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Approximate and exact numerical computation of supersonic flow over an airfoil

Published online by Cambridge University Press:  20 April 2006

Timothy S. Lewis  and
Lawrence Sirovich
Timothy S. Lewis
Affiliation:
Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912
Lawrence Sirovich
Affiliation:
Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912
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Abstract

An approximate solution is developed for two-dimensional, steady, inviscid supersonic flow over an airfoil. This approximation produces accurate results for a wide range of Mach numbers and airfoil thicknesses. It is used as the starting point for a rapidly convergent iterative numerical solution of the exact equations. A co-ordinate system consisting of the principal characteristics and streamlines is employed. Examples computed for a symmetric airfoil reveal several interesting features in the tail shock and the flow behind the airfoil.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 112 , November 1981 , pp. 265 - 282
Copyright
© 1981 Cambridge University Press

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References

Adamson, T. C. 1968 J. Fluid Mech. 34, 735.
Babenko, K. I., Voskresenskiy, G. P., Lyubimov, A. N. & Rusanov, V. V. 1966 Three-dimensional flow of ideal gas past smooth bodies. N.A.S.A. Tech. Transl. F-380.
Caughey, D. A. 1969 Second-order wave structure in supersonic flows. N.A.S.A. CR-1438.
Chong, T. H. & Sirovich, L. 1980 Phys. Fluids 23, 1296.
Eggers, A. J., Syvertson, C. A. & Kraus, S. 1953 N.A.C.A. Rep. no. 1123.
Epstein, P. S. 1931 Proc. Nat. Acad. Sci. 17, 532.
Friedrichs, K. O. 1948 Comm. Pure Appl. Math. 1, 211.
Hayes, W. D. & Probstein, R. F. 1966 Hypersonic Flow Theory, vol. i. Academic.
Holt, M. 1977 Numerical Methods in Fluid Dynamics. Springer.
Jones, J. G. 1963 J. Fluid Mech. 17, 506.
Liepmann, H. W. & Roshko, A. 1957 Elements of Gasdynamics. Wiley.
Lighthill, M. J. 1960 Higher Approximations in Aerodynamic Theory. Princeton University Press.
Mahony, J. J. 1955 J. Aero. Sci. 22, 673.
Mahony, J. J. & Skeat, P. R. 1955 Austr. Aero. Res. Lab., Aero. Note 147.
Meyer, R. E. 1957 Q. Appl. Math. 14, 433.
Meyer, R. E. 1960 Theory of characteristics in inviscid gas dynamics, Handbuch der Physik, vol. ix. Springer.
Salas, M. D. 1976 A.I.A.A. J. 14, 583.
Sirovich, L. & Chong, T. H. 1980 Phys. Fluids 23, 1291.
Taylor, T. D., Ndefo, E. & Masson, B. S. 1972 J. Comp. Phys. 9, 99.