Point-enhanced convolutional neural network: A novel deep learning method for transonic wall-bounded flows

Low order models can be used to accelerate engineering design processes. Ideally, these surrogates should meet the conflicting requirements of large design space coverage, high accuracy and fast evaluation. Within the context of aerospace applications at transonic conditions, this can be challenging due to the associated non-linearity of the flow regime. Different methods have been investigated in the past to predict the flow-field around shapes such as airfoils or cylinders. However, they usually have reduced spatial resolution, limiting the prediction capabilities within the boundary layer which is of interest for transonic wall-bounded flows. This work proposes a novel Point-Enhanced Convolutional Neural Network (PCNN) method that combines the advantages of the well-established PointNet and convolutional neural network approaches. The PCNN model has relatively low memory requirements in the training process, preserves the spatial correlation in the domain and has the same resolution as a traditional computational method. The architecture is used for the flow-field prediction of civil aero-engine nacelles in which it is demonstrated that the flow features of peak isentropic Mach number ($M_{is}$), pre-shock isentropic Mach number and shock location ($X/L_{nac}$) are captured within $\Delta M_{is}$ = 0.02, $\Delta M_{is}=0.04$, $\Delta X/L_{nac}=0.007$, respectively. The PCNN model successfully predicts the integral parameters of the boundary layer, in which the incompressible displacement thickness, momentum thickness and shape factor are typically within 5% of the CFD. Overall, the PCNN method is demonstrated for transonic wall-bounded flows for a range of flow physics that include shock waves and shock-induced separation.