Development of a potential based code for MHD analysis of LLCB TBM

A two dimensional solver is developed for MHD flows with low magnetic Reynolds’ number based on the electrostatic potential formulation for the Lorentz forces and current densities which will be used to calculate the MHD pressure drop inside the channels of liquid breeder based Test Blanket Modules (TBMs). The flow geometry is assumed to be rectangular and perpendicular to the flow direction, with flow and electrostatic potential variations along the flow direction neglected. A structured, non-uniform, collocated grid is used in the calculation, where the velocity ( u), pressure ( p) and electrostatic potential ( ϕ) are calculated at the cell centers, whereas the current densities are calculated at the cell faces. Special relaxation techniques are employed in calculating the electrostatic potential for ensuring the divergence-free condition for current density. The code is benchmarked over a square channel for various Hartmann numbers up to 25,000 with and without insulation coatings by (i) comparing the pressure drop with the approximate analytical results found in literature and (ii) comparing the pressure drop with the ones obtained in our previous calculations based on the induction formulation for the electromagnetic part. Finally the code is used to determine the MHD pressure drop in case of LLCB TBM. The code gives similar results as obtained by us in our previous calculations based on the induction formulation. However, the convergence is much faster in case of potential based code.