I. Theoretical investigation of the reflection of ionizing shocks. II. Theoretical study of sound and shock waves in a two-phase flow

Abstract

PART I The reflection of an ionizing shock from the end wall of a shock tube is studied theoretically following the experimental model of J. Smith. The observed perturbations in the wall pressure history are found to agree with this theory. To describe the first perturbation, a decrease in pressure due to the ionization part in the reflected shock structure, the flow equations are linearized but the rate equations are used in nonlinear form. The second perturbation, an increase in pressure due to the ionization part of the incident shock structure, is studied using Whitham's theory and assuming equilibrium behind the reflected shock. PART II The propagation of sound and shock waves in a two-phase medium is studied theoretically using the flow equations for each component. It is shown that the assumption of constant mass ratio during the sound propagation, used previously in the literature for the case of bubbles suspended in a liquid, is only valid for low frequencies. For high frequencies a larger sound speed is obtained. These two sound speeds give two different Mach numbers. It is found that when both Mach numbers are larger than one, the shock structure in a liquid containing bubbles is given by an initial increase of the pressure, followed by a region in which it oscillates around its final equilibrium value. When the low frequency Mach number is larger than one, and the high frequency Mach number smaller than one, the oscillations disappear and the transition is uniform. The speed of sound of the mixture is also calculated by evaluating the scattering by the suspended phase.