分子气体稀薄效应的动理学建模  

Kinetic modeling of rarefied molecular gas dynamics

作　　者：曾嘉楠 李琪 吴雷 ZENG Jianan;LI Qi;WU Lei(Department of Mechanics and Aerospace Engineering,Southern University of Science and Technology,Shenzhen 518055,China)

机构地区：[1]南方科技大学力学与航空航天工程系,深圳518055

出　　处：《空气动力学学报》2022年第2期1-30,I0001,共31页Acta Aerodynamica Sinica

基　　金：国家自然科学基金(12172162)。

摘　　要：稀薄气体效应,是指气体在特征尺度与其分子平均自由程相当的系统中流动时出现的非平衡效应。相比于单原子气体,分子气体(每个气体分子包含两个及以上原子)流动因同时具有转动、振动等多种自由度的非平衡过程,其稀薄效应更为复杂。分子气体稀薄效应在航空航天、微机电系统和页岩气开采等民生、科技领域广泛存在,而描述该效应的动理学模型与数值模拟方法尚不成熟。本文从单原子气体与玻尔兹曼方程出发,介绍气体动理学建模的相关研究现状,针对分子气体特性详细讨论气体弛豫过程与输运系数的关系。针对典型的稀薄气体流动验证常用的模型方程的精度,并指出直接模拟蒙特卡罗方法在分子气体稀薄流动应用中存在的问题,即在体积黏性确定的情况下无法指定热流弛豫速率及恢复热导率。随后针对此问题,使用吴模型量化研究该弛豫速率在分子气体稀薄流动模拟中导致的宏观量的不确定性,并讨论从分子动力学模拟和瑞利-布里渊散射实验中减小甚至消除不确定性的方法。本文对涉及化学反应的稀薄气体流动建模有指导意义。The rarefaction effects arise when the mean free path of gas molecules is comparable to the characteristic flow length. Compared to monatomic gas, the dynamics of rarefied molecular gas, which consists of two or more atoms in one gas molecule, is more complicated, due to the additional non-equilibrium effects in the rotational and vibrational motions. As the major constituent in the atmosphere of Earth and Mars, rarefied molecular gas dynamics has strong applications in aerospace science, micro-electro-mechanical system, shale gas extraction, and so on. However, the corresponding models and simulation methods are not sophisticated. Starting from the monatomic gas and the Boltzmann equation, we review the development of the kinetic modeling of rarefied gas and the essential connection between the transport coefficients and relaxation processes. Then, we focus on the relaxation process and transport coefficients of molecular gas, and introduce typical kinetic models with the systematic assessment of their accuracy. Meanwhile, we discuss the defect of direct simulation Monte Carlo method in the modeling of rarefied molecular gas, i.e., it cannot specify the thermal relaxation rates (hence cannot recover the thermal conductivities) when the bulk viscosity is determined. Finally, we use the Wu model to quantify the uncertainties, and discuss how to reduce or even eliminate the uncertainties based on the data from the molecular dynamics simulation and Rayleigh-Brillouin scattering experiment. This present article is instructive for the modeling of rarefied gas flows involving chemical reactions.

关 键 词：稀薄气体动力学 玻尔兹曼方程 弛豫过程 平动/内部热导率 Eucken因子 

分 类 号：O356[理学—流体力学] V211.25[理学—力学]