Predicting film-cooling effectiveness of compound-angle holes using a POD-based hybrid deep learning model

Film cooling is a key thermal protection technology for hot-section components in gas turbine engines. Efficient hole design and rapid evaluation of cooling performance are essential for improving the thermal protection of these components. However, compound-angle film-cooling holes introduce significant complexities: the lateral injection breaks jet symmetry and alters the evolution of the counterrotating vortex pair (kidney-type vortices) and spanwise shear layers. These phenomena result in a non-Gaussian spanwise distribution of cooling effectiveness, rendering traditional Gaussian-based prediction models inadequate. This study proposes an advanced deep learning framework specifically designed for accurate 2D film-cooling effectiveness prediction under limited-data conditions. The model integrates proper orthogonal decomposition (POD) for modal feature extraction, a conditional injection mechanism for adaptive parameter modulation, and a transformer-enhanced UNet for high-fidelity reconstruction. The results show that the POD module effectively identifies the dominant physical modes, enabling significant dimensionality reduction and reducing the dependence on large datasets. The conditional injection mechanism adaptively modulates multi-level features according to the input parameters, thereby improving the model robustness across the parameter space. In addition, the Transformer-UNet architecture captures the complex local structures near the hole exit and accurately represents nonlinear regions such as the CRVP and shear layers. The proposed model achieves a mean absolute error of 0.0038 on the test set. Furthermore, the maximum relative errors for area-averaged effectiveness and nonuniformity are maintained at 6.24% and 9.33%, respectively. The framework demonstrates excellent transferability, allowing for application to diverse hole geometries without extensive structural modifications.