Modeling of Electron Energy Phenomena in Hypersonic Flows

Abstract

b0 = scattering parameter for 90 deg, Ze = 12 0kTe , m CV;e = electron specific heat capacity, 3=2 R=Me , J= kg K cs = species charge Ds = species diffusion coefficients, m =s Ee = electron energy, e Cv;eTe 1=2 u v w Ei;f = first ionization energy per unit mass, J=kg Erot = rotational energy Evib = vibrational energy e = elementary charge, 1:6022 10 19 C ee = electron energy per unit mass of electrons, CV;eTe 1=2 u v w ee = modified electron energy per unit mass, e= ee evib;s = vibrational energy per unit mass F = inviscid flux vector H = total enthalpy per unit mass, J=kg Je = electron diffusion flux k = Boltzmann constant, 1:38065 10 23 m kg s 2 K 1 k v 0;j = vibrational-excitation rate coefficient from vibrational state to j, m=s Ms = molecular weight of species s ms = species mass, kg n = unit vector normal to computational cell face ne = electron number density, m 3 pe = electron pressure, Pa Q = vector of conserved variables qe = electron heat flux R = universal gas constant, 8314.3, J=kg mole K Schem;e = electron energy gained by the electrons generated from chemical reactions Se = source term Se;modified = modified source term of the electron energy equation that includes the electron pressure term Sepg = approximation of the work done on electrons by the electric field induced by the electron pressure gradient Sinelastic;e = rate of inelastic energy exchange between electrons and molecules Strans e = energy exchange between translational and electron energies Te = electron temperature, K Ttrans = translational temperature, K Ttr = translational-rotational temperature, K Tve = vibrational-electron-electronic temperature, K U = velocity component normal to computational cell face u = flow velocity Ys = species mass fraction v;s = species characteristic vibrational temperature = thermal conductivity, K W=m D = Debye length, m = viscosity coefficient, N s =m s = species density, kg=m 3 es = collision cross section for electron and s species, m e = electron viscous stress es = electron-vibrational relaxation time, s _ !e = electron-mass production rate by chemical reactions, kg=m s 0 = vacuum permittivity, 8:854 10 , C V 1 m 1