Three-dimensional numerical analysis of magnetohydrodynamic flow bounded by conducting walls under alternating-current magnetic fields

Abstract

Three-dimensional (3D) numerical simulation of incompressible, magnetohydrodynamic (MHD) flows under alternating-current (AC) magnetic fields are carried out, which takes into account the coupling with the electromagnetic fields in the solid and gas regions. A numerical scheme is constructed by combining the Galerkin finite element method and the edge-element based finite element method, which are applied to the discretizations of the Navier–Stokes equations and the electromagnetic field equations, respectively. The solution algorithm for fluid flow is based on an explicit fractional step approach and the simultaneous relaxation of velocity and pressure to satisfy the continuity equation. The electromagnetic field equations are formulated with the use of the magnetic vector potential which is defined on the edge elements. In the proposed numerical scheme, the advection term in the induction equation is not neglected, because the scheme needs to deal with the condition where the advection term is the same order with the diffusion term in that equation. The validity of the numerical scheme is verified through the analysis of the electromagnetic field under a direct-current magnetic field, and numerical simulations of the MHD flows under spatially uniform AC magnetic fields are carried out. It is confirmed that the spatio-temporal mean Lorentz force in the conducting fluid becomes weaker with the increase in the dimensionless frequency due to the skin effect. It is also shown that the flow pattern in a hexahedral closed domain is largely changed when the frequency is getting higher, which is associated with the change in the Lorentz force profile.

Keywords

• magnetohydrodynamic flow
• coupled analysis
• finite element method
• edge element
• alternating-current magnetic field