On the quasi-static approximation in the finite magnetic Reynolds number magnetohydrodynamic flow past a circular cylinder

Abstract

Abstract We consider the classical problem of Magnetohydrodynamic (MHD) flow past a circular cylinder in the presence of an imposed magnetic field aligned to the flow. Our analysis includes the computation of magnetic field in the interior of the cylinder because in an experimental setup, the magnetic field will naturally pass through the cylinder. As such, we have solved the Maxwell’s equations both in the fluid flow region as well as in the interior of the cylinder with appropriate continuity conditions for magnetic field as it penetrates the cylinder. The fully nonlinear MHD equations are solved numerically using a highly accurate finite difference scheme. The influence of magnetic field in controlling boundary layer separation is discussed through the analysis of pressure gradient and the radial and transverse velocity gradients. In fact, magnetic field penetrated inside the cylinder helps to suppress flow separation more effectively than otherwise. A non-monotonic behavior of interaction parameter on the flow separation is observed for low values of magnetic Reynolds numbers ( R m ). Most importantly, we examine the realm of Quasi-Static approximation in the two-dimensional MHD flows against the corresponding computationally expensive fully nonlinear MHD solutions. Our results suggest that even if R m = 0 . 5 , the percentage error in using Quasi-Static approximation can reach up to 17.5%. Thus we have analyzed and quantified the differences between the fully nonlinear treatment and the Quasi-Static approximation for this classical flow configuration for the first time.