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On the outer-edge problem of a hypersonic boundary layer

Published online by Cambridge University Press:  29 March 2006

Richard S. Lee  and
H. K. Cheng
Richard S. Lee
Affiliation:
McDonnell Douglas Astronautics Company-Western Division, Santa Monica, California
H. K. Cheng
Affiliation:
University of Southern California, Los Angeles, California
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Abstract

Existing analytical treatments of the hypersonic strong interaction problem adopt the two-region structure of the classical boundary-layer theory; however, the uneven heating and external vorticity created by the highly curved, leading-edge shock wave leads to the question of the uniform validity of the boundary-layer approximation near the boundary-layer edge. Recently Bush (1966), using a non-linear viscosity-temperature law (μ ∞ Tω, ω < 1) instead of the linear one (μ ∞ T) used by previous investigators, demonstrated the need to analyze separately a transitional layer intermediate between the inviscid region and the boundary layer. In this paper, an asymptotic analysis of the Navier-Stokes equations in von Mises's variables, allowing a three-region structure, is carried out for the case of μ ∞ T. Results, with the second-order effects associated with heating and vorticity accounted for, show that a separate analysis of the transitional region is not strictly necessary in this case, and hence the equivalence of the two-region approach is confirmed. On the other hand, it is shown that the second-order boundary-layer correction owing to the heating and vorticity effects, not considered by Bush, is necessary in order to determine a uniformly valid temperature distribution in the physical variables. Numerical results for an insulated and a cold flat plate, considerably different from those of others, are obtained.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 38 , Issue 1 , 14 August 1969 , pp. 161 - 179
Copyright
© 1969 Cambridge University Press

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References

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