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Hypersonic static aerodynamics for Mars science laboratory entry capsule
Acta Astronautica 103 (2014) 168–175
Contents lists available at ScienceDirect
Acta Astronautica journal homepage: www.elsevier.com/locate/actaastro
Hypersonic static aerodynamics for Mars science laboratory entry capsule Xiaofeng Yang n, Wei Tang, Yewei Gui, Yanxia Du, Guangming Xiao, Lei Liu State key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang, Sichuan 621000, China
a r t i c l e in f o
abstract
Article history: Received 2 April 2014 Received in revised form 29 May 2014 Accepted 21 June 2014 Available online 1 July 2014
The Mars Science Laboratory (MSL) entry capsule has been designed as a lifting entry for sufficient deceleration and precise landing performance. This paper presents the static aerodynamics analysis of the MSL capsule in the hypersonic entry process for exploration mission to Mars. Hypersonic static coefficients were derived from fully three-dimensional computational fluid dynamics solutions with a specified effective specific heat ratio on a typical trajectory state. Aerodynamic performance analysis ascertains the trim characteristics and static stability of the capsule with respect to the center of gravity (CG) location. Analysis results obtained show that CG location determines the trim characteristics and the static stability, and certain CG radial and axial shift alters the lifting entry performance, so that proper aerodynamic configuration and inner equipment layout is needed for CG adjustment to satisfy the static aerodynamics requirements. & 2014 IAA. Published by Elsevier Ltd. All rights reserved.
Keywords: MSL entry capsule Computational fluid dynamics Static aerodynamics Hypersonic
1. Introduction The recent Mars Science Laboratory mission successfully landed on the surface of Mars on August 2012. The MSL entry capsule traveled the entire Martian atmosphere before descending and landing [1,2] and complex lifting entry was selected with a hypersonic lift-to-drag (L/D) of 0.24 at a trimmed angle of attack of 161 for sufficient deceleration and precise landing performance. The center of gravity (CG) of MSL entry capsule is radially offset for the desired angle of attack and L/D [3], the same as the Earth reentry capsules, such as Soyuz. How to predict the lifting entry performances is one of the most important problems for Mars entry capsule design. Though several Mars entry missions have been achieved, small amount of engineering flight data is available. In addition, there exist no ground-based facilities that can reproduce the high-speed and high-temperature Martian
n
Correspondence author. E-mail address: [email protected] (X. Yang).
http://dx.doi.org/10.1016/j.actaastro.2014.06.036 0094-5765/& 2014 IAA. Published by Elsevier Ltd. All rights reserved.
flow that occurs at flight conditions. The computational fluid dynamics (CFD) technique, therefore, turns out to be a significant approach for flight aerodynamic analysis. The capsule entries through different flight regimes from rarefied, then to transitional, and finally to continuum regime and therefore requires different prediction methods. Aerodynamics in the rarefied regime is predicted using the DSMC method, while Navier–Stokes equations are used for the continuum regime. For hypersonic Mars entry, NS solver is believed to be applicable for static aerodynamics prediction. Large amounts of numerical efforts have been made to date to quantify the aerodynamics for various entry capsule configurations during hypersonic flight. Most of the numerical works used the chemical and thermal nonequilibrium model, which is fairly complicated and have not been effectively verified by experiments [4]. For this reason, some computational attempts based on the perfect gas model have been made to avoid the uncertainty of the chemical reacting model, and comparative discussions with the complex reacting model were also performed [5–8]. As the Martian atmosphere, considered as a mixture of 95.7% CO2, 2.7% N2 by volume and some other gases, is
X. Yang et al. / Acta Astronautica 103 (2014) 168–175
relatively thinner than air, the vibrational excitation characteristic temperature is measured to be lower than that of air, and real-gas effects exist when entry capsules fly at a very high velocity, both of which decrease the post-shock effective specific heat ratio γ2 [5]. From this point of view, the assumption of constant γ¼1.4 is no longer valid for Mars entry flowfield, and surface pressure and heatflux for lower γ flow may thus change during the hypersonic entry process. It is demonstrated in statistical thermodynamics [9] that gas thermal properties, such as internal energy and the specific heat, can be expressed in terms of specific heat ratio, gas constant and temperature. The use of an effective specific heat ratio permits hypersonic non-air flow with high temperature real-gas effects to be approximately accounted for [10]. Such approach has been widely used in the rocket combustion flow, hypersonic reentry flow [11,12] and so forth. As for Mars entry mission, a lower value of effective γ for calorically perfect gas simulation is believed to be an effectual approach to accurately predict surface pressure and total coefficients of the MSL entry capsule. The current work is motivated by the need of an improved general understanding of hypersonic static aerodynamics for Mars entry capsules. In this paper, a serial of fully three-dimensional numerical simulations for the MSL entry capsule were performed at different angles of attack for a given flight state with a specified effective specific heat ratio. Those simulations aimed to ascertain the generic aerodynamic performance and the static stability of the capsule with respect to the capsule CG location. The relation between the CG position and the lift-to-drag ratio and pitch behavior were numerically analyzed to better understand the lifting aerodynamic characteristics, as well as the aerodynamic sensitivity. 2. Models and methods 2.1. Geometry and grid generation The proposed geometry for aerodynamics analysis is the MSL entry capsule. The forebody is a 701 sphere cone with a nose radius of 1.125 m and an overall capsule
169
