Three dimensional simulation of electric field and MHD power generation during re-entry

A numerical tool is developed to help design MHD power generation panels onboard a re-entry vehicle. The tool solves the Poisson equation for the electric potential, which arises from the current continuity equation and the generalized Ohm's law with the Hall effect and ion slip. The discretized form of the Poisson equation is presented in this paper, together with a set of relaxation methods. A multigrid library, HYPRE, is also introduced, which uses parallel multigrid methods to solve elliptic partial differential equations with discontinuous and anisotropic coefficients. The code is tested with three cases, and all the results reproduce analytic solutions and those from the literature. The code is used to compute the electric field and current density distribution around a re-entry vehicle with onboard electrodes. We compare the computed current density with previous 2D results. They show a similar pattern in most regions between the electrodes, while near the electrode ends the 2D simulation gives simplified result. Several 3D plots of current density streamtraces are made, and from the plots we categorize the current into five types. We also compute the net current going through each electrode surface and the corresponding power extraction. The computed power extraction is slightly less than the previous result, where the difference is due to the current loss through the electrodes ends and the narrower region between the electrodes.