Reconstruction of temperature and heat flux from Thermal Large Eddy Simulations using Deep Learning

It is paramount to understand the coupling between velocity and temperature for many flows found in nature, or industrial applications, like in solar receivers, found inside concentrated solar power towers. Thermal-Large Eddy Simulation (T-LES) is a set of turbulence and thermal modeling equations for turbulent flows with an important thermal component.T-LES modeling can capture the largest scales of turbulence and heat flux fluctuations at a reasonable cost compared to DNS. However, fluctuations at small scales are not captured.This study develops and compares three different methods to reconstruct the small scales of temperature fluctuations by inverting the numerical T-LES filter. This filter is never fully known. First, a supervised learning method only applicable \textit{a priori}. Second, a weakly supervised learning method, requiring the two point correlation of the temperature. This method is applicable \textit{a posteriori}. A third method is proposed based on the Adaptive Local Deconvolution Method applied in a constrained learning framework with a single filter.The results of the first method highlight the ability of the neural network to generalize the filter inversion from a small number of training examples, on both the temperature fields and on the reconstructed heat flux. The results of the second method show the capability of the network to reconstruct plausible raw data and to fit the statistics of the Direct Numerical Simulation (DNS) on temperature fields. The third method exhibits satisfactory results while involving only a few parameters to learn on temperature and heat flux.