Kinetic theory analysis of steady evaporating flows from a spherical condensed phase into a vacuum

Abstract

Steady evaporating flows from a spherical condensed phase into a vacuum are considered. On the basis of the Boltzmann–Krook–Welander equation, the behavior of the gas (the velocity distribution function as well as the density, velocity, and temperature) from the sphere to downstream infinity is analyzed numerically in detail for the whole range of the Knudsen number. The discontinuity of the velocity distribution function in the gas, a typical behavior of the gas around a convex body, is analyzed accurately. It extends, with appreciable size, to downstream infinity not only for intermediate and large Knudsen numbers but also even for rather small Knudsen numbers. The flow is highly in nonequilibrium over the whole field except for very small Knudsen numbers. The velocity and temperature at downstream infinity take finite values, determined by the Knudsen number, except the temperature at zero Knudsen number. An analytic solution for small Knudsen numbers, especially the temperature at infinity (frozen temperature) is obtained with the aid of the asymptotic theory and the hypersonic expansion.