Kyle M. Hanquist

Conceptual Analysis of Electron Transpiration Cooling for the Leading Edges of Hypersonic Vehicles

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.

Detailed modeling of electron emission for transpiration cooling of hypersonic vehicles

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 radi...

Evaluation of Computational Modeling of Electron Transpiration Cooling at High Enthalpies

A modeling approach for electron transpiration cooling of high-enthalpy flight is evaluated through comparison to a set of experiments performed in a plasma arc tunnel for air and argon. The comparisons include air and argon flow at high enthalpies (27.9 and 11.6  MJ/kg, respectively), with a Mach number of 2.5 to 3. The conversion of the reported enthalpies and Mach numbers to freestream temperatures and velocities is discussed. The numerical approach is described, including implementation of a thermionic emission boundary condition and an electric field model. Also described is the implementation of a finite-rate chemistry model for argon ionization. Materials with different electron emission properties are also investigated, including graphite and tungsten. The comparisons include two different geometries with different leading-edge radii. The numerical results produce a wide range of emitted current due to the uncertainties in freestream conditions and emissive material properties, but they still agre...

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. Nomenclature AR Richardson constant, 1.20 × 10 A/m/K Cs Charge of species s C Thermal speed D Diffusion coefficient E Electric field j Electric current density J Diffusive flux J Current density h Planck constant, 6.63 × 10 m kg/s kB Boltzmann constant, 1.38 × 10 J/K K Mobility ms Mass of species s Ms Molar mass of species s n Number density NAv Avogadro constant, 6.02 × 10 mol p Pressure q Heat transfer Qe Elementary charge, 1.60 × 10 C u Velocity U Drift velocity ∗PhD Candidate, Student Member AIAA. †James E. Knott Professor of Engineering, Fellow AIAA

Comparisons of computations with experiments for electron transpiration cooling at high enthalpies

A modeling approach for electron transpiration cooling of high enthalpy flight is compared to a set of experiments performed in a plasma arc tunnel for nitrogen and argon. The comparisons include nitrogen and argon flow at high enthalpies, 12,000 btu/lb and 5,000 btu/lb respectively, with a Mach number of 2.5 to 3. Converting the provided enthalpies and Mach numbers to freestream temperatures and velocities is discussed. The numerical approach is described including implementation of a thermionic emission boundary condition. Also described is the implementation of a finite-rate chemistry model for argon ionization. Different emissive materials are also investigated including graphite and tungsten. The comparisons include two different geometries with different leading edge radii. The numerical results produce a wide range of emitted current due to the uncertainties in freestream conditions and emissive material properties, but still agree well with the experiments. Future work recommendations are provided that may improve the physical accuracy of the modeling capabilities used in the comparisons. Nomenclature AR Richardson constant, 1.20 × 10 A/m/K Cp Constant pressure specific heat Cs Charge of species s E Electric field j Electric current density Jee Emitted electron current density h Planck constant, 6.63 × 10 m kg/s gj Degeneracy factor of electronic energy level j ht Total enthalpy ∆hi Enthalpy of ionization kb Backward reaction rate coefficient kB Boltzmann constant, 1.38 × 10 J/K kf Forward reaction rate coefficient Ke Equilibrium constant ms Mass of species s M Mach number NAv Avogadro constant, 6.02 × 10 mol p Pressure q Heat transfer Qe Elementary charge, 1.60 × 10 C Qint Internal energy partition function u Freestream velocity Rn Leading edge radius ∗PhD Candidate, Student Member AIAA. †James E. Knott Professor of Engineering, Fellow AIAA

Computational analysis of electron transpiration cooling for hypersonic vehicles

Simulations of a leading edge of a hypersonic vehicle using computational fluid dynamics (CFD) and a material response code are presented in order to investigate the effect in-depth surface conduction has on electron transpiration cooling (ETC). ETC is a recently proposed thermal management approach. Previous numerical studies have shown that ETC can significantly lower the stagnation point surface temperature of sharp leading edges of hypersonic vehicles. However, these studies have neglected the effect of heat also being conducted into the material as opposed to only into the flow via radiative cooling and ETC. A modeling approach is presented for ETC, which includes the boundary conditions for electron emission from the surface, accounting for the electric field and space-charge limit effects within the near-wall plasma sheath. A material response code is used to determine typical values of in-depth surface conduction for the test cases studied. Since ETC materials are still being developed, a parametric study is conducted for a range of material properties pertinent to ETC. The results of this study are used to generate in-depth surface conduction profiles, which are implemented into the CFD framework. The CFD simulations show that including in-depth surface conduction results in lower surface temperatures than predicted with radiative and ETC cooling alone. This is because in-depth surface conduction complements radiative cooling and ETC by moving heat away from the surface, in the case of surface conduction by moving the energy into the material, allowing for a lower surface temperature. The results also show that ETC remains a major mode of heat transfer away from the surface, even with in-depth surface conduction. This suggests that ETC is still a promising mode of thermal management, especially since it transfers energy to the flow instead of into the material. Nomenclature AR Richardson constant, 1.20 × 10 A/m/K Ci Ion acoustic speed D Diffusion coefficient D Drag E Electric field j Electric current density J Current density kB Boltzmann constant, 1.38 × 10 J/K ṁ Mass blowing rate Ms Molar mass of species s n Number density NAv Avogadro constant, 6.02 × 10 mol p Pressure q Heat transfer Qe Elementary charge, 1.60 × 10 C ∗PhD Candidate, Student Member AIAA. †James E. Knott Professor of Engineering, Fellow AIAA

Modeling of electron transpiration cooling for hypersonic vehicles

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 can be used to investigate the feasibility of ETC in a hypersonic environment. A modeling approach is presented for ETC, which includes devloping the boundary conditions for electron emission from the surface, accounting for the electric field and space-charge limit effects within the near-wall plasma sheath. Two different analytical models for space-charge limited emission are discussed. The first model assumes that the electrons are emitted cold from the surface while in the second approach the emitted electrons have a finite temperature. The theory shows that emitted electrons with a finite temperature, referred to as warm emission in the present paper, can reach higher levels of emission. This is important because the benefit of ETC, mainly reduction in the surface temperature, is directly correlated to the level of electron emission from the surface. The space-charge limit models are assessed using 1D direct-kinetic plasma sheath simulations. The simulations agree well with the space-charge limit theory proposed by Takamura et al. for emitted electrons with a finite temperature. Both models are implemented into a CFD code, LeMANS, and run for a test case typical of a leading edge radius in a hypersonic flight environment. The CFD results show finite temperature theory results in a larger reduction in wall temperature because more electron emission is allowed for than the cold emission theory. However, even with the electrons being emitted with a finite temperature, the emission still reaches space-charge limits for the test case considered, which can limit the benefits of ETC. Nomenclature AR Richardson constant, 1.20 × 10 A/m/K C̄ Thermal speed E Electric field j Electric current density J Current density kB Boltzmann constant, 1.38 × 10 J/K ms Mass of species s Ms Molar mass of species s n Number density NAv Avogadro constant, 6.02 × 10 mol ∗PhD Candidate, Department of Aerospace Engineering, Ann Arbor, MI, 48109, USA, AIAA Student Member. †Visiting Research Physicist, Princeton Plasma Physics Laboratory, Princeton, NJ, 08543, USA. ‡James E. Knott Professor, Department of Aerospace Engineering, Ann Arbor, MI, 48109, USA, AIAA Fellow.