diameter of 4.5 m. A 0.125-m-radius shoulder connects the forebody to three-sectional-cone afterbody as described in Fig. 1. The body axis system is used for aerodynamic analysis shown in Fig. 1. Under such system, a pitch-up motion of the entry capsule means a positive angle of attack (α40), and a positive pitch moment pitches the capsule up (Fig. 1). The computational grid for MSL configuration is a multiblock structured grid and has an overall number of approximately 1.4 million cells (half-body). To assure accurate prediction, the grid is everywhere orthogonal to the body at the surface. Grid independence analysis shows that grids for the wall cell Reynolds number Rec ¼ρ1U1dw/ μ1 ¼O(1) can fulfill the accuracy requirement of aerodynamics analysis, where dw is the normal grid distance close to the wall (the wall step). The wall cell Reynolds number for the current analysis is hence 6.4. Fig. 2 shows a cutaway view of the schematic computational grid. 2.2. Numerical method Computational fluid dynamics (CFD) technique was undertaken to predict the aerodynamic force for the MSL entry capsule. A finite volume approach was used to solve the full Navier–Stokes flowfield equations for a calorically perfect gas. The code used the van Leer flux-vector splitting method for the inviscid fluxes with the 2nd order correction using the van Leer limiter. For time integration, the non-iterative implicit method was used for rapid convergence. Constant inflow condition was imposed on the farfield boundary, and the extrapolation was used on the outflow boundary in all solutions. Non-slip wall boundary condition was implemented and the thermal state of the surface is radiative equilibrium to satisfy the 4 relation qw ¼εσTw with a fixed surface emissivity of 0.78. The flowfield is assumed to be steady and laminar. Unsteady effects are weak at these high speeds for long duration entry flight [13], and moreover, unsteady aerodynamic contribution is negligibly small in the afterbody [14]. Transition to turbulence could occur but is weak due to low Reynolds number in the relatively thin Martian atmosphere [4]. Despite of multicomponent mixture existing in the Martian atmosphere, pure CO2 gas was taken into account for simplification. At high-Mach-number flight conditions, a marked decrease of the post-shock specific heat ratio occurs. Effective specific heat ratio, γeff, was specified to take the non-air and high-temperature real-gas effects into account. Such effective value can be determined by matching the density ratio (ρ2/ρ1) across a normal shock for equilibrium flow. An alternative choice of γeff is determined directly from the post-shock total temperature. High-temperature gas viscosity coefficient is assumed to depend only on temperature, and can be specified by Sutherland's law [15]. The dynamic viscosity coefficient μ for CO2 is μ=μ0 ¼ ðT=T 0 Þ3=2 ðT 0 þ CÞ=ðT þCÞ
ð1Þ 5
Fig. 1. MSL geometry and definition of aerodynamic forces.
where the reference viscosity μ0 ¼1.48 10 kg/(m s), the reference temperature T0 ¼293.15 K, and the Sutherland constant C¼240 K. Sutherland's law agrees well with
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Fig. 2. MSL computational grid schematic (the actual grid is twofold refined in each direction).
theoretical calculation from Fenghour [16]. Since both viscous diffusion and heat conduction are driven by molecular motion, the thermal conductivity k have direct correlation with the viscosity coefficient μ, and can be obtained from the Prandtl number as k ¼μcp/Pr. For hightemperature CO2, we assume Pr ¼0.71. For code validation purpose, the available numerical and experimental data of the scaled 701 sphere-cone have been used [17,18], because all of the successful missions to Mars have relied on a 701 sphere-cone configuration. Two freestream conditions are tested, that is, for the inflow enthalpy of 1.89 MJ/kg (U1 ¼ 1908 m/s, p1 ¼ 1010 Pa) and 5.63 MJ/kg (U1 ¼2871 m/s, p1 ¼1614 Pa) using CO2 as the test gas. Calculated results based on an effective specific heat ratio are compared against experiments. The calculation results of the surface pressure for both inflow enthalpy with experimental and DPLR data are shown in Fig. 3. The surface pressure comparison highlights a good agreement between numerical and experimental data, thus confirming reliability of the CFD simulations for Mars entry capsules.
Fig. 3. Surface pressure comparison with experiments for the inflow enthalpy of 1.89 and 5.63 MJ/kg.
2.3. Static aerodynamics analysis method
can be determined as follows:
The total coefficients from integration of calculated surface pressure and shear stress with zero angles of sideslip include the axial (CA), normal (CN), lift (CL) and drag (CD) coefficients for various angles of attack. Just the same as conventional reentry capsules, CA is dominant in all total coefficients for Mars entry capsule configuration, particularly at small angles of attack. The determination of the center of pressure (CP) for the drag-dominant entry vehicle is quite different from that of slender body (Xcp ¼ CM/CN), and the influence of the axial force cannot be neglected. The CP location with zero angles of sideslip
X cp ¼
C M;N CN
Y cp ¼
C M;A CA
Zcp ¼ 0
ð2Þ
where Xcp, Ycp and Zcp are the CP dimensionless coordinate components, CA and CN are the axial and normal force coefficient, and CM,A and CM,N are pitch moment coefficient due to the axial and normal force, respectively. Necessary radial CG offset will be used to meet the requirements of trimmed α and L/D for the lifting entry. Actually, CG is located on the trim line for a certain trimmed α or L/D. The trim line is the total aeroforce line originating from the CP point, as is expressed in the
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following form: Y Y cp C N ¼ X X cp C A
ð3Þ
where X and Y are the dimensionless spatial coordinates. Nevertheless, the trim requirement is not enough, and the pitch stability is of as equal importance as the trim condition. Hence, the CG position cannot be arbitrarily located on the trim line, and must be restricted in a specific interval for pitch stability. Static pitch stability requires that the pitch moment derivative with respect to angle of attack must be negative for stable flight. Thus, CM can be expressed as follows: C M ¼ C A ðY cp Y cg Þ þC N ðX cp X cg Þ
ð4Þ
Since CA, CN, Xcp, and Ycp are all the function of α, the pitch moment derivative is then dC M dC dC N dY cp dX cp ¼ A ðY cp Y cg Þ þ ðX cp X cg Þ C A þC N dα dα dα dα dα ð5Þ The location of CG on the individual trim line determines the trimmed α and L/D, and the shift of CG back and forth on the trim line alters the pitch stability margin. Given the trim condition and required margin of pitch stability, the CG coordinates can be solved by the combination of formulae (3) and (4), expressed as follows: X cg ¼ X cp ΔX Y cg ¼ Y cp ΔYΔX ðdC M =dαÞ þ C A ðdY cp =dαÞ C N ðdX cp =dαÞ ðdC N =dαÞ ðdC A =dαÞðC N =C A Þ CN ΔY ¼ ΔX CA ¼
ð6Þ
