Interpretable Deep Learning for Turbulent Heat Transfer with Prandtl Number Effect

We investigate the prediction and interpretation of Prandtl number effect in turbulent heat transfer using deep learning. Turbulent heat transfer is an important physical phenomenon observed in industries such as heat exchangers and gas turbines, and its prediction is very important. However, the distribution of heat transfer is very different according to Prandtl number (Pr), and this nonlinearity makes it difficult to predict heat transfer. In this study, the turbulent heat transfer was considered for the analysis of the Prandtl effect. First, conditional generative adversarial networks (cGAN) predicted the surface heat flux for Pr = 0.1-7 from wall information, streamwise and spanwise shear stresses. Our model was able to generate heat flux well reflecting the characteristics for Pr. Furthermore, we analyzed the nonlinear relationship between input and output for Pr using a gradient map and decomposition algorithm. Through these methods, we find that the model learns spatially shifting characteristics for strong local heat fluxes for Pr from the same wall shear stresses in predicting heat fluxes.