Effect of roughness on the interaction between low-density gas and the surface of a solid

The effect of roughness on the reflection of molecules of a low-density gas from the surface of a solid is studied. An expression is derived for the transform for a single reflection from a homogeneous roughness which permits simple programming for a computer. A simple approximation to this expression is considered which is applicable over a broad range of roughness parameters and of gas-molecule angles of incidence. Based on this approximation, the angular distributions of reflected molecules are calculated and a comparison is made with similar distributions taken from [1].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 68–75, July–August, 1972.     

The noneouilibrium dissociation of diatomic molecules in a boundary layer

A study is made of the influence of the process of diffusion of diatomic molecules on the rate of their thermal dissociation. On the basis of the ladder model of the dissociation of molecules — truncated harmonic oscillators — an expression is obtained for the macroscopic reaction rate which depends explicitly and exponentially on the square of the gradient of the gas temperature. The molecules constitute a small admixture in a monatomic inert gas. The effect of the diffusion on the rate of dissociation is illustrated by the results of numerical calculation of the flow in the boundary layer around the stagnation point of a blunt body.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Shidkosti i Gaza, No. 1, pp. 161–170, January–February, 1985.     

The flow of a gas consisting of asymmetric dipole molecules in a field of resonance radiation

The special properties of the flow of a molecular gas in a field of continuous radiation the frequency of which is resonant to the frequency of the intermodal vibrational-rotational transition has been considered previously in [1]. However, this did not take account of a possibility of an energy flux arising from translational degrees of freedom of the gas molecules into vibrational degrees of freedom as a result of the rotational-translational (R-T) transfer. This effect was discussed in [2] for the absorption by a gas consisting of diatomic molecules of radiation momentum in the P-branch of a vibrational-rotational transition. As will be shown below, for asymmetric dipole molecules of the type similar to a symmetric and an asymmetric top, this mechanism of the resonance radiation effect may take place not only under absorption of the radiation in the P-branch, but also in the Q-, and even in the R-branch. The investigation of these effects in the flow of a gas consisting of asymmetric dipole molecules in a resonance radiation field forms the subject of the present study.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 123–137, January–February, 1985.In conclusion we may note that the effects considered can have an important effect on the propagation both of continuous, and of intermittent electromagnetic radiation.     

Diffusiophoresis of an aerosol particle in a binary gas mixture

The diffusion force and rate are calculated for the diffusiophoresis of a spherical particle in a binary gas mixture by solving the gas–kinetic equations. Two schemes of diffusiophoresis are considered: constant–pressure diffusion and diffusion of one mixture component through the other fixed component. The problem is solved by the integral–momentum method at arbitrary Knudsen numbers. Diffuse scattering of the gas molecules on the particle surface is assumed. The Lorentzian and Rayleigh models of a binary gas mixture are considered. The dependences of the force and rate of diffusiophoresis on the Knudsen number and the other determining parameters are analyzed. The results obtained are compared with well–known experimental data.     

Calculation of a Heat Flow from a Spherical Particle in a Diatomic Gas

The problem of heat flow from a uniformly heated spherical particle in a diatomic gas is considered. The paper reports results of numerical calculations for an analog of the Bhatnagar–Gross–Krook model of the collision integral under for purely diffuse reflection of the gas molecules from the surface.     

Rarefied gas flow past a sphere with injection

Hypersonic rarefied gas flow over the windward face of a sphere is considered in the presence of distributed injection from the surface of the body. A similar problem was previously solved in [1–3] within the framework of continuum mechanics and in [4] on the basis of model kinetic equations. In the present study the calculations were carried out using the Monte Carlo method of direct statistical modeling [5, 6]. The injected gas was the same as the free-stream gas. A simple monatomic gas model with a rigid sphere interaction potential was employed. The reflection of the molecules from the surface of the body was assumed to be diffuse with total energy accommodation. The calculation procedure using weighting factors is described in [7]. The influence of injection on the mechanical and thermal effect of the gas flow on the body is investigated for various degrees of rarefaction of the medium and injection rates.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 175–179, July–August, 1990.     

