Direct Shocks in a Vibrationally Nonequilibrium Gas

Direct shocks in flows of a high-temperature diatomic gas with rotational and vibrational degrees of freedom are considered. Gas-dynamic parameters and populations of molecular vibrational levels behind a shock are studied for the case of disturbance of vibrational equilibrium in an incident flow.     

Poiseuille flow and thermal creep in a capillary tube on the basis of the kinetic R-model

Flow of a diatomic rarefied gas in a capillary tube of infinite length and an arbitrary cross-section under a given small pressure gradient (Poiseuille flow) or a small temperature gradient (thermal creep) is studied on the basis of a kinetic model that takes account for the rotational degrees of freedom of molecules (R-model). Numerical investigation is carried out for flows between parallel flat plates and in a circular capillary tube at the gas parameters corresponding to nitrogen. The main calculated quantity is the gas flow rate through a tube cross-section. The results are compared with the corresponding data obtained on the basis of the S-model.     

Equation for the number of quanta and the dissociation rate in a diatomic gas

We examine vibrational relaxation in a one-component diatomic gas, the molecules of which are described by a Morse potential. An expression is obtained for the mean number of quanta of a molecule assuming there exists a sharp boundary which separates vibrational levels into two groups. In each group there dominates either vibrational-quantum exchange processes or energy-exchange processes between the vibrational and translational degrees of freedom. By solving numerically the system of equations for the number of quanta and for the dissociation rate for times larger than the vibrational relaxation time, the dependence of the dissociation constant on the number of quanta is obtained.     

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.     

Effect of rotational degrees of freedom of molecules on energy flux in attenuated gas

On the basis of model kinetic equations a solution is obtained by a numerical method for the flow of attenuated gas around a sphere. The effect of rotational degrees of freedom on the energy flux to the body is investigated. Values of the ratio between the energy flux Q and its free-molecular value Q* for monatomic and diatomic gases are compared; for the comparison, the dimensionless temperature of the body, the gas velocity at infinity, and the law of viscosity must be the same in the two cases. For sufficiently cold bodies (when the body temperature is below the equilibrium temperature for a diatomic gas) the difference between Q/Q* for monatomic and diatomic gases is insignificant. For a diatomic gas when the body temperature is close to equilibrium, the ratio Q/Q* is found to have a nonmonotonic dependence on the Knudsen force.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 119–124, September–October, 1977.     

On the theory of vibrational relaxation of diatomic molecules

The relaxation of diatomic molecules (harmonic oscillators) in a relatively light inert gas, which plays the part of a thermostat, is considered within the framework of classical mechanics. The gas-kinetic equation for the distribution function of diatomic molecules is approximated by the Fokker-Planck equation in the space of the energies of translational, rotational and vibrational motions on the assumption of strong nonadiabaticity of the collisions. In the approximation discussed, relaxation processes with different degrees of freedom develop independently, although the characteristic times of these processes are quantities of the same order. The vibrational relaxation time, expressed in terms of the gas-kinetic integral ^*(1,1) (T*), is obtained.     

Application of Model Kinetic Equations to Calculations of Super- and Hypersonic Molecular Gas Flows

For the purpose of taking the internal degrees of freedom into account, threetemperature approximating model equations, which are a generalization of the R- and ES–BGKmodels, are proposed for a diatomic gas. The surface pressure, friction, and heat transfer coefficients are compared with the direct simulation Monte Carlo (DSMC) solution in the problem of flow past a cylinder in the super- and hypersonic flow regimes. The dependence of the surface coefficients on the rotational collision number is analyzed.     

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.     

Expansion of monatomic and diatomic gases from a spherical source into a vacuum in a gravitational field

Steady monatomic and diatomic gas flows from a spherical source into a vacuum in a gravitational field are studied using direct statistical simulation. The qualitative gravitation effect on the flow is shown to be independent of the intermolecular collision model. Three characteristic Jeans parameter ranges can always be distinguished, namely, the subcritical range, on which the flow in a weak gravitational field is similar with the outflow in the absence of gravitation, the supercritical range, on which the outflow velocity remains small even at large distances from the source, and a narrow transitional range between the two former ranges. The presence of internal degrees of freedom of gas molecules displaces the transitional range toward the greater values of the Jeans parameter and leads to an increase in the outflow velocity and the gas temperature; however, in the initial region the latter effect is expressed only slightly. The normalized escape flow is a nonmonotonic function of both the Jeans parameter and the Knudsen number and is different for monatomic and diatomic gases within 50% on the parameter range considered.     

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.     

Effect of inelastic collisions on the first-order slip coefficients for a diatomic gas with rotational degrees of freedom

When solving problems of inhomogeneous gas dynamics in the slip regime, it is necessary to know the boundary conditions for the velocity, temperature, heat fluxes, etc., that is, the boundary conditions for the gas macroparameters. In particular, such problems arise in developing the theory of thermophoresis of moderately large aerosol particles [1].The problem of monatomic and molecular (di- and polyatomic) gas slip along a boundary surface is considered in many publications (see, for example, [2–8]). The first-order effects include the isothermal and thermal gas slips characterized by the coefficients C_m and K_TS, respectively.In contrast to a monatomic gas, the molecules of diatomic and polyatomic gases have internal degrees of freedom, which considerably complicates the kinetic equation [9]. The lack of reliable models for the intermolecular interaction potential predetermines the need to construct model kinetic equations [10].In this study, for a diatomic gas whose molecules have rotational degrees of freedom, we propose a model kinetic equation obtained by developing the approach described in [6]. With the use of this model equation, the problem of diatomic gas slip along a plane surface is solved. As a result, for diatomic gases the coefficients C_m and K_TS, which depend on the thermophysical gas parameters and the intensity of inelastic collisions, are obtained.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 176–182. Original Russian Text Copyright © 2004 by Poddoskin.     

