Vortex structure of steady flow in a rectangular cavity

The vortex structure of the two-dimensional steady flow in a lid-driven rectangular cavity at different depth-to-width ratios and Reynolds numbers is investigated using a lattice Boltzmann method. The aspect ratio varies from 0.1 to 7 and the Reynolds number ranges from 0.01 to 5000. The effects of the aspect ratio and Reynolds number on the size, center position and number of vortices are determined together with the flow pattern in the cavity. The present results not only confirm the vortex structure of Stokes flow reported by previous researchers, but also reveal some new evolution features of the vortices and their structure with the Reynolds number. When the Reynolds number approaches 0, the flow shows a characteristic feature of symmetric vortex structure. On the other hand, as the Reynolds number increases, the sizes and center positions of the vortices in the near-lid region appear to be strongly affected by the inertia force, resulting in an asymmetric vortex structure in this region. The influence of the inertia force decreases along the depth for the deep cavity flow. It is found that there is a critical value of the aspect ratio, which depends on the Reynolds number. When the critical value is exceeded, flow pattern in a certain region of cavity becomes symmetric again. These large symmetric vortices are similar in shape, and their sizes approach a constant.