Focusing of Shock Wave by Underwater Discharge

On Nonlinear Reflection and Focusing Effect

Abstract

This paper purposes to improve the focusing effect by taking account of the nonlinear reflection of underwater shock wave. Reflected shock wave by the ellipsoidal reflector does not focus on a geometrical focal point because of the nonlinear reflection. The nonlinearity between incident and reflection angles on the shock wave focusing is evaluated based on the propagation time of reflected shock wave from a rigid flat plate. The peak pressure of the focused shock wave strongly depends on the wave front distribution, especially on the pressure concentration in the radial direction of the reflector. Higher pressure can be obtained by shifting spark gap position toward the second geometrical focal point. The optimal displacement of the spark gap estimated based on the relationship for the nonlinear reflection agrees with the experimental observation. The shape of reflector is modified taking account of the nonlinear effect. The modified reflector demonstrates significant increase of pressure by focused shock wave compared with the standard ellipsoidal reflector.