Fluid Dynamics Analysis of a Space Vehicle Entering the Mars Atmosphere

This paper reports the results of design analyses of two Manned Braking Systems (MBS) entering the Mars atmosphere, with the aim of supporting design studies of a planetary entry system. Two lifting body configurations with rounded edge delta-like cross section have been analyzed. The preliminary aerodynamic and aerothermodynamic analyses have considered flight conditions compatible with a manned mission entering the Mars atmosphere. However, neither the mission architecture needed to reach Mars from Earth or neighbour Earth space, nor surface exploration have been addressed. All the design analyses have been performed at several levels. Indeed, vehicle aerodynamic assessment has been extensively addressed through simplified design approach as, e.g., hypersonic panel methods (HPM); then, a number of fully three-dimensional computational fluid dynamics (CFD) simulations, both with Euler and Navier-Stokes approximations, of the hypersonic flowfield past the entry vehicle have been performed. The results herein provided have been obtained for a Mars entry scenario compliant with an approach to the red planet both by direct planetary entry and entry after aerobraking (Polishchuk et al., 2006) (Viviani and Pezzella, 2009). These results may be used to provide numerical data for understanding requirements for the human exploration of Mars.


Introduction
This paper reports the results of design analyses of two Manned Braking Systems (MBS) entering the Mars atmosphere, with the aim of supporting design studies of a planetary entry system.Two lifting body configurations with rounded edge delta-like cross section have been analyzed.The preliminary aerodynamic and aerothermodynamic analyses have considered flight conditions compatible with a manned mission entering the Mars atmosphere.However, neither the mission architecture needed to reach Mars from Earth or neighbour Earth space, nor surface exploration have been addressed.All the design analyses have been performed at several levels.Indeed, vehicle aerodynamic assessment has been extensively addressed through simplified design approach as, e.g., hypersonic panel methods (HPM); then, a number of fully three-dimensional computational fluid dynamics (CFD) simulations, both with Euler and Navier-Stokes approximations, of the hypersonic flowfield past the entry vehicle have been performed.The results herein provided have been obtained for a Mars entry scenario compliant with an approach to the red planet both by direct planetary entry and entry after aerobraking (Polishchuk et al., 2006) (Viviani and Pezzella, 2009).These results may be used to provide numerical data for understanding requirements for the human exploration of Mars.

Computational flowfield analysis
CFD analyses have been performed to assess the aerothermal environment that the MBS experiments during descent, thus evaluating several surface loading distributions (e.g., pressure and heat flux).To this aim, several fully three-dimensional numerical computations, both for perfect and chemically reacting gas approximation, have been performed.The vehicle configurations, under investigation in this work, are shown in Fig. 1 These lifting bodies feature an aerodynamic configuration with a compact body about 8 [m] long with a rounded edge delta-like cross section (Hanley et al., 1964).A very preliminary internal layout for a crew of four astronauts is also reported in Fig. 1.

Freestream conditions
The flight scenario considered so far is summarized in Table 1.They refer to entry conditions compatible with a vehicle entering the Mars atmosphere both from a hyperbolic orbit (HO), e.g., direct planetary entry, and an elliptic orbit (EO) e.g., planetary entry after aerobraking (Gupta et al., 1996).(Hanley et al., 1964).Several Mach numbers and different angles of attack () have been investigated and compared each other.The Fluent code together with user defined functions (UDFs), developed in order to simulate mixtures of gas in thermo-chemical non-equilibrium, have been used for CFD computations with a non-equilibrium chemical model suitable for Martian atmosphere (Gupta et al., 1996) (Mack et al., 2008) (Kustova et al., 2009).
For the reacting gas computations, 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 modelled as a reacting gas mixture of 9 species (Ar, CO 2 , N 2 , O 2 , CO, NO, N, O, C) involved in the chemical reactions of Table 2 (Park et al., 1994) (Anderson, 1989).The reaction mechanism and the related chemical kinetics, taken into account in the present work, are summarized in Table 2, where M is the reacting partner (third body) that can be any of the nine reacting species of the gas mixture.Non-equilibrium computations have been performed since one of the most challenging problem facing the design of atmospheric entry vehicle is the phenomenon of "real gas behaviour".At hypersonic speeds, the shock wave produced ahead of the vehicle suddenly elevates the gas temperature in the shock layer.So the gas thermal energy may be comparable with the energy associated with a whole range of gas chemical processes such as: molecular vibrational excitation; dissociation of atmospheric molecules into their atomic forms; formation of other chemical species through recombination reactions; and ionisation of both molecular and atomic species (Park et al., 1994).Table 2. Reactions mechanism and rate parameters (Park et al., 1994).

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Therefore, the gas mixture has to be considered in thermal and chemical non-equilibrium.Finally, the CFD analysis of the MBS have been preceded by a code validation phase performed considering the available numerical and experimental data for the Mars Pathfinder probe at entry peak heating conditions, as summarized in (Viviani et al., 2010) (Gnoffo et al., 1998) (Gnoffo et al., 1996) (Mitcheltree et al., 1995).

