because of the change in g [8]. Therefore, as static aerodynamic instability is associated with changing sonic line location, high temperature effects result in modifying vehicle hypersonic aerodynamics and aerothermodynamics by means of a very abrupt 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

Table 2 Reactions mechanism and rate parameters. Reaction

Third body (M)

Ar (cm3 mol  1 s  1)

br

Td (K)

21

CO2 þ M-CO þOþ M

CO2, CO, N2, O2, NO Ar C, N, O

6.9  10 6.9  1020 1.4  1022

 1.5

63,275

CO þ M-Cþ Oþ M

CO2, CO, N2, O2, NO Ar C, N, O

2.3  1020 2.3  1019 3.4  1020

 1.0

1,29,000

N2 þ M-Nþ N þM

CO2, CO, N2, O2, NO Ar C, N, O

7.0  1021 7.0  1021 3.0  1022

 1.6

1,13,200

O2 þM-Oþ Oþ M

CO2, CO, N2, O2, NO Ar C, N, O

2.0  1021 3.0  1021 3.0  1022

 1.5

59,750

NO þ M-N þ OþM

CO2, CO, N2, O2, NO Ar C, N, O

1.1  1017 5.0  1015 5.0  1015

0.0

75,500

C2 þ M-C þC þ M NCO þM-CO þN þ M NO þ O-Nþ O2 N2 þ O-NO þN CO þ O-C þO2

All All

2.0  1021 6.3  1016 8.4  1012 6.4  1017 3.9  1013

 1.5  0.5 0.0  1.0  0.18

59,750 24,000 19,450 38,370 69,200

2.1  1013

0.0

27,800

CO2 þ O-CO þ O2

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Fig. 3. The MBS panel mesh.

Fig. 4. Pressure coefficient contours for on MBS surface at a ¼01 (left), and at a ¼251 (right) for MN ¼ 20.

SIM 1.8 1.6 1.4 1.2

Lift

1.0

Drag

0.8

L/D

0.6 0.4 0.2 0.0 130

140

160

150

170

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

180

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if the thermal shield is not protecting the vehicle anymore. This is the explanation of the relation that exists between pitching moment coefficient (CMY), and sonic line location. For instance, the change of CMY is associated to the motion of the sonic line location on vehicle leeside. In order to address the real gas effects, the Martian atmosphere has been considered as a reacting gas mixture of 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 chemical kinetics, taken into account in the present non-equilibrium CFD computations, are summarized in Table 2, where M is the reacting partner (third body) that can be any of the nine reacting species. Both reaction mechanism and kinetics are due to Park et al. [10].

4. Numerical analysis 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.

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

Fig. 9. Mars Pathfinder. Comparison of surface pressure to stagnation pressure ratio between present computation and results of Ref. [13].

Fig. 8. Mars Pathfinder. Contours of CO2 and N2 mass fractions at trajectory. peak heating conditions. Axisymmetric computation.

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which are calculated according to Eqs. (3) and (4), respectively: Ci ¼

Fi ð1=2Þr1 v21 Sref

CMj ¼

i ¼ L,D

Mj ð1=2Þr1 v21 Lref Sref

ð3Þ

j¼Y

ð4Þ

The reference parameters that have been chosen for the definition of the aerodynamic forces and moment nondimensional coefficients are the longitudinal reference length (Lref ¼D¼2Rb), equal to the capsule diameter (e.g. 5.0 m), and the reference surface (Sref ¼ pR2b ¼ 19.6 m2), that is the maximum cross-section area of the MBS. The

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pitching moment is computed from the nose of the capsule vehicle. The evaluations of the vehicle aerodynamic database (AEDB) have been mainly performed by means of engineering tools, while a limited number of accurate CFD computations have been carried out in order to verify the attained accuracy, and to focus on some critical design aspects not predictable with simplified tools as, for example, the real gas effects. 4.1. Engineering-based results Engineering based aerodynamic and aerothermodynamic analyses have been extensively performed using a

Fig. 10. The computational domain.

