Numerical investigation of the Lorentz force effect on the vortex transfiguration in a two-dimensional lid-driven cavity

Abstract

Numerical calculations of the two-dimensional unsteady incompressible driven cavity flow in the presence of the Lorentz body force are presented. The Navier—Stokes equations in vorticity-stream function formulation are solved numerically using a uniform grid mesh of 201×201. A second-order central difference approximation is used for spatial derivatives and the solutions march in time with a fourth-order Runge—Kutta method. The unsteady driven cavity flow solution is computed for a Reynolds number of Re=1000. The effects of the Stuart number (ratio of the electromagnetic forces to inertial forces) and penetration depth of the Lorentz force on the lid-driven cavity vortices are investigated. Two new quaternary vortices at the bottom corners of the cavity are observed in the flow field as the Stuart number and penetration depth increase. The primary vortex size also dwindles and eventually breaks down into two tertiary vortices as these parameters increase. The velocity component profiles are also considerably sensitive with respect to these parameters. It should be emphasized that on the basis of extensive comparisons and validations, which are made with benchmark solutions found in the literature, the numerical computations are repeated considering the Lorentz body force effect in the lid-driven cavity. Detailed results are presented in the article.