@article{
 title = {Modeling of Electron Energy Phenomena in Hypersonic Flows},
 type = {article},
 year = {2012},
 volume = {26},
 id = {46b6170d-9554-3060-9f61-1b1e4c02528c},
 created = {2021-07-11T20:32:26.099Z},
 accessed = {2021-07-11},
 file_attached = {true},
 profile_id = {6476e386-2170-33cc-8f65-4c12ee0052f0},
 group_id = {5a9f751c-3662-3c8e-b55d-a8b85890ce20},
 last_modified = {2021-07-11T20:32:38.275Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {false},
 hidden = {false},
 citation_key = {kim:jtht:2012},
 private_publication = {false},
 abstract = {Studies are described for modeling electron energy phenomena for hypersonic flows. The electron energy must be modeled separately from other energy modes because it may have a significant effect on vibrational relaxation 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 for, which include translational-electron, rotational-electron, and vibrational-electron energy relaxation. To avoid a singularity of the Jacobian in the electron energy equation, we introduce a modified electron energy expression. The suggested electron-energy model is implemented into a hypersonic flow code for both explicit and implicit methods. In the present study, we numerically simulate the electron energy with electron-vibrational relaxation for diatomic nitrogen. For the assessment of the electron-energy model, we simulate several cases, which are a plasma wind-tunnel, a radio attenuation measurement (RAM)-C case, the entry of the automated transfer vehicle, and the Stardust reentry capsule. Nomenclature b 0 = scattering parameter for 90 deg, Ze 2 †=12" 0 kT e †, m 2 C V;e = electron specific heat capacity, 3=2† R=M e †, J=kg K† c s = species charge D s = species diffusion coefficients, m 2 =s E e = electron energy, e ‰C v;e T e ‡ 1=2†u 2 ‡ v 2 ‡ w 2 †Š E i;f = first ionization energy per unit mass, J=kg E rot = rotational energy E vib = vibrational energy e = elementary charge, 1:6022 10 19 C e e = electron energy per unit mass of electrons, C V;e T e ‡ 1=2†u 2 ‡ v 2 ‡ w 2 † e e = modified electron energy per unit mass, e =†e e e vib;s = vibrational energy per unit mass F = inviscid flux vector H = total enthalpy per unit mass, J=kg J e = electron diffusion flux k = Boltzmann constant, 1:38065 10 23 ‰m 2 kg s 2 K 1 Š k ev 0;j = vibrational-excitation rate coefficient from vibrational state 0 to j, m 3 =s M s = molecular weight of species s m s = species mass, kg n = unit vector normal to computational cell face n e = electron number density, m 3 p e = electron pressure, Pa Q = vector of conserved variables q e = electron heat flux R = universal gas constant, 8314.3, J=kg mole K S chem;e = electron energy gained by the electrons generated from chemical reactions S e = source term S e;modified = modified source term of the electron energy equation that includes the electron pressure term S epg = approximation of the work done on electrons by the electric field induced by the electron pressure gradient S inelastic;e = rate of inelastic energy exchange between electrons and molecules S transe = energy exchange between translational and electron energies T e = electron temperature, K T trans = translational temperature, K T tr = translational-rotational temperature, K T ve = vibrational-electron-electronic temperature, K U = velocity component normal to computational cell face u = flow velocity Y s = 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 2 e = electron viscous stress es = electron-vibrational relaxation time, s _ ! e = electron-mass production rate by chemical reactions, kg=m 3 s " 0 = vacuum permittivity, 8:854 10 12 , C V 1 m 1},
 bibtype = {article},
 author = {Kim, Minkwan and Gülhan, Ali and Boyd, Iain D},
 doi = {10.2514/1.T3716},
 journal = {Journal of Thermophysics and Heat Transfer},
 number = {2}
}

