Transient Couette Flow of Rarefied Binary Gas Mixtures

Abstract

The transient Couette flow problem of rarefied binary gas mixtures is studied for the nonlinear case, Mi ≥ 1: one of the plates with equal plate temperatures is accelerated impulsively. The method of solution is the Monte Carlo method. The physical space is divided into macroscopically small cells. The change in the distribution function in a cell during a time interval Δt, which should be sufficiently small in comparison with the characteristic times (τD)iα, (τF)iα, and (τC)ij, is obtained by following the test particles for each molecular event through the event; i.e., molecular drift, external force, or molecular collision. The flow field is calculated for Maxwellian molecules and the range of Knudsen number Kn ≥ 0.1 (from free molecular to transition flow regime). The relaxation phenomena of a gas mixture with the boundary effects are observed. Of particular interest are an epochal relaxation due to the molecule-surface collision and the temperature “overshoot” near the moving plate. The steady-state solutions, which are obtained from the long-time results, are also presented. The effects of Knudsen number, mixture ratio, and gas-surface interaction are investigated, and the separation phenomena between the species are observed.

Analysis of numerical techniques of the direct simulation Monte Carlo method in the rarefied gas dynamics

“…Consequently, the application of Algorithm 2 to construct the random process corresponding to equation (3.2) is justified. The numerical technique suggested in [15] can also be obtained from equation (3.1). If Δί« τ λ (τ λ is the free path length of a molecule), then we can assume that the collision frequency v(C) does not change for the time interval Δί.…”

“…Nowadays numerical techniques for simulating a spatially homogeneous relaxation suggested in [2,4,7,15] are widely used. All these schemes are obtained using heuristic arguments on the basis of physical ideas about the relaxation processes in a realistic gas.…”

A comparative study of no-time-counter and majorant collision frequency numerical schemes in DSMC

“…The algorithm is computationally efficient with an O(N) complexity, but the method does not reproduce the collision frequency under certain extreme non-equilibrium conditions. Koura introduced the collision frequency (CF) scheme [5], which is an exact Monte Carlo scheme in which the collision frequency (ν) is computed as the average value of σ T c r over all collision pairs in the cell as…”