This paper presents a novel CFD-driven machine learning framework to develop Reynolds-averaged Navier-Stokes (RANS) models. The CFD-driven training is an extension of the gene expression programming method Weatheritt and Sandberg (2016) [8], but crucially the fitness of candidate models is now evaluated by running RANS calculations in an integrated way, rather than using an algebraic function. Unlike other data-driven methods that fit the Reynolds stresses of trained models to high-fidelity data, the cost function for the CFD-driven training can be defined based on any flow feature from the CFD results. This extends the applicability of the method especially when the training data is limited. Furthermore, the resulting model, which is the one providing the most accurate CFD results at the end of the training, inherently shows good performance in RANS calculations. To demonstrate the potential of this new method, the CFD-driven machine learning approach is applied to model development for wake mixing in turbomachines. A new model is trained based on a high-pressure turbine case and then tested for three additional cases, all representative of modern turbine nozzles. Despite the geometric configurations and operating conditions being different among the cases, the predicted wake mixing profiles are significantly improved in all of these a posteriori tests. Moreover, the model equation is explicitly given and available for analysis, thus it could be deduced that the enhanced wake prediction is predominantly due to the extra diffusion introduced by the CFD-driven model.

本文提出了一种新颖的CFD驱动的机器学习框架，用于开发雷诺平均Navier-Stokes（RANS）模型。CFD驱动的训练是基因表达编程方法Weatheritt and Sandberg（2016）的扩展[8]，但至关重要的是，现在通过集成方式运行RANS计算而不是使用代数函数来评估候选模型的适用性。与将训练后的模型的雷诺应力适合高保真度数据的其他数据驱动方法不同，可以基于CFD结果中的任何流量特征来定义CFD驱动的训练的成本函数。这扩展了该方法的适用性，尤其是在训练数据有限的情况下。此外，结果模型是在训练结束时提供最准确的CFD结果的模型，本质上在RANS计算中显示出良好的性能。为了证明这种新方法的潜力，将CFD驱动的机器学习方法应用于涡轮机尾流混合的模型开发。在高压涡轮机壳体的基础上训练了一个新模型，然后对另外三种情况进行了测试，所有这些均代表了现代涡轮机喷嘴。尽管两种情况下的几何构造和运行条件不同，但在所有这些情况下，预计的尾流混合曲线均得到了显着改善后验测试。此外，模型方程式被明确给出并可供分析，因此可以推断出增强的尾流预测主要归因于CFD驱动模型引入的额外扩散。