Study of instabilities and quasi-two-dimensional turbulence in volumetrically heated magnetohydrodynamic flows in a vertical rectangular duct

Abstract

We consider magnetohydrodynamic (MHD) rectangular duct flows with volumetric heating. The flows are upward, subject to a strong transverse magnetic field perpendicular to the temperature gradient, such that the flow dynamics is quasi-two-dimensional. The internal volumetric heating imitates conditions of a blanket of a fusion power reactor, where a buoyancy-driven flow is imposed on the forced flow. Studies of this mixed-convection flow include analysis for the basic flow, linear stability analysis and Direct Numerical Simulation (DNS)-type computations. The parameter range covers the Hartmann number (Ha) up to 500, the Reynolds number (Re) from 1000 to 10 000, and the Grashof number (Gr) from 105 to 5 × 108. The linear stability analysis predicts two primary instability modes: (i) bulk instability associated with the inflection point in the velocity profile near the “hot” wall and (ii) side-wall boundary layer instability. A mixed instability mode is also possible. An equation for the critical Hartmann number has been obtained as a function of Re and Gr. Effects of Ha, Re, and Gr on turbulent flows are addressed via nonlinear computations that demonstrate two characteristic turbulence regimes. In the “weak” turbulence regime, the induced vortices are localized near the inflection point of the basic velocity profile, while the boundary layer at the wall parallel to the magnetic field is slightly disturbed. In the “strong” turbulence regime, the bulk vortices interact with the boundary layer causing its destabilization and formation of secondary vortices that may travel across the flow, even reaching the opposite wall. In this regime, the key phenomena are vortex-wall and various vortex-vortex interactions. Flow and magnetic field effects on heat transfer are also analyzed.