Fig. 11. Mach number (left), and static pressure contours for MN ¼ 5 and a ¼101.

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3D Panel Methods code developed by CIRA (SIM, Surface Impact Method) in the frame of its research activities on preliminary design of reentry vehicles. This tool, at high supersonic and hypersonic speeds, is able to accomplish the aerodynamic and aerothermodynamic analyses of a complex reentry vehicle configuration using simplified approaches as local surface inclination methods, and approximate boundary-layer methods, respectively. The SIM typical of hypersonics are Newtonian, Modified Newtonian, and Tangent Cone theories. In Fig. 3 a typical mesh surface of the MBS, used for the engineering level computations is shown. MBS aerodynamic results provided by engineeringbased analysis cover a ranging from 1301 to 1801. It is worth noting that the AoA is measured from the capsule apex, as done in the past for Apollo Command Module. As an example of SIM results, Fig. 4 shows the contours of pressure coefficient over the capsule surface at a ¼ 01 (left) and at a ¼ 251 (right) for MN ¼20. The curves of lift, drag, and aerodynamic efficiency are shown in Fig. 5. It collects MBS aerodynamic coefficients, which represent the preliminary aerodynamics assessment of Mars entry capsule.

As an example of the results provided by the validation phase, Fig. 6 shows the Mach number contours comparison among the perfect gas and the equilibrium flow results. Fig. 7 reports the same comparison but for the static temperature contours. Flowfield streamlines are also shown in order to highlight the vortex structures, which arise on the capsule leeside. As one can see, both comparisons between ideal gas and real gas numerical computation underline that real gas effects markedly affects the flowfield around the capsule, and hence its aerodynamic performance. The effects of chemical dissociation can be recognized in Fig. 8. Finally, Fig. 9 recognizes the comparison of surface pressure to stagnation pressure ratio between present computation and results of Ref. [13], as evaluated on the

4.2. Computational fluid dynamics results Computational fluid dynamics analyses are performed to simulate the flowfield past the entering vehicle to assess MBS aerodynamic performance. Both perfect gas, and reacting gas with finite rate chemistry models (see Table 2) are used in fully three-dimensional Euler and Navier–Stokes computations. The CFD analysis of the MBS has been preceded by a code validation phase performed considering the available numerical and experimental data for the Mars Pathfinder probe [7,13]. To this end the freestream conditions of Mars Pathfinder capsule at trajectory peak heating have been analyzed.

Fig. 13. Static temperature contours for MN ¼ 20 and a ¼ 201. Perfect gas computation.

Fig. 12. Mach number (left), and static pressure contours for MN ¼ 20 and a ¼201.

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capsule centerline. As one can see, the comparison highlights a good agreement between numerical and experimental data. Present CFD computations of MBS have been carried out 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 of 829,000 cells (half-body) and is tailored for the freestream conditions summarized in Table 1. The distribution of surface grid points has been dictated by the level of resolution desired in various areas of the vehicle such as the stagnation region and the base fillet, according to the computational scopes. A close-up view of the 3-D mesh on the vehicle surface can be seen on the right-hand side of Fig. 10. Grid refinement in strong gradient regions of flowfield has been made through a solution adaptive approach. The preliminary results of CFD simulations performed so far are summarized hereinafter. For example, the flowfield predicted around the MBS at MN ¼ 5, and a ¼101 can be appreciated in Fig. 11, where the Mach

Fig. 14. Static temperature contours for MN ¼ 20 and a ¼ 201. Nonequilibrium gas computation.

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number and static pressure fields are reported both on the capsule surface, and pitch plane. The same flowfield features are reported in Fig. 12 for MN ¼ 20, and a ¼ 201 in order to appreciate the effect of both the Mach number and the AoA. As shown, when the MBS flies at MN ¼20, and a ¼201 the bow shock is closer to the capsule and the wake flow region is wider. The next comparisons are reported in Figs. 13 and 14 where are shown the static temperature contours for both perfect gas and non-equilibrium gas computations at MN ¼ 20, and a ¼ 201, respectively. Flowfield streamlines are also reported in order to appreciate the complex flow pattern. The maximum flowfield temperature in the case of perfect gas is close to about 40,000 K. This means that thermo-chemical processes occur behind the bow shock as species show vibrational excitation and dissociation.

