Exact solution and CFD simulation of magnetorheological fluid purely tangential flow within an eccentric annulus

Abstract

In this paper, hydrodynamic characteristics of Magnetorheological (MR) fluid flow within an eccentric annulus have been investigated analytically and numerically. The MR fluid obeys the Herschel–Bulkley constitutive relation with a magnetic field dependent on yield stress. While the eccentric ratio or the gap between two cylinders is very small, local flow can be assumed between two parallel plates. With this simplification of motion equation, the effects of the magnetic field, eccentricity ratio and power-law exponent (n=0.25, 0.5 and 1) on the tangential velocity, torque and pressure gradient are analyzed analytically. Then, the results were compared with two-dimensional (2D) simulations for a system of two eccentric cylinders filled with a MR fluid. The Computational Fluid Dynamics (CFD) simulation results show good agreement with analytical solution. A wider range of the various parameters has been studied by the 2-D simulations. The influences of MR effects on flow field are significant and not negligible. The viscosity increases by increasing the magnetic field and eccentricity ratio, consequently providing an enhancement in the yield stresses and total torque required to rotate the inner cylinder.