Reactive and nonreactive vibrational energy exchanges in nonequilibrium hypersonic flows

Josyula, Eswar; Bailey, William F.; Ruffin, Stephen M.

doi:10.1063/1.1608013

Cited by 37 publications

(8 citation statements)

References 25 publications

(24 reference statements)

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“…The availability of ab initio rate parameters for elementary collisional processes has enabled the development of state-to-state (STS) models. [4][5][6][7][8][9][10][11] These models allow for the detailed study of kinetic processes under strong non-equilibrium conditions, for which the distribution of the internal energy levels strongly departs from the equilibrium Maxwell-Boltzmann distribution. The most detailed models developed in the literature are rovibrational STS models.…”

Section: Introductionmentioning

confidence: 99%

Energy transfer models in nitrogen plasmas: Analysis of $\mathbf {\rm N_2(X\,^1\Sigma _g^+){\mbox{--}}\rm N(^4S_u){\mbox{--}}e^-}$N2(XΣg+1)–N(4Su)–e− interaction

Héritier

Jaffe

Laporta

et al. 2014

The Journal of Chemical Physics

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The relaxation of N₂(X¹Σg⁺) molecules in a background gas composed of N((4)S(u)) atoms and free electrons is studied by using an ideal isochoric and isothermic chemical reactor. A rovibrational state-to-state model is developed to study energy transfer process induced by free electron and atomic collisions. The required cross sections and the corresponding rate coefficients are taken from two well-known kinetic databases: NASA Ames kinetic mechanism for the description of the N₂(X¹Σg⁺)-N((4)S(u)) processes and the Phys4Entry database for the electron driven processes, N₂(X¹Σg⁺)-e(-). The evolution of the population densities of each individual rovibrational level is explicitly determined via the numerical solution of the master equation for temperatures ranging from 10000 to 30,000 K. It was found that the distribution of the rovibrational energy levels of N₂(X¹Σg⁺) is strongly influenced by the electron driven collisional processes, which promote the excitation of the low lying vibrational levels. The macroscopic vibrational energy relaxation is governed by the molecule-atom collisions, when free electrons, initially cold are relaxing to the final heat-bath temperature. Thus, the main role of the free electrons is to ensure the equilibration of vibrational and free electron excitation, thus validating the existence of the local equilibrium T(V)-T(e). However, if electrons and heavy particles are assumed to be in equilibrium at the heat bath temperature, electron driven processes dominate the vibrational relaxation. Finally, we have assessed the validity of the Landau-Teller model for the description of the inelastic energy transfer between molecules and free electrons. In the case of free-electron temperatures lower than 10,000 K, Landau-Teller relaxation model gives an accurate description of the vibrational relaxation, while at higher temperatures the error in the predictions can be significant and the model should not be used.

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Section: Introductionmentioning

confidence: 99%

Energy transfer models in nitrogen plasmas: Analysis of $\mathbf {\rm N_2(X\,^1\Sigma _g^+){\mbox{--}}\rm N(^4S_u){\mbox{--}}e^-}$N2(XΣg+1)–N(4Su)–e− interaction

Héritier

Jaffe

Laporta

et al. 2014

The Journal of Chemical Physics

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“…Previous works on this issue have typically resorted to simpler approaches derived from other fields such as gas discharges [7][8][9]. It is not until recently that it has been acknowledged that the specific conditions encountered behind strong shock waves required developing and using more elaborate theoretical approaches [10,11].…”

Section: Introductionmentioning

confidence: 99%

State-Resolved Dissociation Rates for Extremely Nonequilibrium Atmospheric Entries

Silva

Guerra

Loureiro

2007

Journal of Thermophysics and Heat Transfer

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This paper presents the application of the forced harmonic oscillator method to the simulation of state-resolved dissociation processes behind high-temperature shock waves typical of atmospheric reentries. Improvements have been brought to the model, considering a more precise method for the calculation of the different vibrational level energies, therefore increasing the accuracy of the predicted transition probabilities between higher vibrational levels close and above the dissociation limit. The model has been validated against data issued from recent experiments, as well as data issued from semiclassical trajectory calculations for collisions between different species. A good overall agreement is achieved against such other data. A database of reaction rates has been constructed with the purpose of simulating shock-heated nitrogen flows. Dissociation processes behind a shock wave have been simulated for different postshock translational temperatures. At lower temperatures, the well-known ladder-climbing phenomenon is the main dissociation channel behind a shock wave, with dissociation occurring for transitions from the vibrational levels close to the dissociation limit. At higher temperatures, transitions between the different vibrational levels of nitrogen become roughly equiprobable, and the overall range of bound vibrational levels contributes to the dissociation. Nomenclature C k ij = transformation matrix C p = specific heat at constant pressure, J=kg=K C v = specific heat at constant volume, J=kg=K E = level energy, Hz E m = Morse potential well, J h = enthalpy, J=kg J s = Bessel function k B = Boltzmann constant, 1:3806505 10 23 J=K kT = thermal reaction rate, cm 3 =s M = Mach number m = mass, kg m= mass parameter, m AB m C =m AB m C or m AB m CD =m AB m CD P = probability r = internuclear distance, m S VT = vibration-translation steric factor, 4=9 S VV = vibration-vibration steric factor, 1=27 T = macroscopic temperature, K T r = rotational temperature, K T tr = translational temperature, K T tr-r = translational-rotational temperature, K T v = vibrational temperature, K t = time, s Vr = intermolecular potential, J V-T = vibration-translation processes V-V-T = vibration-vibration-translation processes v = vibrational level v = velocity, m=s v = averaged collision velocity, m=s Z = gas-kinetic collisional frequency, Hz = repulsive potential parameter, m 1 = heat capacity ration, C p =C v = mass parameter, m A =m A m B "= two-state first-order V-T transition probability, P1 ! 0 = mass parameter, m A m B =m A m B = two-state first-order V-V-T transition probability, 4P1; 0 ! 0; 1 1=2 = generalized two-state first-order V-V-T transition probability = collision cross section, m 2 ! = vibrational transition frequency, Hz ! e = harmonic oscillator energy, Hz ! e x e = first-order anharmonic oscillator energy, Hz Subscripts f = final vibrational quantum number i = initial vibrational quantum number max = maximum vibrational level before dissociation qbound = vibrational level above the dissociation limit tr =...

