Abstract Turbulence modelling in turbomachinery flows remains a challenge, especially when transition and separation phenomena occur. Recently, several research efforts have been devoted to the improvement of closure models for Reynolds-averaged Navier-Stokes (RANS) equations by means of machine learning approaches which make it possible to extract the knowledge hidden inside the available high-fidelity data (from experiments or from scale-resolving simulations). In this work the use of the field inversion approach is investigated for the augmentation of the Spalart–Allmaras RANS model applied to the flow in low pressure gas turbine cascades. As a first step, the field inversion method is applied to the T106c cascade at two different values of Reynolds number (80000-250000): An adjoint-based gradient method is employed in order to minimise the prediction error on the wall isentropic Mach number distribution. The data obtained by the correction field are then analysed by means of an Artificial Neural Network (ANN) which makes it possible to generalise the correction by finding correlations which depend on physical variables. A study on the definition of the input variables and on the architecture of the ANN is performed. Different kind of corrections are evaluated and a particularly robust correction factor is obtained by limiting the range of the correction in the spirit of intermittency models. Finally, the ANN is introduced in an augmented version of the Spalart–Allmaras model which is tested on the T106c cascade (for values of the Reynolds number not considered during the training) and for the T2 cascade. The prediction ability of the method is investigated by comparing the numerical predictions with the available experimental data not only in terms of wall isentropic Mach number distribution (which was used as goal function during the field inversion) but also in terms of mass-averaged exit angle and kinetic losses.

中文翻译：

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用于涡轮机械流中数据增强 RANS 建模的场反演

摘要 涡轮机械流动中的湍流建模仍然是一个挑战，尤其是在发生过渡和分离现象时。最近，一些研究工作致力于通过机器学习方法改进雷诺平均 Navier-Stokes (RANS) 方程的闭合模型，这使得可以提取隐藏在可用高保真数据中的知识（来自实验或来自尺度解析模拟）。在这项工作中，研究了场反演方法的使用，以增强应用于低压燃气轮机叶栅中的流动的 Spalart-Allmaras RANS 模型。作为第一步，将场反演方法应用于两个不同雷诺数值 (80000-250000) 下的 T106c 级联：采用基于伴随的梯度方法以最小化壁等熵马赫数分布的预测误差。然后通过人工神经网络 (ANN) 分析由校正场获得的数据，这使得通过查找依赖于物理变量的相关性来概括校正成为可能。对输入变量的定义和人工神经网络的架构进行了研究。评估不同类型的校正，并通过本着间歇模型的精神限制校正范围来获得特别稳健的校正因子。最后，ANN 被引入到 Spalart-Allmaras 模型的增强版本中，该模型在 T106c 级联（对于训练期间未考虑的雷诺数值）和 T2 级联进行测试。