The film cooling of cylindrical holes embedded in transverse trenches under superposition has shown promise for protecting the critical components of a high-pressure turbine from thermal damage. To optimize the relevant parameters and provide a suitable film cooling strategy, it is important to predict the effectiveness of lateral-averaged adiabatic film cooling with the trench effect on the surface of a blade. However, high-fidelity semi-empirical correlations for film cooling under superposition conditions with a trench have rarely been examined. This study establishes a gated recurrent unit (GRU) neural network model to predict the effectiveness of lateral-averaged film cooling under multiple-row superposition conditions with a trench. In general, a gated recurrent unit (GRU) neural network model is built with a large sequence of one-dimensional (1D) parameters, including the depth and width of the trench, compound angle, location of the hole, and blowing ratio. The computational fluid dynamics (CFD) method is used to provide a training dataset for the model. After careful testing and validation, the results predicted by the GRU agreed well with the CFD results. Moreover, the performance and robustness of the GRU were better than those of other recurrent neural network model, such as the long short-term memory (LSTM) model. Integrated with the GRU model, the sparrow search algorithm was adopted to optimize the parameters of the trench. The film cooling effectiveness of the optimized case improved by 1.6% compared with the best case, 28.5% compared with the worst case in dataset and 23.5% compared with the no-trench case.
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