NUMERICAL SIMULATION OF MHD FULLY DEVELOPED BUOYANT FLOW AT LOW PR: "DIRECT" VS. "AD HOC" TREATMENT OF THE HARTMANN LAYERS

Computational results were obtained for fully developed free convection MHD flow in a vertical square duct. Two thermal conditions were considered: differential heating along the two side walls, and volumetric heat generation with symmetric cooling through the side walls. The magnetic field vector B was perpendicular to the front/back walls (Hartmann walls), which were supposed to be adiabatic. The Prandtl number was 0.0321, the Grashof number (based on the distance D between the thermally active walls) was 10 5 and the Hartmann number (expressing the magnetic field intensity) was 200 or 1000. Simulations were performed by using a general purpose CFD code (CFX-4.3) in which appropriate terms were implemented in order to model the MHD forces and the behaviour of electrical potential and currents. The method allows the treatment of general, complex configurations of engineering interest, although only the simple above geometry was considered here. In previous work an approximate “ad hoc” treatment was used for the Hartmann layers (thin fluid layers which line the walls perpendicular to the magnetic field, and which are interested by very sharp velocity gradients). On the contrary, in the present paper the Hartmann layers were explicitly resolved by the computational grid and no simplifying assumption was used. Results compared favourably with those based on the “ad hoc” Hartmann layer treatment and showed otherwise unresolved details of the flow and electrical quantities in the near-wall regions.