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A theoretical study of non-equilibrium blunt-body flows

Published online by Cambridge University Press:  28 March 2006

Raul J. Conti
Raul J. Conti
Affiliation:
Department of Aeronautics and Astronautics, Stanford University
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Abstract

Non-equilibrium inviscid flows behind a spherical-segment shock wave are investigated with the method of series truncation. This semi-analytical technique developed at Stanford is based on a systematic co-ordinate-perturbation scheme. The flow variables are expanded in series in powers of the longitudinal curvilinear co-ordinate leading away from the stagnation point. The problem is thus reduced to one of numerical integration of ordinary differential equations for functions of the normal co-ordinate. Unlike the similar situation of the Blasius series in boundary-layer theory, the present scheme–having to deal with elliptic equations–must resort to series truncation. As a consequence, a truncation error is introduced. The present paper shows a simple way of reducing this error.

The simplified air chemistry adopted is based on non-equilibrium dissociation and recombination of oxygen diluted in inert nitrogen. A wide spectrum of non-equilibrium régimes is investigated for a fixed set of flight conditions. In particular, near-frozen flows are followed to the vicinity of the stagnation point through a region of large temperature and concentration gradients located near the body. This equilibrium-drive region, arising from the singular nature of the frozen limit, is studied in some detail.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 24 , Issue 1 , January 1966 , pp. 65 - 88
Copyright
© 1966 Cambridge University Press

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References

Belotserkovskii, O. M. & Dushin, V. K. 1964 Nonequilibrium supersonic gas flow around blunt bodies. Zh. Vych. Mat. i Matem. Fiz. 4, 61.Google Scholar
Bloom, M. H. & Steiger, M. H. 1960 Inviscid flow with non-equilibrium molecular dissociation for pressure distributions encountered in hypersonic flight. J. Aerospace Sci. 27, 821.Google Scholar
Blythe, P. A. 1963 The effects of vibrational relaxation on hypersonic flow past blunt bodies. Aer. Quart. 14, 357.Google Scholar
Chung, Paul 1961 Hypersonic viscous shock layer of nonequilibrium dissociating gas. NASA TR no. R-109.Google Scholar
Conti, R. J. 1964 Stagnation equilibrium layer in nonequilibrium blunt-body flows. AIAA J. 2, 2044.Google Scholar
Ellington, D. 1963 An approximate method for calculating hypersonic nonequilibrium airflows past blunt bodies. Canad. Arm. Res. and Dev. Establ. TR no. 458/63.Google Scholar
Freeman, N. C. 1958 Non-equilibrium flow of an ideal dissociating gas. J. Fluid Mech. 4, 40.Google Scholar
Gibson, W. E. & Marrone, P. V. 1962 A similitude for nonequilibrium phenomena in hypersonic flight. AGARD Meeting on high Temperature Aspects of Hyp. Fluid Dyn., Brussels, Belgium, April 1962.
Hall, J. G., Eschenroeder, A. Q. & Marrone, P. V. 1962 Blunt-nose inviscid airflows with coupled nonequilibrium processes. J. Aero Sci. 29, 1038.Google Scholar
Hayes, D. H. & Probstein, R. F. 1959 Hypersonic Flow Theory. New York: Academic Press.
Kao, H. C. 1964 Hypersonic viscous flow near the stagnation streamline of a blunt body. AIAA J. 2, 1892.Google Scholar
Lee, R. H. & Chu, S. T. 1964 Nonequilibrium inviscid flow about blunt bodies. Aerospace Corp. SSD-TDR-63–369.Google Scholar
Lick, W. 1960 Inviscid flow of a reacting mixture of gases around a blunt body. J. Fluid Mech. 7, 128.Google Scholar
Lin, S. C. & Teare, J. D. 1961 A streamtube approximation for calculation of reaction rates in the inviscid flow field of hypersonic objects. 6th Symp. on Ballistic Mis. and Aer. Tech., vol. 4. New York: Academic Press.
Lun'Kin, Iu. P. & Popov, F. D. 1964 Influence of nonequilibrium dissociation on supersonic flow around blunt bodies. Zh. Vych. Mat. i Matem. Fiz. 4, 896.Google Scholar
Marrone, P. V. 1963 Inviscid, nonequilibrium flow behind bow and normal shock waves, Part I. Cornell Aer. Lab. Rep. no. QM-1626-A-12(I).Google Scholar
Murzinov, I. N. 1961 The flow of gas near the stagnation point of a blunt body with a finite rate of excitation of vibrational degrees of freedom. Akad. Nauk SSSR Mek. i Mashin., no. 6, p. 33.Google Scholar
Schlichting, H. 1960 Boundary Layer Theory, p. 146 (4th ed.). New York: McGraw-Hill.
Shih, W. C. L. & Baron, J. R. 1964 Nonequilibrium blunt-body flow using the method of integral relations. AIAA J. 2, 1062.Google Scholar
Springfield, J. F. 1964 Steady, inviscid flow of a relaxing gas about a blunt body with supersonic velocity. 1964 Heat Tr. and Fl. Mech. Inst., p. 182. Stanford University Press.
Swigart, R. J. 1962 A theory of asymmetric hypersonic blunt-body flows. Stanford U. SUDAER no. 120; also AIAA J. 1, 1034.Google Scholar
Van Dyke, M. D. 1964a The blunt-body problem revisited. Internat. Hyp. Symp., Buffalo, N.Y., 25 June 1964.Google Scholar
Van Dyke, M. D. 1964b The circle at low Reynolds number as a test of the method of series truncation. 11th Internat. Congress of Appl. Mech., Munich, 30 August 1964.Google Scholar