A Conical Thin-Shock-Layer Theory Uniformly Valid in the Entropy Layer

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Report Number: FDL TDR 64-82
Author(s): Melnik, Robert E.
Corporate Author(s): Grumman Aircraft Engineering Corporation
Laboratory: Air Force Flight Dynamics Laboratory
Date of Publication: 1965-01
Pages: 233
Contract: AF 33(657)-7313
DoD Project: 8219
DoD Task: 821902
Identifier: AD0614444

This paper is concerned with the thin-shock-layer theory of hypersonic flow over general conical surfaces. A small parameter, E, representative of the density ratio across the shock wave is introduced and systematic expansions of the exact nonlinear equations of conical flow are constructed. By combining the method of 'inner and outer expansions' with the 'P.L.K.' method the author obtains a two layer solution and the associated composite expansion that is uniformly valid in the entropy layer. Formulas for the first two terms of the various expansions are given in terms of a number of quadratures. The discontinuities of entropy, density, and radial velocity appearing in the limit solution are replaced by regions of rapid variation in the uniformly valid solution. To illustrate the general character of the entropy layer corrections, the first order terms of the expansions were evaluated for two specific cases: the hypersonic flow over a slightly yawed circular cone, and the hypersonic flow in the vicinity of a conical symmetry plane. In both cases all integrations were carried out analytically and explicit solutions were obtained. For the case of a circular cone the present theory reproduced the first order results obtained by Cheng in an earlier analysis.

Provenance: Lockheed Martin Missiles & Fire Control

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