Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-18T18:44:45.240Z Has data issue: false hasContentIssue false

An analytic approach to the method of series truncation for the supersonic blunt body problem

Published online by Cambridge University Press:  28 March 2006

Hsiao C. Kao
Affiliation:
Northrop Corporation, Norair Division, Hawthorne, California

Abstract

A method for obtaining analytic solutions to the problem of blunt bodies in the supersonic stream of an ideal gas is presented. The solutions are written in terms of power series whose coefficients are elementary functions. These solutions are approximate, but the approximation is rational, i.e. any higher approximation can, in principle, be obtained. Some of these higher approximations have been calculated. Examples are presented for various free-stream conditions and prescribed body shapes. These are compared with results from standard numerical procedure and with available experimental measurements.

Type
Research Article
Copyright
© 1967 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

Bazzhin, A. P. & Gladkov, A. A. 1963 Some considerations on the solution of converse problems by a series-expansion method (in Russian) Inzhenernyi Zhurnal 3, 51718.Google Scholar
Bohachevsky, I. O., Rubin, E. L. & Mates, R. E. 1965 A direct method for computation of nonequilibrium flows with detached shock waves. AIAA Paper no. 65–24.Google Scholar
Cheng, H. K. & Gaitatzes, G. A. 1966 Use of the shock layer approximation in the inverse hypersonic blunt body problem AIAA J. 4, 40613.Google Scholar
Conti, R. 1964 Stagnation equilibrium layer in nonequilibrium blunt-body flows AIAA J. 2, 20446.Google Scholar
Conti, R. 1966 A theoretical study of nonequilibrium blunt-body flows J. Fluid Mech. 24, 6588.Google Scholar
Hayes, W. D. & Probstein, R. F. 1959 Hypersonic Flow Theory, chaps. v and vi. New York: Academic Press.
Ince, E. L. 1926 Ordinary Differential Equations, chap. xii. New York: Dover.
Kao, H. C. 1965 A new technique for the direct calculation of blunt-body flow fields AIAA J. 3, 1613.Google Scholar
Kendall, J. M. 1959 Experiments on supersonic blunt-body flows. California Institute of Technology, JPL Progress Rept. no. 20–372.Google Scholar
Lax, P. D. 1954 Weak solutions of nonlinear hyperbolic equations and their numerical computations Communs. Pure and Appl. Math, 7, 15993.Google Scholar
Lomax, H. & Inouye, M. 1964 Numerical analysis of flow properties about blunt bodies moving at supersonic speeds in an equilibrium gas. NASA Tech. Rept. TR-R-204.Google Scholar
Maslen, S. H. 1964 Inviscid hypersonic flow past smooth symmetric bodies AIAA J. 2, 105561.Google Scholar
Swigart, R. J. 1963 A theory of asymmetric hypersonic blunt-body flows AIAA J. 1, 103442.Google Scholar
Van Dyke, M. D. & Gordon, H. D. 1959 Supersonic flow past a family of blunt axisymmetric bodies. NASA Tech. Rept. R-1.Google Scholar
Van Dyke, M. D. 1964 Perturbation methods in fluid mechanics, chap. III. New York: Academic Press.
Van Dyke, M. D. 1965 Hypersonic flow behind a paraboloidal shock wave. J. de MÉcanique, 4, 4, 47793.Google Scholar
Van Dyke, M. D. 1965 The blunt-body problem revisited. Fundamental Phenomena in Hypersonic Flow. Ed. by J. G. Hall. Ithaca, N.Y.: Cornell University Press.
Xerikos, J. & Anderson, W. A. 1965 An experimental investigation of the shock layer surrounding a sphere in supersonic flow AIAA J. 3, 4517.Google Scholar