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.     

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.     

高温气体热化学反应的DSMC微观模型分析

热化学耦合的非平衡现象一直是高温气体热化学问题研究的难点, 制约了诸如爆轰波胞格结构、低温点火速率等现象的分析. 本文以高温氮气离解和氢氧燃烧中的链式置换反应为例, 从微观反应概率、振动态指定的反应速率、热力学非平衡态的宏观反应速率、碰撞后的能量再分配等角度, 分析了直接蒙特卡罗模拟中的典型化学反应模型(TCE, VFD, QK模型)的微观动力学性质. 研究发现, 无论是高活化能的高温离解反应还是低活化能的链式置换反应, 实际参与反应的分子的振动能概率分布都偏离了平衡态的Boltzmann分布, 包含较强振动能额外影响的VFD模型可以很好地模拟高温离解反应, 而TCE (VFD的一个特例)和QK模型对活化能较低的链式置换反应的预测效果相对更好. 此外, 化学反应碰撞后的能量再分配应遵循微观细致平衡原理, 细微的偏差都可能造成平动能和振动能难以达到最终的平衡状态. 直接蒙特卡罗模拟的应用评估结果表明, 化学反应的振动倾向对热化学耦合过程产生了明显的影响, 特别是由于高振动能分子更多地参与了化学反应, 气体平均振动能的下降将影响后续化学反应的进行.      

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.     

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.     

Three-dimensional computer model of nonequilibrium aerophysics of the spacecraft entering in the Martian atmosphere

A three-dimensional computer model of nonequilibrium aerophysics of the spacecraft entering in the Martian atmosphere and landing on the planet surface is presented. The model is based on the system of Navier-Stokes equations, the energy conservation equation in the form of the Fourier-Kirchhoff equation for the translational temperature, the system of equations of vibrational kinetics for six vibrational modes of N₂, O₂, CO₂ and CO molecules, and the equation of selective thermal radiation transfer in the multigroup spectral approximation. The results of two-dimensional and threedimensional calculations of the nonequilibrium flowfield and the convective and radiative heating of the EXOMARS spacecraft surface are presented. The calculations are performed on regular multiblock curvilinear grids using the NERAT-2D and NERAT-3D computer codes developed in the Institute for Problems in Mechanics of the Russian Academy of Sciences.     

Vibrational relaxation of diatomic molecules in a non-Boltzmann thermostat

The action of resonance IR laser radiation on a molecular gas leads, at high-power absorption intensity, to a breakdown in the equilibrium (Boltzmann) energy distribution in the internal degrees of freedom [1]. Under realistic conditions, molecular gases usually are (due to small amounts of impurities or isotopic components) multicomponent systems. In this case resonance IR laser radiation (or other methods of selective action), disturbing the distribution function of the primary gas, does not interact directly with impurities. The problem thus arises of determining the distribution function of the impurity gas interacting with the nonequilibrium (non-Boltzmann) thermostat. The present paper, devoted to the solution of this problem, treats the distribution function of harmonic oscillators A, consisting of a small amount of impurities in a system of harmonic oscillators B with given nonequilibrium distribution functions of vibrational energy. The behavior of a system in a nonequilibrium thermostat was first considered in [2, 3] where, as well as in [4, 5], it was shown that in a non-Maxwellian thermostat with a small amount of harmonic oscillator impurities, a Boltzmann distribution in harmonic oscillator vibrational energies is established under stationary conditions, with a temperature differing from the gas-kinetic temperature of the thermostat, defined in terms of the mean-square velocity. The behavior of a small amount of impurities (heavy monoatomic particles and harmonic oscillators) in a non-Maxwellian thermostat of a light gas was further investigated in [6–8]. Unlike the papers mentioned, the present one considers the behavior of a small amount of harmonic oscillator impurities in a thermostat with a Maxwellian velocity distribution and with a nonequilibrium (non-Boltzmann) distribution in vibrational energies.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 3–10, September–October, 1978.     

