Unified Gas Kinetic Simulations of Lid-Driven Cavity Flows: Effect of Compressibility and Rarefaction on Vortex Structures

We investigate and characterize the effect of compressibility and rarefaction on vortex structures in the benchmark lid-driven cavity flow. Direct numerical simulations are performed, employing the unified gas kinetic scheme to examine the changes in vortex generation mechanisms and the resulting flow structures at different Mach and Knudsen numbers. At high degrees of rarefaction, where inter-molecular interactions are minimal, the molecules mainly collide with the walls. Consequently, the dominant flow structure is a single vortex in the shape of the cavity. It is shown that increasing compressibility or decreasing rarefaction lead to higher molecular density in the cavity corners, due to more frequent inter-molecular collisions. This results in lower flow velocities, creating conditions conducive to the development of secondary and corner vortices. The physical processes underlying vortex formations at different Knudsen numbers, Mach numbers, and cavity shapes are explicated. A parametric map that classifies different regimes of vortex structures as a function of compressibility, rarefaction, and cavity shape is developed.