where, the coefficients CA and CN are obtained from computation, the CP coordinates are from formula (2), and all the derivatives with respect to angle of attack are approximately calculated with central difference. Formula (6) sketches the relationship between the CG location (the offset Ycg and the shift Xcg) and flight requirements, including the trim characteristics (the trimmed α and L/D) and the static pitch stability (the derivative CM,α), which is of vital significance for the aerodynamic configuration design and the capsule cabin layout. 3. Results and discussion 3.1. Hypersonic flowfield Hypersonic flow structure for the MSL entry capsule is complicated, especially for the vortex flow. Steady numerical simulations for a sample hypersonic flowfield at H¼31 km are herein performed. The flight speed is 5164 m/s and the Mach number is 26.1 with an angle of attack α¼-17.051, so that the farfield unit Reynolds number Re1 ¼ 2.363 106/m. The effective value of specific heat ratio here is derived to be 1.16. Fig. 4 shows the main steady structure of the hypersonic flowfield on the symmetry plane. A strong bow shock wave is detached from the surface and lies very close to the heatshield. The gas across the shock wave is compressed to form a shock layer, much thinner than that of the air flow. Inflow
Fig. 4. Hypersonic flow structure for MSL on the symmetry plane.
uniform streamlines are deflected across the shock and travel around the body (Fig. 5). Expansion waves occur near the shoulder due to large deflection angle. The gas gets accelerated in this region and merges into the external inviscid flow downstream from the shoulder. The heatshield boundary layer thickness increases from the stagnation point to the shoulder, and the shear layer appears after the shoulder, resulting in local vortex motion. Consequently, flow separation arises on the backshell (Fig. 5). A large region of recirculating flow leads to a relatively low pressure distribution on the backshell, which has a negligible contribution to the total coefficients. The wake flow after the capsule meets and then accumulates to form the recompression waves, which are nearly parallel to the inflow direction, and grow weaker to the outer flow. Fig. 6 shows the heatshield surface pressure and shear stress distribution on the symmetric line, and their comparison with Ref. [3]. As is expected, surface pressure is the highest at the stagnation point and falls off rapidly as the flow expands around the shoulder and onto the afterbody. Surface shear stress, however, is just the opposite, depending on the streamwise velocity magnitude at the edge of the boundary layer. On the whole, calculated results for both surface pressure and shear stress keep in good agreement with the reference, especially for the surface pressure on the windside, which dominates the total aeroforce coefficients. It is worth mentioning that a certain degree of fluctuation exists for both calculated surface pressure and shear stress in the heatshield leeside, partly because of very high Mach number and very low specific heat ratio. Nevertheless, the overall influence of such fluctuation is relatively weak after integration for aerodynamic analysis. 3.2. Generic aerodynamic performance Regarding aerodynamic performance analysis, computation cases for relative low speed of 3620 m/s (Ma1 ¼16.0) at H¼20.8 km were performed to avoid the leeside fluctuation
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Fig. 5. Streamlines on the symmetry plane and near the surface of MSL.
Fig. 6. Surface pressure and shear stress distribution on MSL symmetry plane.
mentioned above. The angles of attack range from 01 to 411 to obtain the generic aerodynamic performance. Fig. 7 shows the surface pressure distribution for three angles of attack of 61, 17.51 and 291, respectively. The high-pressure region on the surface moves to the windside shoulder region as the magnitude of angle of attack increases. In addition, the stagnation point locations, and the shock and sonic lines on the symmetric plane are also shown in Fig. 7. For angle of attack of 61, the stagnation point is located near the axis on the sphere cone; when the angle of attack increases to 17.51, the stagnation point is moved far away from the axis to the cone frustum section; when to 291, the stagnation point is moved very near to the shoulder. The windside sonic line merges into the boundary layer at the shoulder, while the leeside one at different place depending on the angle of attack. For lower angle of attack, 61 for example, the sonic line merges into the boundary layer at the shoulder, the same as the windside. When the angle of attack increases, the
merging location moves to the sphere-cone junction (for 17.51), even near the axis (for 291), and the sonic line has an inflection in the vicinity of the apex because of strong compressibility. The windside sonic line envelopes high pressure region, which dominates the total aerodynamic coefficients. The integrated axial (CA), normal(CN), lift (CL) and drag (CD) coefficients and the lift-to-drag ratio (L/D), are shown in Fig. 8 as a function of angle of attack from zero to 411. CA is predicted to decrease continuously as the magnitude of the angle of attack increases and CN is just the reverse. Moreover, CA is expected to be dominant in all total coefficients and bears an order of magnitude larger than CN. At small angle of attack, CL and CD are believed to hold the same trend as CN and CA, respectively. As a result, L/D increases with the increase of the magnitude of the angle of attack. It can be expected from computations that a trimmed L/D of 0.27 can be achieved if a trimmed angle of attack of 17.51 holds. The calculated CP locations for various angles of attack are shown in Fig. 9. Since the post-shock high pressure region is deviated from the symmetry axis with the increase of the magnitude of the angle of attack, CP moves away from the axis correspondingly. The trim lines for the given trimmed α or L/D are also shown Fig. 9. When the magnitude of the angle of attack increases, the slope of the trim line increases because of the CP offset, resulting in more skewed trim line with respect to the axis. Such departure from or skewness off the axis required for the trim condition give rise to a specific CG offset. Fig. 10 shows the pitch moment characteristic curves for the trimmed L/D equal to 0.27 with 5 specified CG locations. It can be seen that all the curves meet at the point α¼ 17.51 and CM ¼0, which is the description of trim condition. It can also be seen that the shift back and forth on the trim line affects the slope of the moment characteristic curve. The slope for CG close to the heatshield is negative which symbolizes a static pitch stable flight, while it becomes slightly negative, zero, or even
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Fig. 7. Shock shape and sonic line on the symmetry plane around the MSL body for different angles of attack. (a) a =-6° (b) a =-17.5° (c) a =-29°.
