Validation and verification of a robust 3-D MHD code

Abstract

The present paper aims to establish the MHD module of Anupravaha-1, a general purpose solver for fluid-flow, developed by our research group as a versatile computational tool for simulating MHD flows through complex geometric configurations. The code is capable of handling non-orthogonal, multi-block, structured grids and treats a coupled fluid–wall (conjugate) modeling to include thermal and electro-magnetic effects in the presence of duct walls and electro-thermally coupled manifolds. The solver module is thoroughly validated using various benchmark numerical and analytical results, which include, but not limited to the following variety of problems: (a) 2-D analytical and numerical reference cases of pressure driven flows in straight and curved channels, and natural convection in a rectangular enclosure, for Hartmann numbers Ha ≤ 300. (b) Fully-developed flow through a rectangular duct for Hartmann numbers up to Ha = 15,000, considering the duct walls to be all insulating (the Shercliff's case) and also with only the Hartmann walls partially conducting (Hunt's case II). (c) For the 3-D solver validation, comparative results for (1) the flow through a straight duct in the presence of a non-uniform magnetic field, (2) free convection in a cubical enclosure under a uniform magnetic field, and (3) an electro-magnetically driven flow in a toroidal duct for low Hartmann numbers (Ha ≤ 100), are obtained and discussed. (d) In addition, the implementation of a simple wall treatment method for computing high Hartmann number flows, as typically encountered in liquid metal cooled fusion-blanket applications, is tested using the case of flow through a rectangular duct in the presence of a homogeneous magnetic field for Ha = 10,000–30,000. The performance of the code in the cases considered ranged from good to excellent. Lastly, comparison with the ALEX (Argonne Liquid metal EXperiment), for the case of flow through a rectangular duct in a fringing magnetic field is presented, that revealed the sensitivity of the results to the precise description of the magnetic field.