Three-Dimensional Analysis of the Influence of the Magnetic Flux Density on Minimum PR in a Faraday-Type MHD Channel

Abstract

The magnetohydrodynamic (MHD) behavior and performance characteristic have been revealed by 3-D numerical simulation of the Faraday-type MHD generator. Numerical results show that the generator inlet–outlet pressure ratio (PR) will affect the plasma behaviors and generator performance in the channel. At high PR, the plasma flows at supersonic, and higher electric power [enthalpy extraction rate (EE)] can be obtained. However, at low PR, boundary layer separation occurs with deflected flow of velocity streamlines and vortex in the separated flow region, owing to the oblique shock wave. Therefore, there exists a minimum PR to maximize power generation performance. Under the strong MHD interaction, the Lorentz force causes the loss of Mach number and the increase of static pressure, but it can alleviate the effect of oblique shock for a lower PR. Furthermore, suppressing the boundary layer separation effect gradually evolves into a normal shock wave. When PR is higher, the thermoelectric conversion efficiency increases, and then a weak shock wave will be generated in the channel, which will propagate upstream and evolve into a normal shock wave. Consequently, under a higher magnetic flux density, the minimum PR can be effectively reduced, and the best generator performance can be obtained. In addition, an “ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> ”-shaped velocity profile will be generated due to the significantly increased MHD interaction. The results calculated in the present simulation are valuable and important for setting working gas conditions and evaluating generator performance.