Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-18T18:50:52.640Z Has data issue: false hasContentIssue false
  • English
  • Français

A uniformly valid solution for the hypersonic flow past blunted bodies

Published online by Cambridge University Press:  28 March 2006

W. Schneider
W. Schneider
Affiliation:
Deutsche Versuchsanstalt für Luft- und Raumfahrt, Institut für Theoretische Gasdynamik, Aachen, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

The plane and axisymmetric hypersonic flow past blunted bodies is investigated as an inverse problem (shock shape given). The fluid may behave as a real gas in local thermodynamic equilibrium. Viscosity and heat conduction are neglected. An analytical solution uniformly valid in the whole flow field (from the stagnation region up to large distances from the body nose) is given. The solution is based on two main assumptions: (i) the density ratio ε across the shock is very small, (ii) the pressure at a point P of the disturbed flow field is not very small compared with the pressure immediately behind the shock in the intersection point of the shock surface with its normal through P. Terms O(ε) are neglected in comparison with 1, but it is not necessary for the shock layer to be thin. The change of velocity along streamlines is taken into account. In order to calculate the flow quantities one has to evaluate only two integrals (equations (49) and (53) together with the boundary values (5) and (10)). The application of the solution is illustrated and the accuracy is tested in some examples.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 31 , Issue 2 , 29 January 1968 , pp. 397 - 415
Copyright
© 1968 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Brocher, E. F. 1960 Comments on the behaviour of Sedov's blast-wave solution as γ $1. J. Aero/Space Sci. 27, 955–6.Google Scholar
Busemann, A. 1933 Flüssigkeits- und Gasbewegung. In Handwörterbuch der Naturwissenschaften, vol. iv, 2nd ed., pp. 244–79. Jena: Gustav Fischer.
Cheng, H. K. & Gaitatzes, G. A. 1966 Use of the shock-layer approximation in the inverse hypersonic blunt-body problem AIAA J. 4, 406–13.Google Scholar
Chester, W. 1956 Supersonic flow past a bluff body with a detached shock. Part I, Two-dimensional body J. Fluid Mech. 1, 353–65. Part II, Axisymmetrical body. J. Fluid Mech. 1, 490–6.Google Scholar
Freeman, N. C. 1956 On the theory of hypersonic flow past plane and axially symmetric bluff bodies J. Fluid Mech. 1, 366–87.Google Scholar
Freeman, N. C. 1960 A note on the explosion theory of Sedov with application to the Newtonian theory of unsteady hypersonic flow. J. Aero/Space Sci. 27, 77–8 and 956.Google Scholar
Hayes, W. D. & Probstein, R. F. 1966 Hypersonic Flow Theory, vol. I, 2nd ed. New York: Academic Press.
Honda, M. 1965 Stream-function co-ordinates in rotational flow and analysis of the flow in a shock layer. Part I J. Inst. Math. Applies. 1, 127.Google Scholar
Honda, M. 1966 Stream-function co-ordinates in rotational flow and analysis of the flow in a shock layer. Part II J. Inst. Math. Applies. 2, 55.Google Scholar
Inouye, M. & Lomax, H. 1962 Comparison of experimental and numerical results for the now of a perfect gas about blunt-nosed bodies. NASA TN D-1426.Google Scholar
Lighthill, M. J. 1957 Dynamics of a dissociating gas. Part I. Equilibrium flow J. Fluid Mech. 2, 1–32.Google Scholar
Maslen, S. H. 1964 Inviscid hypersonic flow past smooth symmetric bodies AIAA J. 2, 1055–61.Google Scholar
Mirels, H. 1962 Hypersonic flow over slender bodies associated with power-law shocks. In Advances in Applied Mechanics (H. L. Dryden & Th. v. Karman, eds.), vol. 7, pp. 1–54, 317–19. New York: Academic Press.
Schneider, W. 1966 Über die Theorie dünner Hyperschall-Störschichten. DLR-For-schungsbericht 66–42. Zentralstelle für Luftfahrtdokumentation und -information, München.
Sychev, V. V. 1960 On the theory of hypersonic gas flow with a power-law shock wave. Prikladnaya Matematika i Mekhanika, 24, 518–23, transl. in J. Appl. Math. Mech. 24, 756–64.Google Scholar
Van Dyke, M. D. 1958 A model of supersonic flow past blunt axisymmetric bodies, with application to Chester's solution J. Fluid Mech. 3, 515–22.Google Scholar
Van Dyke, M. D. 1966 The blunt-body problem revisited. In Fundamental Phenomena in Hypersonic Flow (J. G. Hall, ed.), pp. 52–65.
Van Dyke, M. D. & Gordon, H. D. 1959 Supersonic flow past a family of blunt axisymmetric bodies. NASA Tech. Rept. R-1.Google Scholar
Whitham, G. B. 1957 A note on the stand-off distance of the shock in high speed flow past a circular cylinder, Comm. Pure Appl. Math. 10, 531–5.Google Scholar
Yakura, J. K. 1962 Theory of entropy layers and nose bluntness in hypersonic flow. In Hypersonic Flow Research (F. R. Riddell, ed.), pp. 421–70. New York: Academic Press.