Impact of Poisson Equation Boundary Conditions in Modeling Partially Ionized Hypersonic Flows

A vehicle flying at sufficiently high speeds through an atmosphere may ionize surrounding gas via shock waves to create a partially ionized plasma. Though it is the convention to use the ambipolar diffusion approximation when modeling hypersonic flows, studies show that full calculation of electrostatic effects leads to significant differences in quantities of interest, such as electron number density and vehicle surface heat flux. In a 1D setup, when a zero potential gradient is used at the inlet and the vehicle surface potential is fixed to zero, electric fields tend to spike at the shock front and within the plasma sheath at the vehicle surface. To date, no study has explored the impact of other boundary condition configurations. This study seeks to resolve that gap by testing a series of Poisson equation boundary condition configurations for a 1D stagnation streamline for a range of hypersonic flow conditions. Of these configurations, the most important is the floating wall potential boundary condition, which captures realistic behavior of insulated surfaces in the presence of a plasma. The range of hypersonic flow conditions includes both continuum and kinetic regimes, allowing for the additional study of the influence of nonequilibrium behavior on electric field formation.