PREDICTION OF CROSSFLOW TRANSITION BASED ON DEEP NEURAL NETWORKS
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摘要: 基于深度神经网络DNN构建了从层流流场无量纲速度梯度、流向涡强度等物理量到横流转捩模态下间歇因子间的映射关系, 获得一种新的数据驱动转捩模型. 通过将数据驱动转捩模型与SST k-ω湍流模型耦合, 有效简化了转捩模型输运方程求解, 实现高效、准确的亚音速三维边界层横流转捩流场计算. DNN训练数据来自变雷诺数的NLF(2)-0415无限展长后掠翼计算结果, 并以两种工况进行测试, 数据驱动转捩模型预测精度与γ-Reθ转捩模型近似. 将数据驱动转捩模型用于其他典型横流转捩算例的计算, 以验证其泛化能力. 对于变后掠角的NLF(2)-0415后掠翼, 数据驱动转捩模型与γ-Reθt-CF模型预测的转捩位置几乎一致, 并且能够预测出后掠角从45°增长到65°的过程中, 转捩位置先向前再向后移动的现象; 对于标准椭球体, 使用低分辨率网格进行计算, 数据驱动转捩模型依然能够实现转捩位置预测, 对椭球体表面Cf的计算结果与多个平台的横流转捩模型、实验结果基本一致. 研究表明, 以横流转捩相关物理量作为输入对DNN进行训练, 并将获得的数据驱动转捩模型与SST k-ω湍流模型耦合, 可以实现对横流转捩的有效预测, 且具有较强的泛化能力. 数据驱动转捩模型对网格分辨率要求更低, 在保证计算精度的前提下, 具有较高的计算效率.Abstract: This study based on deep neural networks (DNN), produces a mapping from the physical quantities such as dimensionless velocity gradient and streamwise vorticity of laminar flow field to the intermittency of cross flow transition, and obtains a new data driven transition model. The data driven transition model is coupled with the SST k-ω turbulence model, and the process of solving the transport equations is effectively simplified, which realize efficient and accurate numerical simulation of subsonic 3-D cross flow transition. The computational data of NLF(2)-0415 swept airfoil at different Reynolds numbers is used to train DNN, and two cases are used to test. The prediction accuracy of data driven transition model is similar to that of γ-Reθ transition model. Using the data driven transition model to compute other typical examples of cross flow transition, to verify its generalization ability. For the transition locations of NLF(2)-0415 swept airfoil with different swept angles, the simulation results of data driven transition model have similar accuracy to that of γ-Reθ transition model. Moreover, the phenomenon of transition position moving forward and then backward in the process of sweep Angle increasing from 45° to 65° can be predicted by data driven transition model. For the standard ellipsoid, although using low resolution mesh, the data driven transition model has the ability to compute the transition location, and the computed results of Cf are same to those of other transition models and experiments. The results show that coupling data driven transition model (which is obtained from the physical quantities related to cross flow transition) with SST k-ω transition model can realize the general prediction of cross flow transition. On the premise of ensuring computational accuracy, the data driven transition model requires lower resolution mesh and has higher computing efficiency.
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Key words:
- crossflow transition /
- deep neural works /
- supervised learning /
- intermittency
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图 10 间歇因子预测值与计算值对比
Figure 10. Comparison between predicted value and calculated value of intermittency
图 12 数据驱动转捩模型与γ-Reθ转捩模型Cf计算结果
Figure 12. Cf of data driven transition model and γ-Reθ transition model
表 1 NFL(2)-0415后掠翼计算条件
Table 1. Conditions of NFL(2)-0415 airfoil
Case Re/106 m−1 h/μm AoA
/(o)Λ
/(o)Tu∞ νt/ν 1 1.92 3.3 −4 45 0.1 5 2 2.19 3 2.37 4 2.73 5 3.27 
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表 2 交叉验证结果
Table 2. Result of cross validation
DNN Ltrain/10-4 Ltest/10-4 Ltest average/10-4 1 2.68 4.83 4.31 2 1.99 3.68 3 2.54 4.41 4 2.52 4.87 5 2.37 3.74
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表 3 数据驱动转捩模型与γ-Reθt-CF转捩模型对转捩位置的计算结果对比
Table 3. Comparison of xtr between data driven transition model and γ-Reθt-CF transition model
Λ Data driven
transition modelγ-Reθt-CF
transition model45o 0.416 0.424 55 o 0.391 0.395 65 o 0.408 0.413
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