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Analytical prediction of the transition from Mach to regular reflection over cylindrical concave wedges

Published online by Cambridge University Press:  20 April 2006

G. Ben-Dor  and
K. Takayama
G. Ben-Dor
Affiliation:
Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer Sheva, Israel
K. Takayama
Affiliation:
Institute of High Speed Mechanics, Tohoku University, Sendai, Japan
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Abstract

Two formulas, based on analytical considerations, which are capable of predicting the wedge angle of transition from Mach to regular reflection over cylindrical concave wedges, are developed. They are derived using Hornung, Oertel & Sandeman's (1979) conclusion that a Mach reflection can exist only if the corner-generated signals can catch up with the incident shock wave. The good agreement between the present models and the experimental results confirm Hornung et al.'s (1979) concept. The predictions of these models are in better agreement with experimental results than the predictions of Itoh, Okazaki & Itaya's (1981) model. The present models are very simple to use and apply but, like Itoh et al.'s (1981) model, they also lack the ability to account for the dependence of the transition angle on the radius of curvature of the cylindrical wedge.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 158 , September 1985 , pp. 365 - 380
Copyright
© 1985 Cambridge University Press

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References

Ben-Dor G. 1980 AIAA J. 18, 1143.
Ben-Dor, G. & Glass I. I. 1979 J. Fluid Mech. 92, 459.
Ben-Dor, G. & Takayama K. 1981 Can. Aero. & Space J. 27, 128.
Ben-Dor G., Takayama, K. & Kawauchi T. 1980 J. Fluid Mech. 100, 147.
Dewey J. M., Walker D. K., Lock, G. D. & Scotten L. N. 1983 In Shock Tubes and Waves (ed. R. D. Archer & B. E. Milton), pp. 144–149. Sydney Shock Tube Symposium Publishers.
Heilig W. H. 1969 Phys. Fluids Suppl. 12, I, 154.
Henderson, L. F. & Lozzi A. 1975 J. Fluid Mech. 68, 139.
Hornung H. G., Oertel, H. & Sandeman R. J. 1979 J. Fluid Mech. 90, 541.
Itoh, S. & Itaya M. 1979 In Shock Tubes and Waves (ed. A. Lifshitz & J. Rom), pp. 314–323. The Magnes Press, Hebrew University.
Itoh S., Okazaki, N. & Itaya M. 1981 J. Fluid Mech. 108, 383.
Milton B. E. 1975 AIAA J. 13, 1531.
Takayama, K. & Ben-Dor G. 1983 Israel Journal of Technology 21, 197.
Takayama K., Ben-Dor, G. & Gotoh J. 1981 AIAA J. 12, 1238.
Takayama, K. & Sasaki M. 1983 Rep. Inst. High Speed Mech., Tohoku Univ., Vol. 46. Sendai, Japan.
Von Neumann J. 1963 Collected Works, Vol. 6. Pergamon.
Whitham G. B. 1957 J. Fluid Mech. 4, 337.