Numerical analysis of a uniform flow of a rarefied gas past a sphere on the basis of the Boltzmann equation for hard-sphere molecules

Abstract

A slow uniform flow of a rarefied gas past a sphere is investigated on the basis of the linearized Boltzmann equation for hard-sphere molecules and the diffuse reflection condition. With the aid of a similarity solution, the Boltzmann equation is reduced to two simultaneous integrodifferential equations with three independent variables, which are solved numerically. The collision integral is computed efficiently by the use of a numerical collision kernel [Phys. Fluids A 1, 363 (1989)]. The velocity distribution function of the gas molecules, which has discontinuity in the gas, the density, flow velocity, and temperature fields of the gas, and the drag on the sphere are obtained accurately for the whole range of the Knudsen number. In spite of slow flow, the temperature is nonuniform (thermal polarization). From the behavior of the velocity distribution function, the kinetic transition region is clearly seen to separate into the Knudsen layer and the S layer for small Knudsen numbers.