Lattice Boltzmann simulation of lid-driven flow in deep cavities

Abstract

In this paper, the lattice Boltzmann equation (LBE) method is applied for simulation of lid-driven flow in a two-dimensional, rectangular, deep cavity. First, the code is validated for the standard square cavity, and then the results of a deep cavity are presented. Steady results are presented for deep cavities with aspect ratios of 1.5–4, and Reynolds numbers of 50–3200. Several features of the flow, such as the location and strength of the primary vortex, and the corner-eddy dynamics are investigated and compared with previous findings from experiments and theory. Steady results for deep cavities show the existence of corner eddies at the bottom, which coalesce to form a second primary-eddy as the cavity aspect-ratio is increased above a critical value. However, at relatively high Reynolds numbers, the second primary-eddy is formed via a rapid transition of an unsteady wall-eddy. The predicted results from LBE simulations are shown to be consistent with experiments and theory.