The effect of gas motion on the reaction kinetics of vibrationally excited molecules

The effect is considered of gas motion on the kinetics of reactions whose energy threshold is overcome as the result of vibrational excitation of the reactant molecules. The conditions are determined for which such an effect may be realized. An expression is obtained for the rate of thermal dissociation of diatomic molecules considered as harmonic oscillators representing a small impurity in a monoatomic inert gas; the expression depends explicitly and nonlinearly on the divergence of the flow velocity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 100–105, November–December, 1984.     

Calculation of nonequilibrium distribution functions and dissociation rate of diatomic molecules in a boundary layer

The effect of the nonequilibrium velocity and rotation distributions of the dissociating molecules on the population of the upper vibrational levels and the dissociation rate, when the reaction kinetics are strongly influenced by the motion of the gas, is analyzed by solving the Boltzmann equation by a method permitting the calculation of the distribution function under conditions of strong disequilibrium.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 165–172, March–April, 1989.     

Quasiequilibrium model of the kinetics of coupled modes of CO2 molecules

The correct allowance for the influence of anharmonicity in the vibrational spectrum of CO₂ on the level distribution of molecules under nonequilibrium conditions, when the vibrational temperature departs significantly from the gas temperature, has become especially urgent in connection with obtaining generation on a number of long-wavelength transitions of CO₂ molecules [1, 2]. The shifts in the levels of coupled modes (symmetric and deformation) are due mainly to Fermi resonance and can reach a considerable value, comparable with the gas temperature even for low levels. In [3] the main features of the quasisteady level distribution of coupled modes were clarified within the framework of the Treanor model of vibrational kinetics. The influence of the ascending flux of quanta, excited by VV exchange under nonequilibrium conditions, on the vibrational distribution was considered in [4–6]. In the present paper we propose a quasiequilibrium model of CO₂ kinetics, obtained without presuming quasisteadiness of the ascending flux of quanta, and making it possible, in contrast to [3–6] to describe the dynamics of the variation of the distribution of molecules among multiplets as a result of processes of VV exchange and VT relaxation between multiplets, with allowance for possible processes of pumping by outside sources. With a Boltzmann population distribution within the multiplets, having the translational temperature of the gas, the problem of studying relaxation in coupled modes is reduced to the equations for an effective anharmonic oscillator with levels corresponding to the multiplets of CO₂ molecules. In this case the levels of the effective oscillator are degenerate with a multiplicity equal to the number of levels in the corresponding multiplet, and they have an anharmonicity constant dependent on the gas temperature. The population distribution of the effective oscillator can be studied by methods developed for the investigation cf a one-mode anharmonic oscillator. The proposed quasiequilibrium model was used for a numerical calculations of the temporal evolution of the distribution function of CO₂ molecules over the levels of coupled modes under the conditions of an extremely maintained discharge.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 16–22, May–June, 1986.     

Estimation of the effect of vibrational excitation of diatomic molecules on their diffusional transport and dissociation in a boundary layer

Relations for the diffusion fluxes of vibrationally highly excited diatomic molecules are found by means of the Chapman-Enskog method. On the basis of these relations a quantitative estimate of the changes in the diffusion coefficients under vibrational excitation and the corresponding changes in the macroscopic dissociation rate is obtained under conditions of disequilibrium of the upper vibrational levels of the dissociating molecules caused by the diffusion processes. The diffusion relations obtained are used in deriving the boundary conditions for the equations of level vibrational kinetics. A simplified version of this derivation is presented for noncatalytic and catalytic surfaces.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 169–182, January–February, 1996.     

Model of the physico-chemical kinetics behind the front of a very intense shock wave in air

A model of the physico-chemical kinetics of the reactions taking place behind the front of an intense shock wave propagating in air with a speed of 9–14 km/s is proposed. The problem of describing the chemical reactions, namely, molecular dissociation and exchange reactions involving vibrationally excited molecules in the absence of vibrational equilibrium, is solved. The vital role of the vibrational excitation delay in the dissociation of oxygen and nitrogen is established. The rate of the exchange reaction between nitrogen molecules and oxygen atoms in the shock wave depends only slightly on the vibrational excitation level. It is demonstrated that the rate constants for thermally nonequilibrium dissociation reactions can be represented within the framework of the one-temperature approximation at constant vibrational temperatures of the dissociating species satisfying quasi-stationary conditions.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 169–182, March–April, 1995.     

Kinetics of the deactivation of the vibrations of highly excited oscillators in an inert gas medium,taking account of spontaneous radiation

In the diffusion approximation, the article discusses the kinetics of the process of deactivation of the vibrations of radiating anharmonic and harmonic oscillators in an inert gas medium. Limiting solutions are given for the purely radiational deactivation of a classical Morse oscillator and of a harmonic oscillator. It is shown that, with an increase in the effect of spontaneous radiation, the role of the anharmonic character of the vibrations in the process of deactivation increases; the initial (or arbitrary) distribution relaxes more slowly the higher its energy level, i.e., the greater the effect of the anharmonic character of the vibrations. The results are of importance for systems with a considerable population of the upper vibrational levels of the molecules, which may arise as a result of a chemical reaction or by the optical pumping of a gas.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 62–67, July–August, 1972.The author thanks N. N. Magretova for carrying out the numerical calculation.     

