可压缩稠密气体各向同性湍流的数值模拟研究

       稠密气体是一种特殊的非理想气体，具有很高的实际应用价值。可压缩各向同性湍流是一种基本的湍流形式，被许多学者们深入研究且相关成果对推动湍流发展有很大的意义。由于稠密气体的特殊热力学性质，在可压缩稠密气体各向同性湍流中出现了许多新的现象，流场性质也与理想气体湍流有较大不同。因此对 可压缩稠密气体各向同性湍流的研究既具有实际意义也有很高的学术价值。本文采用高精度直接数值模拟的方法对可压缩稠密气体各向同性湍流场进行求解。相应湍流场的湍流马赫数为 1.0，泰勒雷诺数为 153.0，流场具有强可压缩的特性。本文采用了一种混合格式来离散控制方程，流场中的激波区域采用七阶 WENO 格式 处理，而光滑区域则采用八阶紧致中心差分格式来处理。同时，气体的热力学性 质采用 Martin­Hou 状态方程来描述。

       本文主要的研究内容包括流场的小尺度结构统计性质以及局部拓扑结构的特征。流场的初始热力学状态位于逆温带中，这个区域的气体动力学基本导数为负值。湍流场在初始条件下开始演化，当达到稳定状态后，流场中存在三种不同的气体区域：Bethe–Zel’dovich–Thompson（BZT）区域，classical dense gas（CDG）区域，以及 usual gas（UG）区域。不同气体区域的流场性质有所不同，在本文中我们通过比较三个气体区域的流动特征来分析稠密气体效应的影响。

       在本文中研究了不同气体区域中的拟涡能生成项的统计特性。基于亥姆霍兹 分解，可以发现不同气体区域中的拟涡能生成项主要来自于它的剪切分量。同时，稠密气体效应会削弱压缩区域中的拟涡能生成并减小膨胀区域的拟涡能损失。另 一方面，将拟涡能生成项在速度梯度张量的三个特征方向上分解后发现，第一特征方向的分量造成拟涡能损失而第三特征方向的分量贡献拟涡能生成。稠密气体效应则会降低所有分量的幅值。进一步地，本文基于速度梯度张量的三个不变量，分析了不同气体区域中局部拓扑结构的特征。在膨胀区域，稠密气体效应会显著减少膨胀的涡结构并削弱这部分结构对拟涡能损失的贡献。

   Dense gas is a special real gas, which has high practical application value. Compressible isotropic turbulence is a basic form of turbulence, which has been deeply studied by many scholars, and the relevant results are of great significance to promote the development of turbulence. Due to the special thermodynamic properties of dense gas, many new phenomena have appeared in the compressible isotropic turbulence of dense gas, and the flow field properties are quite different from those of ideal gas turbulence. Therefore, the study of compressible isotropic turbulence of dense gas has both practical significance and high academic value. In this paper, the compressible isotropic turbulence of dense gas is solved by high-precision direct numerical simulation. The turbulent Mach number in the flow field is 1.0, and the Taylor Reynolds number is 153.0. The flow field has strong compressibility. Moreover, a hybrid scheme is used to discretize the governing equations. The shock region in the flow field is treated by the seventh-order WENO scheme, while the smooth region is treated by the eighth-order compact central difference scheme. At the same time, the thermodynamic properties of the gas are described by Martin-Hou equation of state.

  The main research contents of this study include the statistical properties of small-scale structure and the characteristics of local topology. The initial thermodynamic state of the flow field is located in the inversion zone, where the fundamental derivative of gas dynamics is negative. When the flow field reaches a stationary state, it contains three distinct gas regions: the Bethe-Zel'dovich-Thompson (BZT) region, the classical dense gas (CDG) region, and the usual gas (UG) region. The flow field properties of different gas regions are different. In this paper, we analyze the influence of dense gas effect by comparing the flow characteristics of three gas regions.

  The effects of different gas regions on the statistical properties of the enstrophy production term are investigated in this study. Based on Helmholtz decomposition, it is discovered that the solenoidal component is primarily responsible for enstrophy production. The dense gas effect reduces enstrophy production in the compression region and weakens enstrophy loss in the expansion region. Decomposing the enstrophy generation term in the three characteristic directions of the velocity gradient tensor, on the other hand, reveals that the component in the first characteristic direction causes enstrophy loss, while the component in the third characteristic direction contributes to enstrophy generation. The amplitude of all components will be reduced due to the dense gas effect. Furthermore, the flow topology properties based on the three invariants of the velocity gradient tensor are investigated. The dense gas effect significantly reduces the expansive vortex structure in the expansion region, weakening its contribution to enstrophy loss.

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