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Hypersonic Flow with Attached Shock Waves over Delta Wings

Published online by Cambridge University Press:  07 June 2016

B. A. Woods*
Affiliation:
School of Mathematics, University of Leeds*
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Summary

Hypersonic conical flows over delta wings are treated in the thin-shock-layer approximation due to Messiter. The equations are hyperbolic throughout, even in regions where the full equations are elliptic, and have not hitherto been solved for flows with attached shock waves. The concept of the simple wave has been used to construct a class of solutions for such flows; they contain discontinuities in flow variables and shock slope but, for the case of flow over a delta wing with lateral symmetry, agreement with results of numerical solutions of the full equations is good. The method is applied to plane delta wings at yaw, and to wings with anhedral and dihedral. For the flow at the tip of a rectangular wing, it is shown that two distinct solutions may be constructed.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society. 1970

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References

1. Messiter, A. F. Lift of slender delta wings according to Newtonian Theory. AIAA Journal, Vol. 1, No. 4, pp 794-802, April 1963.Google Scholar
2. Squire, L. C. Calculated pressure distributions and shock shapes on thick conical wings at high supersonic speeds. Aeronautical Quarterly, Vol. XVIII, pp 185-206, May 1967.CrossRefGoogle Scholar
3. Küchemann, D. Hypersonic aircraft and their aerodynamic problems. Progress in Aeronautical Sciences, Vol. 6, Pergamon Press, Oxford, 1965.Google Scholar
4. Hayes, W. D. and Probstein, R. F. Hypersonic flow theory. 2nd Edition, Vol. 1, Academic Press, New York, 1966.Google Scholar
5. Squire, L. C. Calculated pressure distributions and shock shapes on conical wings with attached shock waves. Aeronautical Quarterly, Vol. XIX, pp 31-50, February 1968.Google Scholar
6. Cole, J. D. and Bratnerd, J. J. Slender wings at high angles of attack in hypersonic flows. Hypersonic Flow Research (“Progress in Astronautics and Rocketry”, Vol. 7) edited by Riddell, F. R., Academic Press, New York, 1962.Google Scholar
7. Courant, R. and K. O., Friedrichs Supersonic flow and shock waves. Interscience Press, New York, 1948.Google Scholar
8. Babaev, D. A. Numerical solution of the problem of supersonic flow past the lower surface of a delta wing. (Translated from Russian.) AIAA Journal, Vol. 1, No. 9, pp 2224-2231, September 1963.Google Scholar
9. Babaev, D. A. Flow about a triangular wing for large values of M. (Translated from Russian.) USSR Computational Mathematics and Mathematical Physics. Vol. 3, No. 2, pp 528-532. 1963.Google Scholar
10. Malmuth, N. D. Three-dimensional perturbations on hypersonic wedge flow, AIAA Journal. Vol. 2, No. 8, pp 1383-1389, August 1964.Google Scholar
11. Melnik, R. E. and Scheuing, R. A. Shock layer structure and entropy layers in hypersonic conical flows. Hypersonic Flow Research, edited by Riddell, F. R., Academic Press, New York, 1962.Google Scholar
12. Melnik, R. E. A conical thin-shock-layer theory uniformly valid in the entropy layer. Grumman Aircraft Engineering Corporation, FDL-TDR-64-82, January 1965.Google Scholar