Thermal dissociation of diatomic molecules in a nonisothermal boundary layer in the presence of exchange reactions

The effect of an inhomogeneous temperature field in a boundary layer on the kinetics of dissociation of diatomic molecules simulated by truncated harmonic oscillators is considered in a multicomponent mixture in the presence of exchange reactions which take place at lower vibrational levels as compared with dissociation.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 163–172, January–February, 1995.     

Inverted population of Co2 molecules in expanding gas streams

The system of equations of hydrodynamics, which describes the process of escape of the mixtures CO₂ + N₂ + He, H₂O from a nozzle, is solved numerically in conjunction with the equations of the kinetics of the excitation of the vibrational degrees of freedom of the molecules. It is found that an inverted population of the CO₂ molecules with respect to the transition [00 °1] – [10 °0], is produced under certain conditions at the exit from the nozzle. The magnitude of the inversion depends both on the nozzle configuration and on the initial values of the gas temperature and pressure. It is shown that for a specified nozzle configuration there exist optimal values of these parameters, at which the inverted population of the CO₂ molecules reaches approximately 10¹⁵ cm^–3.Translated from Zhumal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 24–34, September–October, 1971.     

Thermal dissociation of diatomic molecules in a nonisothermal two-temperature boundary layer

Nonequilibrium thermal dissociation in a nonisothermal boundary layer in a mixture of Morse anharmonic oscillators — molecules of a diatomic gas and its atoms — is considered within the framework of the ladder mechanism. The local nonlinear nonequilibrium corrections to the two-temperature macroscopic dissociation rate, which depend, in particular, on the translational and vibrational temperature gradients and the degree of dissociation, are determined.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 191–201, March–April, 1996.     

Formation of inversion in jet of CO2-H2O-N2 gas mixture expanding through a slot

A calculation is made of the kinetics of vibrational relaxation of CO₂ molecules in a CO₂ -H₂O-N₂ mixture escaping into a vacuum from a slot. The examination of vibrational relaxation led to a solution of the kinetic equations corresponding to the most important channels of energy exchange in vibration-vibration and vibration-translation processes. It proved possible to consider the dynamics of a nonequilibrium gas in an approximation of the adiabatic motion of a medium with an effective adiabatic index corresponding to a certain degree of freezing in of the vibrational component of the heat capacity of the gas. The calculated values of the gain index agree well with experimental data. The gain index was calculated with allowance for Doppler and Lorentz mechanisms of line broadening. The results of the calculation were analyzed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 25–31, November–December, 1973.The authors thank A. S. Biryukov and N. N. Sobolev for advice and comments and É. A. Ashratov and G. K. Bunin for conducting the gasdynamical calculation on an electronic computer.     

Transonic outflow of an imperfect gas from a vessel with plane walls

Transonic isentropic imperfect gas flows^* were investigated in the one-dimensional formulation in [2–5]. The problem of the transonic outflow of a jet of thermally perfect gas with equilibrium excitation of the vibrational degrees of freedom of the molecules (calorically imperfect gas) was investigated in the two-dimensional formulation in [6]. Below the problem of the transonic outflow of a real (thermally and calorically imperfect) gas from a vessel with plane walls is considered. A method of solution is proposed. Calculation results characterizing the effect of the angle between the walls and the stagnation parameters on the transonic outflow of air are presented.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 88–95, November–December, 1993.The authors are grateful to G. Yu. Stepanov for his interest in their work.     

Kinetic equations for vibrational relaxation in a mixture of polyatomic gases

Kinetic equations are derived for the relaxation of the vibrational energy in a mixture of polyatomic gases, which are ones with molecules simulated by harmonic oscillators. The most general case is envisaged, where the energy relaxation occurs not only via vibrational-translational transitions but also via multiquantum vibrational exchange involving an arbitrary number of vibrational modes. The analysis also incorporates the possible degeneracy of each mode when the molecules colliding are the same. An expression is derived that extends previous results [1–6] and that relates the vibrational temperatures in the case of quasiequilibrium. Equations are derived for the vibrational relaxation for the CO₂-N₂ case.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 29–37, November–December, 1972.We are indebted to L. A. Shelepin for valuable discussions on the results.     

Influence of excitation of internal degrees of freedom of molecules on the process of weak evaporation or condensation

A study is made of the process of weak evaporation (or condensation) with allowance for excitation of vibrational and rotational degrees of freedom of diatomic molecules. The solution to the corresponding Knudsen layer problem is obtained on the basis of a model kinetic equation of the type of the Morse equation [1]. A relation is obtained that establishes the connection between the rate of evaporation (or condensation) and the parameters of the surface and the gas above it. The boundary conditions of slip for the equations of gas dynamics are analyzed. The results are compared with the evaporation or condensation in the case of a monatomic gas. The introduction of accommodation coefficients for an evaporating surface is considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6. pp. 98–110, November–December, 1979.     

