Lattice Boltzmann Simulation of Incompressible Fluid Flow in Two-sided Converging and Diverging Lid-driven Square Cavity

Abstract

The present study focuses on the predictions of flow behavior, streamlines and some other factors of a two adjacent-sided converging and diverging lid-driven square cavity filled with fluid. In the diverging case, the top wall of the cavity is considered to be in motion from left to right, and the left wall is considered to be in motion from top to bottom simultaneously with identical speeds. It is found that for a low Reynolds number, the flow behavior seems to be symmetric with respect to one of the diagonals of the cavity, and at a critical Reynolds number 1121, the symmetry of the flow behavior blows up, and an asymmetric form is obtained due to the increased inertia and turbulence effects. Any increment in the Reynolds number above the critical Reynolds number develops this asymmetry gradually more and more. In the second phenomenon, the converging phenomenon, the top wall of the cavity is assumed to be in motion from left to right, and the right wall is assumed to be in motion from bottom to top simultaneously with identical speeds so that they converge at the corner of the cavity. This case gives rise to two critical Reynolds numbers Re = 969 and Re = 2053 and the flow behavior for both asymmetric states was found to be opposite. Furthermore, the rate of convergence of the present methodology, lattice Boltzmann methodology, for various Reynolds numbers is found to be very high except for the critical and their nearby Reynolds numbers.