Limits for thermionic emission from leading edges of hypersonic vehicles

Simulations of electron transpiration cooling (ETC) on the leading edge of a hypersonic vehicle using computational fluid dynamics (CFD) are presented. The thermionic emission boundary condition and electric field model including forced diffusion are discussed. Different analytical models are used to describe the plasma sheath physics in order to avoid resolving the sheath in the computational domain. The first analytical model does not account for emission in the sheath model, so the emission is only limited by the surface temperature. The second approach models the emissive surface as electronically floated, which greatly limits the emission. The last analytical approach biases the emissive surface, which makes it possible to overcome space-charge limits. Each approach is compared and a parametric study is performed to understand the effects that the material work function, freestream velocity, and leading edge geometry has on the ETC effect. The numerical results reveal that modeling the sheath as a floated surface results in the emission, and thus ETC benefits, being greatly limited. However, if the surface is negatively biased, the results show that the emission can overcome space-charge limits and achieve the ideal ETC benefits predicted by temperature limited emission. The study also shows that, along with negatively biasing the surface, emission is enhanced by increasing the number of electrons in the external flowfield by increasing the freestream velocity.