Predicting the wall-shear stress and wall pressure through convolutional neural networks

Abstract

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 $y_{\mathrm{target}}^{+}$, using the sampled velocity fluctuations in wall-parallel planes located farther from the wall, at $y_{\mathrm{input}}^{+}$. 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 $R{e}_{\tau }=180$ 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 $R{e}_{\tau }=550$, 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 $R{e}_{\tau }=180$ 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.

33 pages, 10 figures. arXiv admin note: substantial text overlap with arXiv:2107.07340

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• A deep learning approach to wall-shear stress quantification: From numerical training to zero-shot experimental application