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Abstract
The heat transfer over various reentry axisymmetric configurations is studied numerically by solving time-dependent compressible laminar Navier-Stokes equations. The governing fluid flow equations are disrectized in spatial coordinates employing a finite volume approach, which reduces the equations to semi-discretized ordinary differential equations. Temporal integration is performed using multi-stage Runge-Kutta time stepping scheme. A local time step is used to achieve steady state solution. The numerical simulation is carried out on a mono-block structured grid. The numerical computation is carried out for freestream Mach number of 5.0. The numerical scheme captures well all the essential flow field features such as bow shock wave, sonic line, expansion fan on the corner, recompression shock wave and recirculating flow in the base region. Comparisons of the flow field, surface pressure, skin friction coefficient and wall heat flux results are made between different configurations of the reentry capsules such as ARD (ESA’ s Atmospheric Reentry Demonstrator), CARINA, Apollo, Muses-C (Mu Science Engineering Satellite), OREX (Orbital Reentry Experiments) and Beagle-2. The effects of geometrical parameters of the different reentry capsules on surface pressure, skin friction coefficients and heat flux and forebody aerodynamic drag are analyzed. Base pressure is independent of the forebody shape of the reentry capsules. The effects of module geometry on the flow field are numerically analyzed which may be useful for optimization of the reentry capsule.
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References
- Gnoffo, P.A., Price, J.M. and Braum, R.D., "On the Computation of Near Wake", Aerobrake Flow Fields, AIAA Paper 91-1371, June 1991.
- Grasso, F. and Marinir, M., "Solution of Hypersonic Flows with Total Variation Diminishing Multigrid Techniques", Computer and Fluids, Vol. 23, No. 5, 1995, pp. 571-592.
- Venkatapathy, E., Palmer, G., and Prabhu, D.K., "AFE Base Computations", AIAA Paper 91-1372, June 1991.
- Allen, J.S. and Cheng, S.I., "Numerical Solution of the Compressible Navier-Stokes Equations for the Near Wake", Physics of Fluids, Vol. 13, No. 1, 1970, pp. 37-52.
- Weinbaum, S., "Rapid Expansion of a Expansion of a Supersonic Boundary Layer and its Applications to the Near Wake", AIAA Journal, Vol. 4, No. 2, 1966, pp. 217-226.
- Osu, H., Abe, T., Ohnishi, Y., Sasoh, A. and Takayama, K., "Numerical Investigation of High Enthalpy Flow Generated by Expansion Tube", AIAA Journal, Vol. 40, No. 12, 2002, pp. 2423-2430.
- Grasso, F. and Pettinelli, C., "Analysis of Laminar Near Wake Hypersonic Flow", Journal of Spacecraft and Rockets, Vol. 32, No. 6, 1995, pp. 970-980.
- Tai, C-S. and Kao, A.F., "Navier-Stokes Solver for Hypersonic Flow Over a Slander Cone", Journal of Spacecraft and Rockets, Vol. 31, No. 1, 1994, pp.215-222.
- Lamb, J.P. and Oberkampf, W.L., "Review and Development of Base Pressure and Base Heating Correlations in Supersonic Flow", Journal of Spacecraft and Rockets, Vol. 32, No. 1, 1995, pp. 8-23.
- Wood, A.W., Gnoffo, P.A. and Rault, D.F.G., "Aero- dynamic Analysis of Commercial Experiment Trans- port Reentry Capsule", Journal of Spacecraft and Rockets, Vol. 34, No. 5, 1996, pp. 643-646.
- Teramoto, S., Hiraki, K. and Fujii, K., "Numerical Analysis of Dynamic Stability of a Reentry Capsule at Transonic Speed", AIAA Journal, Vol. 39, No. 4, April 2001, pp. 646-653.
- Y amamoto, Y . and Y oshioka, M., "CFD and FEM Coupling Analysis of OREX Aero-thermodynamic Flight Data", AIAA 95-2087.
- Tam, L.T., "LU-SGS Implicit Scheme for Entry Ve- hicle Flow Computation and Comparison with Aero- dynamic Data", AIAA 92-2671 CP, 1992.
- Liever, P.A., Habchi, S.D., Burnell, S. I. and Lingard, J.S., "Computational Fluid Dynamics Prediction of the Beagle 2 Aerodynamic Data Base", Journal of Spacecraft and Rockets, Vol. 40, No. 5, 2003, pp.632-638.
- Haas, B.L. and Venkatapathy, E., "Mars Path Finder Computations Including Base Heating Predictions", AIAA 95-2086, 1995.
- Longo, J.M.A., Orlowski, M. and Bruck., "Considerations of CFD Modeling for the Design of Reentry Vehicle", Aerospace Science Technology, Vol.4, 2000, pp. 337-345.
- Sietzen, F., "Heir to Apollo: Shaping the CEV, Aero- space America, January 2006, pp. 30- 36.
- Mehta, R.C., "Computation of Flow Field Over Reentry Capsules at Supersonic Mac h Numbers", Computational Fluid Dynamics Journal, Vol. 13, Oct. 2004, pp. 585-596.
