Research and application of SST turbulence surrogate model based on neural network
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摘要:
针对传统湍流模型参数众多且获取复杂流动数据慢的问题，研究多种神经网络算法用于求解超声速流动中雷诺平均（Navier-Stokes）求解器的湍流代理模型。以超声速流动条件下的凹槽为例，应用拉丁超立方抽样方法，获取标准SST湍流模型的9个参数样本空间；采用自主研发的高超声速内外流耦合数值模拟软件AHL3D，在来流马赫数为2.92下开展数值模拟，获得壁面压力数据，构建数据集；搭建了深度神经网络（deep neural networks, DNN）、残差神经网络（residual neural network, ResNet）、长短时记忆网络（long short-term memory, LSTM）等多种模型对数据集进行训练，从而形成SST湍流代理模型。实验结果表明：在给定SST湍流模型系数下，3种神经网络代理模型均能高精度地预测壁面压力，可决系数达到了0.99以上，与数值模拟求解器结果基本一致，可用于快速获取不同湍流模型参数下的壁面压力。
Abstract:In view of the problem that traditional turbulence model has many parameters and is slow to obtain complex flow data, various kinds of neural network algorithms were studied to construct the turbulence surrogate model of the Navier-Stokes solver in supersonic flow. The cavity under supersonic flow conditions was taken as the research object, and the Latin hypercube sampling method was used to obtain the sample space of nine parameters of the standard SST turbulence model. The independently developed hypersonic internal and external flow coupling numerical simulation software AHL3D was used to carry out numerical simulation at the incoming flow Mach number of 2.92 Ma to obtain the wall pressure data, and then the dataset was constructed. Various kinds of models such as deep neural networks (DNN), residual neural network (ResNet), and long short-term memory (LSTM), which were trained by the training dataset, were used to build the SST turbulence surrogate model. The experimental results showed that: under certain SST turbulence model parameters, these three neural network surrogate models can predict the wall pressure with high accuracy, and the coefficient of determination was above 0.99, which was basically consistent with the results of the numerical simulation solver, and can be used to quickly obtain the wall pressure under different turbulence model parameters.
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Key words:
- cavity /
- SST turbulence surrogate model /
- neural networks /
- turbulence surrogate model /
- wall pressure
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图 5 壁面压力计算结果与实验结果对比
Figure 5. Comparison between the calculated results and the experimental results for wall pressure
图 6 摩阻系数计算结果与实验结果对比
Figure 6. Comparison between the calculated results and the experimental results for frictional coefficient
图 7 流场速度剖面计算结果与实验结果的对比
Figure 7. Comparison between the calculated results and the experimental results for velocity profile of flow field
图 11 模型系数的对壁面压力的影响大小
Figure 11. Influence of turbulence model parameters on wall pressure
图 17 在M1下的基于DNN的壁面压力曲线预测结果
Figure 17. Prediction results of wall pressure curve based on DNN under M1
图 18 在M1下的基于ResNet的壁面压力曲线预测结果
Figure 18. Prediction results of wall pressure curve based on ResNet under M1
图 20 在M2下的基于DNN的壁面压力曲线预测结果
Figure 20. Prediction results of wall pressure curve based on DNN under M2
图 21 在M2下的基于ResNet的壁面压力曲线预测结果
Figure 21. Prediction results of wall pressure curve based on ResNet under M2
图 22 在M2下的基于LSTM的壁面压力曲线预测结果
Figure 22. Prediction results of wall pressure curve based on LSTM under M2
图 24 在M3下的基于DNN的壁面压力曲线预测结果
Figure 24. Prediction results of wall pressure curve based on DNN under M3
图 25 在M3下的基于ResNet的壁面压力曲线预测结果
Figure 25. Prediction results of wall pressure curve based on ResNet under M3
图 26 在M3下的基于LSTM的壁面压力曲线预测结果
Figure 26. Prediction results of wall pressure curve based on LSTM under M3
表 1 SST湍流模型系数及区间
Table 1. SST turbulence model parameters and intervals
系数 标称值 最小值 最大值 $ {\sigma _{{\text{k1}}}} $ 0.85 0.7 1.0 $ {\sigma _{{\text{k2}}}} $ 1.0 0.8 1.2 $ {\sigma _{{\text{w1}}}} $ 0.5 0.3 0.7 $ {\sigma _{{\text{w2}}}} $ 0.856 0.7 1.0 $ {\beta ^*}/{\beta _1} $ 1.20 1.19 1.31 $ {\beta ^*}/{\beta _2} $ 1.0870 1.05 1.45 $ \,{\beta ^*} $ 0.09 0.0776 0.1016 $ \kappa $ 0.41 0.38 0.42 $ {a_1} $ 0.31 0.31 0.40 
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