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Theoretical study of the transonic flow past wedge profiles with detached shock waves

Published online by Cambridge University Press:  20 April 2006

Michel Abboud
Michel Abboud
Affiliation:
Institut für Strömungslehre und Strömungsmaschinen, Universität (TH) Karlsruhe
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Abstract

This report presents a numerical study of the two-dimensional, steady and inviscid flow of a perfect gas past wedge profiles with detached shock waves for free-stream Mach numbers between 1.05 and 1.44.

Utilizing the hodograph transformation, a boundary-value problem for the mixed flow is formulated in the hodograph plane and subsequently solved by a finite-difference scheme, iterating respectively between the elliptic and hyperbolic regions. The use of boundary-fitted coordinates and a graded lattice failed to achieve satisfactory results, owing to either convergence difficulties or numerical inaccuracies introduced through the coordinate generator. On the other hand, Cartesian coordinates presented no convergence problems and yielded accurate results.

After transforming the solution back to the physical plane, the flow field between the shock wave and the limiting Mach wave is determined. A comparison of the results with experiments and other theories shows a good agreement both for the pressure distribution on the wedge and for the shock stand-off distance.

Also of special interest is a quantitative comparison of the results with the small-disturbance theory (solution of the Tricomi equation) and the limiting case of the free-stream Mach number 1.

Moreover, an example of the flow past round-nosed wedges, with and without an angle of attack, is treated using the inverse method.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 146 , September 1984 , pp. 181 - 201
Copyright
© 1984 Cambridge University Press

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