可压缩瑞利泰勒湍流的流动机理和建模研究

瑞利泰勒湍流是流体力学的一个基本问题，在很多自然现象和工程应用中广泛存在。超新星爆炸和惯性约束核聚变处于大密度比和强可压缩的极端情况，本文重点关注中、高阿德伍德数和强可压缩的瑞利泰勒湍流。本文开展了二维和三维可压缩瑞利泰勒湍流的直接数值模拟，研究了流动压缩性的影响；发展了可压缩瑞利泰勒湍流的大涡模拟模型和快速预测方法。主要工作如下：
    
    （1）  数值模拟了不同分层参数和不同阿德伍德数的二维可压缩瑞利泰勒湍流。模拟发现，在小阿德伍德数的情况下，密度分层抑制气泡厚度的增长，但在大阿德伍德数的情况下，膨胀压缩运动促进气泡厚度的增长。研究表明，膨胀压缩运动随着阿德伍德数和分层参数的增大而增强。混合层内，膨胀运动占主导，这形成一个向上的推力促进气泡发展；而混合层外，压缩运动更强。流动压缩性对能量传输起着关键作用，密度分层抑制势能向动能的转化，而膨胀压缩运动促进内能和动能的转化。
    
    （2）  通过数值模拟研究了流动压缩性对三维瑞利泰勒湍流的混合和能量传输的影响。研究发现，流动压缩性对大尺度动能的产生起着重要作用，小分层参数时，动能主要来源于势能，大分层参数时，其主要来源于内能。内能向动能的转化促进气泡厚度的增长。通过滤波方法研究了动能的尺度间传输，研究发现，无量纲亚格子动能流量的统计值与分层参数基本无关，但流动压缩性对大尺度上的逆向传输有促进作用；压缩运动促进动能的正向传输，而膨胀运动促进动能的逆向传输。
        
    （3）  把常系数空间梯度模型（CSGM）用于可压缩瑞利泰勒湍流的大涡模拟，进一步提高了大涡模拟的预测精度。相邻点的梯度信息被加入到CSGM模型中，以提高模型精度。先验研究表明，CSGM模型比传统的亚格子模型具有更高的精度。后验研究中，CSGM模型准确预测了亚格子项的概率密度函数。作为一种结构模型，CSGM模型可以重构小的气泡和尖钉结构，从而对混合厚度给出了更好的预测。CSGM模型在预测质量分数场、速度和涡量场、温度和压力场的瞬时结构和统计量方面具有优异的性能，特别是对于温度场的预测。
    
    （4）  把傅里叶神经算子（FNO）用于可压缩瑞利泰勒湍流的大涡模拟，不仅提高了预测精度，还明显提升了预测速度。FNO模型在预测各种统计量和瞬时结构方面都优于隐式大涡模拟和传统的亚格子模型，特别是对温度场的预测，远好于传统大涡模拟方法。使用短时间、低雷诺数的数据训练的FNO模型，在后验测试中表现出了优良的长时间预测的泛化性能以及一定程度的高雷诺数的泛化能力。

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