Direct numerical simulation of electromagnetically forced flows using OpenFOAM

We present direct numerical simulation results of a conducting fluid subject to the Lorentz force resulting from an external static magnetic field normal to the electric current direction. This research discipline, generally known as electromagnetic forcing flows, is motivated by many engineering and physical applications such as plasma physics, geophysics, weather prediction and solid melting processes. In this paper, a computational fluid dynamics (CFD) code is developed using the open source C++ library OpenFOAM. The solver is based on the electric potential method coupled to the Navier-Stokes equations. The code is then benchmarked to other well-known solvers using different numerical techniques and to the experiment. Excellent agreement is obtained for the forced toroidal channel flow, with three-dimensional dynamics, as well as for the confined vortex-pair in a cylindrical container, with quasi-two-dimensional dynamics. Quasi-two-dimensional forced flow in the presence of non-uniform magnetic field at low Hartmann number is also used for comparison. Furthermore, qualitative comparison with the experiment is made where we are able to successfully simulate the vortex pairs generated by the Lorentz force and the effect of the magnetic field gradient leading to the so-called gradB jets in accordance with the experiment.