Fig. 8. The total coefficient curves.
positive for CG shifting backwards, causing a neutral or unstable flight. 3.3. Center of gravity discussion There exists a close relationship between the CG location and flight behaviors. In accordance with formula (6), we bring out the distribution of the trimmed α or L/D and the static pitch stability margin in the CG plane, as shown in Fig. 11. If the requirements of the trim condition and the static pitch stability are determinate, the needed CG is then exactly located from Fig. 11. In other words, CG location determines trim characteristics and stability,
Fig. 9. The center of pressure for various α and the trimline for the given trimmed α or L/D.
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Table 1 The sensitivity of aerodynamic performance to the CG position. Xcg ¼ 0.28, Ycg ¼ 0.024 to Xcg to Ycg
dCM/dα 0.0050 0.0200
L/D 0.290 6.950
almost horizontal in the concerned range of angle of attack. A radial CG offset of 1% reference diameter from the symmetry axis would result in a trimmed L/D as high as 0.07 and a pitch derivative as high as 0.003/1. In consequence, a small radial bias of CG may cause remarkable flight performance deviation for lifting entry, which should be paid close attention to in the process of aerodynamic design. 4. Conclusions Fig. 10. Pitch moment characteristic curves for 5 different CG locations with the trimmed L/D equal to 0.27.
Fig. 11. The trimmed α or L/D and the static pitch stability margin distribution in the CG plane (solid: stability margin isoline, dashed: trimmed α isoline).
which is meaningful for further aerodynamic design. As for the MSL entry capsule, CG is located near the volumetric center (30% of the total length) on the assumption of relatively uniform mass distribution. Supposing that the required trimmed angle of attack is 17.51 (or 0.27 for the trimmed L/D), we can offset CG for a dimensionless distance of 0.0045 in the radial direction. In addition, such offset can hold a static pitch stability margin of 0.003/1 at least, that is, both of the trim condition and static pitch stability are fulfilled for typical hypersonic lifting entry. Apart from CG discussion above, the sensitivity of total coefficients to the bias of CG also plays a significant role in aerodynamic design. A remarkable change of the trim characteristics and static pitch stability due to a small CG bias should be avoided. Sensitivity analysis from Table 1 shows that it is more radially sensitive than axially, especially for the trimmed L/D, because the trim line is
This paper deals with the static aerodynamic analysis for Mars exploration mission. A series of fully threedimensional Navier–Stokes computations of the hypersonic flowfield past an MSL-shaped capsule has been performed for the entry conditions with an effective specific heat ratio. Hypersonic continuum static coefficients were numerically predicted at the given state on the hypersonic trajectory. Aerodynamic performance analysis shows CG location determines trim characteristics and stability, which can be guidance on aerodynamic design. A CG radial offset of a dimensionless distance of 0.0045 achieves a trimmed L/D of 0.27 and a static pitch stability margin of at least 0.003/1, which can fulfill the hypersonic lifting entry. Finally, sensitivity study shows that a small radial bias of CG may cause remarkable flight performance deviation for lifting entry, which should be paid close attention to. Consequently, proper aerodynamic configuration and cabin equipment layout is needed for CG adjustment to meet the static aerodynamics requirements. This investigation provides researchers with guidelines for the optimization of the design of the Mars entry capsule.
Acknowledgments This research is partly supported by the National Natural Science Foundation of China (Grant No. 91216204). References [1] R.D. Braun, R.M. Manning, Mars exploration entry, descent, and landing challenges, J. Spacecr. Rockets 44 (2) (2007) 310–323. [2] R. Prakash, P.D. Burkhart, A. Chen, K.A. Comeaux, C.S. Guernsey, D.M. Kipp, D.W. Way, Mars Science Laboratory entry, descent, and landing system overview, in: Proceedings of Aerospace Conference, IEEE, 2008, pp. 1–18. [3] K.T. Edquist, A.A. Dyakonov, M.J. Wright, C.Y. Tang, Aerothermodynamic environments definition for the Mars Science Laboratory entry capsule, AIAA Pap. 1206 (2007) 8–11. [4] M.J. Wright, C.Y. Tang, K.T. Edquist, B.R. Hollis, P. Krasa, C.A. Campbell, A review of aerothermal modeling for Mars entry missions, AIAA Pap. 443 (2010) 4–7. [5] P.A. Gnoffo, K.J. Weilmuenster, R.D. Braun, C.I. Cruz, Effects of sonic line transition on aerothermodynamics of the Mars pathfinder probe, in: Proceedings of AIAA, 1995, 1825-CP p.
