Numerical Simulations of Shock Focusing over Concave Surfaces

Abstract

This paper describes the numerical study of a shock focusing, that is, a planar shock wave impacting a concave surface. Cylindrical and parabolic reflectors are studied for different curvatures, depths and incident Mach numbers. Computations are carried out using a high-order low-dissipation bandwidth-optimized weighted essentially nonoscillatory method and both inviscid and viscous two-dimensional flow models are considered. The obtained results agree well with the experimental observations made by Skews et al. (Skews, B. W., Kleine, H., Barber, T., and Iannuccelli, M., Flow Features in a Cavity During Shock Wave Impact, 16th Australian Fluid Mechanics Conference, Univ. of Queensland, Brisbane, Australia, 2007) and Izumi et al. (Izumi, K., Aso, S., and Nishida, M., Experimental and Computational Studies Focusing Processes of Shock Waves Reflected from Parabolic Reflectors, Shock Waves, Vol. 3, No. 3,1994, pp. 213-222) for the parabolic one. In the case of cylindrical reflectors, shocks interaction and fine structures as Kelvin-Helmholtz instabilities are recovered, and the computed angles of the transition from an inverse Mach reflection to a transitional regular reflection compare favorably with the analytical model of Ben-Dor (Ben-Dor, G., Shock Wave Reflection Phenomena, Springer-Verlag, New York, 1992) for relatively weak incident shock waves (M s ≤ 2). In the case of parabolic reflectors, the three types of focalization process are addressed and their own structure analyzed.