Drag and Pressure Fields for the Mhd Flow around a Circular Cylinder at Intermediate Reynolds Numbers

Steady incompressible flow around a circular cylinder in an external magnetic field that is aligned with fluid flow direction is studied for Re (Reynolds number) up to 40 and the interaction parameter in the range 0 ≤N ≤ 15 (or 0 ≤M ≤ 30), where M is the Hartmann number related to N by the relation M = √2N Re, 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 for Re = 10 is suppressed completely when N < 1 and it started growing again when N ≥ 9. For Re = 20 and 40, the suppression is not complete and in addition to that the rear separation bubble started increasing when N ≥ 3. The drag coefficient decreases for low values of N (< 0.1) and then increases with increase of N . The pressure drag coefficient, total drag coefficient, and pressure at rear stagnation point vary with √ N . It is also found that the upstream and downstream pressures on the surface of the cylinder increase for low values of N (< 0.1) and rear pressure inversion occurs with further increase of N . These results are in agreement with experimental findings.