Computation and experimental validation of N_{2}-CH_{4}-Ar mixture flows behind normal shock wave

Different vibration-dissociation-vibration coupling models have been used to compute the nonequilibrium N-CH-Ar mixture flow behind a normal shock wave. A three-temperature model was used and the diffuse nature of vibrational relaxation at high temperatures was accounted for. The numerical results obtained with the Treanor and Marrone model (preferential or non preferential) and the Park model of vibration-dissociation-vibration coupling are compared. These results show that the temperatures and the concentrations are mainly affected by the value of the characteristic temperature U in the preferential model of Marrone and Treanor. An assessment of the more realistic model was realized by comparing numerical results with shock tube experiments. The influence of argon addition on the nonequilibrium emission of CN behind the shock wave was also numerically studied and compared to experimental measurements. Received 1 September 1995 / Accepted 10 December 1996     

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.     

Influence of vibration-dissociation coupling on heat transfer and hypersonic drag

A numerical investigation is carried out within the framework of the multicomponent total viscous shock layer model [6, 7], according to which when Re 100 the flow near a blunt body can be divided into a shock wave zone and a viscous shock layer. At the inner edge of the shock wave the generalized Rankine-Hugoniot relations are imposed, and in the shock layer the complete system of viscous shock layer equations is solved with allowance for vibrational relaxation and nonequilibrium dissociation and ionization reactions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 141–151, May–June, 1990.     

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%.     

Experimental and numerical studies of weak blast waves in air

Effects of viscosity and vibrational nonequilibrium on the profile of a weak, spherical N-wave in air are experimentally and numerically studied. Weak blast waves were generated, in a quiescent air dome, by spark discharges and exploding wires and observed by high frequency response microphones over 40 meters. Some similarity relationships were obtained from the blast wave experiments. For observed N-waves having less than 100 Pa peak overpressure, the peak overpressure p _f and the duration of the positive phaset _d+ are found to vary with the radial distance from the sourcer as p _f r ^–1.38 andt _d + r ^0.19, whilst the rise time of the blast wave t _f linearly increases with distance. Similar trends were also found for the negative phase of the blast wave. Numerical simulations were carried out to compare with the blast wave data. The Navier-Stokes equations for spherical symmetric flows were solved by coupling with a relaxation equation for vibrational excitation of oxygen using the random choice method (RCM) adapted to supercomputing with an operator splitting technique. The resultant N-wave profiles are in good agreement with the experimental results. The numerical results clearly indicate that the wave-easing process due to the dispersive effect of vibrational relaxation plays a dominant role in determining the rise time of the N-wave.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Comparison of different approaches to the calculation of chemically nonequilibrium flow with allowance for vibrational relaxation

Chemically nonequilibrium flows with allowance for vibrational relaxation are investigated numerically within the framework of the hypersonic viscous shock layer equations with reference to the example of the flow in the neighborhood of the critical line of the “Buran” orbital vehicle in its motion along a re-entry trajectory. It is found that the vibrational temperatures of the molecular components differ markedly. The distinctive feature of the model in question, as compared with a model with one average vibrational temperature, is the stronger effect on the flow characteristics over the thermally stressed part of the trajectory. The models proposed in the literature for dissociation from an effective vibrational level are compared with the model for dissociation with a certain probability from all the vibrational levels. It is shown that the use of an approximation of the total dissociation constant as a function of translational temperature only may lead to a considerable variation from the results of calculations with allowance for vibrational relaxation on the basis of the equilibrium dissociation rate constant. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 138–146, March–April, 1994.     

Dissociation of anharmonic molecules by means of high-power infrared emission

The kinetics of nonequilibrium molecular dissociation when vibrations are excited by high-power infrared emission is investigated for a model of anharmonic oscillators. The case when exchange of vibrational quanta during collision with molecules in the lower states plays a fundamental role in the formation of the vibratory distributionfunction at the upper level is analyzed. Dependences of the “vibration temperature” and the rate constant for nonequilibrium dissociation, as a function of the optical pumping probability are obtained for different pumping conditions. The results are compared with similar calculations for a harmonic model.     

