Machine learning for the prediction of the local skin friction factors and Nusselt numbers in turbulent flows past rough surfaces

Turbulent flows past rough surfaces can create substantial energy losses in engineering equipment. During the last decades, developing accurate correlations to predict the thermal and hydrodynamic behavior of rough surfaces has proven to be a difficult challenge. In this work, we investigate the applicability of convolutional neural networks to perform a direct image-to-image translation between the height map of a rough surface and its detailed local skin friction factors and Nusselt numbers. Additionally, we propose the usage of separable convolutional modules to reduce the total number of trainable parameters, and PReLU activation functions to increase the expressivity of the neural networks created. Our final predictions are improved by a new filtering methodology, which is able to combine the results of multiple neural networks while discarding non-physical oscillations likely caused by over-fitting. The main study is based on a new DNS database formed by 80 flow cases at a friction Reynolds number of Re_τ=180 obtained by applying random shifts to the Fourier spectrum of the grit-blasted surface originally scanned by Busse et al. (2015). The results show that machine learning can accurately predict the skin friction values and Nusselt numbers for a rough surface. A detailed comparison with existing correlations in the literature revealed that the maximum errors generated by deep learning were only 8.1% for the global skin friction factors C_f¯ and 2.9% for the Nusselt numbers Nu¯, whereas the best classical correlations identified reached errors of 24.9% and 13.5% for C_f¯ and Nu¯ respectively. The deep learning results also proved stable with respect to rough surfaces with abrupt changes in their roughness elements, and only presented a minor sensitivity with respect to variations in the dataset size.