Electronic edition ISSN 1574-0579

Development and verification of a finite-volume solver for a disk magnetohydrodynamic generator

Liu Wei Nan^1,2 - Li Zhen Hao^1,2 - Zhao Ling Zhi^1,2,3 - Peng AiWu^1,2,3

¹ School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
² Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100190, China
³ State Key Laboratory of High Density Electromagnetic Power and Systems, Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100190, China

Abstract
A disk magnetohydrodynamic (MHD) generator involves strong coupling among highvelocity compressible flow, non-equilibrium plasma transport, Hall current conduction, electromagnetic forces, and an external electrical load. This study develops a twodimensional axisymmetric finite-volume solver for the complete flow passage of the disk MHD generator. The compressible Navier–Stokes equations are discretized using an AUSM-type flux with second-order reconstruction and advanced by a two-stage strongstability-preserving Runge–Kutta scheme. Species transport and electron energy equations are solved using consistent face mass fluxes. Charge conservation and the generalized Ohm’s law, including the Hall effect, are combined to obtain the electric potential equation, whereas the flow and electromagnetic fields are coupled through the Lorentz force, Joule heating, electromagnetic work, and electron-heavy-particle energy exchange. Terminal voltage, current, and external-load power are updated during the transient calculation. Unlike the CIP-based formulations commonly employed in previous disk generator simulations, the present method adopts a conservative control-volume formulation for the flow and plasma equations, providing consistent transport of mass, species, and energy across cell faces. The compressible flow module is cross-compared with ANSYS Fluent, and the coupled solver is verified against a published two-dimensional disk MHD benchmark. The predicted maximum Mach number and static pressure differ from the reference values by 4.3 per cent and 5.4 per cent, respectively, whereas the calculated output power is 5.14 kW, corresponding to a deviation of only 0.78 per cent. The developed solver is subsequently applied to a disk MHD generator under an axial magnetic field of 7.0 T. Electromagnetic braking decreases the characteristic Mach number from 2.21 to 0.93 and increases the static pressure from 37.9 to 153.35 kPa. Strong spatial nonuniformities are observed in the electron temperature, electrical conductivity, Hall parameter, electric potential, and current density fields. The results demonstrate that the proposed finite-volume framework can reliably capture the coupled compressible flow and electromagnetic characteristics of disk MHD generators and provides an extensible numerical tool for strong field operating condition analysis. Table 1, Figs 10, Refs 28.