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

The flow of liquid metals in straight rectangular channels with an externally applied transversemagnetic field is considered for breeding blankets in tokamak fusion reactors. Under thetokamak magnetic field, the liquid metal experiences the magnetohydrodynamic (MHD) effectthat enhances the laminarization of the flow. In geometric singularities, or under certain flowconditions, the combination of Lorentz forces, momentum, and buoyant forces may trigger theformation of vortical structures. The generated vortices will align with the direction of themagnetic field, and therefore the use of a quasi-two-dimensional (Q2D) model is convenient tostudy them assuming that the walls are electrically insulating and the Hartmann number Ha=BL root sigma/mu is high enough. Using this model is computationally affordable, allowingextensive parametric analyses. To identify the presence of eddies in the two-dimensionaldomain, the application of the bi-dimensional fast Fourier transform (FFT2) is foreseen as anadequate detection method. This work presents a methodology to systematically calculate liquidmetal 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 andof the FFT2 method proposed to automatically identify eddies. The sensitivity of the detectionmethod is analyzed to subsequently apply it in parametric analyses.