Magnetoconvection in a horizontal duct flow at very high Hartmann and Grashof numbers

TL;DR

This study uses simulations and stability analysis to explore magnetoconvection in a horizontal duct at extreme Hartmann and Grashof numbers, revealing flow instabilities and the limits of two-dimensional approximations.

Contribution

It extends understanding of magnetoconvective flows at very high control parameters relevant to nuclear fusion reactors, validating a 2D approximation and analyzing its limitations.

Findings

Instability to quasi-2D rolls persists at high parameters.

High-amplitude temperature fluctuations due to flow transport.

Classical 2D approximation accuracy decreases at extreme Grashof numbers.

Abstract

Direct numerical simulations and linear stability analysis are carried out to study mixed convection in a horizontal duct with constant-rate heating applied at the bottom and imposed transverse horizontal magnetic field. A two-dimensional approximation corresponding to the asymptotic limit of very strong magnetic field effect is validated and applied, together with full three-dimensional analysis, to investigate the flow's behaviour in the previously unexplored range of control parameters corresponding to typical conditions of a liquid metal blanket of a nuclear fusion reactor (Hartmann numbers up to $10^4$ and Grashof numbers up to $10^{10}$). It is found that the instability to quasi-two-dimensional rolls parallel to the magnetic field discovered at smaller Hartmann and Grashof numbers in earlier studies also occurs in this parameter range. Transport of the rolls by the mean flow leads to magnetoconvective temperature fluctuations of exceptionally high amplitudes. It is also demonstrated that quasi-two-dimensional structure of flows at very high Hartmann numbers does not guarantee accuracy of the classical two-dimensional approximation. The accuracy deteriorates at the highest Grashof numbers considered in the study.