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.     

Investigation of heat transfer at the critical point of a sphere around which flows a hypersonic flow of carbon dioxide gas

The article gives the numerical results of an investigation of flow near the leading critical flow line with the hypersonic flow of carbon dioxide gas around a sphere. The investigation was made on the basis of a simplified system of Navier-Stokes equations for a five-component model of the gas, taking account of dissociation-recombination relaxation processes of the components of the gas, as well as of the excitation and deactivation of the vibrational degrees of freedom of molecules of carbon dioxide gas. The calculations were made in a range of values of the pressure in the oncoming flow from 10^?7 to 10^?3 atm, and of the velocity from 4.5 to 8 km/sec for a sphere of radius 2 m. The surface of the sphere was assumed to be either ideally catalytic or chemically neutral. The dependence of the heat-transfer parameter on the determining parameters of the flow is obtained.     

Influence of Vibrational Relaxation on the Pulsation Activity in Flows of an Excited Diatomic Gas

The influence of vibrational relaxation on the nonlinear evolution of a large vortex structure in a shear flow of a highly nonequilibrium diatomic gas is studied. Calculations are performed using the equations of twotemperature gas dynamics for a viscous heatconducting gas. Relaxation of the temperature of vibrational levels of gas molecules to equilibrium is described by the Landau–Teller equation. The contribution of the relaxation of rotational levels is taken into account by the bulk viscosity in the stress tensor. It is shown that in the presence of only the relaxation process with no viscous dissipation, the damping of the kinetic energy of perturbations and Reynolds stresses increases by up to 10 % compared to the case of thermal equilibrium. For high (actually attainable) degrees of excitation of the vibrational mode, moderate dynamic and bulk viscosities, and a typical relaxation time comparable to flow time, the relative effect of perturbation damping reaches 15%.     

Diffusion equation in the theory of vibrational relaxation of diatomic molecules

A kinetic equation is obtained for the distribution function of anharmonic oscillators with respect to the vibrational energy; it enables one in the diffusion approximation to describe the vibrational relaxation of diatomic molecules in a medium of inert gas when there is a weak interaction between the oscillators and a thermal bath. The main difference from the equation for harmonic oscillators is in the appearance in the diffusion coefficient of an adiabaticity function that characterizes the variation of the adiabaticity factor because of the anharmoni-city of the vibrations. It follows from the form of this function that the greatest difference between the relaxation of anharmonic and harmonic oscillators is to be expected in the case of adiabatic interaction of oscillators with particles of the inert gas.     

Boundary conditions for flows of multiatomic gases

We consider the problem of obtaining macroscopic boundary conditions for the equations of a strongly nonuniform, multitemperature boundary later in a gas with translational, rotational, and vibrational degrees of freedom and for arbitrary catalyticity of the solid surface with respect to various vibrational modes. The boundary conditions are analyzed on surfaces with properties favorable to flow modes with population inversion in the quantum equations.     

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.     

双原子分子晶体振动弛豫过程的分子动力学研究

用分子动力学方法研究瞬时加热振动自由度后的能量弛豫过程.晶元包含128个双原子分子,采用周期性边界条件和体心立方结构,对于分子内和分子间原子相互作用采用双莫尔斯势.发现平衡时间的对数与因子,f_21之间存在线性关系,而f_21正比于分子内振动与格波振动的频率比.     

转动非平衡玻尔兹曼模型方程统一算法与全流域绕流计算应用

基于过去开展稀薄自由分子流到连续流气体运动论统一算法框架,采用转动惯量描述气体分子自旋运动,确立含转动非平衡效应各流域统一玻尔兹曼模型方程.基于转动能量对分布函数守恒积分,得到计及转动非平衡效应气体分子速度分布函数方程组,使用离散速度坐标法对分布函数方程所依赖速度空间离散降维;应用拓展计算流体力学有限差分方法,构造直接求解分子速度分布函数的气体动理论数值格式;基于物面质量流量通量守恒与能量平衡关系,发展计及转动非平衡气体动理论边界条件数学模型及数值处理方法,提出模拟各流域转动非平衡效应玻尔兹曼模型方程统一算法.通过高、低不同马赫数1:5～25氮气激波结构与自由分子流到连续流全飞行流域不同克努森数（9×10-4～10）Ramp制动器、圆球、尖双锥飞行器、飞船返回舱外形体再入跨流域绕流模拟研究,将计算结果与有关实验数据、稀薄流DSMC模拟值等结果对比分析,验证统一算法模拟自由分子流到连续流再入过程高超声速绕流问题的可靠性与精度.