基于动态迭代近似反卷积模型的可压缩湍流大涡模拟研究

可压缩湍流的大涡模拟研究对于航空航天等领域的发展非常重要。目前针对
密度不加权大涡模拟的研究相对较少，只有少部分从事相关亚格子（subgrid-scale，SGS）未闭项的建模分析。稠密气体因其特殊的物理性质受到了科研工作者们广泛的关注，针对稠密气体开展大涡模拟的研究具有很高的科研价值和实际意义，但是稠密气体复杂的状态方程会给大涡模拟的建模带来困难。本文使用袁泽龙等人提出的动态迭代近似反卷积模型（dynamic iterative approximate deconvolution，DIAD）开展可压缩各向同性湍流的大涡模拟研究，通过与其他传统亚格子湍流模型的结果进行对比详细评估DIAD 模型的表现和性能。本文的主要的研究内容如下：

（1）分别研究了初始湍流马赫数为0.4 和0.8 两种情况下的可压缩各向同性
衰减湍流密度不加权大涡模拟的亚格子封闭问题。与密度加权大涡模拟相比，使
用密度不加权滤波得到的控制方程中拥有更多的亚格子未封闭项。研究中使用不
同的亚格子模型对未封闭项进行重构，包括梯度模型（gradient model，GM），近似反卷积模型（approximate deconvolution model，ADM），动态Smagorinsky 模型（dynamic Smagorinsky model，DSM），动态混合模型（dynamic mixed model，DMM），以及DIAD 模型。此次研究是在(2𝜋)3 的计算域中使用1283 的均匀网格开展大涡模拟计算。研究中推导出了适合于密度不加权方法的GM、DSM 和DMM 模型的具体公式。此外，本文还首次将DIAD 模型应用到可压缩湍流的研究中。在先验检验中，GM、ADM 和DIAD 模型的相关系数均大于0.9。其中，DIAD 模型的相关系数大于0.98，相对误差小于0.2，优于其他亚格子模型。在密度不加权大涡模拟的后验检验中，DIAD 模型能够很好的预测湍流的各种统计量和流动结构，包括速度的能谱、亚格子通量的概率密度函数以及亚格子热通量、亚格子动能通量和涡量的瞬时空间结构。

（2）开展了初始湍流马赫数为0.4 和0.8 时稠密气体可压缩衰减各向同性湍
流的大涡模拟。DIAD 模型被用来对稠密气体控制方程中的亚格子未封闭项进行研
究，这种模型采用近似反卷积的方法可以方便的对稠密气体中的热力学相关项进
行建模。此次研究在(2𝜋)3 的计算域中使用643 的均匀网格进行大涡模拟的计算。在先验检验中，除亚格子内能通量外，DIAD 模型所重构的其他亚格子项的相关系数均大于0.98，相对误差均小于0.2。DIAD 模型在后验检验中可以很好地预测热力学量相关亚格子项的概率密度函数。此外，研究中还使用DIAD 模型和DSM 模型进行了不对热力学相关亚格子未封闭项进行建模的分析，结果显示热力学相关亚格子未封闭项对湍流场的影响较小。DIAD 模型在预测稠密气体可压缩湍流的各种统计量和结构比DSM 模型更有优势，包括速度和热力学变量的能谱，归一化亚格子动能通量、亚格子应力偏差和应变率张量的概率密度函数以及涡量的瞬时空间结构。

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