Fig. 16. The static temperature field on the capsule symmetry plane and on two flowfield cross. sections at MN ¼ 20 and a ¼ 201. Static pressure contour on capsule forebody. Perfect gas computation.

Fig. 15. Contours of CO2 and N2 mass fractions on MBS pitch plane.

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This is clearly shown in Fig. 14 since the maximum flowfield temperature reaches only about 8000 K. The contour fields of carbon dioxide and nitrogen dioxide, taking into account for the flow species dissociation, which arises at MN ¼20, and a ¼201 are shown for the capsule pitch plane in Fig. 15. Fig. 16 shows the static temperature contours on capsule symmetry plane and two flowfield cross sections together with the static pressure contours on capsule surface at MN ¼20, and a ¼201, considering the Mars atmosphere as a perfect gas. The MBS bow shock structure around the descent vehicle can be appreciated con-

sidering contour fields of static temperature and Mach number reported in Figs. 16 and 17, respectively. In the latter figure the shock wave that envelopes the capsule can be clearly recognized through the iso-Mach surface together with the Mach number contours reported on a downstream cross plane. Moreover, in Fig. 17 a number of streamtraces are also shown in order to highlight the recirculating flowfield region at the capsule leeside. Note that, at capsule leeward take place two counter rotating vortices that are clearly shown also in Figs. 13–15. The curves of lift, drag, aerodynamic efficiency, and of pitching moment coefficients are shown in Figs. 18 and 19.

Fig. 17. Mach number contours for MBS bow shock and on two flowfield cross sections at MN ¼20 and a ¼ 201. Static pressure contour on capsule forebody. Perfect gas computation.

CL

CD

1.8

0.6

1.6 0.5

1.4

0.4

1.2 1.0

0.3 0.2 0.1 0.0 130

0.8

SIM Crowder & Moote CFD M = 5 PG CFD M = 20 PG CFD (Air) M = 19 RG CFD M = 10 RG CFD M = 20 RG

140

150 160 AoA (deg)

SIM Crowder & Moote CFD M = 5 PG CFD M = 20 PG CFD (Air) M = 19 RG CFD M = 10 RG CFD M = 20 RG

0.6 0.4 0.2 170

180

0.0 130

140

150 160 AoA (deg)

170

Fig. 18. Lift and drag coefficients versus a. Comparison between panel methods, CFD results and experimental data.

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L/D SIM Crowder & Moote CFD M = 5 PG CFD M = 20 PG CFD (Air) M = 19 RG CFD M = 10 RG CFD M = 20 RG

0.7 0.6 0.5

CMy (pole @ nose), Lref = 5 m

0.12

0.8

985

0.10 0.08 0.06

0.4 0.3

0.04

0.2 0.02

0.1 0.0 130

140

150 160 AoA (deg)

170

180

0.00 130

SIM SIM Crowder & Moote CFD M = 5 PG CFD M=5 PG CFD M = 20 PG CFD (Air) M = 19 RG CFD CFD M=10 M = 10RG RG CFD M=20 M = 20RG RG

140

170

150 160 AoA (deg)

180

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

AoA = 10 deg 1.2

1.0

1.0

0.8

0.8 Pw/Pt2

Pw/Pt2

AoA = 0 deg 1.2

0.6 0.4

0.6 0.4

Eq.(5)

0.2

0.2

CFD Perfect gas

Eq.(5)

Ref. 15

0.0 -1.2

-0.8

-0.4

0.0 s/Rb

CFD Perfect gas

0.4

0.8

1.2

0.0 -1.2

-0.8

-0.4

0.0 s/Rb

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].

