Control of pressure distribution in shock generators with elliptic and parabolic cross-sections

Theoretical investigation of liquid shock generating devices with elliptically and parabolically shaped chambers is presented. A device of such kind with an elliptic geometry has been previously fabricated and tested experimentally. Experimental observations confirmed the results of earlier theoretical analysis of the problem, showing that shock waves produced by an electric discharge at one of the foci of the elliptic chamber will converge at the second focus after the reflection from the cavity wall. In the present paper a previous two-dimensional model is extended to account for the height variation in the chamber. Expression for the pressure distribution behind the converging wave front is obtained and a relation between the shape of the upper bounding surface of the chamber and pressure distribution behind the converging wave front is investigated. It is shown that a desired pressure distribution may be obtained by an appropriate choice of the upper surface of the chamber.