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“…Inviscid flow modeling has been carried out by Ruffin [1,2], Josyula et al [3,4], and Giordano et al [5]. Concerning viscous flows, Candler et al [6] and, in particular, the University of Bari (Bari group) carried out a number of simulations under thermochemical nonequilibrium conditions for N 2 =N, O 2 =O, and air mixtures [7][8][9][10][11].…”

mentioning

confidence: 98%

State-to-State Simulation of Nonequilibrium Nitrogen Stagnation-Line Flows: Fluid Dynamics and Vibrational Kinetics

Orsini¹,

Rini²,

Taviani³

et al. 2008

Journal of Thermophysics and Heat Transfer

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An advanced model of fluid dynamics and nonequilibrium vibrational-chemical kinetics in high-temperature viscous flows along the stagnation line is proposed. The present model takes into account detailed state-to-state kinetics and state-dependent transport properties. Fluid dynamics equations are self-consistently coupled to vibrational kinetics, and state-dependent transport terms are properly incorporated in the governing equations. As an example, vibrational kinetics, macroscopic flow parameters, and heat transfer in a N 2 =N mixture are calculated for different flow conditions. A comparison with thermal equilibrium and vibrational frozen flows is presented, showing the important role of detailed kinetics coupled to fluid dynamics. Several models of chemical and vibrational kinetics are assessed and a strong dependence of the flow parameters and surface heat flux on the chemical model is demonstrated. Nomenclature c fr p = mixture frozen specific heat at constant pressure D ij = binary diffusion coefficients D = Fick's diffusion coefficient F = reduced tangential velocity, u=u f = stream function g = dimensionless enthalpy, h=h H M=A j;N = state-specific dissociation rate coefficients h i , h = species and mixture enthalpy per unit mass i, j, k = vibrational quantum number or species indices J i = dimensionless mass diffusion flux J y i = mass diffusion flux normal to the body surface K k;l i;j = rate coefficients for vibrational transitions k f=b r = forward/backward chemical reaction rates l 0 = Chapman-Rubesin parameter M i , M = species and mixture molar mass m i = species molecular mass Ns = total number of species (including vibrational levels) Nv = number of vibrational levels n i , n = species and mixture number density Pr = Prandtl number p = mixture pressure q w = surface heat flux r = local body radius S i , S T = source terms in simplified equations Sc = Schmidt number T = gas temperature u = velocity tangential to the body surface V = auxiliary variable in the Lees-Dorodnitsyn transformation v= velocity normal to the body surface _ W i = dimensionless species source term in the bulk _ W cat i = dimensionless species source term at the wall w = parameters at the body surface _ w i = species source term x, y = Cartesian coordinates x i , y i = species molar and mass fractions = parameters at the boundary-layer edge = first Lees-Dorodnitsyn coordinate = reduced temperature, T=T = thermal conductivity coefficient = shear viscosity coefficient 0 ir , 00 ir = stoichiometric coefficients of reactants and products = second Lees-Dorodnitsyn coordinate i , = species and mixture density

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Reactive and nonreactive vibrational energy exchanges in nonequilibrium hypersonic flows

Cited by 37 publications

References 25 publications

Energy transfer models in nitrogen plasmas: Analysis of $\mathbf {\rm N_2(X\,^1\Sigma _g^+){\mbox{--}}\rm N(^4S_u){\mbox{--}}e^-}$N2(XΣg+1)–N(4Su)–e− interaction

Energy transfer models in nitrogen plasmas: Analysis of $\mathbf {\rm N_2(X\,^1\Sigma _g^+){\mbox{--}}\rm N(^4S_u){\mbox{--}}e^-}$N2(XΣg+1)–N(4Su)–e− interaction

State-Resolved Dissociation Rates for Extremely Nonequilibrium Atmospheric Entries

State-to-State Simulation of Nonequilibrium Nitrogen Stagnation-Line Flows: Fluid Dynamics and Vibrational Kinetics

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