Hostname: page-component-7479d7b7d-k7p5g Total loading time: 0 Render date: 2024-07-14T00:45:22.808Z Has data issue: false hasContentIssue false
  • English
  • Français

Diffraction of a plane shock by an analytic blunt body

Published online by Cambridge University Press:  29 March 2006

John P. Moran  and
William K. Van Moorhem
John P. Moran
Affiliation:
University of Minnesota, Minneapolis
William K. Van Moorhem
Affiliation:
Cornell University, Ithaca, N.Y.
Get access Rights & Permissions [Opens in a new window]

Abstract

A study is made of the transient flow which results from the impingement of a plane shock on a blunt body. The analysis is based on Taylor-series expansions in the space and time variables of the flow properties and of the shape of the reflected shock. Coefficients of the series are determined numerically so as to satisfy the exact equations of motion and shock jump conditions. Convergence problems are ameliorated by recasting the series into continued fractions. While the analysis does not treat the transition from regular to Mach reflexion, it remains valid for all time in the subsonic region of the flow if the incident shock is sufficiently strong. In any case, it is accurate enough where it is valid to be useful for evaluation of more conventional numerical methods.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 38 , Issue 1 , 14 August 1969 , pp. 127 - 136
Copyright
© 1969 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

Ambrosio, A. & Wortman, A. 1962 Stagnation point shock detachment distance for flow around spheres and cylinders. ARS J. 32, 282.Google Scholar
Barnwell, R. W. 1967 Numerical results for the diffraction of a normal shock wave by a sphere and for the subsequent transient flow. NASA Tech. Rep. no. R-268.Google Scholar
Bogoslavskii, K. E. 1966 Nonstationary interaction of blunt bodies with a shock wave Sov. Phys.-Doklady, 11, 290–292.Google Scholar
Domb, C. 1965 Statistical mechanics of critical behaviour in magnetic materials. Magnetism, II A. New York: Academic Press.
Henrici, P. 1963 Some applications of the quotient-difference algorithm Proc. Symp. Appl. Math. 15, 159–183.Google Scholar
Lax, P. D. 1954 Weak solutions of nonlinear hyperbolic equations and their numerical computation Comm. Pure Appl. Math. 7, 159–193.Google Scholar
Leavitt, J. 1968 Computational aspects of the detached shock problem. AIAA J. 6, 1084–1088.Google Scholar
Moran, J. P. 1969 Initial stages of axisymmetric shock-on-shock interaction for blunt bodies. Phys. Fluids, to appear.Google Scholar
Pack, D. E. 1964 The reflexion and diffraction of shock waves J. Fluid Mech. 18, 549–576.Google Scholar
Shanks, D. 1955 Nonlinear transformations of divergent and slowly convergent sequences J. Math. Phys. 34, 1–42.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, 515–522.Google Scholar
Van Dyke, M. D. 1966 The blunt-body problem revisited. Fundamental Problems in Hypersonic Flow. Cornell University Press.
Van Tuyl, A. 1960 The use of rational approximations in the calculation of flows with detached shocks J. Aero. Sci. 27, 559–560.Google Scholar
Van Tuyl, A. 1967 Use of rational approximations in the calculation of flows past blunt bodies AIAA J. 5, 218–225.Google Scholar
Wall, H. S. 1948 Continued Fractions. New York: Van Nostrand.