The Production and Stability of Converging Shock Waves

Abstract

Converging shock waves offer interesting possibilities of attaining very high temperatures and pressures. A theoretical treatment by G. Guderley which we have confirmed and extended by the method of characteristics indicated that the strength of a strong converging cylindrical or spherical shock varies inversely with a power (0.396 for γ=1.4) of the surface area of the wave, thus becoming very great close to the center of convergence. The experimental production of high temperatures and pressures by means of these converging shocks depends on their ``stability'' of form. A converging wave is said to be stable if it approaches perfect cylindrical or spherical shape, thus damping out random disturbances as it propagates. The experimental work of L. G. Smith on Mach reflection is applied to show that these converging waves are stable for the shock range (M≤2.4) covered by his experiments. Smith's work and the theoretical work of Lighthill indicate that the stability decreases greatly at high Mach numbers. The simplest experimental method of achieving a cylindrical converging shock is by the use of a shock tube with a converging channel. This, however, results in the hottest region of the gas being in close thermal contact with the cold walls. An axially symmetric shock tube has been designed and constructed which produces a complete converging cylindrical shock rather than just a sector and in which the region of convergence is comparatively well isolated thermally from the walls. It has been found possible to converge a moderate strength shock wave (M=1.7) sufficiently to produce considerable luminosity at the center of convergence. Schlieren photographs are presented showing various phases of the formation and stability of these converging waves.