In particular the capsule’s thermal shield nose is assumed as pole for pitching moment calculation (i.e. 0,0,0). Both those figures collect MBS aerodynamic coefficients compared with some experimental data, reported in order to highlight accuracy of engineering-based results. As one can see, experimental and numerical data compare very well, thus confirming that engineeringbased estimations represent a reliable preliminary aerodynamics of Mars entry capsule. In those figures are also reported the CFD results for MN ¼ 20, and a ¼201 obtained for both perfect and reacting gas approximations. By comparing those numerical results it follows that real gas effects increase both the aerodynamic drag and pitching moment coefficient, whereas the lift is only slighted influenced. Note that, Figs. 18 and 19 report the Crowder–Moote and CFD results (CFD air M¼19 RG), respectively, available for the Apollo capsule in air since, as said before, the static coefficients available for the air adequately represent the

static coefficients for an aerodynamic braking vehicle in the Mars atmosphere [14]. The next set of comparisons, among experimental and numerical results, are reported in Figs. 20 and 21, respectively. It displays the pressure ratio Pw/Pt2 comparison, on the capsule pitch plane forward thermal shield, among present CFD results, and wind tunnel (WT) experimental data provided in Ref. [15], for four AoA (i.e. 01, 101, 201, and 281). Experimental data, available only for a ¼01 and 201, refers to a test performed in the Tunnel C at Arnold Engineering and Development center (AEDC) at freestream Mach number of 10.18, and a Reynolds number RND of 1.1  106 [15]. As further comparison note that the pressure distribution (Pw) on the capsule centerline can be evaluated considering that MN theory states that: Pw P1 ¼ sin2 y þ cos2 y Pt2 Pt2

ð5Þ

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AoA = 28 deg 1.2

1.0

1.0

0.8

0.8 Pw/Pt2

Pw/Pt2

g 1.2

0.6

0.6 0.4

0.4 Eq.(5)

0.2

Eq.(5)

0.2

CFD Perfect gas

CFD Perfect gas

Ref. 15

0.0 -1.2

-0.8

-0.4

0.0 s/Rb

0.4

0.8

1.2

0.0 -1.2

-0.8

-0.4

0.0 s/Rb

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].

As one can see, numerical, experimental, and theoretical data compare well for all the AoAs, thus confirming reliability of the CFD simulations. Finally, it is worth noting that the differences existing between numerical and MN pressures, at the capsule corner (i.e. s/Rb ¼ 0.965), are due to the vehicle forebody, which is a truncated spherical cap. This means that the streamwise velocity gradients must be relatively large (i.e. above the value needed for a full hemisphere) in order to produce sonic flow at capsule corner [15].

5. Concluding remarks The paper deals with the aerodynamic analysis of a manned braking system for Mars exploration mission. To this end, a number of fully 3D Navier–Stokes, and Euler CFD computations of the hypersonic flowfield past an Apollo-shaped MBS has been performed in the framework of a loading environment for Mars entry conditions. These evaluations have been aimed to carry out only a preliminary AEDB for the MBS configuration, in compliance with the Phase-A design level. The range between Mach 2, and Mach 20 has been analyzed, with the goal to provide aerodynamic database for the flight mechanics analyses. The aerodynamic coefficients have been provided as a function of Mach number and angle of attack (zero sideslip angle) according to the ‘‘space-based’’ design approach. In the present analysis only continuum regime (hypersonic speed ranges) with the flow modeled both as perfect gas and reacting gas mixture has been studied. Engineering-based analysis based on hypersonic panel methods have been extensively used in order to rapidly develop a very preliminary capsule aerodynamic database. Finally, numerical results show that real gas effects increase both the aerodynamic drag and pitching moment coefficient, whereas the lift is only slighted influenced. Moreover, several results comparison highlight that experimental and CFD aerodynamic findings available for the Apollo capsule in air adequately represent the static coefficients of the MBS in the Mars atmosphere.

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