Shock Waves

, 15:31 | Cite as

Numerical simulation of supersonic flow past reentry capsules

Original Article


The flow fields over ARD (ESA's atmospheric reentry demonstrator), OREX (orbital reentry experiments) and spherically blunted cone-flare reentry configurations are numerically obtained by solving time-dependent, axisymmetric, compressible Navier–Stokes equations for freestream Mach numbers range of 1.2–6.0. The fluid dynamics are discretized in spatial coordinates employing a finite volume approach which reduces the governing equations to semi discretized ordinary differential equations. Temporal integration is performed using the multistage Runge–Kutta time-stepping scheme. A local time step is used to achieve steady-state solution. The numerical simulation is carried out on a structured grid. The flow-field features around the reentry capsule, such as bow shock wave, sonic line, expansion fan and recirculating flow in the base region are obtained. A good agreement is found between the calculated value of aerodynamic drag coefficient of the spherically blunted cone/fare reentry configuration with the experimental data. The effects of geometrical parameters, such as radius of the spherical cap, half cone angle, with sharp shoulder edge and with smooth shoulder edge on the flow-field have been numerically investigated for various reentry configuration which will be useful for optimization of the reentry capsule.


Supersonic flows Computational fluid dynamics Reentry capsules 


  1. 1.
    Chester, W.: Supersonic flow past a bluff body with a detached shock. J. Fluid Mech. 1, 353–365 (1956)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Freeman, N.C.: On the theory of hypersonic flow past plane and axially symmetric bluff bodies. J. Fluid Mech. 1, 353–365 (1956)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Lighthill, M.J.: Dynamics of a dissociating gas, Part 1: Equilibrium flow. J. Fluid Mech. 2, 1–32 (1957)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Venkatapathy, E., Palmer, G., Prabhu, D.K.: AFE base computations including base heating predictions. AIAA Paper 91–1372 (June 1991)Google Scholar
  5. 5.
    Haas, B.L., Venkatapathy, E.: Mars Pathfinder computations including base heating predictions. AIAA Paper 95–2086 (1995)Google Scholar
  6. 6.
    Wood, W.A., Gnoffo, D.F.G., Rault, D.F.G.: Commercial Experiment Transport reentry capsule. J. Spacecraft Rockets 33(5), 643–646 (1996)CrossRefGoogle Scholar
  7. 7.
    Yamamoto, Y., Yoshioka, M.: CFD and FEM coupling analysis of OREX aerothermodynamic flight data. AIAA Paper 95–2087 (1995)Google Scholar
  8. 8.
    Tam, L.T.: LU-SGS Implicit Scheme for entry vehicle flow computation and comparison with aerodynamic flight data. AIAA paper 95–2671 CP (1992)Google Scholar
  9. 9.
    Menne, S.: Computation of non-winged vehicle aerodynamics in the low supersonic rane. In: Proceedings of the Second European Symposium on Aerothermodynamics for Space Vehicles, ESTEC, Noordwiik, The Netherlands, pp. 73–78, 21–25 November 1994.Google Scholar
  10. 10.
    Solazzo, M.A., Sansone, A., Gasbarri, P.: Aerodynamic characterization of the Carina reentry module in the low supersonic regimes. In: Proceedings of the Second European Symposium on Aerothermodynamics for Space Vehicles, ESTEC, Noordwiik, pp. 41–47, 21–25 November 1994Google Scholar
  11. 11.
    Walpot, L.: Numerical Analysis of the ARD capsule in S4 wind tunnel. In: Proceedings of the Fourth European Symposium on Aerothermodynamics for Space Applications, Capua, Italy, pp. 523–527, 15–18 October ESA, 2001Google Scholar
  12. 12.
    Lamb, J.P., Oberkampf, W.L.: Review and development of base pressure and base heating correlations in supersonic flow. J. Spacecraft Rockets 32(1), 8–23 (1995)CrossRefGoogle Scholar
  13. 13.
    Liever, P.A., Habchi, S.D., Burnell, S.I., Lingard, J.S.: Computational prediction of the Beagle 2 aerodynamic database. J. Spacecraft Rockets 40(5), 632–638 (2003)Google Scholar
  14. 14.
    Osu, H., Abe, T., Ohnishi, Y., Sasoh, A., Takayama, K.: Numerical investigation of high-enthaly flow generated by expansion tube. AIAA J. 40(12), 2423–2430 (2002)Google Scholar
  15. 15.
    Tai, C-S., Kao, A-F.: Navier-Stokes solver for hypersonic flow over a slander cone. J. Spacecraft Rockets 31(1), 215–222 (1994)CrossRefGoogle Scholar
  16. 16.
    Teramoto, S., Hiraki, K., Fujii, K.: Numerical analysis of dynamic stability of a reentry capsule at transonic speeds. AIAA J 39(4), 646–653 (2001)CrossRefGoogle Scholar
  17. 17.
    Teramoto, S., Fujii, K.: Mechanism of dynamic instability of a reentry capsule at transonic speeds. AIAA J 40(12), 2467–2475 (2002)Google Scholar
  18. 18.
    Otten, H.B.A.: Preliminary computational investigation on aerodynamic phenomena on DELFT aerospace reentry test vehicle. In: Proceedings of the Fourth Symposium on Aerothermodynamics for Space Applications, Capua, Italy, pp. 207–213, ESA, 15–18 October 2001Google Scholar
  19. 19.
    Peyret, R., Viviand, H.: Computational Methods for Fluid Flow. Springer-Verlag, New York (1993)Google Scholar
  20. 20.
    Jameson, A., Schmidt, W., Turkel, E.: Numerical solution of Euler equations by finite volume methods using Runge-Kutta time stepping schemes. AIAA Paper 81–1259 (1981)Google Scholar
  21. 21.
    Mehta, R.C.: Comparitive study of surface pressure fluctuations over bulbous heat shield at mach 0.95. Comput. & Fluids 30(6), 689–709 (2001)MATHCrossRefGoogle Scholar
  22. 22.
    Mehta, R.C.: Numerical heat transfer study over spiked blunt bodies at Mach 6.8. J. Spacecraft Rockets 37(5), 700–703 (2000)MathSciNetGoogle Scholar
  23. 23.
    Shang, J.S.: Numerical simulation of wing-fuselage interference aerodynamic. AIAA Paper 81–0084 (1981)Google Scholar
  24. 24.
    Mehta, R.C.: Flowfield over bulbous heat shield in transonic and low supersonic speeds. J. Spacecraft Rockets 35(1), 102–105 (1998) AIAA Paper 97–2256 (1997)MathSciNetGoogle Scholar
  25. 25.
    Bertin, J.J.: Hypersonic Aerothermodynamics. p. 297. AIAA Education Series, AIAA Press, VA, USA pp. 297 (1994)Google Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Aerodynamics DivisionVikram Sarabhai Space CentreTrivandrumIndia

Personalised recommendations