Grid-based kinetic models are promising in that the numerical noise inherent in particle-based methods is essentially eliminated. Here, we call such grid-based techniques a direct kinetic (DK) model. Velocity distribution functions are directly obtained by solving kinetic equations, such as the Vlasov equation, in discretized phase space, i.e., both physical and velocity space. In solving the kinetic equations that are hyperbolic partial differential equations, we employ a conservative, positivity-preserving numerical scheme, which is necessary for robust calculations of problems particularly including ionization. Test cases described in this paper include plasma sheaths with electron emission and injection and expansion of neutral atom flow in a two-dimensional configuration. A unifying kinetic theory of space charge limited sheaths for both floating and conducting surfaces is presented. The improved theory is verified using the collisionless DK simulation, particularly for small sheath potentials that particle-based kinetic simulations may struggle due to statistical noise. For benchmarking of the grid-based and particle-based kinetic simulations, hybrid simulations of Hall thruster discharge plasma are performed. While numerical diffusion occurs in the phase space in the DK simulation, ionization oscillations are well resolved since ionization events can be taken into account deterministically at every time step.

Electron transpiration cooling (ETC) is a recently proposed approach to manage the high heating loads experienced at the sharp leading edges of hypersonic vehicles. Computational fluid dynamics (CFD) can be used to investigate the feasibility of ETC in a hypersonic environment. A modeling approach is presented for ETC, which includes developing the boundary conditions for electron emission from the surface, accounting for the space-charge limit effects of the near-wall plasma sheath. The space-charge limit models are assessed using 1D direct-kinetic plasma sheath simulations, taking into account the thermionically emitted electrons from the surface. The simulations agree well with the space-charge limit theory proposed by Takamura et al. for emitted electrons with a finite temperature, especially at low values of wall bias, which validates the use of the theoretical model for the hypersonic CFD code. The CFD code with the analytical sheath models is then used for a test case typical of a leading edge radius in a hypersonic flight environment. The CFD results show that ETC can lower the surface temperature of sharp leading edges of hypersonic vehicles, especially at higher velocities, due to the increase in ionized species enabling higher electron heat extraction from the surface. The CFD results also show that space-charge limit effects can limit the ETC reduction of surface temperatures, in comparison to thermionic emission assuming no effects of the electric field within the sheath.

Recent progress is presented in an ongoing effort to perform a conceptual analysis of possible electron transpiration cooling using thermo-electric materials at the leading edges of hypersonic vehicles. The implementation of a new boundary condition in the CFD code LeMANS to model the thermionic emission of electrons from the leading edges of hypersonic vehicles is described. A parametric study is performed to understand the effects of the material work function, the freestream velocity, and the leading edge geometry on this cooling effect. The numerical results reveal that lower material work functions, higher freestream velocities, and smaller leading edges can increase the cooling effect due to larger emission current densities. The numerical results also show that the electric field produced by the electron emission may not have a significant effect on the predicted properties. Future work recommendations are provided that may improve the physical accuracy of the modeling capabilities used in this study.

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