- Peyret, R. and Viviand, H., "Computational Methods for Fluid Flow", Springer-Verlag, New York, 1993.
- Jameson, A., Schmidt, W. and Turkel, E., "Numerical Solution of Euler Equations by Finite Volume Methods Using Runge-Kutta Time Stepping Schemes", AIAA 81-1259, 1981.
- Mehta, R.C., "Numerical Analysis of Aerodynamic Drag Coefficient for Various Reentry Configurations at High Speed", AIAA 2006-3173, 2006.
- Mehta, R.C., Numerical Simulation of Supersonic Flow Past Reentry Capsules, Shock Waves", DOI 10.1007/s 00193-005-0003-0, 2006.
References
Gnoffo, P.A., Price, J.M. and Braum, R.D., "On the Computation of Near Wake", Aerobrake Flow Fields, AIAA Paper 91-1371, June 1991.
Grasso, F. and Marinir, M., "Solution of Hypersonic Flows with Total Variation Diminishing Multigrid Techniques", Computer and Fluids, Vol. 23, No. 5, 1995, pp. 571-592.
Venkatapathy, E., Palmer, G., and Prabhu, D.K., "AFE Base Computations", AIAA Paper 91-1372, June 1991.
Allen, J.S. and Cheng, S.I., "Numerical Solution of the Compressible Navier-Stokes Equations for the Near Wake", Physics of Fluids, Vol. 13, No. 1, 1970, pp. 37-52.
Weinbaum, S., "Rapid Expansion of a Expansion of a Supersonic Boundary Layer and its Applications to the Near Wake", AIAA Journal, Vol. 4, No. 2, 1966, pp. 217-226.
Osu, H., Abe, T., Ohnishi, Y., Sasoh, A. and Takayama, K., "Numerical Investigation of High Enthalpy Flow Generated by Expansion Tube", AIAA Journal, Vol. 40, No. 12, 2002, pp. 2423-2430.
Grasso, F. and Pettinelli, C., "Analysis of Laminar Near Wake Hypersonic Flow", Journal of Spacecraft and Rockets, Vol. 32, No. 6, 1995, pp. 970-980.
Tai, C-S. and Kao, A.F., "Navier-Stokes Solver for Hypersonic Flow Over a Slander Cone", Journal of Spacecraft and Rockets, Vol. 31, No. 1, 1994, pp.215-222.
Lamb, J.P. and Oberkampf, W.L., "Review and Development of Base Pressure and Base Heating Correlations in Supersonic Flow", Journal of Spacecraft and Rockets, Vol. 32, No. 1, 1995, pp. 8-23.
Wood, A.W., Gnoffo, P.A. and Rault, D.F.G., "Aero- dynamic Analysis of Commercial Experiment Trans- port Reentry Capsule", Journal of Spacecraft and Rockets, Vol. 34, No. 5, 1996, pp. 643-646.
Teramoto, S., Hiraki, K. and Fujii, K., "Numerical Analysis of Dynamic Stability of a Reentry Capsule at Transonic Speed", AIAA Journal, Vol. 39, No. 4, April 2001, pp. 646-653.
Y amamoto, Y . and Y oshioka, M., "CFD and FEM Coupling Analysis of OREX Aero-thermodynamic Flight Data", AIAA 95-2087.
Tam, L.T., "LU-SGS Implicit Scheme for Entry Ve- hicle Flow Computation and Comparison with Aero- dynamic Data", AIAA 92-2671 CP, 1992.
Liever, P.A., Habchi, S.D., Burnell, S. I. and Lingard, J.S., "Computational Fluid Dynamics Prediction of the Beagle 2 Aerodynamic Data Base", Journal of Spacecraft and Rockets, Vol. 40, No. 5, 2003, pp.632-638.
Haas, B.L. and Venkatapathy, E., "Mars Path Finder Computations Including Base Heating Predictions", AIAA 95-2086, 1995.
Longo, J.M.A., Orlowski, M. and Bruck., "Considerations of CFD Modeling for the Design of Reentry Vehicle", Aerospace Science Technology, Vol.4, 2000, pp. 337-345.
Sietzen, F., "Heir to Apollo: Shaping the CEV, Aero- space America, January 2006, pp. 30- 36.
Mehta, R.C., "Computation of Flow Field Over Reentry Capsules at Supersonic Mac h Numbers", Computational Fluid Dynamics Journal, Vol. 13, Oct. 2004, pp. 585-596.
Peyret, R. and Viviand, H., "Computational Methods for Fluid Flow", Springer-Verlag, New York, 1993.
Jameson, A., Schmidt, W. and Turkel, E., "Numerical Solution of Euler Equations by Finite Volume Methods Using Runge-Kutta Time Stepping Schemes", AIAA 81-1259, 1981.
Mehta, R.C., "Numerical Analysis of Aerodynamic Drag Coefficient for Various Reentry Configurations at High Speed", AIAA 2006-3173, 2006.
Mehta, R.C., Numerical Simulation of Supersonic Flow Past Reentry Capsules, Shock Waves", DOI 10.1007/s 00193-005-0003-0, 2006.