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

Abstract

The flow of liquid metals in straight rectangular channels with an externally applied transverse magnetic field is considered for breeding blankets in tokamak fusion reactors. Under the tokamak magnetic field, the liquid metal experiences the magnetohydrodynamic (MHD) effect that enhances the laminarization of the flow. In geometric singularities, or under certain flow conditions, the combination of Lorentz forces, momentum, and buoyant forces may trigger the formation of vortical structures. The generated vortices will align with the direction of the magnetic field, and therefore the use of a quasi-two-dimensional (Q2D) model is convenient to study them assuming that the walls are electrically insulating and the Hartmann number $\textbf{Ha} = B L \sqrt{\sigma/\mu}$ is high enough. Using this model is computationally affordable, allowing extensive parametric analyses. To identify the presence of eddies in the two-dimensional domain, the application of the bi-dimensional fast Fourier transform (FFT2) is foreseen as an adequate detection method. This work presents a methodology to systematically calculate liquid metal MHD flows with a Q2D model and evaluate the formation of eddies in the flow domain. The work includes a description of the validation and verification of the Q2D MHD model and of the FFT2 method proposed to automatically identify eddies. The sensitivity of the detection method is analyzed to subsequently apply it in parametric analyses.