On the Role of Vibrational Excitation in Hypersonic Flow Computations

Abstract. The paper investigates the influence of the thermochemical modeling on the flow-field properties for both compressing and expanding flows. For the nitrogen hypersonic flow over a cylinder a comparison between a model neglecting vibrational energy and two-temperature Park's nonequilibrium model has been performed in a wide variety of experimental and free flight conditions. It is shown that the differences are confined in a thin layer behind the bow shock while the overall flow properties are slightly affected. For the expanding air flows inside hypersonic facilities, besides the two models mentioned above, vibrational equilibrium and CVDV model have been compared. It was found that vibrational nonequilibrium can not be disregarded but no discernible differences have been observed between Park's and CVDV model results, unless the enthalpy is very large.Sommario. L'articolo analizza l'influenza della modellizzazione termochimica sul campo fluidodinamico nel caso di flussi ipersonici sia in compressione che in espansione. Per il flusso di azoto attorno ad un cilindro è stato effettuato un confronto fra un modello che trascura l'energia vibrazionale ed il modello di non-equilibrio a due temperature di Park. L'analisi è stata condotta per un ampio intervallo di variazione dei parametri caratteristici comprendente condizioni sia di volo che di prove in laboratorio. Il confronto ha mostrato che l'effetto del non-equilibrio vibrazionale è sempre limitato ad una regione molto sottile dietro l'onda d'urto e che l'influenza sulle proprietà generali del flusso è in ogni caso modesta. Per il caso dei flussi in espansione in gallerie ipersoniche si è invece assunto come gas l'aria ed oltre ai due modelli già menzionati sono stati utilizzati anche il modello di equilibrio vibrazionale ed il modello CVDV. Si è osservato che per i flussi in espansione il non-equilibrio vibrazionale non può essere trascurato ma che comunque i modelli di Park e CVDV sono sostanzialmente equivalenti tranne nei casi di valori molto elevati dell'entalpia totale.     

Dissociation rate constants for oxygen at temperatures up to 11000 K

Measurements of the absorption and vibrational temperature evolution of molecular oxygen behind the shock wave front in regimes with temperatures near the front varying over the range 4000–11 000 K made it possible to determine the dissociation rate constant for O₂ molecules under both thermal equilibrium and nonequilibrium conditions. The dependence of the dissociation rate constant on the ratio T _v /T, that is, on the deviation from the thermal equilibrium conditions, is demonstrated experimentally. The corresponding expression for the two-temperature dissociation rate constant is proposed.     

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.     

Experimental and numerical studies of rotational relaxation behind a strong shock wave in air

This paper describes the experimental and numerical investigations of unknown characteristics of the rotational nonequilibrium phenomena behind a strong shock wave in air. Experiments were carried out using a piston-driven shock tube with helium as driving gas and air as driven (test) gas, operated as a two-stage shock tube. In the experiments, emission spectra of NO were measured to evaluate the rotational temperature behind a strong shock wave. The numerical calculations use the computational code for the thermal and chemical nonequilibrium flow behind a strong shock wave developed by the present author's group, where 11 chemical species (N, O, NO, N, O, N, O, NO, N, O, e) and 48 chemical reactions of high-temperature air are considered. The thermal nonequilibrium is expressed by introducing an 8 temperature model composed of translational temperature, rotational and vibrational temperatures for N, O, NO, and electron temperature. The coupling of a rotation, vibration and dissociation (CRVD) model was incorporated to take sufficiently into account the rotational nonequilibrium. The calculations were conducted for the same conditions as the experimental ones. From the calculated flow properties, emission spectra were re-constructed using the code for computing spectra of high temperature air “SPRADIAN”. Furthermore, rotational and vibrational temperatures of NO (0,1) were determined from a curve fitting method and compared with the computed results. Received 12 September 2001 / Accepted 18 February 2002     

考虑振动非平衡的可压缩库埃特流动及其传热

新型近空间高超声速飞行器大多具有尖头薄翼的外形,驻点下游机身附近的强剪切流动及气动加热具有显著的非平衡特征.由于加热总量预估和实验测热数据辨识的需要,工程上越来越关注强剪切非平衡流动及气动加热预测问题.本文结合理论建模和直接模拟蒙特卡洛数值模拟,研究了振动非平衡条件下的可压缩库埃特流动的气动力/热问题.首先基于参考温度...     

