标题： 气固流动的滤波两相流模型闭合的机器学习方法：子网格拖曳力和固体相应力模型 显示英文标题

标题： Machine learning approaches to close the filtered two-fluid model for gas-solid flows: Models for subgrid drag force and solid phase stress

摘要： 气固两相流通常通过双流体模型在工业尺度上进行模拟。然而，这些模拟需要非常精细的网格才能准确预测流动，这在计算资源方面提出了极高的要求。为了解决这个问题，开发了滤波双流体模型，其中大尺度流动场通过数值求解，而小尺度波动则通过次网格建模来考虑。在这项研究中，我们对周期域内的稀疏气固两相流进行了精细网格双流体模拟，并应用显式滤波生成数据集。然后，这些数据集被用于开发人工神经网络（ANN）模型，用于滤波双流体模型的闭合问题，例如滤波后的拖曳力和固体相应力。先前发现的适用于密集流动状态的子网格拖曳力ANN模型输入变量集也被证明适用于稀疏状态。此外，我们提出了一种伽利略不变张量基神经网络（TBNN）模型，用于滤波后的固体相应力，可以很好地捕捉由次网格速度波动引起的固体相应力的各向异性特性。最后，将该新的TBNN模型的预测结果与简单涡粘性ANN模型的结果进行了比较。 显示英文摘要

摘要： Gas-particle flows are commonly simulated through two-fluid model at industrial-scale. However, these simulations need very fine grid to have accurate flow predictions, which is prohibitively demanding in terms of computational resources. To circumvent this problem, the filtered two-fluid model has been developed, where large-scale flow field is numerically resolved and small-scale fluctuations are accounted for through subgrid-scale modeling. In this study, we have performed fine-grid two-fluid simulations of dilute gas-particle flows in periodic domains and applied explicit filtering to generate datasets. Then, these datasets have been used to develop artificial neural network (ANN) models for closures such as the filtered drag force and solid phase stress for the filtered two-fluid model. The set of input variables for the subgrid drag force ANN model that has been found previously to work well for dense flow regimes is found to work as well for the dilute regime. In addition, we present a Galilean invariant tensor basis neural network (TBNN) model for the filtered solid phase stress which can capture nicely the anisotropic nature of the solid phase stress arising from subgrid-scale velocity fluctuations. Finally, the predictions provided by this new TBNN model are compared with those obtained from a simple eddy-viscosity ANN model.