Sonic Line and Stand–Off Distance on Re–entry Capsule Shapes

  • Hans G. Hornung
  • Jan Martinez Schramm
  • Klaus Hannemann
Conference paper


In hypersonic flow over a sphere, the shock wave stand–off distance is related to the density ratio by
where Δ is the stand–off distance, r is the sphere radius, ρ  ∞  is the free–stream density and \(\overline\rho\) is the average density along the stagnation streamline, see e. g., Hornung [1]. For a sharp cone of a given angle, the stand–off distance increases linearly with \(\rho_\infty/\overline\rho\) from a critical onset point and is scaled by the base radius R of the cone, see e. g., Leyva [2]. For a spherically blunted cone, one may therefore expect a transition to occur between sphere behavior and sharp cone behavior. This would be undesirable for stability and heat–flux reasons. A possibly more benign shape is an oblate ellipsoid, as suggested by Brown [5]. We study features of such flows on the basis of perfect–gas computations. Since the density ratio is very sensitive to reaction rate in flows with vibrational and chemical relaxation, these phenomena are very important in entry of vehicles into atmospheres such as that of Mars. The computations are therefore extended to include the effects of reacting CO2 flows.


Density Ratio Standoff Distance Sonic Line Oblate Ellipsoid Sharp Cone 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Hornung, H.G.: Nonequilibrium dissociating flow over spheres and circular cylinders. J. Fluid Mech. 64, 725–736 (1972)Google Scholar
  2. 2.
    Leyva, I.A.: Shock detachment from a cone in reacting flow. In: Ball, G.J., Hillier, R., Roberts, G.T. (eds.) Proceedings of the 22nd International Symposium on Shock Waves, Southampton University Media (2000)Google Scholar
  3. 3.
    Quirk, J.J.: Amrita–A computational facility (for CFD modelling) VKI 29th CFD Lecture Series (1998), ISSN 0377-8312,
  4. 4.
    Schwamborn, D., Gerhold, T., Heinrich, R.: The DLR TAU Code: Recent Applications in Research and Industry. In: Proceedings of the European Conference on Computational Fluid Dynamics ECCOMAS CFD (2006),
  5. 5.
    Brown, J.L.: The Effect of Forebody Geometry on Turbulent Heating and Thermal Protections System Sizing for Future Mars Mission Concepts. In: 4th Interplanetary Planetary Probe Workshop (IPPW4), Pasadena, CA (June 2006)Google Scholar
  6. 6.
    Krasil’nikov, A.V., Nikulin, A.N., Kholodov, A.S.: Some features of flow over spherically blunted cones of large vertex angles. Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza (2), 179–181 (1975)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Hans G. Hornung
    • 1
  • Jan Martinez Schramm
    • 2
  • Klaus Hannemann
    • 2
  1. 1.GALCIT, CaltechPasadenaUSA
  2. 2.DLR-AS/RFGöttingenGermany

Personalised recommendations