Gas-dynamic boundary conditions of evaporation and condensation: Numerical analysis of the Knudsen layer

Abstract

The gas-dynamic Euler equations require two boundary conditions to be specified at the surface of evaporated condensed phase and one condition at the surface of condensation. In the commonly considered three-parameter space of the temperature and pressure ratios and the Mach number this corresponds to a three-dimensional curve in the case of evaporation and to a surface in the case of condensation. To obtain the conditions of evaporation and condensation the steady-state Knudsen layer is numerically studied by the discrete velocity method applied to a Boltzmann equation with a relaxation collision term. Simple models of Mott-Smith type based on the conservation laws and analytical approximations of the velocity distribution function in the Knudsen layer may give satisfactory description of the gas-dynamic evaporation and condensation conditions while in general they inadequately represent the detailed structure of the distribution function. One of the reasons why the models deviate from the calculations is that they do not allow different parallel and perpendicular temperatures of the velocity distribution. Under evaporation, the Knudsen layer thickness increases with the Mach number $\mathrm{M.}$ Under condensation, it is inversely proportional to $M$ when $M$ is low. Numerical results are obtained and an analytical model is proposed for the vapor temperature considerably less than the condensed phase one (up to 10 times) what is typical for back condensation under pulsed laser ablation.