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 for $\text{Re}$ (Reynolds number) up to 40 and the interaction parameter in the range $0\le N\le 15$ (or $0\le M\le 30$), where $M$ is the Hartmann number related to $N$ by the relation $M=\sqrt{2N\text{Re}}$, 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 $\text{Re}=10$ is suppressed completely when $N<1$ and it started growing again when $N\ge 9$. For $\text{Re}=20$ and 40, the suppression is not complete and in addition to that the rear separation bubble started increasing when $N\ge 3$. The drag coefficient decreases for low values of $N$ $\left(<0.1\right)$ and then increases with increase of $N$. The pressure drag coefficient, total drag coefficient, and pressure at rear stagnation point vary with $\sqrt{N}$. It is also found that the upstream and downstream pressures on the surface of the cylinder increase for low values of $N$ $\left(<0.1\right)$ and rear pressure inversion occurs with further increase of $N$. These results are in agreement with experimental findings.