Drag and pressure fields for the MHD flow around a circular cylinder at intermediate Reynolds numbers

Abstract

Steady incompressible flow around a circular cylinder in an external magnetic field that is aligned with fluid flow direction is studied forRe(Reynolds number) up to 40 and the interaction parameter in the range0≤N≤15(or0≤M≤30), whereMis the Hartmann number related toNby the relationM=2NRe, using finite difference method. The pressure-Poisson equation is solved to find pressure fields in the flow region. The multigrid method with defect correction technique is used to achieve the second-order accurate solution of complete nonlinear Navier-Stokes equations. It is found that the boundary layer separation at rear stagnation point forRe=10is suppressed completely whenN<1and it started growing again whenN≥9. ForRe=20and 40, the suppression is not complete and in addition to that the rear separation bubble started increasing whenN≥3. The drag coefficient decreases for low values ofN(<0.1)and then increases with increase ofN. The pressure drag coefficient, total drag coefficient, and pressure at rear stagnation point vary withN. It is also found that the upstream and downstream pressures on the surface of the cylinder increase for low values ofN(<0.1)and rear pressure inversion occurs with further increase ofN. These results are in agreement with experimental findings.