Boundary-driven nonequilibrium gas flow in a grooved channel via kinetic theory

Abstract

The nonequilibrium flow of a gas in a two-dimensional grooved channel, due to the motion of the wall of the channel, is investigated based on kinetic theory. The presence of the rectangular grooves that are placed periodically on the stationary wall results in a two-dimensional flow pattern. The problem is modeled by the linearized Bhatnagar-Gross-Krook (BGK) and S-model kinetic equations, which are solved for the corresponding perturbed distribution functions by the discrete velocity method. Maxwell diffuse type reflecting boundary conditions are used to model the gas-surface interaction, while periodic boundary conditions are imposed at the inlet and outlet of the channel. The computed macroscopic quantities of practical interest include velocity profiles, contours of pressure, density, and temperature, as well as the flow rate and the heat flux through the channel and the drag coefficient along the moving boundary. The results are valid in the whole range of the Knudsen number, from the free molecular regime through the transition and slip regimes up to the hydrodynamic limit, for various values of the depth and the width of the groove and the periodic length of the channel. A comparison between the BGK and S-model results is performed. Several interesting flow patterns and characteristics are examined in terms of the geometrical parameters of the flow configuration, including an unexpected behavior of the velocity profile across the channel at large Knudsen numbers.