Physics-encoded convolutional neural network to predict the mass flow rates of the holes in double-wall systems

Novel double-wall effusion cooling system shows a remarkable potential for thermal protection of gas turbine blades due to its high cooling effectiveness. Achieving precise assessment of the mass flow rate across every hole within the double-wall blade is essential for refined design. Compared to existing approaches such as computational fluid dynamics (CFD) methods, porous media equivalent methods, and flow network methods, machine learning methods demonstrate superior efficiency and accuracy. However, the commonly used fully connected neural network (FCNN) will suffer from excessive model size and data demand. To address the limitation, a physics-encoded convolutional neural network (PeCNN) is proposed in the present study. By treating all holes as an integral input and performing convolutional calculations on its elements, PeCNN is able to learn the flow interactions among holes, enabling a holistic modeling of the entire system. Additionally, an edge identification feature is added in the input to learn the wall-limited effects at the edge. A customized dot product layer is designed to ensure that the mass flow rates are strictly equal to 0 at positions where the hole diameters are 0. Mass conservation is introduced to the loss function to prompt equal mass flow rates of film holes and impingement holes. These physical constraints are intended to further improve the accuracy and robustness. The models were trained and tested by numerical datasets. For the film holes and impingement holes in the test set consisting of two-dimensional hole clusters, the mean relative errors of the model are only 3.41% and 5.22%, respectively.