Relaxation,propagation of sound,and transfer processes in molecular gases

Taking account of rotational and vibrational degrees of freedom of the molecules, a system of equations has been obtained for a molecular gas which describes slightly nonequilibrium states with a length and time on the order of magnitude of the length and time of the rotational and vibrational relaxation. By solving this system, which describes the propagation of sound and the transfer process, the absorption coefficient, the dispersion of the velocity of sound, the transfer coefficients (in particular, the thermal conductivity coefficient), and an expression for the total tensor of the pressures have been found and analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 53–67, September–October, 1970.The author thanks V. M. Zhdanov for his valuable advice and remarks, and also Yu, Ya. Polyak and B. M. Chistoserdov for their useful evaluations.     

Investigation of the inverted medium of a quasi-stationary CO2 laser with pulsed excitation

The results of an investigation of the inverted medium of a quasi-stationary CO₂ laser is presented. The medium is distinguished by the fact that the time of flight of individual molecules through the discharge gaps is less than the relaxation time of the 00 °1 CO₂ laser level. The emitted power, the gain, the saturation intensity, and the gas temperature are measured. Using the experimental data, the distribution of the molecules in the vibrational and rotational states of the inverted medium is calculated. The maximum power density attained in this experimental model is 25 W/cm³. For comparison, the characteristics of a model in which cold CO₂ is added to the flow of excited nitrogen are investigated. It is shown that in this case the output power level is determined by the efficiency with which the jets are mixed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 23–29, January–February, 1973.The authors thank V. M. Fedorov for useful discussions and A. A. Borynyak for his help with the experiments.     

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.     

Shift of chemical equilibrium in a resonance infrared radiation field

The degree of displacement of chemical equilibrium in dissociation reactions, including three-particle recombination due to laser radiation at an isolated vibrational degree of freedom of the molecules, is determined. Dependences of the vibrational temperature and the chemical equilibrium constant on the vibrational excitation probability are obtained.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 10–12, January–February, 1976.The authors wish to express their appreciation to R. V. Khokhlov for support and interest in the work.     

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.     

Approximating kinetic equation for weakly nonequilibrium states of polyatomic gases

The aim of the present paper is to construct an approximate kinetic equation that, first, takes into account correctly the possibility of excitation of both rotational and vibrational degrees of freedom of the molecules and, second, is valid for any law of intermolecular interaction.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 183–187, March–April, 1982.We thank M, Ya. Alievskio for helpful consultations.     

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.     

Propagation of small disturbances in a relaxing and radiating diatomic gas in vibrational nonequilibrium

In radiation gasdynamical problems, where the primary object of investigation is a moving gas, the influence of radiation on the parameters of the gas flow is usually neglected to avoid overcomplication of the problem. The growth and behavior of initial disturbances in a scattering, radiating, absorbing, viscous, heat-conducting gas characterized by local thermodynamic equilibrium has been investigated previously [1]. However, for low pressures (p10^–4 to 10^–3 technical atm) and fairly high temperatures of the active molecular degrees of freedom (T10³ to 3·10³K) the distribution of the molecules among the vibrational levels can differ markedly from the equilibrium distribution due to the or der-of-magnitude closeness of the vibrational relaxation time _c associated with collisions and the radiative deactivation time * of excited molecules [2, 3]. We now analyze normal modes in a vibrationally nonequilibrium medium with allowance for radiation scattering in the vibrational-rotational band. We formulate a dispersion relation and discuss some limiting cases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 168–171, September–October, 1976.The author is grateful to V. I. Kruglov, Yu. V. Khodyko, and M. A. El'yashevich for their interest and discussions.     

Rotation-vibration-dissociation interaction in a multicomponent nonequilibrium viscous shock layer

A new, simple and physically adequate method of calculating vibrationally nonequilibrium dissociation constants is proposed on the basis of a dissociation model which takes into account the equilibrium excitation of the rotational degrees of freedom of the molecules and the nonequilibrium excitation of vibrational quantum states. This rotation-vibration-dissociation interaction model contains only the indeterminacy associated with the indeterminacy of the experimental data on the interaction potentials and the collision cross sections of the components. In the case of thermodynamic equilibrium the model gives values of the dissociation constants close to those generally accepted. The use of this model in multicomponent nonequilibrium total viscous shock layer calculations gives values for the shock detachment distance within 5% of the experimental values. The indeterminacy in the values of the vibrational energy lost by air molecules during dissociation and recovered during recombination does not lead to serious errors in the macrocharacteristics of the flow. The nonequilibrium excitation of vibrational degrees of freedom proves to be not so important in computing the macrocharacteristics of the flow as previously assumed and the existing algorithms for calculating chemically nonequilibrium flows on the assumption of thermodynamic equilibrium can be used with satisfactory accuracy for calculating the values of the heat flux, the position of the shock wave, and the temperature and pressure in the shock layer for partially dissociated and ionized air.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 166–180, November–December, 1994.     

Nonequilibrium dissociation of diatomic molecules in flows with convective and diffusive particle transport

The nonequilibrium effects in the kinetics of the thermal dissociation which occurs in a streaming gas of diatomic molecules are investigated. Expressions are obtained for the macroscopic reaction rate and the vibrational energy distribution of the molecules, taking into account the influence of the gas motion. Cases of flows with convective and diffusive particle transport are considered. The dissociating molecules are simulated by cutoff harmonic oscillators. The vibrational kinetics is described in the framework of the so-called diffusion approximation.Translated fron Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 147–153, November–December, 1985.     

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.     

Problems of the theory of monomolecular dissociation of a one-component gas and dissociation constant of CO2 at high temperatures

Equations determining the temperature of vibrations and dissociation constant of polyatomic molecules with consideration of fast exchange of vibrational quanta are formulated. The equations are simplified considerably if different groups of oscillators have similar temperatures of vibrations. In the case of practical interest, it is sufficient to know the vibrational relaxation time and monomolecular dissociation constant at high densities for solving the problem in a harmonic approximation. Quantitative results are obtained for carbon monoxide.Translated from Zhurnal Prikladnoi Mekhanika i Tekhnicheskaya Fiziki, No. 3, pp. 46–52, May–June, 1972.The author thanks S. A. Losev and N. A. Generalov for additional measurement data and I. S. Zaslonko for useful discussions.     

Ionization mechanism in a low-density hypersonic stream

It is shown that the ionization mechanism due to the direct collision of molecules replaces the mechanism of associative ionization in the hypersonic flow of air around a blunt body as the density diminishes. The value of the Reynolds number for which this transition occurs is found. The results of computations of a viscous nonequilibrium shock layer are compared with experimental results of American researchers. Good agreement is obtained between results on the distribution of the electron concentrations in the shock layer. It is shown that the barodiffusion process exerts a great influence on the distribution of the electron concentration in the shock layer at low Reynolds numbers.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 160–163, May–June, 1976.The author is grateful to V. V. Lunev and V. G. Voronkin for discussing this research.     

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.     

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.     

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.     

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.     

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.     

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.     

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.