Convolution- compacted vision transformers for prediction of local wall heat flux at multiple Prandtl numbers in turbulent channel flow

Sammanfattning: Predicting wall heat flux accurately in wall-bounded turbulent flows is critical fora variety of engineering applications, including thermal management systems andenergy-efficient designs. Traditional methods, which rely on expensive numericalsimulations, are hampered by increasing complexity and extremly high computationcost. Recent advances in deep neural networks (DNNs), however, offer an effectivesolution by predicting wall heat flux using non-intrusive measurements derivedfrom off-wall quantities. This study introduces a novel approach, the convolution-compacted vision transformer (ViT), which integrates convolutional neural networks(CNNs) and ViT to predict instantaneous fields of wall heat flux accurately based onoff-wall quantities including velocity components at three directions and temperature.Our method is applied to an existing database of wall-bounded turbulent flowsobtained from direct numerical simulations (DNS). We first conduct an ablationstudy to examine the effects of incorporating convolution-based modules into ViTarchitectures and report on the impact of different modules. Subsequently, we utilizefully-convolutional neural networks (FCNs) with various architectures to identify thedistinctions between FCN models and the convolution-compacted ViT. Our optimizedViT model surpasses the FCN models in terms of instantaneous field predictions,learning turbulence statistics, and accurately capturing energy spectra. Finally, weundertake a sensitivity analysis using a gradient map to enhance the understandingof the nonlinear relationship established by DNN models, thus augmenting theinterpretability of these models