Numerical simulations of MHD flows past obstacles in a duct under externally applied magnetic field

摘要

In this thesis, we simulate the flow of an electrically conducting fluid past an obstacle placed inside a duct under the influence of an externally applied magnetic field. Three different obstacles are considered: a circular and a square cylinder spanning over the full height of the duct and a square cylinder spanning over the half height of the duct. The magnetic field is oriented along the cylinder axis and the duct is electrically insulating. In a first stage of the thesis, we perform a parametric study over both Ha and Re in the case where both Ha ≫ 1and N ≫ 1 with 2D simulations using the quasi-2D flow model by [165]. In particular, we provide the first explanation of the collapse of the regular Kármán vortex street observed experimentally by [180]. We also derive two different scaling laws linking the evolutions of the flow coefficients and either Re/Ha or Re/Ha0.8. The second phase of the thesis is dedicated to the development of a 3D MHD capable code to solve the flow equations with the inductionless approximation. This code is used to investigate the 3D MHD flow past a truncated square cylinder in a duct. We explain the different stages of elaboration of our code and validate its performances to MHD duct flows and cylinder wakes. We also implement a wall function at the interface between the Hartmann layers and the bulk flow. The non-MHD flow past the truncated cylinder is simulated for 10 ≤ Re ≤ 400. In particular, the early stages of the unsteady flow regime is characterised by a regular symmetric procession of hairpin vortices. We explain the formation mechanism of these vortices and its evolution when Re is increased. Finally, we investigate the MHD flow past the electrically insulating truncated cylinder at Ha=100 and 200 for Re up to 1000. The flow dynamics is strongly 2D with the presence of a Hunt’s wake at very low Re. The unsteady regime leads to the development of a Kármán vortex street. Switching to a perfectly conducting truncated square cylinder enhances the braking of the flow by the Lorentz force in the region above the cylinder tip.NB some of the mathematical symbols in this abstract may not display correctly; please consult the PDF file for the definitive version of the abstract.