Numerical results
The aerodynamic analysis of MBS is shown in term of lift (C L ), drag (C D ) and pitching moment (C My ) coefficients which are calculated according to Eq. ( 1) and Eq. ( 2), respectively.
The reference parameters L ref (e.g., longitudinal reference length) and S ref (e.g., reference surface) are the vehicle length (e.g., 8 m) and planform area (e.g., 32 m 2 ).The pitching moment is computed from the vehicle nose (i.e.0, 0, 0).Engineering based aerodynamic analysis has been extensively performed by using a 3D Panel Methods code developed by CIRA, namely HPM (Viviani and Pezzella, 2009).This tool, at high supersonic and hypersonic speeds, is able to accomplish the aerodynamic and aerothermodynamic analyses of a complex re-entry vehicle configuration by using simplified approaches as local surface inclination methods and approximate boundary-layer methods, respectively.The SIM typical of hypersonics are based on Newtonian, Modified Newtonian, and Prandtl-Mayer theories (Anderson, 1989).Typical surface meshes of the MBS, used for the engineering level computations, are shown in Fig. 2. MBS aerodynamic results, provided by engineering-based analysis, cover  ranging from 0 to 50 deg.Present CFD computations for the MBS have been carried out on a 3-D multiblock structured grid close to that shown in Fig. 3.The grid consists of about 20 blocks and 900.000 cells (half body).Both computational domains are tailored for the free-stream conditions of 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 one, according to the computational scopes.Fig. 3 shows also a close-up view of the 3-D mesh on the vehicle surface and pitch plane.Grid refinement in strong gradient regions of flowfield has been made through a solution adaptive approach.

Fig. 3. Example of computational mesh domains for Euler CFD simulations
The preliminary results of CFD simulations performed so far are summarized hereinafter.For example, Fig. 6 shows the static temperature contours on the vehicle symmetry plane and static pressure contours on vehicle surface at M  =20 and =20 deg, considering the Mars atmosphere as a reacting gas mixture.As shown, the MBS bow shock structure around the descent vehicle can be appreciated as well., 1989).This results in a thinner shock layer around the entry vehicle (e.g., lower stand-off distance).
Under conditions where dissociation exists, the aerodynamics of vehicle 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 (Gnoffo et al., 1998) (Viviani et al., 2010).The curves of lift and drag coefficients are shown in Fig. 7.Those curves collect MBS aerodynamic coefficients compared with available numerical data both for perfect gas and reacting gas approximations, reported in order to highlight accuracy of both numerical and engineering-based results (Viviani et al., 2010).As one can see, engineering and numerical data compare very well, thus confirming engineering-based estimations represent reliable preliminary aerodynamics of a Mars entry vehicle.Moreover, real gas effects increase the aerodynamic drag coefficient whereas the lift is only slightly influenced.
As far as CFD results for the second configuration are concerned, Fig. 8 shows the Mach number contour field that takes place around the vehicle when it is flying at the peak heating conditions of entry by EO (e.g., M  =22, =40 deg, and H=44.20 km).
In particular, the left side of Fig. 8 shows the Mach contour field on the vehicle pitch plane while at the right side of Fig. 8 gives an idea of the bow shock shape that envelopes the vehicle since the Mach field is reported on three different flowfield cross sections.
As shown, a thin shock layer envelopes the entry vehicle windside with a strong expansion that characterizes the flow at the end of the vehicle.The CO mass fraction field around the vehicle for the same freestream conditions is shown in Fig. 9 where some streamtraces colored by Mach number are also reported.

Conclusion
The paper deals with the flowfield analysis of two braking systems for manned exploration mission to Mars.
A number of fully 3D Navier-Stokes and Euler CFD computations of the hypersonic flowfield past two lifting body vehicles have been performed for several freestream conditions of a proposed Mars entry loading environment.These evaluations have been aimed at carrying out only a preliminary design of the MBS configuration, in compliance with the Phase-A design level.The range between Mach 2 and Mach 26 has been analyzed, to provide both aerodynamic databases according to both the space-based and trajectory-based design approaches.Numerical results show that real gas effects increase both the aerodynamic drag and pitching moment coefficient, whereas the lift is only slightly influenced.

Fig. 2 .
Fig. 2. Example of panel mesh for engineering-based aerodynamic analysis.

Fig. 4 .
Fig. 4. Results for M  =20 and =20 deg.(Left) static temperature field on vehicle symmetry plane; (right) static pressure contour on vehicle surface for non-equilibrium reacting gas At the same flight conditions, Fig. 5 reports on chemical dissociation of the flow in the shock layer considering the contours of CO 2 mass fraction on MBS pitch plane.As a consequence, flow dissociation determines a large density ratio  across the strong bow shock compared with a flow of the same gas where no dissociation takes place(Viviani and Pezzella, 2009)  (Anderson, 1989).This results in a thinner shock layer around the entry vehicle (e.g., lower stand-off distance).

Fig. 5 .Fig. 6 .
Fig. 5. Results for M  =20 and =20 deg.Contours of CO 2 mass fraction Moreover, Fig. 6 shows CFD results for M  =21 and =40 deg.The left side reports pressure coefficient contours (C p ) on vehicle surface and on two cross sections; whereas on the right C p contours on vehicle surface and Mach number contours on three cross sections have been shown.

Fig. 7 .
Fig. 7. C L and C D versus .Comparison between panel methods and CFD results for perfect and reacting gas approximations.

Fig. 8 .
Fig. 8. Mach contours on the vehicle pitch plane and three flowfield cross sections at the EOPH conditions.

Fig. 9 .
Fig. 9. CO mass fraction at the EOPH conditions on three cross sections with streamtraces colored by Mach number As shown the CO concentration reaches its maximum value close to the body.Fig. 10 shows the temperature comparison among non-equilibrium flow (right side of pilot) and perfect gas computation, evaluated at three flowfield cross sections (x=1.5 [m], 5.5 [m] and 9.5 [m]).It is clearly evident how real gas phenomena affect the vehicle shock layer, thus confirming all the conclusions highlighted before.