A vortex pair-constraint Gaussian superposition method for predicting film cooling effectiveness of converging slot hole in turbine blade

Accurate prediction of film cooling effectiveness is essential for the thermal protection of turbine blades. As a novel high-performance film hole, converging slot holes provide superior lateral coverage by generating three interacting vortex pairs, resulting in much more complex flow structures than the formed by cylindrical or fan-shaped holes, which typically produce a single vortex pair. Existing empirical correlations and unconstrained machine learning approaches, which are primarily developed based on simpler vortex structures, lack the generalization capability required to accurately predict the film cooling performance of converging slot holes. This study proposes a novel Vortex Pair-constraint Gaussian superposition method (VP-GSM) to predict the film cooling effectiveness of converging slot holes. The method identifies the three vortex pairs generated by the converging slot holes via Q-criterion analysis and reconstructs the film cooling effectiveness distribution through a superposition of three corresponding Gaussian functions. The results show that for single hole configurations, the method achieves an average relative error of 2.94% for the area-averaged film cooling effectiveness compared to CFD-computed results on flat plate models, representing a 57% improvement in prediction accuracy over direct prediction approach. For multi-row configurations, an improved Sellers superposition method introduces a correction factor to account for the complex vortex interactions induced by multiple rows, reducing prediction errors by up to 11.90% compared to the conventional Sellers superposition approach.