Modeling of Electron Temperature in Hypersonic Flows

Studies are described for an electron temperature model for hypersonic flow. The elec-tron temperature is needed to be calculated separately, because it may have a significant effect on vibrational temperature and chemical reactions. Whenever flows are in a strong thermal nonequilibrium state, an electron energy equation should be considered. In the considered electron energy equation, the electron energy relaxations of each energy mode are accounted which include translational-electron, rotational-electron, and vibrational-electron energy relaxation. In order to avoid the singularity of the Jacobian in the electron energy equation, we introduce a modified electron energy expression. The suggested elec-tron temperature model is implemented into a hypersonic flow code for both explicit and implicit methods. In the present study, we numerically calculate the electron temperature with electron-vibrational relaxation for diatomic nitrogen. For the assessment of the elec-tron temperature model, we simulate several cases which are a cylinder flow, a RAM-C case, the entry of the Automated Transfer Vehicle (ATV), and the Stardust reentry capsule. Nomenclature ée Modified electron energy per unit mass, ée = ρe ρ εe R ̄ Universal gas constant, 8314.3 [J/kg ·mole ·K] ω̇e Electron mass production rate by chemical reactions, kg/m3sec λD Debye length, [m]−→ Je Electron diffusion flux−→qe Electron heat flux−→u Flow velocity ρs Species density, kg/m−3 σes Collision cross section for electron and s species, m2 τes Electron-vibrational relaxation time, [sec