Numerical simulations of a cylinder wake under a strong axial magnetic field

We study the flow of a liquid metal in a square duct past a circular cylinder in a strong externally imposed magnetic field. In these conditions, the flow is quasi-two-dimensional, which allows us to model it using a two-dimensional (2D) model. We perform a parametric study by varying the two control parameters Re and Ha (Ha₂ is the ratio of Lorentz to viscous forces) in the ranges [0...6000] and [0...2160], respectively. The flow is found to exhibit a sequence of four regimes. The first three regimes are similar to those of the non-magnetohydrodynamic (non-MHD) 2D circular wake, with transitions controlled by the friction parameter Re/Ha. The fourth one is characterized by vortices raising from boundary layer separations at the duct side walls, which strongly disturbs the Kármán vortex street. This provides the first explanation for the breakup of the 2D Kármán vortex street first observed experimentally by Frank, Barleon, and Müller [Phys. Fluids 13, 2287 (2001)]. We also show that, for high values of Ha (Ha≥1120), the transition to the fourth regime occurs for Re∝0.56Ha, and that it is accompanied by a sudden drop in the Strouhal number. In the first three regimes, we show that the drag coefficient and the length of the steady recirculation regions located behind the cylinder are controlled by the parameter Re/Ha^4/5. Also, the free shear layer that separates the recirculation region from the free stream is similar to a free MHD parallel layer, with a thickness of the order of Ha^-1/2 that is quite different to that of the non-MHD case, and therefore strongly influences the dynamics of this region. We also present one case at Re=3×10⁴ and Ha=1120, where this layer undergoes an instability of the Kelvin-Helmholtz-type.