Numerical Model of Thermionic- and Photo- emission Electron Heat Spreading

Abstract: Thermionic emission has been exploited to give rise to the theory of thermionic cooling also known as electron transpiration cooling, which can potentially serve as a powerful and engineerable cooling mode for hypersonic leading edges that can reach temperatures exceeding 2000 {\deg}C. However, the contribution to this cooling mode by photoexcited electrons remains relatively unexplored. Here, we present a numerical model of thermionic emission and photoemission driven cooling and heat spreading, examining the trajectories of electrons emitted based on a random energy model within a prescribed potential space. By simulating surfaces with two different temperature gradients, and imposing potential spaces derived for Cartesian, cylindrical, and spherical coordinate systems, we demonstrate that heat spreading can be significant for temperature gradients on a length scale comparable to the electron spreading distance. Additionally, by testing two different leading edge radii, we find that heat spreading affects a larger percentage of surface area for a smaller leading edge radius.