{"_id":"Gbwqf6YnYFFHYp2gp","bibbaseid":"kim-glhan-boyd-modelingofelectronenergyphenomenainhypersonicflows-2012","author_short":["Kim, M.","Gülhan, A.","Boyd, I., D."],"bibdata":{"title":"Modeling of Electron Energy Phenomena in Hypersonic Flows","type":"article","year":"2012","volume":"26","id":"46b6170d-9554-3060-9f61-1b1e4c02528c","created":"2021-07-11T20:32:26.099Z","accessed":"2021-07-11","file_attached":"true","profile_id":"6476e386-2170-33cc-8f65-4c12ee0052f0","group_id":"5a9f751c-3662-3c8e-b55d-a8b85890ce20","last_modified":"2021-07-11T20:32:38.275Z","read":false,"starred":false,"authored":false,"confirmed":false,"hidden":false,"citation_key":"kim:jtht:2012","private_publication":false,"abstract":"Studies are described for modeling electron energy phenomena for hypersonic flows. The electron energy must be modeled separately from other energy modes because it may have a significant effect on vibrational relaxation 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 for, which include translational-electron, rotational-electron, and vibrational-electron energy relaxation. To avoid a singularity of the Jacobian in the electron energy equation, we introduce a modified electron energy expression. The suggested electron-energy model is implemented into a hypersonic flow code for both explicit and implicit methods. In the present study, we numerically simulate the electron energy with electron-vibrational relaxation for diatomic nitrogen. For the assessment of the electron-energy model, we simulate several cases, which are a plasma wind-tunnel, a radio attenuation measurement (RAM)-C case, the entry of the automated transfer vehicle, and the Stardust reentry capsule. Nomenclature b 0 = scattering parameter for 90 deg, Ze 2 †=12\" 0 kT e †, m 2 C V;e = electron specific heat capacity, 3=2† R=M e †, J=kg K† c s = species charge D s = species diffusion coefficients, m 2 =s E e = electron energy, e ‰C v;e T e ‡ 1=2†u 2 ‡ v 2 ‡ w 2 †Š E i;f = first ionization energy per unit mass, J=kg E rot = rotational energy E vib = vibrational energy e = elementary charge, 1:6022 10 19 C e e = electron energy per unit mass of electrons, C V;e T e ‡ 1=2†u 2 ‡ v 2 ‡ w 2 † e e = modified electron energy per unit mass, e =†e e e vib;s = vibrational energy per unit mass F = inviscid flux vector H = total enthalpy per unit mass, J=kg J e = electron diffusion flux k = Boltzmann constant, 1:38065 10 23 ‰m 2 kg s 2 K 1 Š k ev 0;j = vibrational-excitation rate coefficient from vibrational state 0 to j, m 3 =s M s = molecular weight of species s m s = species mass, kg n = unit vector normal to computational cell face n e = electron number density, m 3 p e = electron pressure, Pa Q = vector of conserved variables q e = electron heat flux R = universal gas constant, 8314.3, J=kg mole K S chem;e = electron energy gained by the electrons generated from chemical reactions S e = source term S e;modified = modified source term of the electron energy equation that includes the electron pressure term S epg = approximation of the work done on electrons by the electric field induced by the electron pressure gradient S inelastic;e = rate of inelastic energy exchange between electrons and molecules S transe = energy exchange between translational and electron energies T e = electron temperature, K T trans = translational temperature, K T tr = translational-rotational temperature, K T ve = vibrational-electron-electronic temperature, K U = velocity component normal to computational cell face u = flow velocity Y s = 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 2 e = electron viscous stress es = electron-vibrational relaxation time, s _ ! e = electron-mass production rate by chemical reactions, kg=m 3 s \" 0 = vacuum permittivity, 8:854 10 12 , C V 1 m 1","bibtype":"article","author":"Kim, Minkwan and Gülhan, Ali and Boyd, Iain D","doi":"10.2514/1.T3716","journal":"Journal of Thermophysics and Heat Transfer","number":"2","bibtex":"@article{\n title = {Modeling of Electron Energy Phenomena in Hypersonic Flows},\n type = {article},\n year = {2012},\n volume = {26},\n id = {46b6170d-9554-3060-9f61-1b1e4c02528c},\n created = {2021-07-11T20:32:26.099Z},\n accessed = {2021-07-11},\n file_attached = {true},\n profile_id = {6476e386-2170-33cc-8f65-4c12ee0052f0},\n group_id = {5a9f751c-3662-3c8e-b55d-a8b85890ce20},\n last_modified = {2021-07-11T20:32:38.275Z},\n read = {false},\n starred = {false},\n authored = {false},\n confirmed = {false},\n hidden = {false},\n citation_key = {kim:jtht:2012},\n