Prediction of multi-physics field distribution on gas turbine endwall using an optimized surrogate model with various deep learning frames
Authors: Zhang Weixin , Liu Zhao , Song Yu , Lu Yixuan , Feng Zhenping 
Published: December 2023

Purpose
To improve the speed and accuracy of turbine blade film cooling design process, the most advanced deep learning models were introduced into this study to investigate the most suitable define for prediction work. This paper aims to create a generative surrogate model that can be applied on multi-objective optimization problems.

Design/methodology/approach
The latest backbone in the field of computer vision (Swin-Transformer, 2021) was introduced and improved as the surrogate function for prediction of the multi-physics field distribution (film cooling effectiveness, pressure, density and velocity). The basic samples were generated by Latin hypercube sampling method and the numerical method adopt for the calculation was validated experimentally at first. The training and testing samples were calculated at experimental conditions. At last, the surrogate model predicted results were verified by experiment in a linear cascade.

Findings
The results indicated that comparing with the Multi-Scale Pix2Pix Model, the Swin-Transformer U-Net model presented higher accuracy and computing speed on the prediction of contour results. The computation time for each step of the Swin-Transformer U-Net model is one-third of the original model, especially in the case of multi-physics field prediction. The correlation index reached more than 99.2% and the first-order error was lower than 0.3% for multi-physics field. The predictions of the data-driven surrogate model are consistent with the predictions of the computational fluid dynamics results, and both are very close to the experimental results. The application of the Swin-Transformer model on enlarging the different structure samples will reduce the cost of numerical calculations as well as experiments.

Research limitations/implications
The number of U-Net layers and sample scales has a proper relationship according to equation (8). Too many layers of U-Net will lead to unnecessary nonlinear variation, whereas too few layers will lead to insufficient feature extraction. In the case of Swin-Transformer U-Net model, incorrect number of U-Net layer will reduce the prediction accuracy. The multi-scale Pix2Pix model owns higher accuracy in predicting a single physical field, but the calculation speed is too slow. The Swin-Transformer model is fast in prediction and training (nearly three times faster than multi Pix2Pix model), but the predicted contours have more noise. The neural network predicted results and numerical calculations are consistent with the experimental distribution.

Originality/value
This paper creates a generative surrogate model that can be applied on multi-objective optimization problems. The generative adversarial networks using new backbone is chosen to adjust the output from single contour to multi-physics fields, which will generate more results simultaneously than traditional surrogate models and reduce the time-cost. And it is more applicable to multi-objective spatial optimization algorithms. The Swin-Transformer surrogate model is three times faster to computation speed than the Multi Pix2Pix model. In the prediction results of multi-physics fields, the prediction results of the Swin-Transformer model are more accurate.