Numerical investigation of the effect of rotational relaxation rate on the nitrogen shock wave structure

The nitrogen rotational relaxation process is numerically investigated on the basis of the Monte-Carlo method and the calculation of the classic three-dimensional equations of motion of rigid-rotator molecules. The dependence of the relaxation parameterZ _R on the initial values of the translational and rotational temperaturesT _t andT _R and the asymmetry parameter in the molecular interaction potential is obtained. The problem of the shock wave structure is solved using the Pullin phenomenological model whose parameters are determined on the basis of the solution of the relaxation problem with exact calculation of the molecular interaction. The dependence of the flow fields and the relative thickness of the density profile on the quantityZ _R is obtained and the calculated data are compared with the results of experiments. It is shown that the data are in better agreement for larger values of the asymmetry parameter.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 159–167, July–August, 1995.     

Rotational relaxation of nitrogen in a viscous shock layer at low reynolds numbers

The viscous shock-layer model is used to examine relaxation of rotational degrees of freedom of molecular nitrogen in flow of a rarefied gas near the stagnation flow line around a sphere. It is shown that in the strongly smeared shock-wave region the rotational degrees of freedom can exhibit substantial nonequilibrium, leading to the increase of temperature and an increase of shock-layer thickness as compared with the equilibrium values. The influence of rotational relaxation on the shock-wave structure is discussed, and boundaries are found for the flow regions when rotational relaxation plays on important role,A comparison is made between the results of numerical calculations and experimentally obtained density profiles available in the literature near the stagnation line in flow of a rarefied gas over a sphere [1, 2]. Quite good agreement is obtained between the results of the calculation and experimental data over a wide range of Reynolds numbers.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 172–175, July–August, 1977.     

Possibility of forming an inverted distribution over the rotational levels of nitrogen in an expanding gas stream

A number of theoretical papers have been devoted to an investigation of the relaxation kinetics of the population of a system of rotational levels of molecules in a stream of gas freely expanding from a sonic nozzle [1–3]. The complexity of the task of constructing models of relaxation and of collisions consistent in accuracy, however, as well as the difficulties in solving the resulting system of kinetic and gas-dynamic equations, lead to the necessity of using substantial approximations. Some disagreement between the experimental data and calculated results [1, 2] requires an evaluation of the accuracy of the various approximations used and further refinement of the theoretical models. In contrast to [1], in order to bring out the possible mutual influence of nonequilibrium energy exchange between the degrees of freedom of nitrogen molecules and the variation of the gas-dynamic parameters, the calculation presented below is based on a numerical solution of a self-consistent system of kinetic and gas-dynamic equations for the populations of rotational states and the temperature, density, and velocity of gas in the stream. Collisional probabilities of rotational transitions, calculated with allowance for the long-range part of the potential of the interaction between molecules [4], are used for this.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 9–16, May–June, 1986.     

Vibrational-translational relaxation of anharmonic oscillators at low temperatures

An approximate analytic solution is found to the problem of the vibrational-translational relaxation of anharmonic oscillators at translational temperatures which are small compared with the energy difference between adjacent levels of the oscillator. The deviation of the obtained distribution from the Boltzmann distribution in the relaxation process is analyzed. A study is made of the behavior of the vibrational energy near equilibrium at temperatures such that dissociation has only a small effect on the rate of vibrational relaxation.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 3–8, March–April, 1976.The author wishes to thank M. B. Zheleznyak and A. Kh. Mnatsakanyan for a useful discussion of the work.     

Spectroscopic determination of rotational temperature in rarefied hypersonic flow by glow-discharge excitation of luminescence

The use of the relative intensity method for measurement of the rotational temperature of nitrogen in a rarefied air flow by means of glow-discharge excitation of luminescence is described. Special features of measurement of the rotational temperature at low static pressure of the gas in the flow are noted. Profiles of the rotational temperature along the stagnation line in the case of transverse flow over a cylinder are obtained. The dependence of the measurement error on the temperature is discussed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 139–143, March–April, 1971.     

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.     

Flow of a supersonic low-density jet of nitrogen and nitrogen-hydrogen mixture over a blunt body

This paper gives the results of electron-beam measurements of the rotational temperature of nitrogen and its concentration in front of a spherically blunt cylinder situated on the axis of a supersonic rarefied jet of nitrogen and nitrogen-hydrogen mixture.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 50–55, November–December, 1972.     

Sound absorption in a shock wave

It was shown in [1–4] that the reflection of a sound wave or its transmission through a shock front should be accompanied by attenuation or intensification of the wave is regarded as a discontinuity. In accordance with current representations [5, 6], a shock wave includes a viscous shock and a lengthy relaxation zone. Equilibrium is established with respect to translational and rotational degrees of freedom in the viscous shock and with respect to internal degrees of freedom in the relaxation zone. The result of the interaction of the shock and sound waves is determined by the relationship between the length of the sound wave and the width of the shock wave.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 90–94, May–June, 1986.     

