A Conservative Numerical Method for Solving the Generalized Boltzmann Equation for an Inert Mixture of Diatomic Gases
A Conservative Numerical Method for Solving the Generalized Boltzmann Equation for an Inert Mixture of Diatomic Gases
复制标题
求解双原子气体惰性混合物广义玻尔兹曼方程的保守数值方法
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
R. Agarwal
中科院分区：
文献类型：
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作者：
Felix G. TCheremisine;R. Agarwal
本文介绍了在过渡流和稀薄流区，用广义Boltzmann方程（GBE）计算非反应双原子气体（如氮和氧）混合物中高超声速非平衡激波（SW）流的计算方法。在GBE中，内部和平移的自由度被认为是在量子和经典力学的框架分别。可用于标准玻尔兹曼方程的计算框架（对于具有平移自由度的单原子气体）通过包括GBE中的旋转和振动自由度来扩展。GBE的解需要对双原子气体分子的跃迁几率、弹性和非弹性截面等进行建模，这是求解碰撞积分所需要的。整个问题，包括振动-平移（VT）和旋转-平移（RT）的能量转移是通过应用一个三阶段分裂程序的GBE解决。这三个阶段包括自由分子运输、VT弛豫和RT弛豫。为了计算混合气体中的激波结构，需要在冲量空间而不是标准速度空间中建立GBE。此外，到目前为止，中性气体混合物中SW的计算仅针对一维问题进行，并且它们假设解在速度空间中具有圆柱对称性。在本文中，我们描述了适用于二维和三维流动的多组分中性混合物的一般数值方法的发展。开发了一个三维程序，并应用于计算中性二元混合物中的SW。
This paper describes the computational methodology for computing hypersonic nonequilibrium shock wave (SW) flows in a mixture of non reacting diatomic gases such as Nitrogen and Oxygen using the Generalized Boltzmann Equation (GBE) at Knudsen numbers in transitional and rarefied flow regimes. In the GBE, the internal and translational degrees of freedom are considered in the framework of quantum and classical mechanics respectively. The computational framework available for the standard Boltzmann equation (for a monoatomic gas with translational degrees of freedom) is extended by including both the rotational and vibrational degrees of freedom in the GBE. The solution of GBE requires modeling of transition probabilities, elastic and inelastic cross-sections etc. of a diatomic gas molecule, needed for the solution of the collision integral. The whole problem that includes both the vibrational - translational (VT) and rotational - translational (RT) energy transfers is solved by applying a three-stage splitting procedure to the GBE. The three stages consist of free molecular transport, VT relaxation, and RT relaxation. For computation of shock structure in a mixture of gases, the GBE needs to be formulated in impulse space instead of the standard velocity space. Furthermore, till now, the computations of SW in neutral gas mixtures have been performed only for 1D problem and they assume cylindrical symmetry of the solution in the velocity space. In this paper, we describe the development of a general numerical method for multicomponent neutral mixtures applicable to 2D and 3D flows. A 3D code has been developed and applied to compute the SW in neutral binary mixture.