Enhancing generalization in endwall film cooling prediction: Incorporating the superposition principle into transformer-based neural operators

In this study, a physics-enhanced neural operator framework is proposed to enhance the generalization prediction ability of the cooling layout of a turbine end wall with variable number of film holes. Specifically, inspired by the film cooling superposition principle, the superposition-based deep neural operator (SDNO) network is proposed, which divides the turbine end wall's temperature field prediction into two stages. In the first stage, the cooling layout of a turbine end wall is divided into several sub-parts, and a transformer-based neural operator network, namely Calculate Net, is designed to predict the temperature field of each sub-part. Then, in the second stage, another neural operator network, i.e., Superposition Net, is designed to combine all the temperature fields of each sub-part and obtain the final superposed field of full cooling layout. Additionally, instead of directly taking the film cooling layout as binary pixel data, a signed distance function which is sensitive to the variable locations of cooling holes is designed to preprocess the input layout information. Furthermore, the proposed end wall film cooling prediction model is trained with samples varying the number of film holes from 1 to 5 at different locations. Then, the trained prediction shows excellent generalization prediction ability, which can accurately predict the film effectiveness of the cooling layout with 10–20 film cooling holes that are unseen in the training samples. In the meantime, the proposed SDNO network also shows remarkable better prediction accuracy. With the above, the effectiveness of the SDNO has been well demonstrated.