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On a singular point in the Newtonian theory of hypersonic flow

Published online by Cambridge University Press:  28 March 2006

N. C. Freeman
N. C. Freeman
Affiliation:
National Physical Laboratory, Teddington, England
This research was undertaken while the author was on leave of absence at Princeton University.
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Abstract

An examination of the Newtonian inviscid theory of hypersonic flow past a sphere is made in the neighbourhood of the singular point which occurs at θ = 60°. A uniformly valid theory is developed in this neighbourhood which exhibits the limiting detached ‘free-layer’ behaviour postulated by Hayes and Lighthill in the limit as γ → 1. A complete solution is obtained which gives details of streamline and shock wave shape, pressure distribution, etc. for γ − 1 small.

Reasons are given why the empirical ‘modified’ Newtonian theory of Lees proves to be a good approximation to experimentally determined pressure distributions.

A novel check to the theory is provided by a simple power-law relation between the pressure on the sphere surface and the distance of the shock wave away from sphere at the same point.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 8 , Issue 1 , May 1960 , pp. 109 - 122
Copyright
© 1960 Cambridge University Press

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References

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