Comparison of the core flow approximation and full solution approach for MHD flow in non-symmetric and multiple adjacent ducts

AbstractThe core flow approximation method has been used extensively in the past several years to model MHD flow at high Hartmann number and interaction parameter. This method assumes that inertial and viscous forces and the induced magnetic field are negligible, thus transforming the governing equations to a set of linear equations. The resulting equations are much easier to solve than the original set of equations, and as a result this method has been applied to several geometries. Benchmarking to experimental results has been done with excellent results for a limited number of geometries, but more investigation is necessary to determine the validity and applicability of the core flow approach. In this paper, results of the core flow analysis are compared with results from a two-dimensional full solution analysis (which included inertial and viscous terms) to further evaluate the core flow method. In particular, comparison is made for a rectangular duct geometry with an oblique magnetic field, a rectangular duct with a magnetic field parallel to one set of walls but without symmetry about the plane between the two side walls, and multiple adjacent rectangular ducts where the magnetic field is parallel to one set of walls. Special attention is paid to assumptions used in the core flow approximation dealing with the electric current flowing in the side layers. These comparisons are done for fully developed flow, and the results show that the core flow approximation can predict flow in these geometries with accuracy that is within design limits.