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Diffraction of shock waves by a moving thin wing

Published online by Cambridge University Press:  29 March 2006

L. Ting
Affiliation:
New York University, Bronx, N.Y.
M. Gunzburger
Affiliation:
New York University, Bronx, N.Y.

Abstract

An analytical solution is obtained for the flow field due to the impinging of a plane shock wave of arbitrary strength by a thin wing moving in the opposite direction. The planform and the thickness distribution of the wing can be arbitrary and the speed of the wing can be either supersonic or subsonic relative to the undisturbed stream ahead of the shock or to that behind the shock. The solution is a generalization of the previous solution of Ting & Ludloff for the diffraction of shock wave by a two-dimensional stationary airfoil to a three-dimensional wing moving with supersonic or subsonic speed relative to the stream ahead of or behind the shock. The solution is employed for the analysis of the changes in aerodynamic forces when an airplane encounters a blast wave or a shock wave of another airplane. It is also used to study the diffraction of a shock wave or an N-wave advancing over flat terrains.

Type
Research Article
Copyright
© 1970 Cambridge University Press

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References

Arora, N. L. 1968 An integral-transform method for shock-shock interaction studies. J. Fluid Mech. 34, 209.Google Scholar
Arora, N. L. 1969 Integral transforms for shock-shock interaction—three dimensional planar wings. J. Appl. Math. Phys. 20, 244.Google Scholar
Baker, E. B. & Copson, E. T. 1950 The Mathematical Theory of Huygen's Principle. Oxford University Press.
Blankenship, V. D. 1965 Shock-shock interaction on a slender supersonic cone. J. Fluid Mech. 22, 599.Google Scholar
Chester, W. 1954 The diffraction and reflection of shock waves. Quart. J. Mech. Appl. Math. 7, 57.Google Scholar
Chow, F. & Gunzburger, M. 1969 Numerical program and examples for diffraction of shock by wings. New York University Report NYU-AA-69-8.Google Scholar
Donovan, A. F. & Lawrence, H. R. 1957 Aerodynamic Components of Aircraft at High Speeds. Section A. Princeton, N.J.: Princeton University Press.
Gunzburger, M. 1969 Diffraction of shock wave by a thin wing-symmetric and anti-symmetric problem. Ph.D. Thesis, School of Engineering and Science, New York University.
Liepman, H. W. & Roshko, A. 1957 Elements of Gasdynamics. New York: John Wiley.
Lighthill, M. J. 1949 The diffraction of blast I. Proc. Roy. Soc. A 198, 454.Google Scholar
Ludloff, H. F. & Friedman, M. B. 1952 Diffraction of blasts by axisymmetric bodies. J. Aero. Sci. 19, 425.Google Scholar
Smyrl, J. F. 1963 The impact of a shock wave on a thin two-dimensional aerofoil moving at supersonic speed. J. Fluid Mech. 15, 223.Google Scholar
Ter-Minassiants, S. M. 1969 The diffraction accompanying the regular reflexion of a plane obliquely impinging shock wave from the walls of an obtuse wedge. J. Fluid Mech. 35, 391.Google Scholar
Ting, L. & Ludloff, H. F. 1952 Aerodynamics of blasts. J. Aero. Sci. 19, 317.Google Scholar