Supersonic flow past blunt bodies involving fast nonequilibrium processes

In the numerical integration of the system of equations of relaxation gasdynamics the solution may become unstable. Instability arises in those cases when the characteristic time for the nonequilibrium process becomes less than the characteristic flow time. To ensure stability it is necessary to reduce the integration step. With approach to equilibrium conditions, when the process rate increases, the step reduction may lead to excessive computational time. Preceding studies have overcome the difficulty in solving the one-dimensional [1–3] and two dimensional [4] problems by various techniques, the basic idea being the use of implicit difference schemes for approximating the relaxation equations.In the present paper analogous considerations are used to develop a scheme for calculating supersonic flow past blunt bodies with fast non-equilibrium processes within the framework of [5]. The basic coordinate system , is used to approximate the equations, just as in [5]. However the relaxation equation is solved along a streamline element. Calculations are presented for the air flow past a sphere with account for the oxygen dissociation reaction. The validity of the binary similarity law for this model is verified. As an example of the applicability of the technique, a calculation is made of the flow of a chemically reacting mixture with heat release about a sphere.     

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.     

Possibility of the occurrence of dissociation reactions of multiatomic molecules during rapid cooling in an expanding supersonic stream

We investigate the possibility of the occurrence of the reaction involving the dissociation of N₂O and the exchange reaction N₂O+CON₂+CO₂ during rapid cooling of a gas mixture due to supersonic expansion in a nozzle. A numerical solution of the equations for the balance of vibrational energy and the kinetics of the chemical reactions under nonequilibrium conditions is given. We find the values of the parameters that are necessary for the experimental observation of the phenomena considered.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 48–53, March–April, 1973.     

高温非平衡流动中的氧分子振动态精细分析

高超声速流动在头激波压缩后常处于高 温条件下的热化学非平衡状态. 本文采用态-态方法和双温度模型计算分析了一维正激波后和高超声速钝体绕流驻点线上的氧气热化学非平衡流动. 态-态方法将氧气的每个振动能级当成独立的组分,通过耦合 Euler 方程或驻点线上的降维 Navier-Stokes 方程,数值求解得 到了高温流动中的精细热化学非平衡状态. 而双温度模型假设氧气的振动能级服从 Boltzmann 分布,通过求解振动能方程得到振动温度. 一维正激波后热化学松弛过程的计算结果表明,态-态计算预测的温度分布和氧原子浓度分布较好地吻合了文 献中的实验结果,而经典的双温度模型的预测结果误差较大,且不同双温度模型的计算结果比较发散. 态-态方法详细地给出了所有振动能级的变化过程. 无论是正激波还是脱体激波后的流场,都是高振动能级首先得到激发;但是数密度大的低振动能级先达到热平衡,而高能级 分子要经过很长距离后才能达到热平衡. 在驻点附近,复合反应生成的氧气分子处于高振动能级,导致高振动能级分子数密度显著高于平衡分布. 计算还发现,经典双温度模型的离解反应速率明显偏离态-态计算结果,无法准确体现振动离解耦合效应对离解反应 速率的影响,但是 Park 双温度模型将离解失去的振动能取为 0.3$\sim 高超声速流动在头激波压缩后常处于高 温条件下的热化学非平衡状态. 本文采用态-态方法和双温度模型计算分析了一维正激波后和高超声速钝体绕流驻点线上的氧气热化学非平衡流动. 态-态方法将氧气的每个振动能级当成独立的组分,通过耦合 Euler 方程或驻点线上的降维 Navier-Stokes 方程,数值求解得 到了高温流动中的精细热化学非平衡状态. 而双温度模型假设氧气的振动能级服从 Boltzmann 分布,通过求解振动能方程得到振动温度. 一维正激波后热化学松弛过程的计算结果表明,态-态计算预测的温度分布和氧原子浓度分布较好地吻合了文 献中的实验结果,而经典的双温度模型的预测结果误差较大,且不同双温度模型的计算结果比较发散. 态-态方法详细地给出了所有振动能级的变化过程. 无论是正激波还是脱体激波后的流场,都是高振动能级首先得到激发;但是数密度大的低振动能级先达到热平衡,而高能级 分子要经过很长距离后才能达到热平衡. 在驻点附近,复合反应生成的氧气分子处于高振动能级,导致高振动能级分子数密度显著高于平衡分布. 计算还发现,经典双温度模型的离解反应速率明显偏离态-态计算结果,无法准确体现振动离解耦合效应对离解反应 速率的影响,但是 Park 双温度模型将离解失去的振动能取为 0.3$\sim $0.5 倍分子离解能是比较合理的.     

