Nonequilibrium Radiation behind the Strong Shock Waves in Marsian and Titan Atmospheres: Numerical Rebuilding of Experimental Data

Abstract

The computati onal model of nonequili brium radi ation emitted in the relaxati on zone behind shock front is presented in the paper. The hydrodynamic description of relaxati on zone is performed in the framework of Euler equations. The model includes different physical chemical processes such as chemical kinetics, relaxati on of vi brational energy. Also the equation for the determinati on of electron gas temperature is solved. The "justoverl appi ng" line model is used for the calculation of the s pectral emissivity. The presented model is used in order to obtain vari ous characteristics of radiation (spectral emissivity, spatial distri buti on of s pectral emissivity integrated over s pecific wavelength region, maxi mum val ue of the nonequili brium radi ation) behind shock front for the conditi ons which are relevant to the experi mental data obtained on different facilities. Comparison of experi mental and theoretical data is presented in the paper. The reasons for the discrepancies are discussed. Nomenclature x = distance behind the shock front p = pressure ρ = density u = velocity T = translational temperature of the heavy particles x i = mo lar fract ion of i-th chemical co mponent m i = mass of i-th chemical co mponent T V,i,j = vibrational temperature of j-th mode of i-th molecu le θ i,j = characteristic vibrational temperature of j-th mode of i-th mo lecule g i,j = degeneracy of j-th mode of i-th molecu le N s = total number of chemical co mponents N M = number of diato mic and triato mic molecu les among chemical co mponentslar concentrations of i-th chemical co mponent k f i , k r i = forward and reverse rate constant of i-th chemical react ion N r = total number of chemical react ions a ij , b ij = stoichiometric coefficients of the j-th forward and reverse reactions for the i-th chemical co mponent K eq i = equilibriu m constant of i-th reaction e m , e 0 m = number of v ibrational quanta of the m-th vib rational mode and equilibriu m (with translational 2 temperature) nu mber of vibrat ional quanta of the m-th vibrat ional mode Q m VT = term accounting for the translational-vibrational energy exchange of the m-th vibrat ional mode Q m CV = term accounting for the loss and gain of vibrational quanta due to chemical reactions in which the mth vibrational mode participate N VT,m = total number of VT reactions τ m = relaxation time of the m-th vibrational mode τ m,i = relaxation time of the m-th vibrational mode in the i-th VT react ion n e = volume concentration of electrons T e = temperature of electron gas Q ei = term accounting for the contribution of electron-ion collisions to the change of the energy of electron gas Q ea = term accounting for the contribution of electron-atom collisions to the change of the energy of electron gas Q ai = term accounting for the contribution of associative ionization and dissociative recomb ination reactions to the change of the energy of electron gas Q ion = term accounting for the contribution of ionization reactions to the change of the energy of electron gas Q ...

Particle Methods for Nonequilibrium Hypersonic and Plasma Flows

“…It is connected with the square of moment of vibronic transition in accordance with the following relation: The full description of the model can be found in [28][29][30]. It is worth noting that what is presented here is actually a framework.…”

“…Since then our group is involved in this area of scientific researches [28][29][30]. Two parts of activities are distinguished in this area.…”

Advanced Models in Shock Waves

“…(5) on the electronic energy states of atoms, and on the electronic and rovibronic energy states of molecules as well as on the temperature of free electrons (for electron impact processes). Selected models, reported in literature [13,15,17,22] and briefly discussed in the next sections, differ mainly in the way they consider the influence of internal distributions on the chemical rates [23]. These differences reflect also on the radiation model, since the calculated emissivity and absorption coefficients are directly related to the adopted model for the distribution of population over the available atomic and molecular quantum states, i.e.…”

“…Since then our group is involved in this area of scientific research [11][12][13]. In this section, an hybrid collisional-radiative model for the relaxation zone behind a shock is presented.…”

“…The first model, devoted to the study of non-equilibrium spectral intensity of radiation emitted by the shock-heated gases for comparison with available shock tube experimental data, has been developed in the Laboratory of Radiative Gas Dynamics in Moscow [11][12][13]. After an hybrid collisionalradiative (CR) model coupled to an Euler solver and a radiative transfer equation (RTE), used to investigate the dynamics of the electronic levels of the atoms behind a strong shock wave, has been developed in a joint collaboration between research groups in France and Belgium [14][15][16].…”