The combination of turbulence big data with artificial intelligence is an active research topic for turbulence study. This work constructs black-box algebraic models to substitute the traditional turbulence model by the artificial neural networks (ANN), rather than correcting the existing turbulence models in most of current studies. We mainly focused on flows past airfoils at high Reynolds (Re) numbers. Our previous work has developed a turbulence model for flows at different Mach (Ma) number and angles of attack (AOA) with fixed Re number and achieved satisfying results. Nevertheless, for turbulence with variable Re numbers, the generalization ability of the model can not be enhanced effectively by simply increasing the train data. To model the nonlinearity of various turbulent effects at high Re number, prior knowledge about scaling analysis is integrated into the model design and deep neural networks (DNN) is adopted as the framework. Considering the different scaling characteristics, the flow field is divided into different regions and two individual ANN models are built separately. Besides, the combination of regularization, limiters, and stability training is adopted to enhance the robustness of the proposed model. The results of Spallart-Allmaras (SA) model are used as the datasets and reference to the modeling evaluation. The proposed model is trained by six flows around NACA0012 airfoil and applicative to different free stream conditions and airfoils. It is found that the results calculated by the proposed model, such as eddy viscosity, velocity profile, drag coefficient and so on, agree well with reference data, which validate the generalization ability of the model. This work shows the prospect of turbulence modeling by machine learning methods.

湍流大数据与人工智能的结合是湍流研究的活跃研究主题。这项工作构建了黑盒代数模型，以通过人工神经网络（ANN）代替传统的湍流模型，而不是校正当前大多数研究中的现有湍流模型。我们主要关注雷诺数（Re）高的翼型流动。我们之前的工作已经开发出了一个湍流模型，用于在不同的马赫数（Ma）和固定Re数的迎角（AOA）下流动，并取得了令人满意的结果。然而，对于具有可变Re数的湍流，仅通过增加火车数据不能有效地增强模型的泛化能力。为了模拟高Re数下各种湍流效应的非线性，将有关缩放分析的先验知识集成到模型设计中，并采用深度神经网络（DNN）作为框架。考虑到不同的缩放特性，将流场划分为不同的区域，并分别构建两个单独的ANN模型。此外，将正则化，限制器和稳定性训练相结合以增强所提出模型的鲁棒性。Spallart-Allmaras（SA）模型的结果用作数据集，并为建模评估提供参考。拟议的模型由围绕NACA0012机翼的六股流训练，适用于不同的自由流条件和机翼。结果表明，该模型计算得到的结果，如涡流粘度，速度分布，阻力系数等，与参考数据吻合良好，验证了模型的泛化能力。这项工作显示了通过机器学习方法进行湍流建模的前景。