Traditional turbulence models encounter limitations when simulating intricate flows within transonic axial compressors. In contrast, recent advancements in machine learning turbulence models have demonstrated enhanced potential in refining the precision of turbulence modeling. Notably, the tensor basis neural network (TBNN) methodology has successfully developed non-linear eddy viscosity turbulence models. These models possess the capability to capture the anisotropic characteristic of Reynolds stress. However, applying machine learning non-linear eddy viscosity models to aircraft turbomachinery remains relatively infrequent. Current research mainly focuses on linear eddy viscosity turbulence models based on the Boussinesq hypothesis that presupposes isotropy in Reynolds stress. In this work, we introduce a non-linear eddy viscosity turbulence model, denoted as the --SST-TBNN model based on the TBNN framework. This model has been employed to simulate the transonic axial compressor NASA Rotor 37. The TBNN is trained using large eddy simulation (LES) results datasets. The importance of input scalar features is analyzed using the random forest method, from which significant and low-degree variables are selected as inputs for the TBNN. Furthermore, this study proposes including the turbulent Mach number as one of the extra features, representing fluid compressibility, thereby extending the computational mass flow rate range of compressor. Additionally, this paper proposes a method involving the weighted average of Reynolds stress, combining the high-precision but less robust TBNN predictions with results based on the Boussinesq assumption to enhance the turbulence model's robustness. The trained --SST-TBNN model undergoes validation on Rotor 37, where it exhibits a marked improvement in the prediction of overall performance, tip-gap vortex, and radial distribution of flow parameters. The model also displays a commendable capacity for generalization.

中文翻译：

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基于张量神经网络的跨音速轴向压气机流动湍流模型

传统的湍流模型在模拟跨音速轴流压缩机内的复杂流动时遇到限制。相比之下，机器学习湍流模型的最新进展已证明在提高湍流建模精度方面具有更大的潜力。值得注意的是，张量基神经网络（TBNN）方法已成功开发了非线性涡粘性湍流模型。这些模型能够捕捉雷诺应力的各向异性特征。然而，将机器学习非线性涡粘模型应用于飞机涡轮机械仍然相对较少。目前的研究主要集中在基于布辛涅斯克假设的线性涡粘性湍流模型，该假设假设雷诺应力具有各向同性。在这项工作中，我们引入了一种非线性涡粘性湍流模型，表示为基于 TBNN 框架的--SST-TBNN 模型。该模型已用于模拟跨音速轴流压缩机 NASA Rotor 37。TBNN 使用大涡模拟 (LES) 结果数据集进行训练。使用随机森林方法分析输入标量特征的重要性，从中选择显着和低度变量作为 TBNN 的输入。此外，本研究建议将湍流马赫数作为额外特征之一，代表流体的可压缩性，从而扩展压缩机的计算质量流量范围。此外，本文提出了一种涉及雷诺应力加权平均的方法，将高精度但鲁棒性较差的TBNN预测与基于Boussinesq假设的结果相结合，以增强湍流模型的鲁棒性。经过训练的 --SST-TBNN 模型在 Rotor 37 上进行了验证，在整体性能、叶尖间隙涡流和流动参数的径向分布的预测方面表现出显着的改进。该模型还显示出值得称赞的泛化能力。