Assessing the ambipolar diffusion approximation for rarefied hypersonic plasma shock layers

Under hypersonic entry conditions into an atmosphere, gas may be ionized via strong shock waves to create a plasma. Parts of the flow, such as upstream of the shock layer, may be characterized with the continuum approach. Other parts of the flow, such as immediately post-shock or at the vehicle surface, require a kinetic modeling approach to capture the significant departure of velocity distributions from equilibrium conditions, thus leading to the breakdown of continuum assumptions. Particle-based kinetic methods often employ the ambipolar-diffusion approximation to model plasma effects without the added computational expense of solving the Poisson equation, even though the ambipolar-diffusion approximation is derived from continuum assumptions. In this study, we assess the validity of the ambipolar diffusion approximation by comparing simulations of a 1D3V stagnation streamline from a standard direct simulation Monte Carlo model with an Eulerian grid-based Boltzmann-Poisson-BGK solver. The degree of continuum breakdown is characterized by a Knudsen number calculated from local flow conditions and gradients. Predictions of continuum breakdown via local Knudsen numbers are compared between the simulation models. Additionally, differences between the models in macroscopic properties of interest, such as surface heat flux and charge separation, are investigated.