Flow around a circular cylinder in an external magnetic field at high Reynolds numbers

Purpose - To study the steady viscous incompressible electrically conducting fluid flow past a circular cylinder under the influence of an external magnetic field at high Reynolds numbers (Re). Design/methodology/approach - The finite difference method is applied to solve the governing non-linear Navier-Stokes equations. First order upwind difference scheme is applied to the convective terms. The multigrid method with coarse grid correction is used to enhance the convergence rate. The defect correction technique is employed to achieve the second order accuracy. Findings - A non-monotonic behavior in separation angle when N >= 5 and separation length when N >= 3 is found with the increase of external magnetic field. The drag coefficient is found to increase with increase of N. The pressure drag coefficient, total drag coefficient and rear pressure are found to exhibit a linear dependence with N-0.5. The pressure Poisson equation is solved to find pressure fields in the flow region. It is found that the upstream base pressure increases with increase of external magnetic field while the downstream base pressure decreases with the increase of the external magnetic field. Originality/value - The non-monotonic behaviors in the separation angle and separation length at high Re are explained through pressure fields which are found first time for this problem. The linear dependence of the pressure drag coefficient, total drag coefficient and the pressure at rear stagnation point with N-0.5 is in agreement with experimental findings.