Physics-informed deep learning cascade loss model

Abstract

The design procedure of aero-engine compressor requires empirical models such as cascade loss model and deviation model. With accurate predictions of basic cascade performance by empirical model, better designs would be obtained and the cost would be reduced. A number of empirical models have been developed and most of them build mathematical equations based on experimental data. It is difficult to modify and broaden the scope of application for empirical models because of its inadequate ability to fit strong nonlinear function relationship and lack of data. Neural networks, which are widely used nowadays, are applied to solve this problem but a simple end-to-end neural network only slightly improves the model performance due to the neglect of flow field details and the similarity of different samples. A promising way to solve the problems is to embed the physics mechanism or flow field details into neural networks as intermediate variables to guide the learning of models. A physics-informed deep learning cascade loss model is proposed. By adjusting the architecture of neural network and the data structure, model can build the relationship of input and output in a more reasonable way while providing a prediction of flow fields. This paper verified the superiority of deep learning model, which has no physics informed, with a 22.3% error reduction when compared to empirical models. A physics-informed model is built and trained with the velocity distribution in boundary layer is chosen as intermediate variable and the influencing factors of physics-informed models are explored. The error of physics-informed model decreases 57.4% overall, and over 60% at high Mach numbers and high incidences compared to empirical model. The physics informed deep learning model is promising to replace the empirical models in compressor design since it shows better performance and gives a local description of the cascade flow field, which can be utilized in subsequent cascade design.