Department of Mathematics and Mechanics, Saint Petersburg State University, 198504 Universitetskiy prospekt, 28, Saint Petersburg, Russia.
Phys Rev E. 2016 Mar;93(3):033127. doi: 10.1103/PhysRevE.93.033127. Epub 2016 Mar 28.
We study coupling of vibrational relaxation and chemical reactions in nonequilibrium viscous multitemperature flows. A general theoretical model is proposed on the basis of the Chapman-Enskog method modified for strongly nonequilibrium reacting flows; the model differs from models commonly used in computational fluid dynamics since it is able to capture additional cross-coupling terms arising in viscous flow due to compressibility and mutual influence of all nonequilibrium processes occurring in a mixture. The set of fluid dynamic equations is derived starting from the Boltzmann equation; the relaxation terms in these equations are described using the kinetic transport theory formalism. Reaction and relaxation rates depend on the distribution function and thus differ in the zero-order and first-order approximations of the Chapman-Enskog method. An algorithm for the calculation of multitemperature reaction and relaxation rates in both inviscid and viscous flows is proposed for the harmonic oscillator model. This algorithm is applied to estimate the mutual effect of vibrational relaxation and dissociation in binary mixtures of N(2) and N, and O(2) and O, under various nonequilibrium conditions. It is shown that modification of the Landau-Teller expression for the VT relaxation term works rather well in nitrogen, whereas it fails to predict correctly the relaxation rate in oxygen at high temperatures. In oxygen (in contrast to nitrogen), the first-order cross effects of dissociation and VT relaxation are found to be significant. A method for calculation of vibrational relaxation time based on the kinetic theory definition is suggested. Two-temperature dissociation rate coefficients are calculated in the zero- and first-order approximations and compared to other models.
我们研究了非平衡粘性多温度流中振动弛豫和化学反应的耦合。基于Chapman-Enskog 方法进行了修正，以适应强非平衡反应流动，提出了一个通用的理论模型；该模型与计算流体动力学中常用的模型不同，因为它能够捕捉由于压缩性和混合物中发生的所有非平衡过程的相互影响而在粘性流中产生的附加交叉耦合项。从玻尔兹曼方程出发推导出流体动力学方程组；这些方程中的弛豫项使用动力学输运理论形式来描述。反应和弛豫速率取决于分布函数，因此在Chapman-Enskog 方法的零阶和一阶近似中有所不同。针对谐振子模型，提出了用于计算无粘和粘性流中多温度反应和弛豫速率的算法。该算法用于估计在各种非平衡条件下 N(2)和 N、O(2)和 O 二元混合物中振动弛豫和离解的相互影响。结果表明，对于氮，Landau-Teller 表达式对 VT 弛豫项的修正效果相当好，而在高温下无法正确预测氧的弛豫速率。在氧中（与氮相反），发现离解和 VT 弛豫的一阶交叉效应非常显著。提出了一种基于动力学理论定义的振动弛豫时间计算方法。在零阶和一阶近似中计算了两温度离解速率系数，并与其他模型进行了比较。