Effect of laser radiation on the vibrational distribution of CO2

In connection with progress in the field of CO₂ lasers, questions of the vibrational kinetics of molecules of CO₂ have been discussed in many communications. In a majority of cases of practical importance, the distribution of CO₂ is due to processes of vibrational exchange (V-V) on which is based the well-known thermodynamic model [1]. In other cases, the V-V exchange does not determine the vibrational distribution, since the perturbation is small; therefore, it is found sufficient to consider a small number of levels of CO₂ (usually three), whose populations satisfy the linear equations of the balance [2]. There is the possibility of conditions where the vibrations are strongly excited and, at the same time, V-V processes are insignificant (a very small CO₂ impurity in the inert gas, with a high degree of ionization). Then the number of equations becomes large. The present article discusses one such case: the excitation of a steady-state vibrational distribution in a glow discharge by laser radiation, whose solution is rather graphic.     

Thermal slip boundary conditions in vibrational nonequilibrium flows

This paper deals with new thermal jump boundary conditions at the wall in polyatomic gas flows. The calculations and results especially concern vibrational nonequilibrium conditions when the dissociation effects may be neglected. First the usual conditions are briefly described. Then the boundary conditions proposed in the paper are justified on the basis of previous experimental results and by developing direct heat flux calculations at the wall. Analytical expressions and numerical values of the various fluxes are presented.     

稠密流体中双原子分子振动弛豫的非谐性及质量效应

利用分子动力学计算机模拟方法研究了稠密流体中双原子分子的振动弛豫问题，证实了双原产分子的振动弛豫速率随着其非谐性的增大而加快，同时，其速率也随其质量因子的变大而加速。     

稠密流体中双原子分子振动弛豫的非谐性及质量效应

利用分子动力学计算机模拟方法研究了稠密流体中双原子分子的振动弛豫问题，证实了双原产分子的振动弛豫速率随着其非谐性的增大而加快，同时，其速率也随其质量因子的变大而加速。     

An extension of CVDV model to Zeldovich exchange reactions for hypersonic non-equilibrium air flows

A new preferential vibration-dissociation-exchange reactions coupling model – labelled CVDEV – resulting from an extension of the well-known Treanor and Marrone CVDV model, has been derived to take into account the coupling between the vibrational excitation of the and molecules and the two Zeldovich exchange reactions. Analytical expressions for the exchange reactions coupling factor and for the average vibrational energy lost – or gained – by a molecule through an exchange reaction have been developed. The influence of such a coupling has been shown by means of numerical simulations of hypersonic air flows through normal and bow shock waves. Code-to-code comparisons between our model and other recent approaches have been conducted. The infrared radiation of nitric oxide behind a normal shock wave resulting from computations with the CVDEV model has been compared with other coupling model results and to recent shock tube experimental data. These comparisons have shown a good agreement of our model results with the experimental data. In this context, the results show the prominent influence of vibration coupling on the first Zeldovich reaction, and the absence of vibration coupling effects on the second Zeldovich reaction. Received 30 June 1997 / Accepted 3 December 1997     

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.     

高超声速三维热化学非平衡流场的数值模拟

对三维高超声速热化学非平衡流场进行数值模拟,采用双温度热化学非平衡、11组元空气模型,考虑振动-离解耦合．差分格式采用沈清博士提出的“迎风型NND”格式,用熵修正方法消除了高超声速流数值模拟中的“carbuncle现象”．与LU-SGS方法结合,提高了单步计算效率和收敛性．数值模拟结果与文献结果进行了对比,并在弹道靶中进行了钢质圆球的弓形激波位置实验验证．计算结果与文献、实验的对比说明,三维热化学非平衡流计算程序可以精确地捕捉到强弓形激波,得到合理的空气动力系数．     

Effect of freestream nonequilibrium on flow past a wedge

We examine the effect of flow freezing in the nozzle of a hypersonic wind tunnel on the parameters of nonequilibrium flow past a wedge.Zhigulev's solution [1] for vibrational relaxation is extended to the nonequilibrium freestream case.It is shown that in this case the perturbations of the frozen-flow parameters behind the oblique shock wave can change sign if the flow in the working section deviates significantly from equilibrium.A method is proposed for converting experimental results obtained in tunnels with frozen flow to the case of equilibrium freestream flow past the body.The author wishes to thank O. Yu. Polyanskyi and V. P. Agavonov for their interest in this study.