Three-dimensional double-diffusive convection of conducting fluid under a magnetic field

The work aims to study the convection and diffusion of metallic fluid and the tritium in a cavity under the external magnetic field. The solver based on the finite volume method and the consistent and conservative scheme is developed to solve the Navier-Stokes equation considering the Lorentz force, concentration, and thermal buoyancy. The coupling effects of the magnetic field, the internal volumetric heat source, and the concentration difference between the left and right walls of the cavity are investigated. It is found that both the rotation direction and strength of the main circulation flow are controlled by the concentration buoyancy and the thermal buoyancy only regulates the global flow in the cavity. A larger concentration difference or a stronger internal heat source can lead to unstable flow. However, the stronger magnetic field suppresses the main circulation flow and small secondary vortices. The power law scaling of the Sherwood number vs the ratio of the Rayleigh number of the concentration to the Hartman number based on the force balance agrees with the numerical simulation. Four types of flow modes (large-amplitude low-frequency, large-amplitude high-frequency, small-amplitude low-frequency, and stable modes) are observed under the coupled multi-physics fields of the magnetic field, concentration difference, and heat source. The correlation function describing the influence of magnetic field and concentration strength on mass transfer is concluded.