Magnetoconvection in a horizontal duct flow at very high Hartmann and 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. 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-twodimensional 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.

Toward full simulations for a liquid metal blanket: part 2. Computations of MHD flows with volumetric heating for a PbLi blanket prototype at Ha ∼ 104 and Gr ∼ 1012

“…For many blanket flows, this model was proven to serve as a good approximation and could be used instead of full 3D flow equations. However, as suggested in several studies [25,48,49], the accuracy of this model, under some circumstances, can deteriorate, especially at high Gr numbers. First of all, this applies to the temperature field as there is no direct physical mechanism that might be responsible for the two-dimensionalization of the temperature field as it happens with the velocity field.…”