Numerical simulation of the two-dimensional MHD flow around a circular cylinder

In the present paper the time-dependent, two-dimensional, incompressible MHD flow around a circular cylinder is investigated numerically using a finite difference method in stream function-vorticity formulation. The calculations are restricted to the typical situation of liquid metal flows under laboratory conditions where the magnetic Reynolds number is small. The flow is investigated in the parameter range of Re < 10000 and magnetic interaction parameter N < 20 (N = Ha²/Re).
To validate the numerical method, a comparison with the few published numerical results (MOCHIMARU, TSINOBER) is performed, and a good agreement is found. Furthermore, the influence of different outer boundary conditions is tested.
The two cases of a magnetic field aligned to the flow as well as perpendicular to it are investigated in detail. The influence of the magnetic forces on the flow is shown in stream function and vorticity isoline plots for different Reynolds numbers and interaction parameters. The vorticity and pressure distribution at the cylinder surface and the induced magnetic field are calculated and compared with experimental results. The occurrence of a large, but slow recirculation eddy behind the cylinder for a strong aligned magnetic field is discussed. The motion of the fluid becomes more and more stagnant in that region for increasing magnetic fields.
The downstream wake is characterized by the velocity profiles, and the farfield of the vorticity is discussed.
As expected, the influence of the magnetic field on the flow in general is a stabilizing one. In particular, the suppression of an instationary wake flow can be achieved by the magnetic forces. A stability line in the (Re,N)-plane is extracted from the numerical simulations. This result will be compared with a linear stability analysis based on a Galerkin approach.