基于DUGKS-LES的槽道湍流大涡模拟研究

随着计算机技术和计算方法的快速发展，大涡数值模拟逐渐成为一种研究湍流流动的重要工具，然而在科学研究与工程应用中，基于介观方法的大涡模拟研究相对较少。本文首先通过离散统一气体动理学方法（Discrete unified gas kinetic scheme，简称DUGKS）对槽道湍流展开直接数值模拟，验证了DUGKS的高数值稳定性、非均匀网格实施的便捷性。然后，在并行的DUGKS框架下耦合了两类（壁面模型和壁面自适应模型）大涡模拟方法，并对不同雷诺数下的槽道湍流进行了大涡模拟。从湍流统计特征的角度讨论不同雷诺数下的槽道湍流的流动特性，同时在与相关学者的已有成果对比之后对不同大涡模拟模型在DUGKS框架下的效果展开分析。全文研究的主要内容和结论如下：
（1）为了进一步检验DUGKS方法并为大涡模拟方法提供对照数据，本文首先利用DUGKS对180及395雷诺数的槽道湍流展开了直接数值模拟。结果表明，DUGKS具备较好的数值稳定性，且可以利用非均匀、非各向同性特征突出的网格进行湍流模拟，在较低的网格分辨率下得到准确的数值结果。在流向流域相对槽道宽度较大的工况下，即使使用长宽比大于20的设置，仍然数值稳定。但高雷诺数槽道湍流算例的计算量更大，往往需要较长时间才能进入充分发展阶段，借助低雷诺数下的计算结果建立初始场，可有效减少这一过程所需的时间；
（2）本文通过耦合标准离壁Smagorinsky亚格子模型和Musker壁面模型，实现了第一类DUGKS-LES介观大涡模拟算法。推导了在DUGKS框架下实现大涡模拟有效总应力和修正分布函数非平衡态的关系式；在通过壁面函数逆求解壁面剪切应力时，设计了可以保证收敛性的快速牛顿迭代法，同时利用逆问题的近似解进一步提高了迭代效率。结果表明，算法在不同雷诺数下的槽道湍流算例中均表现良好，流向速度、雷诺应力、脉动速度等湍流统计量的平均相对误差均可以保持在12%以内，与相关文献的结果进行比较时DUGKS-LES方法在准确性上具备明显的优势；
（3）本文利用非均匀网格下的差分格式，在DUGKS中耦合了WALE和Vreman两种壁面自适应亚格子模型，从而实现了第二类DUGKS-LES介观大涡模拟算法。通过与标准Smagorinsky模型结果的比较，验证了这两个模型在近壁区域对涡粘系数有一定的自适应调整特性，且由于不受Musker函数的限制，对数律区域的流向速度模拟效果优于耦合了Musker壁面函数的LES算法。与相关文献相比，本文将算例设置拓展到了更高的湍流雷诺数，结果显示，即使使用较低的网格分辨率仍可以实现较为精确的湍流大涡模拟。 对于雷诺应力和湍流速度脉动，WALE与Vreman模型可以将标准Smagorinsky模型的误差减少50%。
本文的研究为使用DUGKS方法进行湍流大涡模拟提供了多种技术手段；通过对槽道湍流统计特征的分析，总结了常用的大涡模拟模型的性能差异；通过对比不同湍流雷诺数下流场的湍流统计量，增进了对不同雷诺数下槽道湍流物理性质的认识，对于探索复杂流动物理具有一定的科学意义和应用价值。

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