Dependence of slip coefficients on the nature of the interaction between gas molecules and a wall

A method of solution of the boundary-value problems of kinetic gas theory is developed, making it possible to use the boundary conditions in the most general form. The generalized Maxwell boundary condition that takes into account the dependence of the accommodation coefficient on the angle of incidence of gas molecules is considered as an example.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 149–152, September–October, 1986.     

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.     

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.     

Slow rotation of a sphere in a confined volume of a dilute gas

The axially symmetric motion of a gas in a volume confined between an external immobile surface of rotation and a coaxial surface of a rotating sphere is considered. A solution is obtained by the moment method based on the Boltzmann equation with a collision integral of Maxwellian molecules. The gas-velocity distribution and an expression for the friction torque exerted on the sphere are obtained for arbitrary Knudsen numbers and for an arbitrary shape of the outer surface. The proportionality of the gas slip velocity over the surface of the sphere to the friction strain is shown. The friction torque is investigated for specific shapes of the outer surface. The motion of a gas filling the space between concentric spheres, each of which rotates about an arbitrary axis, is treated. In the limiting case of small Knudsen numbers the expressions obtained are compared with the corresponding results for a continuous medium.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 117–124, July–August, 1978.The authors are grateful to the participants of the seminars guided by G. I. Petrov and A. M. Golovnyi for discussions concerning this work.     

Numerical modeling of flow with chemical reactions in a strong shock wave with approximate allowance for translational nonequilibrium

The effect of translational nonequilibrium on the course of chemical reactions in a shock wave is studied using the beam–gas model extended to the case of a multicomponent gas. For Arrhenius reactions of general form with collisions between beam and gas molecules, a modified expression of reaction rate is obtained that takes into account the relative motion of the two media. A procedure for numerical solution of the problem is considered, and calculation results for a shock wave in a dissociating air at an oncoming flow velocity of 6000 m/sec are given.     

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.     

Numerical investigation of nitrogen rotational relaxation

The nitrogen rotational relaxation process is numerically investigated on the basis of a Monte-Carlo solution of the spatially homogeneous problem for the kinetic equation. The interaction of the molecules is described by the three-dimensional equations of motion within the framework of classical mechanics, the use of which for a gas such as nitrogen is justified at not very low temperatures. The dependence of the relaxation process on the initial values of the translational and rotational temperatures and the asymmetry parameter in the interaction potential is considered.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 124–132, March–April, 1993.The author wishes to thank V. S. Galkin for discussing the work.     

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.     

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.     

Heat transfer in a very rarefied gas

A one-dimensional problem of heat transfer in a rarefied gas is considered. It relates to the nonmonotonic variation of the heat flux between two plates when the temperature of one of them is reduced. Attention is drawn to a paradox that arises in this problem if the interaction of the molecules of the gas with the surface is described by means of accommodation coefficients.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1. pp. 195–198, January–February, 1980.     

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.     

Influence of real gas properties on the integral aerodynamic coefficients

The results of mathematically modeling axisymmetric hypersonic flow past an ellipsoid are presented. The calculation data are obtained on the basis of a numerical solution of the complete Navier—Stokes equations using a finite-difference method. The investigation is carried out for the problem of laminar flow over the windward side of the body. The effect of the elongation of the ellipsoid on the total heat flux and the viscous and pressure drag is considered. Results are obtained for three different gas (air) models: the perfect gas, chemical equilibrium and chemical nonequilibrium models. For the latter model various sets of catalyticity coefficients are considered. The effect of the real properties of air on the integral aerodynamic characteristics of ellipsoids with different elongations is analyzed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 156–164, July–August, 1992.     

Influence of the macrotransport processes in gases on the change in the hydrodynamic parameters in the presence of a resonance radiation pulse

The effect of a resonance radiation pulse on the gas parameters is investigated. It is assumed that the pulse duration is large enough for the diffusion and heat conduction to be taken into account. It is shown that the diffusion and heat conduction may be significantly influenced by the processes of excitation of the internal degrees of freedom of the molecules.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 120–128, July–August, 1992.