A transfer learning method to assimilate numerical data with experimental data for effusion cooling

Effusion cooling was one of the most important external cooling technologies for airfoils in gas turbines and aeroengines. Due to the complicated flow field of effusion cooling, simulations were in lack of fidelity, while experimental measurements were expensive and slow. Therefore, the industry has been continuously seeking for mathematical tools that could integrate simulation data with experimental data for effusion cooling, to achieve high fidelity and fast prediction. Deep learning techniques, maturing in recent years, are potential tools to fulfill such demands. However, it was also known that generalization accuracy of machine learning models was still insufficient for small scale datasets. The present study proposed a transfer learning method based on an iterative neural operator to assimilate numerical data with experimental data for effusion cooling. Reynolds Averaged Navier Stokes simulations were conducted to collect source data. A pre-trained machine learning model was built up on the source dataset and transferred to three separately sets of target data. The target datasets included an experimental dataset obtained in this study and two experimental datasets in the literature, each with less than 20 data, different data size and different variables. Ten non-transferred models and three transferred models were evaluated for the accuracy, training speed and data dependence. Results showed that the iterative neural operator model could precisely capture the nonlinear characteristic of effusion, and predict the local effusion cooling effectiveness of random hole configurations with a high quality. Compared with a direct machine learning approach, transfer learning significantly reduced the requirements for the number of training samples (reduced by 2-3 times) and training epochs (reduced by 5-6 times) to reach the same accuracy. Meanwhile, when the data cost and training cost were identical, transfer learning reduced the errors by 63.7% for experi-mental data, 41.8% for literature dataset 1, and 46.2% for literature dataset 2 respectively. The efforts were expected to provide a robust solution to modelling experimental data of effusion cooling using limited sample number and limited time with the aid of relatively bigger numerical datasets.