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.     

Diagnostics of rarefied gases using hot-wire anemometer

Hot-wire anemometry has been quite widely used in recent years to study low-density flows [1–3]. High sensitivity and good spatial resolution of the method make its application effective in flows with large gradients. The technique permits the determination of two thermodynamic quantities, the coefficient of heat transfer h and recovery temperature T_r. Relations coupling h and T_r with flow parameters were obtained in [4]. These relations were generalized in [3] for the case of unequal accommodation of translational and internal energy of molecules on the wire surface and nonequilibrium energy distribution in internal degrees of freedom. In order to obtain a more detailed information on the distribution of gasdynamic parameters, the hot-wire anemometer is, as a rule, used in conjunction with other diagnostic tools like the Pitot tube or electron beam [2]. The present work deals with the application of a twin-wire (perpendicular and parallel to the flow direction) hot-wire anemometer in rarefied flows without the benefit of other techniques. Furthermore, the influence of differences in the accommodation coefficients of translational and internal energies and the degree of rarefaction on the hot-wire anemometer is also investigated.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 126–130, September–October, 1986.In conclusion, the authors acknowledge A. K. Rebrov for useful discussions stimulating development of studies with hot-wire anemometry.     

One-dimensional nonequilibrium air flow

A solution is found for the problem of steady quasi-one-dimensional air flow in a stream tube with nonequilibrium chemical reactions, ionization reactions, and nonequilibrium excitation of the vibrational degrees of freedom in the molecular components. We consider the inverse problem: for a given pressure distribution find the distributions of all the other gas-thermodynamic quantities and the streamtube sections. The use of an implicit scheme for approximating the equations makes it possible to carry out the calculations over the entire range of variation in the degree of nonequilibrium — from the frozen state to equilibrium. We discuss the nature of the variation in temperature, vibrational energies, and component concentrations along the stream tube. A numerical analysis is made of the transition to equilibrium flow.     

On the Reasonability of Taking the Volume Viscosity Coefficient into Account in Gas Dynamic Problems

The flow models are considered in the first (Navier–Stokes) approximation. The effect of the volume viscosity coefficient on the solutions obtained is investigated with reference to the problem of the plane shock wave profile. It is shown that taking the volume viscosity coefficient into account makes it possible to improve the solution for the flows with low dynamic nonequilibrium for which the first-approximation models are justified. It is preferable to use two-temperature flow models under the conditions of high dynamic nonequilibrium.     

Monte Carlo analysis of dissociation and recombination behind strong shock waves in nitrogen

Computations are presented for the relaxation zone behind strong, one-dimensional shock waves in nitrogen. The analysis is performed with the direct simulation Monte Carlo method (DSMC). The DSMC code is vectorized for efficient use on a supercomputer. The code simulates translational, rotational and vibrational energy exchange and dissociative and recombinative chemical reactions. A new model is proposed for the treatment of three body recombination collisions in the DSMC technique which usually simulates binary collision events. The new model represents improvement over previous models in that it can be employed with a large range of chemical rate data, does not introduce into the flow field troublesome pairs of atoms which may recombine upon further collision (pseudo-particles) and is compatible with the vectorized code. The computational results are compared with existing experimental data. It is shown that the derivation of chemical rate coefficients must account for the degree of vibrational nonequilibrium in the flow. A nonequilibrium chemistry model is employed together with equilibrium rate data to compute successfully the flow in several different nitrogen shock waves.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.