The Linearized Rayleigh Problem in a Rarefied Gas Flow According to the Bgk Model

摘要

The classical Rayleigh problem was formulated using the BGK kinetic equation, and the numerical evaluation is carried out on an IBM 7094. The results describe the macroscopic velocity q sub x, the shear stress P sub xy, the tangential heat flux Q sub x, and the temperature field T' in the near-free-molecule flow. These results are obtained for a wide range of values of lambda t (the number of inter-molecular collisions in a time t). The flow picture is physically plausible, and agrees in regions of common validity with other available results. For example, the velocity-slip on the surface, which is half of the impulsive velocity, V, in the free-molecule limit, decreases with increasing collision numbers (lambda t), and finally vanishes in the Rayleigh limit (or the continuum limit). The boundary layer thickness also decreases with increasing lambda t. The initial formulation of the problem involves only the first power of q sub x which is much smaller than the local speed of sound. Using a higher approximation by retaining the (q sub x) squared term, the temperature fields are obtained for the near-free-molecule flow. In further work it is proposed to use these results so that the compressibility effects may be included through an iteration scheme. (Author)