The objective of this study is to assess the capability of convolution-based neural networks to predict wall quantities in a turbulent open channel flow. The first tests are performed by training a fully-convolutional network (FCN) to predict the 2D velocity-fluctuation fields at the inner-scaled wall-normal location $y^{+}_{\rm target}$, using the sampled velocity fluctuations in wall-parallel planes located farther from the wall, at $y^{+}_{\rm input}$. The predictions from the FCN are compared against the predictions from a proposed R-Net architecture. Since the R-Net model is found to perform better than the FCN model, the former architecture is optimized to predict the 2D streamwise and spanwise wall-shear-stress components and the wall pressure from the sampled velocity-fluctuation fields farther from the wall. The dataset is obtained from DNS of open channel flow at $Re_{\tau} = 180$ and $550$. The turbulent velocity-fluctuation fields are sampled at various inner-scaled wall-normal locations, along with the wall-shear stress and the wall pressure. At $Re_{\tau}=550$, both FCN and R-Net can take advantage of the self-similarity in the logarithmic region of the flow and predict the velocity-fluctuation fields at $y^{+} = 50$ using the velocity-fluctuation fields at $y^{+} = 100$ as input with about 10% error in prediction of streamwise-fluctuations intensity. Further, the R-Net is also able to predict the wall-shear-stress and wall-pressure fields using the velocity-fluctuation fields at $y^+ = 50$ with around 10% error in the intensity of the corresponding fluctuations at both $Re_{\tau} = 180$ and $550$. These results are an encouraging starting point to develop neural-network-based approaches for modelling turbulence near the wall in large-eddy simulations.

翻译：本研究旨在评估基于卷积的神经网络预测湍流明渠流动中壁面量的能力。首先通过训练全卷积网络（FCN）进行测试，利用距壁面较远位置$y^{+}_{\rm input}$处的壁面平行平面上的采样速度脉动，预测内尺度法向位置$y^{+}_{\rm target}$上的二维速度脉动场。将FCN的预测结果与所提出的R-Net架构的预测结果进行对比。由于R-Net模型的性能优于FCN模型，因此对前者架构进行优化，利用距壁面较远位置的采样速度脉动场预测二维流向和展向壁面剪切应力分量及壁面压力。数据集来源于$Re_{\tau} = 180$和$550$条件下明渠流动的直接数值模拟（DNS）。在不同内尺度法向位置采集湍流速度脉动场，同时获取壁面剪切应力和壁面压力数据。在$Re_{\tau}=550$时，FCN和R-Net均可利用流动对数区的自相似性，以$y^{+} = 100$处的速度脉动场作为输入预测$y^{+} = 50$处的速度脉动场，流向脉动强度预测误差约为10%。此外，R-Net还能利用$y^{+} = 50$处的速度脉动场预测壁面剪切应力和壁面压力场，在$Re_{\tau} = 180$和$550$条件下对应脉动强度误差均在10%左右。这些结果为在大涡模拟中发展基于神经网络的近壁湍流建模方法提供了令人鼓舞的起点。