Data-driven optimization of rough surfaces for convective heat transfer enhancement

Dimpled surface designs are known to be effective at enhancing convective heat transfer. However, optimizing these surfaces can be challenging due to the large parameter space created by the different combinations between geometrical features. In this paper, we combine a machine learning framework with a GPU-accelerated DNS solver to quickly assess the performance of a very large number of surface configurations, and to identify optimal designs. Our neural network can be trained to predict 2-D images with the local Nusselt numbers of rough surfaces within a few hours (in a single GPU), based on their original height maps. During evaluation, our neural network coupled with our parameterized geometrical formulation can evaluate one million dimpled surface designs in less than 45 min using a 64-core CPU architecture; with a low RAM memory footprint per core. Moreover, the GPU-accelerated DNS solver can calculate the Nusselt number of a rough surface within a few hours as well. The study considers a diverse parameter space including dimples with multiple depth profiles, major radiuses, corner effects, and inclination angles. To predict optimal designs, a basic reinforcement loop is created. In the first stage, only randomly chosen dimpled surface designs are selected as training data. The Nusselt numbers for each design are extracted from Direct Numerical Simulations (DNS), performed by the GPU-accelerated turbulent flow solver. Then, a convolutional neural network is trained, and different surface designs in our parameter space are evaluated. In order to advance the reinforcement learning loop, additional DNS cases are run for the optimal predicted surface, and other closely related geometrical variations. After adding these new DNS cases to the training set, the neural network is re-trained, and the process is repeated. Starting from the first iteration of the reinforcement learning loop, our results shows that machine learning can predict remarkably optimized dimpled surface designs, with high Nusselt numbers verified through DNS. Moreover, we find that machine learning chooses dimple configurations that enhance the interaction between roughness elements, even if other dimples with shorter radius (and equal depth) have more heat transfer area. The optimal surface has elongated dimples with opposite inclination angles, which create a zig-zag pattern for the flow near the walls. Additionally, we have shown that at different Reynolds numbers, the optimal geometry is different as well. We analyze other plausible optimal dimpled surface designs within our parameter space, and we find that machine learning correctly identified the adequate parameters to maximize heat transfer. Therefore, we conclude that machine learning is a highly effective tool to identify optimized designs for convective heat transfer enhancement.