Non-equilibrium vapour condensation on a shock-tube endwall behind a reflected shock wave

Abstract

This paper deals theoretically with a filmwise condensation of a vapour on the endwall of a shock tube behind a reflected shock wave. The gas dynamics, accompanied by heat and mass transfer at the vapour-liquid interface, is treated by the method of matched asymptotic expansions. The first and second approximate solutions are obtained and evaluated numerically. It is clarified that there exists a transition process on the growth of a liquid film, that is, the liquid film grows approximately in proportion to the time t in the early stages after the reflection of the shock wave, and after some time, it grows in proportion to the square root of the time. This transition process from the t-dependent growth to the t^½-dependent one is mainly controlled by the intensity of condensation. In the t-dependent growth region, the growth rate of the liquid film is proportional to the condensation parameter, depending both upon an initial condition and upon thermal properties of the vapour and the liquid film, while in the t^½-dependent growth region it becomes independent of the condensation parameter and is controlled only by thermal properties of the vapour, liquid film and shock-tube endwall. This result suggests that the measurement of the condensation parameter by shock tubes should be made in the t-dependent growth region immediately after the reflection of the shock wave.