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Supersonic flow of a vibrationally relaxing gas past a circular cone

Published online by Cambridge University Press:  12 April 2006

James Kao
Affiliation:
Department of the Mechanics of Fluids, University of Manchester, England Present address: Koninklijke/Shell Exploratie en Produktie Laboratorium, Volmorlaan 6, Rijswijk (Z.H.), Holland.
J. P. Hodgson
Affiliation:
Department of the Mechanics of Fluids, University of Manchester, England

Abstract

The steady supersonic flow of a vibrationally relaxing gas past a cone is studied using numerical methods. Near the tip of the cone the flow is obtained by means of a coordinate expansion and built on to this is a characteristic network used to obtain the remainder of the flow. Of particular interest is the development of the frozen shock at the tip into a relaxation-dominated wave at distances large compared with the width of the wave. The numerical results are presented in a concise similarity form which will permit accurate extrapolation to very weak waves in atmospheric air.

Type
Research Article
Copyright
© 1978 Cambridge University Press

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References

Blythe, P. A. 1969 Non-linear wave propagation in a relaxing gas. J. Fluid Mech. 37, 31.Google Scholar
Cabannes, H. & Stael, C. 1961 Singularities of attached shock waves in steady axially symmetric flow. J. Fluid Mech. 10, 289.Google Scholar
Chester, W. 1956 Supersonic flow past a bluff body with a detached shock. Part II. Axisymmetrical flow. J. Fluid Mech. 1, 490.Google Scholar
Chou, D. C. & Chu, B. T. 1971 On the decay of weak waves in axisymmetric non-equilibrium flow. J. Fluid Mech. 50, 355.Google Scholar
Clarke, J. F. & Sinai, Y. L. 1977 The wave system attached to a slender body in a supersonic relaxing gas stream. Basic results: the cone. J. Fluid Mech. 79, 499.Google Scholar
Dain, C. G. & Hodgson, J. P. 1975 The development of weak waves in the unsteady one-dimensional flow of a vibrationally relaxing gas ahead of an impulsively started piston. J. Fluid Mech. 69, 129.Google Scholar
Hodgson, J. P. & Johannesen, N. H. 1971 Real-gas effects in very weak shock waves in the atmosphere and the structure of sonic bangs. J. Fluid Mech. 50, 17.Google Scholar
Hodgson, J. P. & Johannesen, N. H. 1976 The effects of vibrational relaxation on the development of weak non-linear waves in air. Proc. 6th Int. Symp. Non-Linear Acoust., Moscow Staté Univ. pp. 3040.
Hornby, R. P. & Johannesen, N. H. 1975 The development of weak waves in the steady flow of a gas with vibrational relaxation past a thin wedge. J. Fluid Mech. 69, 109.Google Scholar
Khodyko, Y. V. 1964 Flow of a relaxing gas around a thin cone of revolution. N.A.S.A. Tech. Trans. F-334.Google Scholar
Kopal, Z. 1947 Tables of supersonic flow around cones. M.I.T. Centre Anal. Rep. no. 1.Google Scholar
Lighthill, M. J. 1956 Viscosity in waves of finite amplitude. In Surveys in Mechanics (ed. Batchelor & Davies), pp. 250351. Cambridge University Press.
Sedney, R. & Gerber, N. 1963 Non-equilibrium flow over a cone. A.I.A.A. J. 1, 11.Google Scholar
Sedney, R. & Gerber, N. 1967 Shock curvature and gradients at the tip of pointed axisymmetric bodies in non-equilibrium flow. J. Fluid Mech. 29, 765.Google Scholar
Taylor, G. I. & Maccoll, J. W. 1933 The pressure on a cone moving at high speeds. Proc. Roy. Soc. A 139, 838.Google Scholar
Vincenti, W. G. & Kruger, C. H. 1965 Physical Gas Dynamics, pp. 206 et seq. Wiley.