Modeling of Magnetohydrodynamics in Nozzle Arc: A Mathematically and Numerically Efficient Approach

This paper deals with the numerical modeling of magnetohydrodynamics (MHD) phenomenon inside a nozzle arc. Previous work for MHD simulation shows that current density is computed from current continuity equation and thereafter the magnetic field is computed by either of the three approaches: A1-Biot-Savart Law; A2-magnetic vector potential equation; and A3-Ampere's Law. An alternative approach-called here as A4-is proposed here for nozzle arc application. This approach starts with computation of magnetic field from magnetic induction equation, and then current density is computed from Ampere's Law. The proposed approach is shown to give good agreement with other approaches (reported in the published literature) for low- as well as high-current applications. It is demonstrated that the A4 approach offers two advantages over the most commonly used A2 approach: 1) A4 approach achieves almost same computational accuracy with much less computation time and is thus numerically more efficient and 2) A4 approach is mathematically more efficient as it can be nondimensionalized and used for parametric investigation. A hybrid model is also proposed to demonstrate that the A4 model predicts arc characteristics accurately with little effect of singularity issue.