The driven cavity flow over the whole range of the Knudsen number

Abstract

The flow of a rarefied gas in a rectangular enclosure due to the motion of the upper wall is solved over the whole range of the Knudsen number. The formulation is based on the two–dimensional linearized Bhatnagar-Gross-Krook (BGK) kinetic equation with Maxwell diffuse-specular boundary conditions. The integro-differential equations are solved numerically implementing the discrete velocity method. The discontinuity at the boundaries between stationary and moving walls is treated accordingly. A detailed investigation of the rarefaction effects on the flow pattern and quantities is presented over the whole range of the Knudsen number and various aspect (height/width) ratios. Numerical results of flow characteristics, including the streamlines, the velocity profiles, the pressure and temperature contours, and the drag force of the moving wall, are presented for different aspect ratios and various degrees of gas rarefaction from the free molecular through the transition up to the continuum limit. On several occasions, depending upon the flow parameters, in addition to the main vortex, corner eddies are created. As the depth of the cavity is increased, these eddies grow and merge into additional vortices under the top one. The mesoscale kinetic-type approach proves to be efficient and suitable for problems that incorporate multiscale physics, such as the present nonequilibrium flow.