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[6] D.K. Prabhu, D.A. Saunders, On heatshield shapes for Mars entry capsules, in: Proceedings of AIAA, 2002, 1221 p. [7] A. Viviani, G. Pezzella, Aerodynamic analysis of a capsule vehicle for a manned exploration mission to Mars, in: Proceedings of the 16th AIAA/DLR/DGLR International Space Planes and Hypersonic Systems and Technologies Conference, AIAA, 2009, 7386 p. [8] P.A. Liever, S.D. Habchi, S.I. Burnell, J.S. Lingard, CFD prediction of the Beagle 2 aerodynamic database, in: AIAA (2002) 0683. [9] E.H. Hirschel, C. Weiland, Selected aerothermodynamic design problems of hypersonic flight vehicles, Springer Press, New York, 2009. [10] J.D. Anderson, Jr., Hypersonic and high-temperature gas dynamics, AIAA, 2006. [11] G.J. Brauckmann, J.W. Paulson Jr., K.J. Weilmuenster, Experimental and computational analysis of shuttle orbiter hypersonic trim anomaly, J. Spacecr. Rockets 32 (5) (1995) 758–764. [12] K.J. Weilmuenster, H.H. Hamilton, A comparison of computed space shuttle orbiter surface pressures with flight measurements, AIAA, 1982, 0937 p.
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[13] R.A. Mitcheltree, P.A. Gnoffo, Wake flow about the Mars pathfinder entry vehicle, J. Spacecr. Rockets 32.5 (1995) 771–776. [14] K.T. Edquist, P.N. Desai, M. Schoenenberger, Aerodynamics for the Mars Phoenix entry capsule, in: Proceedings of AIAA/AAS Astrodynamics Specialist Conference and Exhibit, AIAA, 2008, 7219 p. [15] R.C. Weast, CRC Handbook of Chemistry and Physics, 65th ed. Chemical Rubber Company Press, Cleveland, 1984. [16] A Fenghour, W.A. Wakeham, V. Vesovic, The viscosity of carbon dioxide, J. Phys. Chem. Ref. Data 27 (1) (1998) 31–44. [17] M.S. Holden, T.P. Wadhams, G.J. Smolinski, M.G. MacLean, J. Harvey, B.J. Walker, Experimental and numerical studies on hypersonic vehicle performance in the LENS shock and expansion tunnels, AIAA Pap. 125 (2006) 2006. [18] M. MacLean, M.S. Holden, Catalytic effects on heat transfer measurements for aerothermal studies with CO2, AIAA Pap. 182 (2006) 9–12.
Contents lists available at ScienceDirect
Acta Astronautica journal homepage: www.elsevier.com/locate/actaastro
Hypersonic static aerodynamics for Mars science laboratory entry capsule Xiaofeng Yang n, Wei Tang, Yewei Gui, Yanxia Du, Guangming Xiao, Lei Liu State key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang, Sichuan 621000, China
a r t i c l e in f o
abstract
Article history: Received 2 April 2014 Received in revised form 29 May 2014 Accepted 21 June 2014 Available online 1 July 2014
The Mars Science Laboratory (MSL) entry capsule has been designed as a lifting entry for sufficient deceleration and precise landing performance. This paper presents the static aerodynamics analysis of the MSL capsule in the hypersonic entry process for exploration mission to Mars. Hypersonic static coefficients were derived from fully three-dimensional computational fluid dynamics solutions with a specified effective specific heat ratio on a typical trajectory state. Aerodynamic performance analysis ascertains the trim characteristics and static stability of the capsule with respect to the center of gravity (CG) location. Analysis results obtained show that CG location determines the trim characteristics and the static stability, and certain CG radial and axial shift alters the lifting entry performance, so that proper aerodynamic configuration and inner equipment layout is needed for CG adjustment to satisfy the static aerodynamics requirements. & 2014 IAA. Published by Elsevier Ltd. All rights reserved.
Keywords: MSL entry capsule Computational fluid dynamics Static aerodynamics Hypersonic
1. Introduction The recent Mars Science Laboratory mission successfully landed on the surface of Mars on August 2012. The MSL entry capsule traveled the entire Martian atmosphere before descending and landing [1,2] and complex lifting entry was selected with a hypersonic lift-to-drag (L/D) of 0.24 at a trimmed angle of attack of 161 for sufficient deceleration and precise landing performance. The center of gravity (CG) of MSL entry capsule is radially offset for the desired angle of attack and L/D [3], the same as the Earth reentry capsules, such as Soyuz. How to predict the lifting entry performances is one of the most important problems for Mars entry capsule design. Though several Mars entry missions have been achieved, small amount of engineering flight data is available. In addition, there exist no ground-based facilities that can reproduce the high-speed and high-temperature Martian
n
Correspondence author. E-mail address: [email protected] (X. Yang).
http://dx.doi.org/10.1016/j.actaastro.2014.06.036 0094-5765/& 2014 IAA. Published by Elsevier Ltd. All rights reserved.
