Interpretable deep learning for prediction of Prandtl number effect in turbulent heat transfer

We propose an interpretable deep learning (DL) model that extracts physical features from turbulence data. Based on a conditional generative adversarial network combined with a new decomposition algorithm for the Prandtl number effect, we developed a DL model that is capable of predicting the local surface heat flux very accurately using only the wall-shear stress information and Prandtl number as inputs in channel turbulence. The considered range of Prandtl number is, with a focus on the subrange of. Through an investigation of the gradient maps of the trained prediction model, we were able to identify the nonlinear physical relationship between the wall-shear stresses and heat flux, which is quite diverse depending on the Prandtl number. Furthermore, the decomposition algorithm, which is used to separate the Prandtl number dependent field from the common field of the surface heat flux, helps not only in learning for good prediction of an arbitrary Prandtl number but also in analysing the effect of the Prandtl number on the determination of the heat flux for the given turbulent flow fields. We demonstrate that a physical interpretation of a trained network is possible.