Oscillatory Couette flow of rarefied binary gas mixtures

Abstract

The oscillatory Couette flow of binary gas mixtures is numerically investigated on the basis of the McCormack model. The dependence of the velocity and shear stress amplitudes and the penetration depth on the gas rarefaction and the oscillation parameters is studied numerically. Two typical mixtures of noble gases, i.e., a neon–argon (Ne–Ar) mixture with a molecular mass ratio less than 2 and a helium–xeon (He–Xe) mixture with a molecular mass ratio of about 32, are considered to explore the influences of the molecular mass ratio and molar concentration. It is found that the Ne–Ar mixture exhibits similar behavior with a single gas, while significant deviations can be observed between a single gas and the He–Xe mixture. Particularly when the gases are in the transitional and near-continuum regimes and the oscillation frequency is high, the amplitudes of velocity and shear stress for the He–Xe mixture vary non-monotonically between the plates as the molar concentration of the light species He exceeds 50% due to the oscillation superposition of the two species. These findings are helpful to design the structure of micro-electromechanical devices.

High-order Unified Gas-kinetic Scheme

“…Both plates are isothermal wall with 273K. Zhang [31] introduced two parameters which characterizes the flow field. One is the rarefaction parameter δ, and the other is oscillation parameter θ.…”

A discrete unified gas-kinetic scheme for multi-species rarefied flows

“…The DUGKS is a finite volume method that exhibits good UP properties due to coupled particle transport and collision effect in the flux reconstruction [21,[26][27][28]. The DUGKS has already been adopted successfully for flows of single-species gases [29][30][31][32] and binary gas mixtures [33,34] from continuum to free molecular regimes.…”

A direct relaxation process for particle methods in gas kinetic theory

“…The multi-scale mechanism from the continuum flow to the rarefied flow (or from the macroscopic flow to the microscopic flow) is crucial for the force and heat loaded on nearspace and reentry vehicles, the control of spacecraft by thrusters 1,2 , the propelling and cooling of Micro-Electro-Mechanical System (MEMS) 3,4 , etc. Since the continuum flow and rarefied flow often exist simultaneously in a singe multi-scale flow field, the modeling and prediction become complicated: The continuum flow is governed by the Navier-Stokes (N-S) equation, and the rarefied flow is governed by the Boltzmann equation, while there is no multi-scale governing equation for the transitional flow between continuum and rarefied ones.…”