Computational Study of the Interaction of a Planar Shock Wave with a Cylinder/Sphere: The Reflected Wave Velocity

The interaction of shock waves with rigid obstacles is of significant interest in aerodynamic science and other engineering applications. During the interaction of a shock wave with an obstacle, a very complex wave pattern which affects the shockwave induced flow is formed. The interaction process depends on a variety of physical parameters such as the shape of the obstacle, the shock wave strength and the type of gas in which the interaction occurs. In the present paper, the interaction of a planar shock wave with a cylinder and a sphere is investigated. Our investigation follows closely the recentwork of Sadot et al. [1] which dealt with shock tube experiments with low Mach number shocks, in the range 1.1 to 1.4. An empirical relation was proposed for the trajectory of the reflected wave. This relation was expressed in terms of non-dimensional distance and time and was shown to be applicable for the investigated range of Mach numbers, cylinder diameters and a general ideal gas. The purpose of the present work is to focus on the backward reflected wave, and in particular, on its velocity change as it progresses away from the leading edge of the cylinder/sphere. It is expected that the reflected wave initially propagates at the velocity of shock reflection from a rigid wall, and asymptotically decelerates to the velocity corresponding to that of a sonic wave in the shocked region. This theoretical behavior is born out by fine mesh hydro-code computations of the interaction problem. The paper is organized as follows: in Section 2 a theoretical background for the limiting velocities of the reflected shock is given, followed by a brief description of the numerical codes and the problem setup (Section 3). The results of simulations for various cases by different CFD codes are given in Section 4. We conclude (Section 5) with a summary and suggestion of future work.