Validity of quasi-2D models for magneto-convection

Abstract

For applications in nuclear fusion reactors where magnetic fields are very strong, liquid metal flows in the cores of ducts can often be regarded as inertialess and practically inviscid, while viscous effects are localized in thin boundary layers. The intense electromagnetic Lorentz forces, resulting from the interaction of induced electric currents and imposed magnetic field, tend to remove flow variations along magnetic field lines and they force the fluid to circulate mainly in planes perpendicular to the field. The established quasi-two dimensional magnetohydrodynamic flow can be predicted by means of an approximate model by reducing the basic governing equations to a 2D problem by analytical integration along magnetic field lines. Such models have been applied in the past by numerous authors to investigate duct flow problems and magneto-convection. However, limitations of those Q2D approaches have never been systematically studied.

Computational modeling of magnetoconvection: Effects of discretization method, grid refinement and grid stretching

“…The combination of the discretized gradient components in (14) and (15) and divergence in (16) gives the consistent second-order approximation of the Laplacian in the left-hand side of (2) on a compact stencil. Finally, the components of the Lorentz force in the momentum equation are computed immediately at the respective centers of the cell faces as…”

“…The model can only be rigorously derived if the walls of the flow domain are perfectly electrically insulated. The fact that it becomes invalid in convection flow with electrically conducting walls was highlighted in [15].…”

“…It has been recently understood that the suppression of turbulence by the magnetic field does not necessarily mean that the flow acquires a simple laminar steady-state form. On the contrary, growth of the MHD-specific convection instability modes that have weak or zero variations along the magnetic field lines and, thus, are not suppressed, may lead to unsteady, essentially nonlinear and complex flow dynamics [7][8][9][10][11][12][13][14][15][16].…”

Validation and verification of a quasi two-dimensional turbulence model and an eddy detection method for liquid metal magnetohydrodynamics flows

“…The use of these Q2D models is constrained by the assumption of electrically insulating walls, as assessed by Bühler et al [11]. Therefore, using Q2D models is especially interesting for the assessment of the transport phenomena in the DCLL blanket projected in Fernandez's et al latest proposal [6].…”