Research Projects

Several engineering applications involve flows of liquid metals which are, at least partially, driven by thermal gradients and influenced by magnetic fields. Such flows are termed magnetoconvection, and they occur in, for example, electromagnetic stirring of melts in casting processes, liquid metal batteries, and cooling blankets in nuclear fusion reactors. The flow in these applications is highly turbulent; hence, cost-effective but accurate numerical simulations of such flows require appropriate subgrid-scale models. The relevant parameters for these models can be determined from the statistics of small-scale turbulence in magnetoconvection. These statistics are the energy spectrum, rate of energy transfer through different scales, and structure functions. Studies on small-scale turbulence statistics exist for either thermally-driven flows without magnetic field effects or purely magnetohydrodynamic flows without thermal forcing [J. Phys. A. 55, 013002 (2022)]. However, turbulence in liquid metal flows that are both thermally driven and influenced by magnetic fields becomes more intricate due to the combined effects of buoyancy and magnetic fields on the small-scale statistics and has not been addressed before. In this project, we will, for the first time, study the small-scale statistics of liquid metal convection for a wide range of thermal forcing (due to buoyancy) and magnetic field strengths. Towards this objective, we will conduct direct numerical simulations of the above flow in a cube of unit dimensions that is heated from below and cooled from above for different governing parameters. Two configurations for the imposed magnetic field will be considered: a horizontal magnetic field (perpendicular to the direction of gravity) and a vertical magnetic field (parallel to the direction of gravity). A second-order finite-difference solver [J. Comput. Phys. 474, 111784 (2023)] will be used for our simulations. We will obtain the Fourier transform of our numerical data and compute the anisotropic energy spectra, the rates of energy injection, cascade, and dissipation at different scales. The effects of anisotropy on the energy transfer mechanisms will be analyzed, and the scaling of the aforementioned spectral quantities with wavenumber will be obtained. We will also compute the structure functions to quantify the dynamics of turbulent flow in real space. Further, the viscous and thermal dissipation rates in the bulk and boundary layers of the flow will be determined, and their dependence on the governing parameters will be analyzed. Finally, we will arrive at phenomenologies for liquid-metal magnetoconvection, which will help determine the parameters for subgrid-scale models for simulating such flows in complex geometries.