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首页> 外文期刊>Journal of Computational Physics >On derivation and verification of a kinetic model for quantum vibrational energy of polyatomic gases in the gas-kinetic unified algorithm
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On derivation and verification of a kinetic model for quantum vibrational energy of polyatomic gases in the gas-kinetic unified algorithm

机译：气体动力学统一算法中多样性气体量子振动能量衍生和验证

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摘要

In this paper, a kinetic Boltzmann model equation involving internal degrees of freedom is constructed for thermodynamic non-equilibrium polyatomic gases, in which the continuous distribution mode of rotational energy and discrete quantum effect of the vibrational energy are both considered, respectively. By theoretically analyzing the "recurrence feature" of this model, it is found that the root of the quantum effect comes from the translational rotational-vibrational relaxation term (G(3)(t,r,v)), because of the additional term relative to the continuous distribution mode of vibrational energy. Besides, some important properties of this model are also analyzed and proved, including the conservative property and entropy inequality. Then, the balance equations on each vibrational energy level and balance equations about macroscopic variables are derived by the moment method. The corresponding thermodynamic relationship in the hydrodynamic limit is also analyzed by the simplified version of Chapman-Enskog method, and the correct Prandtl number is obtained. Numerical methods and wall surface boundary condition to solve this model equation are presented here. Finally, planar flows past a cylinder with different Mach numbers are numerically simulated to test and verify the reliability of this model, and to analyze the influence rules of the excited quantum vibrational energy for polyatomic gas flows. (c) 2020 Published by Elsevier Inc.
机译：本文建立了热力学非平衡多原子气体的含内自由度的动力学玻尔兹曼模型方程，其中分别考虑了转动能的连续分布模式和振动能的离散量子效应。通过对该模型的“重现性”进行理论分析，发现量子效应的根源来自于平移-旋转振动弛豫项（G（3）（t，r，v）），因为与振动能量的连续分布模式相关的附加项。此外，还分析和证明了该模型的一些重要性质，包括保守性和熵不等式。然后，用矩量法导出了各振动能级上的平衡方程和宏观变量的平衡方程。用简化的Chapman-Enskog方法分析了水动力极限下相应的热力学关系，得到了正确的普朗特数。本文给出了求解该模型方程的数值方法和壁面边界条件。最后，对不同马赫数的圆柱绕流进行了数值模拟，验证了该模型的可靠性，并分析了激发量子振动能对多原子气体流动的影响规律。（c） 2020年由爱思唯尔公司出版。

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