Integrated Multimode, Multiphase Cooling of High-Speed Leading Edges

Hypersonic air vehicles are increasingly relevant to planned commercial and defense applications. These vehicles are subjected to extreme temperatures and stresses that can severely limit functional performance. As a result, aerodynamic design requirements must be balanced with thermal management considerations for sustained flight at hypersonic speeds, with specific attention devoted to the leading edge because of extreme local heat fluxes in this region. Thermionic cooling has been proposed as a thermal management technique for hypersonic leading edges, but heat conduction into the surface has been neglected in such models. Here, a multimode cooling model is reported that estimates surface temperatures around the stagnation point, the location of maximum heat flux near the leading edge. The leading edge is modeled using a heat-balance integral formulation of one-dimensional heat conduction with phase change and combined radiative, thermionic, and evaporative heat fluxes at the surface. A well-known, low-work-function emitter material, lanthanum hexaboride, is analyzed, and the wall temperature is predicted to reach just below the melting point of the emitter material at Mach 5 and 10 when the emission current is calculated by the Richardson–Dushman equation. Conduction into the surface is a significant percentage of the total cooling at short times and low Mach numbers, while additional cooling modes begin to dominate at longer times. However, when space-charge effects are considered, the wall temperature reaches the melting point of the emitter at Mach 10 and 15, and the molten material is quickly removed by the high enthalpy flow. Our model predicts the emission current decreases significantly but approaches the Richardson current at Mach 15 if the surface is negatively biased. The results presented here can impact material selection and provide inputs for higher-fidelity models and experiments, leading to a more robust thermal design of hypersonic vehicles.