Focusing of strong shocks in an elliptic cavity

Abstract.

Focusing of strong shock waves in a gas-filled thin chamber with an elliptic boundary is investigated theoretically and numerically. The process of reflection and convergence of cylindrical shocks generated at one of the focal points of the chamber is studied by means of Whitham's theory of geometrical shock dynamics (1957, 1959). The current calculations are based on the modified version of this theory, which takes into account the non-homogeneous flow ahead of the advancing shock, Apazidis and Lesser (1996). There are two main results of the present study indicating a qualitatively different behavior of strong shocks as compared to the linear acoustic case. (1) - the form of the reflected shock is not cylindrical and (2) - the reflected, converging shock does not focus at the geometrical second focal point of the chamber. The dependence of the form of the reflected shock and the location of its focusing point on the strength of the shock and the eccentricity of the chamber is investigated.