Three-dimensional magnetohydrodynamic flow around a 180° sharp bend under transverse magnetic field

Abstract

This study attempts to characterize the variation of pressure loss and the evolution of vortex structures in the steady three-dimensional flow around a 180° sharp bend under a transverse magnetic field. This study is conducted with the Reynolds number, 100≤Re≤400, and Hartmann number, 0≤Ha≤2000. This range of Re and Ha captures both complex three-dimensional structures and the inception of quasi-two-dimensional flows. Numerical simulations display how the pressure loss across the bend region (Δp0) and the vortex structures undergo four regimes by increasing Ha for fixed Re. These regimes are referred to as regimes I–IV. N1c, N2c, and N3c, the critical values of interaction number Nc for the first appearance of regimes II–IV, are recognized at values 0.8, 3.2, and 40, respectively. In regime I (N≤0.8), Δp0 increases slightly and the magnetohydrodynamic flow promotes the recirculating bubble. In regime II (0.8<N≤3.2), as Δp0 decreases, the scope of the recirculating bubble reaches its peak. In regime III (3.2<N≤40), Δp0 grows, while the shrinkage of the recirculating bubble is triggered. Simultaneously, the flow tends to be two-dimensional [J. Sommeria and R. Moreau, “Why, how, and when, MHD turbulence becomes two-dimensional,” J. Fluid Mech. 118, 507 (1982)]. In regime IV (40<N), Δp0 is linearly dependent on Ha/Re. The non-monotonic behavior of the recirculating bubble length is caused by the redistribution of momentum at low Ha and by the predominant effect of the Lorentz force at large Ha. The law of how to distinguish the three-dimensional (3D) flow and quasi-two-dimensional (Q2D) flow is discovered by assessing the recirculating bubble length in the center plane.