Mixed convection in volumetrically heated magnetohydrodynamic flows around a 180-degree sharp bend

Abstract

Magnetohydrodynamic (MHD) flows around a 180-degree sharp bend with volumetric heating are considered. The flows are first upward in the inlet channel and then downward in the outlet channel, subject to a strong transverse magnetic field perpendicular to the direction of exponential decay of the volumetric heating, such that the flow dynamics are quasi-two-dimensional. The work is motivated by the design of liquid metal blankets with U-shaped ducts for future nuclear fusion reactors, in which the main component of the very strong magnetic field is perpendicular to the flow direction and very strong volumetric heating is applied. The flow is found to be steady-state or oscillating depending on the strengths of the internal volumetric heating and magnetic field. A parametric study of the instability leading to the oscillations is performed, which covers the Hartmann number (Ha) from 102 to 104, the Reynolds number (Re) up to 105, and the Grashof number (Gr) from 104 to 1010. The stability threshold can be identified by the parameter Gr/(HaRe) with the threshold value around 32. The high-amplitude low-frequency oscillations of temperature result from the quasi-periodic breakdown of the recirculation bubbles, which attributes to the Kelvin-Helmholtz instability of shear layers.