-
结合机器学习的湍流模型是流体力学领域的研究热点之一. 现有方法主要将实验/数值的数据用于重构或修正湍流涡黏性和雷诺应力, 鲜有针对转捩问题的研究. 本文利用深度残差网络(ResNet)重构了间歇因子与流场平均量间的映射函数, 并与Spallart-Allmaras (SA)模型耦合, 发展了一种类代数转捩模型. 结合高精度加权紧致非线性格式(WCNS-E6E5)在转捩平板和S809翼型算例中进行了验证, 并与四方程的SST- γ-Reθ转捩模型进行了对比, 结果表明: 纯数据驱动的ResNet模型能够准确预测间歇场, 很大程度上改善了SA模型对自然转捩流动的模拟能力; 训练数据仅基于两个零压力梯度转捩平板, 模型能够应用于S809翼型不同迎角的情况, 预测的升阻力特性和摩擦系数分布接近SST- γ-Reθ转捩模型的结果; 在此基础上, 相较SST- γ-Reθ模型节省了超过30%的计算成本. 本研究显示了机器学习方法在转捩模型构建中的强大潜力.Turbulence model combined with machine learning is one of the research hotspots in fluid mechanics. The existing approaches reconstruct or modify the turbulence eddy viscosity or Reynolds stress based on the experimental/numerical data. In this paper, we reconstruct the mapping function between intermittency and the mean flow variables by deep neural network (ResNet), developing an quasi-algebraic transition model coupled with the Spallart-Allmaras (SA) model. We mainly concentrate on the natural transition flows and take the results calculated by the computational fluid dynamics solver with the SST- γ-Reθmodel as the training data. Seventeen local mean flow quantities satisfying the Galilean invariants are selected as the input features. Five-time cross validation is performed to avoid overfitting. Combining with the high-precision weighted compact nonlinear format, S&K, T3a- transition plate and S809 airfoil are used to test the performance of the model. The results are compared with those from the SST- γ-Reθtransition model, showing that the pure data-driven ResNet model can predict the intermittent field accurately, which greatly improves the ability of SA model to simulate the natural transition flow. For the example of S&K and T3a- transition plate, the comparison of wall friction shows that the SA-ResNet model is in good agreement with the experimental result, but the BC model, which is also an algebraic model, predicts the transition position of the T3a- transition plate model prematurely. The training data do not contain any numerical solution about airfoil, but the model can still be applied to the case of S809 airfoil with different attack angles. The predicted results of lift resistance characteristics, frictional coefficient distribution and transition position are close to the results from the SST- γ-Reθtransition model. On this basis, another advantage of the model is the solution efficiency. The efficiency is improved more significantly in the case with larger mesh quantity. With the same convergence accuracy, the CPU time required by the SA-ResNet model for the S&K plate case is 85.6% that of the SST- γ-Reθtransition model, while the CPU time required by the S809 airfoil with a larger mesh volume is only 67.2% that of the later model. This study demonstrates the great potential of machine learning in the construction of transition models.
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] -
Feature Sign Feature Sign Density $\rho $ Scalar function 3[19] ${\rm Tr}({ {{S} }^3})$ Nearest wall distance ${d_w}$ Scalar function 4[19] ${\rm Tr}({ {{\varOmega } }^2}{{S} })$ Turbulence intensity Tu Scalar function 5[19] ${\rm Tr}({ {{\varOmega } }^2}{ {{S} }^2})$ Kinematic viscosity $\nu $ Normalized strain rate ${{\left\| {{S}} \right\|} / {\left( {\left\| {{S}} \right\|{\rm{ + }}\left\| {{\varOmega }} \right\|} \right)}}$ Eddy viscosity ${\nu _t}$ Vortex Reynolds number (strain rate) ${{\rho d_w^2 S} / \mu }$ Reciprocal of local velocity $1/U$ Vortex Reynolds number (vorticity) ${{\rho d_w^2\Omega } / \mu }$ Scalar function 1[19] ${\rm Tr}({ {{S} }^2})$ Q criterion[34] $\dfrac{ {\dfrac{1}{2}\left( { { {\left\| {{\varOmega } } \right\|}^2} - { {\left\| {{S} } \right\|}^2} } \right)} }{ {\dfrac{1}{2}\left( { { {\left\| {{\varOmega } } \right\|}^2} - { {\left\| {{S} } \right\|}^2} } \right) + { {\left\| {{S} } \right\|}^2} } }$ Scalar function 2[19] ${\rm Tr}({ {{\varOmega } }^2})$ Ratio of modified viscosity to
kinematic viscosity (χ)${{\widetilde \nu } / \nu }$ Dimensionless quantity similar to
turbulent viscosity${{{\nu _t}} / {\left( {U{d_w}} \right)}}$ 
下载:
导出CSV
Fold Training error Validation error 1 0.011719 0.013654 2 0.012549 0.010681 3 0.015313 0.018738 4 0.012985 0.015888 5 0.015822 0.014451 下载:
导出CSV
ComputingTime SA SA-ResNet SST-γ-Reθ S&K 1.0 1.11 1.30 T3A- 1.0 1.33 1.49 S809 (α= 3°) 1.0 1.20 1.78 下载:
导出CSV
-
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40]
下载:
计量
- 文章访问数:6162
- PDF下载量:114
- 被引次数:0