Aspect Ratio Effect on Multiple Flow Solutions in a Two-Sided Parallel Motion Lid-Driven Cavity

Abstract

Abstract A continuation method, accompanied with a linear stability analysis, is employed to investigate the bifurcation diagram of the flow solutions, as well as the multiple flow states in a cavity with different aspect ratios for parallel motion of two facing lids. The Reynolds number proportional to the wall velocity is used as the continuation parameter, and the evolution of the bifurcation diagrams in cases with different aspect ratios is illustrated. The induced flow patterns are highly dependent upon both the aspect ratios and the moving velocity of the walls. Three different types of bifurcation diagrams and their corresponding flow states are classified according to the aspect ratios. One stable symmetric flow state and one stable asymmetric flow state are identified. The stable asymmetric flow state is obtained at a high aspect ratio and a low Reynolds number. Meanwhile, the regions of stable and unstable flows are distinguished according to the different aspect ratios.