flow that occurs at flight conditions. The computational fluid dynamics (CFD) technique, therefore, turns out to be a significant approach for flight aerodynamic analysis. The capsule entries through different flight regimes from rarefied, then to transitional, and finally to continuum regime and therefore requires different prediction methods. Aerodynamics in the rarefied regime is predicted using the DSMC method, while Navier–Stokes equations are used for the continuum regime. For hypersonic Mars entry, NS solver is believed to be applicable for static aerodynamics prediction. Large amounts of numerical efforts have been made to date to quantify the aerodynamics for various entry capsule configurations during hypersonic flight. Most of the numerical works used the chemical and thermal nonequilibrium model, which is fairly complicated and have not been effectively verified by experiments [4]. For this reason, some computational attempts based on the perfect gas model have been made to avoid the uncertainty of the chemical reacting model, and comparative discussions with the complex reacting model were also performed [5–8]. As the Martian atmosphere, considered as a mixture of 95.7% CO2, 2.7% N2 by volume and some other gases, is
X. Yang et al. / Acta Astronautica 103 (2014) 168–175
relatively thinner than air, the vibrational excitation characteristic temperature is measured to be lower than that of air, and real-gas effects exist when entry capsules fly at a very high velocity, both of which decrease the post-shock effective specific heat ratio γ2 [5]. From this point of view, the assumption of constant γ¼1.4 is no longer valid for Mars entry flowfield, and surface pressure and heatflux for lower γ flow may thus change during the hypersonic entry process. It is demonstrated in statistical thermodynamics [9] that gas thermal properties, such as internal energy and the specific heat, can be expressed in terms of specific heat ratio, gas constant and temperature. The use of an effective specific heat ratio permits hypersonic non-air flow with high temperature real-gas effects to be approximately accounted for [10]. Such approach has been widely used in the rocket combustion flow, hypersonic reentry flow [11,12] and so forth. As for Mars entry mission, a lower value of effective γ for calorically perfect gas simulation is believed to be an effectual approach to accurately predict surface pressure and total coefficients of the MSL entry capsule. The current work is motivated by the need of an improved general understanding of hypersonic static aerodynamics for Mars entry capsules. In this paper, a serial of fully three-dimensional numerical simulations for the MSL entry capsule were performed at different angles of attack for a given flight state with a specified effective specific heat ratio. Those simulations aimed to ascertain the generic aerodynamic performance and the static stability of the capsule with respect to the capsule CG location. The relation between the CG position and the lift-to-drag ratio and pitch behavior were numerically analyzed to better understand the lifting aerodynamic characteristics, as well as the aerodynamic sensitivity. 2. Models and methods 2.1. Geometry and grid generation The proposed geometry for aerodynamics analysis is the MSL entry capsule. The forebody is a 701 sphere cone with a nose radius of 1.125 m and an overall capsule
169
diameter of 4.5 m. A 0.125-m-radius shoulder connects the forebody to three-sectional-cone afterbody as described in Fig. 1. The body axis system is used for aerodynamic analysis shown in Fig. 1. Under such system, a pitch-up motion of the entry capsule means a positive angle of attack (α40), and a positive pitch moment pitches the capsule up (Fig. 1). The computational grid for MSL configuration is a multiblock structured grid and has an overall number of approximately 1.4 million cells (half-body). To assure accurate prediction, the grid is everywhere orthogonal to the body at the surface. Grid independence analysis shows that grids for the wall cell Reynolds number Rec ¼ρ1U1dw/ μ1 ¼O(1) can fulfill the accuracy requirement of aerodynamics analysis, where dw is the normal grid distance close to the wall (the wall step). The wall cell Reynolds number for the current analysis is hence 6.4. Fig. 2 shows a cutaway view of the schematic computational grid. 2.2. Numerical method Computational fluid dynamics (CFD) technique was undertaken to predict the aerodynamic force for the MSL entry capsule. A finite volume approach was used to solve the full Navier–Stokes flowfield equations for a calorically perfect gas. The code used the van Leer flux-vector splitting method for the inviscid fluxes with the 2nd order correction using the van Leer limiter. For time integration, the non-iterative implicit method was used for rapid convergence. Constant inflow condition was imposed on the farfield boundary, and the extrapolation was used on the outflow boundary in all solutions. Non-slip wall boundary condition was implemented and the thermal state of the surface is radiative equilibrium to satisfy the 4 relation qw ¼εσTw with a fixed surface emissivity of 0.78. The flowfield is assumed to be steady and laminar. Unsteady effects are weak at these high speeds for long duration entry flight [13], and moreover, unsteady aerodynamic contribution is negligibly small in the afterbody [14]. Transition to turbulence could occur but is weak due to low Reynolds number in the relatively thin Martian atmosphere [4]. Despite of multicomponent mixture existing in the Martian atmosphere, pure CO2 gas was taken into account for simplification. At high-Mach-number flight conditions, a marked decrease of the post-shock specific heat ratio occurs. Effective specific heat ratio, γeff, was specified to take the non-air and high-temperature real-gas effects into account. Such effective value can be determined by matching the density ratio (ρ2/ρ1) across a normal shock for equilibrium flow. An alternative choice of γeff is determined directly from the post-shock total temperature. High-temperature gas viscosity coefficient is assumed to depend only on temperature, and can be specified by Sutherland's law [15]. The dynamic viscosity coefficient μ for CO2 is μ=μ0 ¼ ðT=T 0 Þ3=2 ðT 0 þ CÞ=ðT þCÞ
ð1Þ 5
Fig. 1. MSL geometry and definition of aerodynamic forces.
where the reference viscosity μ0 ¼1.48 10 kg/(m s), the reference temperature T0 ¼293.15 K, and the Sutherland constant C¼240 K. Sutherland's law agrees well with
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Fig. 2. MSL computational grid schematic (the actual grid is twofold refined in each direction).
theoretical calculation from Fenghour [16]. Since both viscous diffusion and heat conduction are driven by molecular motion, the thermal conductivity k have direct correlation with the viscosity coefficient μ, and can be obtained from the Prandtl number as k ¼μcp/Pr. For hightemperature CO2, we assume Pr ¼0.71. For code validation purpose, the available numerical and experimental data of the scaled 701 sphere-cone have been used [17,18], because all of the successful missions to Mars have relied on a 701 sphere-cone configuration. Two freestream conditions are tested, that is, for the inflow enthalpy of 1.89 MJ/kg (U1 ¼ 1908 m/s, p1 ¼ 1010 Pa) and 5.63 MJ/kg (U1 ¼2871 m/s, p1 ¼1614 Pa) using CO2 as the test gas. Calculated results based on an effective specific heat ratio are compared against experiments. The calculation results of the surface pressure for both inflow enthalpy with experimental and DPLR data are shown in Fig. 3. The surface pressure comparison highlights a good agreement between numerical and experimental data, thus confirming reliability of the CFD simulations for Mars entry capsules.
Fig. 3. Surface pressure comparison with experiments for the inflow enthalpy of 1.89 and 5.63 MJ/kg.
