Qiu Ruofan, Yang Xinyuan, Bao Yue, You Yancheng, Jin Hua
School of Aerospace Engineering, Xiamen University, Xiamen 361005, China.
Entropy (Basel). 2024 Feb 26;26(3):200. doi: 10.3390/e26030200.
A shock wave is a flow phenomenon that needs to be considered in the development of high-speed aircraft and engines. The traditional computational fluid dynamics (CFD) method describes it from the perspective of macroscopic variables, such as the Mach number, pressure, density, and temperature. The thickness of the shock wave is close to the level of the molecular free path, and molecular motion has a strong influence on the shock wave. According to the analysis of the Chapman-Enskog approach, the nonequilibrium effect is the source term that causes the fluid system to deviate from the equilibrium state. The nonequilibrium effect can be used to obtain a description of the physical characteristics of shock waves that are different from the macroscopic variables. The basic idea of the nonequilibrium effect approach is to obtain the nonequilibrium moment of the molecular velocity distribution function by solving the Boltzmann-Bhatnagar-Gross-Krook (Boltzmann BGK) equations or multiple relaxation times Boltzmann (MRT-Boltzmann) equations and to explore the nonequilibrium effect near the shock wave from the molecular motion level. This article introduces the theory and understanding of the nonequilibrium effect approach and reviews the research progress of nonequilibrium behavior in shock-related flow phenomena. The role of nonequilibrium moments played on the macroscopic governing equations of fluids is discussed, the physical meaning of nonequilibrium moments is given from the perspective of molecular motion, and the relationship between nonequilibrium moments and equilibrium moments is analyzed. Studies on the nonequilibrium effects of shock problems, such as the Riemann problem, shock reflection, shock wave/boundary layer interaction, and detonation wave, are introduced. It reveals the nonequilibrium behavior of the shock wave from the mesoscopic level, which is different from the traditional macro perspective and shows the application potential of the mesoscopic kinetic approach of the nonequilibrium effect in the shock problem.
激波是高速飞行器和发动机发展过程中需要考虑的一种流动现象。传统的计算流体动力学（CFD）方法从宏观变量的角度来描述它，比如马赫数、压力、密度和温度。激波的厚度接近分子自由程的水平，分子运动对激波有很强的影响。根据查普曼 - 恩斯科格方法的分析，非平衡效应是导致流体系统偏离平衡态的源项。非平衡效应可用于获得与宏观变量不同的激波物理特性描述。非平衡效应方法的基本思想是通过求解玻尔兹曼 - 巴特纳格尔 - 格罗斯 - 克鲁克（Boltzmann BGK）方程或多松弛时间玻尔兹曼（MRT - Boltzmann）方程来获得分子速度分布函数的非平衡矩，并从分子运动层面探索激波附近的非平衡效应。本文介绍了非平衡效应方法的理论和理解，并综述了激波相关流动现象中非平衡行为的研究进展。讨论了非平衡矩在流体宏观控制方程中所起的作用，从分子运动的角度给出了非平衡矩的物理意义，并分析了非平衡矩与平衡矩之间的关系。介绍了对激波问题如黎曼问题、激波反射、激波/边界层相互作用和爆轰波等的非平衡效应研究。它从细观层面揭示了激波的非平衡行为，这与传统的宏观视角不同，并展示了非平衡效应的细观动力学方法在激波问题中的应用潜力。