Transmission of waves in a liquid through absorbing layers and subsequent interaction of the waves with an obstacle

The propagation of waves in porous media is investigated both experimentally [1, 2] and by numerical simulation [3–5]. The influence of the relaxation properties of porous media on the propagation of waves has been investigated theoretically and compared with experiments [3, 4]. The interaction of a wave in air that passes through a layer of porous medium before interacting with an obstacle has been investigated with allowance for the relaxation properties [5]. In the present paper, in which the relaxation properties are also taken into account, a similar investigation is made into the interaction with an obstacle of a wave in a liquid that passes through a layer of a porous medium before encountering the obstacle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 53–53, March–April, 1983.     

Numerical investigation of the flow of nitrogen past a sphere with allowance for rotational relaxation

The supersonic flow of nitrogen past a sphere is studied in the framework of the complete Navier-Stokes equations and the relaxation equation with allowance for rotational-translational relaxation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 170–174, March–April, 1980.I thank V. N. Gusev for interest in the work and valuable discussions and V. K. Molodtsov for assisting in the development of the numerical algorithm for solving the problem.     

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.     

Mechanisms of brittle-ductile transition in toughened thermoplastics

The objective of this work was to investigate the mechanism of brittle-ductile transition in toughened polymers. Two systems, namely, a rubber-toughened nylon 66 (Zytel ST-801) and a high impact polystyrene (HIPS), were chosen for this study. The samples were prepared by injection molding and were tested in three-point bending under various loading rates and temperatures. The brittle-ductile transition temperature (T_b–d) was determined from the observed fracture behavior as a function of temperature. Molecular relaxation temperatures of the polymers were measured by mechanical spectroscopy at various frequencies. The correlation between temperature and loading rate was estimated using the Arrhenius equation. The results show that T_b–d of Zytel ST-801 is only slightly affected by the loading rate, whereas T_b–d of HIPS strongly increases with deformation rate. It is found that for the former, within the experimental errors, an increase in T_b–d with loading rate corresponds to the shift in the secondary relaxation temperature T_b of the nylon 66 matrix. For the latter however, the increase in T_b–d is related to the glass/rubber relaxation of the polystyrene matrix. It seems that the type of molecular relaxation controlling the brittle-ductile transition corresponds to that with lower activation energy.     

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.     

Investigation of the Nitrogen Shock Wave Structure on the Basis of Trajectory Calculations of the Molecular Interaction

The shock wave structure in a diatomic gas is investigated using the direct statistical simulation (Monte-Carlo) method. The energy exchange between translational and rotational degrees of freedom (TR-exchange) is calculated by solving the dynamic problem of the interaction between rigid-rotator molecules within the framework of classical mechanics. The density profiles calculated are compared with the experimental data and on this basis the nitrogen rotational relaxation time is estimated. The possibility of using simplified intermolecular interaction models, namely, the variable-diameter sphere model employed together with a phenomenological consideration of the TR-exchange, is studied. Gasdynamic parameter profiles in the shock wave are analyzed. Simple approximations of the velocity gradient and translational and rotational temperature profiles are obtained on the basis of a parametric calculation of the shock wave structure. This makes it possible approximately to describe the gasdynamic parameter profiles in terms of elementary functions.     

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.     

Effect of surface catalytic activity on nonequilibrium heat transfer in a subsonic jet of dissociated nitrogen

The present paper investigates experimentally and numerically the effect of the heterogeneous recombination of atoms on the heat transfer of models in a subsonic jet of dissociated nitrogen for the conditions of an experiment in the VGU-2 plasma generator and determines the effective probabilities of the heterogeneous recombination of nitrogen atoms for a number of materials at high temperatures.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 166–172, May–June, 1985.     

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.     

A linear viscoelastic model for solid polyethylene

Stress relaxation tests have been carried out on a blue, pipe grade PE 80 medium density polyethylene (BP Chemicals), to provide thermo-viscoelastic rheology for use in calculating thermal stresses in pipe production. Stresses up to 4 MPa were used, with strains up to about 2%, in tests at temperatures from 23° to 90°C. Within this range a linear viscoelastic model was applicable, provided the initial ramp strain rate was less than 7×10^–5 s^–1. The stress relaxation data was fitted directly by a model incorporating an elastic response to volumetric strains, and a generalised linear solid model, consisting of two Maxwell elements and a purely elastic element in parallel, for deviatoric strains. Arrhenius type temperature dependence of relaxation times and shear moduli is found, and within experimental accuracy the temperature dependence of all these model parameters is the same. As a consequence, and provided that the duration of the strain ramp is sufficiently short relative to relaxation times, the model leads to time-temperature superposition of the relaxation moduli, using the same shift factor on both the response magnitude and time axes.     

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.