2.3. Static aerodynamics analysis method
can be determined as follows:
The total coefficients from integration of calculated surface pressure and shear stress with zero angles of sideslip include the axial (CA), normal (CN), lift (CL) and drag (CD) coefficients for various angles of attack. Just the same as conventional reentry capsules, CA is dominant in all total coefficients for Mars entry capsule configuration, particularly at small angles of attack. The determination of the center of pressure (CP) for the drag-dominant entry vehicle is quite different from that of slender body (Xcp ¼ CM/CN), and the influence of the axial force cannot be neglected. The CP location with zero angles of sideslip
X cp ¼
C M;N CN
Y cp ¼
C M;A CA
Zcp ¼ 0
ð2Þ
where Xcp, Ycp and Zcp are the CP dimensionless coordinate components, CA and CN are the axial and normal force coefficient, and CM,A and CM,N are pitch moment coefficient due to the axial and normal force, respectively. Necessary radial CG offset will be used to meet the requirements of trimmed α and L/D for the lifting entry. Actually, CG is located on the trim line for a certain trimmed α or L/D. The trim line is the total aeroforce line originating from the CP point, as is expressed in the
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following form: Y Y cp C N ¼ X X cp C A
ð3Þ
where X and Y are the dimensionless spatial coordinates. Nevertheless, the trim requirement is not enough, and the pitch stability is of as equal importance as the trim condition. Hence, the CG position cannot be arbitrarily located on the trim line, and must be restricted in a specific interval for pitch stability. Static pitch stability requires that the pitch moment derivative with respect to angle of attack must be negative for stable flight. Thus, CM can be expressed as follows: C M ¼ C A ðY cp Y cg Þ þC N ðX cp X cg Þ
ð4Þ
Since CA, CN, Xcp, and Ycp are all the function of α, the pitch moment derivative is then dC M dC dC N dY cp dX cp ¼ A ðY cp Y cg Þ þ ðX cp X cg Þ C A þC N dα dα dα dα dα ð5Þ The location of CG on the individual trim line determines the trimmed α and L/D, and the shift of CG back and forth on the trim line alters the pitch stability margin. Given the trim condition and required margin of pitch stability, the CG coordinates can be solved by the combination of formulae (3) and (4), expressed as follows: X cg ¼ X cp ΔX Y cg ¼ Y cp ΔYΔX ðdC M =dαÞ þ C A ðdY cp =dαÞ C N ðdX cp =dαÞ ðdC N =dαÞ ðdC A =dαÞðC N =C A Þ CN ΔY ¼ ΔX CA ¼
ð6Þ
where, the coefficients CA and CN are obtained from computation, the CP coordinates are from formula (2), and all the derivatives with respect to angle of attack are approximately calculated with central difference. Formula (6) sketches the relationship between the CG location (the offset Ycg and the shift Xcg) and flight requirements, including the trim characteristics (the trimmed α and L/D) and the static pitch stability (the derivative CM,α), which is of vital significance for the aerodynamic configuration design and the capsule cabin layout. 3. Results and discussion 3.1. Hypersonic flowfield Hypersonic flow structure for the MSL entry capsule is complicated, especially for the vortex flow. Steady numerical simulations for a sample hypersonic flowfield at H¼31 km are herein performed. The flight speed is 5164 m/s and the Mach number is 26.1 with an angle of attack α¼-17.051, so that the farfield unit Reynolds number Re1 ¼ 2.363 106/m. The effective value of specific heat ratio here is derived to be 1.16. Fig. 4 shows the main steady structure of the hypersonic flowfield on the symmetry plane. A strong bow shock wave is detached from the surface and lies very close to the heatshield. The gas across the shock wave is compressed to form a shock layer, much thinner than that of the air flow. Inflow
Fig. 4. Hypersonic flow structure for MSL on the symmetry plane.
uniform streamlines are deflected across the shock and travel around the body (Fig. 5). Expansion waves occur near the shoulder due to large deflection angle. The gas gets accelerated in this region and merges into the external inviscid flow downstream from the shoulder. The heatshield boundary layer thickness increases from the stagnation point to the shoulder, and the shear layer appears after the shoulder, resulting in local vortex motion. Consequently, flow separation arises on the backshell (Fig. 5). A large region of recirculating flow leads to a relatively low pressure distribution on the backshell, which has a negligible contribution to the total coefficients. The wake flow after the capsule meets and then accumulates to form the recompression waves, which are nearly parallel to the inflow direction, and grow weaker to the outer flow. Fig. 6 shows the heatshield surface pressure and shear stress distribution on the symmetric line, and their comparison with Ref. [3]. As is expected, surface pressure is the highest at the stagnation point and falls off rapidly as the flow expands around the shoulder and onto the afterbody. Surface shear stress, however, is just the opposite, depending on the streamwise velocity magnitude at the edge of the boundary layer. On the whole, calculated results for both surface pressure and shear stress keep in good agreement with the reference, especially for the surface pressure on the windside, which dominates the total aeroforce coefficients. It is worth mentioning that a certain degree of fluctuation exists for both calculated surface pressure and shear stress in the heatshield leeside, partly because of very high Mach number and very low specific heat ratio. Nevertheless, the overall influence of such fluctuation is relatively weak after integration for aerodynamic analysis. 3.2. Generic aerodynamic performance Regarding aerodynamic performance analysis, computation cases for relative low speed of 3620 m/s (Ma1 ¼16.0) at H¼20.8 km were performed to avoid the leeside fluctuation
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Fig. 5. Streamlines on the symmetry plane and near the surface of MSL.
