3D Numerical study of magnetohydrodynamic instability in liquid metal taylor-couette flow

Abstract

This purpose is about a 3D study of magnetohydrodynamic (MHD) instability in liquid matal Taylor-Couette flow, this problem is receiving more and more research interest due to its application in the engineering, oceanography and the astrophysical research The Taylor-Couette system consists of two coaxial cylinders in differential rotation, which is considered as a hydrodynamic model system, allowed researchers to progress in understanding the laminar-turbulent transition phenomena. A set of states found in narrow gap of Taylor-Couette systems where the outer cylinder is held fixed and the inner cylinder speed increased. The symmetry breaking parameter is the Taylor number Ta that gives a measure of the ratio of centrifugal forces to viscous forces. When the liquid is replaced by an electrically conducting fluid and an external magnetic field is applied, this leads to MHD Taylor-Couette flow. Additional body force, Lorentz force, acting on the fluid arises. Lorentz force is in the direction perpendicular to both magnetic and electric fields. The behaviour of flow depends on strength and geometry of applied field, magnetic and electric properties of the liquid, cylinders and endplates. In this work, the MHD instability Taylor-Couette flow is considered for liquid sodium with its magnetic Prandtl number Pm <1. The results of pressure and angular momentum in the Taylor-Couette flow under the effect of an external uniform axial magnetic field B=4 Tesla are investigated numerically for the different cases of electrically conducting or insulating walls at the Ekman cell, at the middle of the first Taylor-votex flow (TVF) and between two cells.