Analysis of Nonequilibrium Dissociation Kinetics in a Boundary Layer Using Various Reaction Models

Values of the nonequilibrium macroscopic reaction rate for a nonisothermal boundary layer of a monatomic diluent gas are calculated using a number of models for thermal dissociation of diatomic molecules — anharmonic Morse oscillators. Analysis is performed for conditions where the diffusive transfer of excited molecules has a significant effect on the population of their upper vibrational levels, which does not only amount to change in vibrational temperature. Under the joint influence of diffusive transfer of molecules, vibrational exchanges, and reactions involving vibrationally excited particles, the local vibrational distribution functions are substantially nonequilibrium. The kinetic models considered take into account the possible contribution of the energy of molecular translational and rotational degrees of freedom to the energy required to overcome the reaction threshold. The effect of multiquantum vibrational—translational exchanges on the distribution of dissociating molecules in their upper vibrational levels is taken into account approximately.     

Theory of two-component gasdynamic laser

In the present paper a numerical calculation is made of the vibrational relaxation of a binary mixture of molecular nitrogen and carbon dioxide gas. The calculation is performed for the entire range of variation of the concentrations of the components and over a wide range of mixture temperatures and pressures for various geometries of the supersonic part of the nozzle (throat dimensions, degree of expansion). It is shown that population inversion of the CO₂ molecules exists within a certain range of variation of the parameters of the mixture and the nozzle. The population inversion of the vibrational levels and the gain of the gaseous mixture are calculated as functions of these parameters and of distance measured from the critical cross section of the nozzle. The energy characteristics of the two-component gasdynamic laser are optimized.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 23–30, May–June, 1974.     

Nonequilibrium condensation of metal vapor mixed with an inert gas in nozzle expansion in cluster beam generators

A closed mathematical model of flows of a mixture consisting of a homogeneously condensible vapor and an inert gas is described. This model is a further development of the pure metal vapor condensation model [1 – 4] and, as distinct from the latter, makes it possible to take into account the effect of molecules of inert gas not only on the thermodynamics of the mixture but on the detailed kinetics of the processes of the cluster formation and breakdown. The results of numerical calculations of the formation of iron and silver clusters in experimental installations are presented.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 80–91, May–June, 1995.     

Study of vibrational deactivation of molecules of carbon dioxide gas during cooling of stream in a supersonic nozzle

The vibrational temperature of the antisymmetrical type of vibrations (v ₃) of the CO₂ molecule at the exit of a supersonic nozzle is measured in the present work using the method of recording the infrared emission. Freezing in of thev ₃-type vibrations was observed during the flow of undiluted carbon dioxide in a nozzle. In this case the vibrational temperature T₃ considerably exceeded the translational temperature. On the basis of a comparison of the experimental results with calculation it can be concluded that vibrational deactivation of CO₂ molecules occurs three to five times faster than the excitation of the vibrations during heating in a shock wave. All the experiments were conducted under the following conditions: maximum expansion of gas in nozzle A/A* = 115, temperature range 1900–2400 °K, pressure range 1–17.5 atm.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 32–40, November–December, 1973.The authors are grateful to U. G. Pirumov and É. A. Ashratov for the calculation of the nozzle profile and the distribution of streamlines as well as for a discussion of the results.     

Nonequilibrium hypersonic flow of carbon dioxide gas over blunt bodies

The Navier-Stokes equations are used to investigate hypersonic flow of carbon dioxide gas over blunt bodies with allowance for nonequilibrium development of chemical reactions and vibrational relaxation of the CO₂ molecules. The problem is solved by the method of stabilization by means of an implicit difference scheme that includes the use of Newton's iterative process. The results are given of calculations of the flow field, the convective heat flux, and the frictional stresses on the surface of blunt cones with spherical noses. The influence of admixtures on the flow field and the heat fluxes is investigated. The results of the calculations are compared with the locally self-similar solution for the neighborhood of the front stagnation point.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 199–202, September–October, 1979.     

A Knudsen layer in a flow with two-temperature relaxation

The boundary conditions are considered for the hydrodynamic equation of [1, 2] for highly nonequilibrium diatomic gas with vibrational relaxation.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 38–43, November–December, 1972.     

Transonic flow of a gas jet from a vessel with plane walls

The problem of transonic flow of a gas jet with equilibrium excitation of the vibrational degrees of freedom of the molecules from an infinite symmetrical vessel with plane walls is reduced to a generalized Tricomi boundary-value problem for an equation of Chaplygin type. It is solved using a difference scheme [13] based on the decomposition of the difference operator in accordance with the type of differential operator. Calculation results are presented for a mixture of oxygen and nitrogen simulating air. The effect of the angle between the walls, the stagnation temperature and the back-pressure coefficient on the flow coefficient is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 128–135, November–December, 1987.The authors are grateful to F. Yu. Stepanov for his useful comments.