Fig. 6. Surface pressure and shear stress distribution on MSL symmetry plane.
mentioned above. The angles of attack range from 01 to 411 to obtain the generic aerodynamic performance. Fig. 7 shows the surface pressure distribution for three angles of attack of 61, 17.51 and 291, respectively. The high-pressure region on the surface moves to the windside shoulder region as the magnitude of angle of attack increases. In addition, the stagnation point locations, and the shock and sonic lines on the symmetric plane are also shown in Fig. 7. For angle of attack of 61, the stagnation point is located near the axis on the sphere cone; when the angle of attack increases to 17.51, the stagnation point is moved far away from the axis to the cone frustum section; when to 291, the stagnation point is moved very near to the shoulder. The windside sonic line merges into the boundary layer at the shoulder, while the leeside one at different place depending on the angle of attack. For lower angle of attack, 61 for example, the sonic line merges into the boundary layer at the shoulder, the same as the windside. When the angle of attack increases, the
merging location moves to the sphere-cone junction (for 17.51), even near the axis (for 291), and the sonic line has an inflection in the vicinity of the apex because of strong compressibility. The windside sonic line envelopes high pressure region, which dominates the total aerodynamic coefficients. The integrated axial (CA), normal(CN), lift (CL) and drag (CD) coefficients and the lift-to-drag ratio (L/D), are shown in Fig. 8 as a function of angle of attack from zero to 411. CA is predicted to decrease continuously as the magnitude of the angle of attack increases and CN is just the reverse. Moreover, CA is expected to be dominant in all total coefficients and bears an order of magnitude larger than CN. At small angle of attack, CL and CD are believed to hold the same trend as CN and CA, respectively. As a result, L/D increases with the increase of the magnitude of the angle of attack. It can be expected from computations that a trimmed L/D of 0.27 can be achieved if a trimmed angle of attack of 17.51 holds. The calculated CP locations for various angles of attack are shown in Fig. 9. Since the post-shock high pressure region is deviated from the symmetry axis with the increase of the magnitude of the angle of attack, CP moves away from the axis correspondingly. The trim lines for the given trimmed α or L/D are also shown Fig. 9. When the magnitude of the angle of attack increases, the slope of the trim line increases because of the CP offset, resulting in more skewed trim line with respect to the axis. Such departure from or skewness off the axis required for the trim condition give rise to a specific CG offset. Fig. 10 shows the pitch moment characteristic curves for the trimmed L/D equal to 0.27 with 5 specified CG locations. It can be seen that all the curves meet at the point α¼ 17.51 and CM ¼0, which is the description of trim condition. It can also be seen that the shift back and forth on the trim line affects the slope of the moment characteristic curve. The slope for CG close to the heatshield is negative which symbolizes a static pitch stable flight, while it becomes slightly negative, zero, or even
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Fig. 7. Shock shape and sonic line on the symmetry plane around the MSL body for different angles of attack. (a) a =-6° (b) a =-17.5° (c) a =-29°.
Fig. 8. The total coefficient curves.
positive for CG shifting backwards, causing a neutral or unstable flight. 3.3. Center of gravity discussion There exists a close relationship between the CG location and flight behaviors. In accordance with formula (6), we bring out the distribution of the trimmed α or L/D and the static pitch stability margin in the CG plane, as shown in Fig. 11. If the requirements of the trim condition and the static pitch stability are determinate, the needed CG is then exactly located from Fig. 11. In other words, CG location determines trim characteristics and stability,
Fig. 9. The center of pressure for various α and the trimline for the given trimmed α or L/D.
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Table 1 The sensitivity of aerodynamic performance to the CG position. Xcg ¼ 0.28, Ycg ¼ 0.024 to Xcg to Ycg
dCM/dα 0.0050 0.0200
L/D 0.290 6.950
almost horizontal in the concerned range of angle of attack. A radial CG offset of 1% reference diameter from the symmetry axis would result in a trimmed L/D as high as 0.07 and a pitch derivative as high as 0.003/1. In consequence, a small radial bias of CG may cause remarkable flight performance deviation for lifting entry, which should be paid close attention to in the process of aerodynamic design. 4. Conclusions Fig. 10. Pitch moment characteristic curves for 5 different CG locations with the trimmed L/D equal to 0.27.
Fig. 11. The trimmed α or L/D and the static pitch stability margin distribution in the CG plane (solid: stability margin isoline, dashed: trimmed α isoline).
which is meaningful for further aerodynamic design. As for the MSL entry capsule, CG is located near the volumetric center (30% of the total length) on the assumption of relatively uniform mass distribution. Supposing that the required trimmed angle of attack is 17.51 (or 0.27 for the trimmed L/D), we can offset CG for a dimensionless distance of 0.0045 in the radial direction. In addition, such offset can hold a static pitch stability margin of 0.003/1 at least, that is, both of the trim condition and static pitch stability are fulfilled for typical hypersonic lifting entry. Apart from CG discussion above, the sensitivity of total coefficients to the bias of CG also plays a significant role in aerodynamic design. A remarkable change of the trim characteristics and static pitch stability due to a small CG bias should be avoided. Sensitivity analysis from Table 1 shows that it is more radially sensitive than axially, especially for the trimmed L/D, because the trim line is
This paper deals with the static aerodynamic analysis for Mars exploration mission. A series of fully threedimensional Navier–Stokes computations of the hypersonic flowfield past an MSL-shaped capsule has been performed for the entry conditions with an effective specific heat ratio. Hypersonic continuum static coefficients were numerically predicted at the given state on the hypersonic trajectory. Aerodynamic performance analysis shows CG location determines trim characteristics and stability, which can be guidance on aerodynamic design. A CG radial offset of a dimensionless distance of 0.0045 achieves a trimmed L/D of 0.27 and a static pitch stability margin of at least 0.003/1, which can fulfill the hypersonic lifting entry. Finally, sensitivity study shows that a small radial bias of CG may cause remarkable flight performance deviation for lifting entry, which should be paid close attention to. Consequently, proper aerodynamic configuration and cabin equipment layout is needed for CG adjustment to meet the static aerodynamics requirements. This investigation provides researchers with guidelines for the optimization of the design of the Mars entry capsule.
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