面向目标的雷诺应力数据加权用于复杂流动中的湍流模型学习

中文摘要 AI 辅助

数据驱动的雷诺平均纳维-斯托克斯（RANS）方程湍流模型为提高复杂流动预测提供了一条有前景的途径。此类模型，特别是湍流本构关系，可以在不评估训练期间RANS方程的情况下，从高保真雷诺应力数据中高效学习。然而，传统损失函数对所有张量分量和空间误差赋予相等权重，尽管它们对感兴趣量（QoI）的影响可能显著不同；因此，减少总体应力误差并不一定导致改进的QoI预测。针对流动级观测的训练考虑了这种依赖性，但需要重复且可能昂贵的RANS求解。在典型剪切流中，物理推理可以识别剪切分量是唯一对平均流预测相关的分量。受此例启发，我们提出了一种面向目标的方法来选择复杂流动中雷诺应力训练数据并赋予权重。对于指定的QoI，单次离线伴随评估量化了其对每个雷诺应力分量局部扰动的敏感性。这些敏感性被转换为监督损失中的固定权重，从而无需进一步的RANS求解即可进行训练。我们在方形管道和周期性丘陵流动中验证了该加权方法，然后将其应用于横流中的气膜冷却射流，尽管仅使用速度相关的QoI，该方法仍比均匀加权训练改善了速度和冷却效率预测。除了湍流建模之外，这项工作还提出了一种更广泛的策略，用于将监督学习与下游预测目标对齐，同时保持训练效率。

英文摘要

Data-driven turbulence models for the Reynolds-averaged Navier-Stokes (RANS) equations offer a promising route to improving predictions of complex flows. Such models, specifically the turbulence constitutive relations, can be learned efficiently from high-fidelity Reynolds-stress data without evaluating the RANS equations during training. However, conventional losses weight all tensor-component and spatial errors equally, although their influence on a quantity of interest (QoI) can differ significantly; reducing the aggregate stress error therefore does not necessarily lead to an improved QoI prediction. Training against flow-level observations accounts for this dependence but requires repeated, potentially expensive RANS solutions. In canonical shear flows, physical reasoning can identify the shear component as the only one relevant for the mean-flow prediction. Motivated by this example, we propose a goal-oriented method to select and weight Reynolds-stress training data for complex flows. For a specified QoI, a single offline adjoint evaluation quantifies its sensitivity to local perturbations of each Reynolds-stress component. These sensitivities are converted into fixed weights in the supervised loss, enabling training without further RANS solutions. We validate the weighting in square-duct and periodic-hill flows, then apply it to a film-cooling jet in crossflow, where it improves velocity and cooling-effectiveness predictions over uniformly weighted training despite using a velocity-only QoI. Beyond turbulence modelling, this work suggests a broader strategy for aligning supervised learning with downstream prediction goals while preserving training efficiency.

发表机构

• University of Stuttgart（斯图加特大学）
• Gwangju Institute of Science and Technology（光州科学技术院）

机构由 AI 辅助整理，请以论文原文为准。