private_publication = {false},\n abstract = {Studies are described for modeling electron energy phenomena for hypersonic flows. The electron energy must be modeled separately from other energy modes because it may have a significant effect on vibrational relaxation 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 for, which include translational-electron, rotational-electron, and vibrational-electron energy relaxation. To avoid a singularity of the Jacobian in the electron energy equation, we introduce a modified electron energy expression. The suggested electron-energy model is implemented into a hypersonic flow code for both explicit and implicit methods. In the present study, we numerically simulate the electron energy with electron-vibrational relaxation for diatomic nitrogen. For the assessment of the electron-energy model, we simulate several cases, which are a plasma wind-tunnel, a radio attenuation measurement (RAM)-C case, the entry of the automated transfer vehicle, and the Stardust reentry capsule. Nomenclature b 0 = scattering parameter for 90 deg, Ze 2 †=12\" 0 kT e †, m 2 C V;e = electron specific heat capacity, 3=2† R=M e †, J=kg K† c s = species charge D s = species diffusion coefficients, m 2 =s E e = electron energy, e ‰C v;e T e ‡ 1=2†u 2 ‡ v 2 ‡ w 2 †Š E i;f = first ionization energy per unit mass, J=kg E rot = rotational energy E vib = vibrational energy e = elementary charge, 1:6022 10 19 C e e = electron energy per unit mass of electrons, C V;e T e ‡ 1=2†u 2 ‡ v 2 ‡ w 2 † e e = modified electron energy per unit mass, e =†e e e vib;s = vibrational energy per unit mass F = inviscid flux vector H = total enthalpy per unit mass, J=kg J e = electron diffusion flux k = Boltzmann constant, 1:38065 10 23 ‰m 2 kg s 2 K 1 Š k ev 0;j = vibrational-excitation rate coefficient from vibrational state 0 to j, m 3 =s M s = molecular weight of species s m s = species mass, kg n = unit vector normal to computational cell face n e = electron number density, m 3 p e = electron pressure, Pa Q = vector of conserved variables q e = electron heat flux R = universal gas constant, 8314.3, J=kg mole K S chem;e = electron energy gained by the electrons generated from chemical reactions S e = source term S e;modified = modified source term of the electron energy equation that includes the electron pressure term S epg = approximation of the work done on electrons by the electric field induced by the electron pressure gradient S inelastic;e = rate of inelastic energy exchange between electrons and molecules S transe = energy exchange between translational and electron energies T e = electron temperature, K T trans = translational temperature, K T tr = translational-rotational temperature, K T ve = vibrational-electron-electronic temperature, K U = velocity component normal to computational cell face u = flow velocity Y s = 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 2 e = electron viscous stress es = electron-vibrational relaxation time, s _ ! e = electron-mass production rate by chemical reactions, kg=m 3 s \" 0 = vacuum permittivity, 8:854 10 12 , C V 1 m 1},\n bibtype = {article},\n author = {Kim, Minkwan and Gülhan, Ali and Boyd, Iain D},\n doi = {10.2514/1.T3716},\n journal = {Journal of Thermophysics and Heat Transfer},\n number = {2}\n}","author_short":["Kim, M.","Gülhan, A.","Boyd, I., D."],"urls":{"Paper":"https://bibbase.org/service/mendeley/6476e386-2170-33cc-8f65-4c12ee0052f0/file/0b67359b-ad4b-5397-03e0-02d54a53aa74/Kim_Gülhan_Boyd___2011___Modeling_of_Electron_Energy_Phenomena_in_Hypersonic_Flows.pdf.pdf"},"biburl":"https://bibbase.org/service/mendeley/6476e386-2170-33cc-8f65-4c12ee0052f0","bibbaseid":"kim-glhan-boyd-modelingofelectronenergyphenomenainhypersonicflows-2012","role":"author","metadata":{"authorlinks":{}}},"bibtype":"article","biburl":"https://bibbase.org/service/mendeley/6476e386-2170-33cc-8f65-4c12ee0052f0","dataSources":["qwkM8ZucCwtxbnXfc","ya2CyA73rpZseyrZ8","2252seNhipfTmjEBQ"],"keywords":[],"search_terms":["modeling","electron","energy","phenomena","hypersonic","flows","kim","gülhan","boyd"],"title":"Modeling of Electron Energy Phenomena in Hypersonic Flows","year":2012}