Numerical investigation of axisymmetric shock wave focusing over paraboloidal reflectors

The problem of a plane shock wave incident to a paraboloidal reflector is numerically investigated. The numerical solver used is developed by an improved, implicit, upwind total variation diminishing scheme in a finite-volume approach. The real-gas effect is taken into account if high temperature occurs. The solver is validated on four test problems. The complicated flow fields of axisymmetric shock wave focusing for different-depth reflectors at various incident shock Mach numbers are studied. An interesting result of a maximum pressure happening at the reflector center is found. This is due to the occurrence of an implosion phenomenon. A maximum temperature might occur at the reflector center or at other locations, depending on the incident shock Mach number and the reflector depth. Moreover, vortical flows induced by shock wave focusing and their formation mechanism are explored. It was found that the vortices near the reflector are caused by a ring-shaped shock/slipline interaction. Owing to the slipline on the symmetry axis, a jet flow is induced, resulting in the formation of vortices near the symmetry axis. Received 13 January 1998 / Accepted 10 November 1998