Rarefaction effects on shear driven oscillatory gas flows: A direct simulation Monte Carlo study in the entire Knudsen regime

A complete mathematical description of oscillatory Couette flows within the framework of kinetic theory is not available in the literature. Motivated by this and their vast engineering applications, we present a parametric study of time-periodic oscillatory Couette flows using the unsteady direct simulation Monte Carlo (DSMC) method. Computations are performed as a function of the Knudsen (Kn) and Stokes (β) numbers, in the entire Knudsen regime (Kn⩽100) and a wide range of Stokes numbers (β⩽7.5). The DSMC results are validated using a recently developed semianalytical/empirical model that is applicable for quasisteady flows (β⩽0.25) in the entire Knudsen regime, and for any Stokes number flow in the slip flow regime (Kn⩽0.1). In addition, we derived an analytical solution of the linearized collisionless Boltzmann equation for oscillatory Couette flows, and utilized this to validate the DSMC results in the free-molecular flow regime. Dynamic response of the flow, including the velocity profiles, phase angle, wave speed, shear stress, and the penetration depth for high Stokes number flows are presented. Increasing the Stokes number at fixed Kn, we observed formation of “bounded Stokes layers,” as expected. However, increasing the Knudsen number at fixed β results in “bounded rarefaction layers,” where the penetration depth continuously decreases with increasing the Kn. Interplay between the rarefaction and unsteadiness contributes to this interesting flow physics, and also introduces a new characteristic length scale to the problem.