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

V. Shatrov¹ - G. Mutschke² - G. Gerbeth²

¹ Institute of Theoretical and Applied Mechanics, Perm, Russia
² Research Center Rossendorf, PO Box 51 01 19, D-01314 Dresden, Germany

Abstract
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 flow is studied in the parameter range Re < 2000 and N < 10 (N = Ha2/Re). The two cases of a magnetic field aligned to the flow as well as the transverse to it are investigated in detail. The vorticity and the pressure distribution at the cylinder surface are calculated and compared with experimental results. The occurrence of a large, but slow recirculating eddy behind the cylinder for a strong aligned magnetic field is found where the fluid motion becomes more and more stagnant for increasing magnetic fields. As expected, the influence of the magnetic field on the unsteady flow in general is a stabilizing one. In particular, the suppression of an non-stationary wake flow can be achieved by the MHD forces. A neutral stability line in (Re, N)-plane is extracted from the numerical simulations. This result will be compared with a linear stability analysis based on a Galerkin approach. Figs 10, refs 10.