Numerical study on the magnetohydrodynamics of an oscillatory flow under inductionless and core-side-layer approximations

Abstract

A harmonically-driven, incompressible, electrically conducting, and viscous magnetohydrodynamic flow through a thin walled duct of rectangular cross section interacting with a uniform magnetic field transverse to its motion direction is numerically investigated. Spectral collocation method is used to solve the Navier-Stokes equation under the inductionless approximation for the magnetic field in the gradient formulation for the problem. Flow is considered fully developed in the direction perpendicular to the applied external magnetic field, laminar in regime, and feasible to be core-side-layer approximated. Flow structure and key features are numerically inquired regarding prospective alternating power generation applications in a liquid metal magnetodydrodynamic generator rectangular channel configuration. It is found that in the side layer and its vicinity the emerging flow structures/patterns depend mainly on the Hartmann number and oscillatory interaction parameter ratio. Formulation developed and tested with these calculations admits implementation of a generator configuration by means of load resistance attachment and walls conductivity optimization.