Towards a better understanding of wall-driven square cavity flows using the lattice Boltzmann method

Abstract

Wall-driven flow in square cavities has been studied extensively, yet it appears some main flow characteristics have not been fully investigated. Previous research on the classic lid-driven cavity (S1) flow has produced the critical Reynolds numbers separating the laminar steady and unsteady flows. Wall-driven cavities with two opposing walls moving at the same speed and the same (S2p) or opposite (S2a) directions have seldom been studied in the literature and no critical Reynolds numbers characterizing transitional flows have ever been investigated. After validating the LBM code for the three configurations studied, extensive numerical simulations have been undertaken to provide approximate ranges for the critical Hopf and Neimark-Sacker bifurcations for the classic and two two-sided cavity configurations. The threshold for transition to chaotic motion is also reported. The symmetries of the solutions are monitored across the various bifurcations for the two-sided wall driven cavities. The mirror-symmetry of the base solution for case S2p is lost at the Hopf bifurcation. The exact same scenario occurs with the pi-rotational symmetry of the base state for case S2a.