Deep learning-aided active subspace exploration of free-stream effects for fan-shaped film cooling

Film cooling plays a critical role in protecting engine components from high temperatures that can influence safety and performance of gas turbines. However, the process is fraught with uncertainties due to complex inflow conditions and geometrical configurations. These uncertainties significantly impact cooling effectiveness, underscoring the importance of identifying the dominant factors in a quantified manner. Traditional methods, such as the Monte Carlo approach, encounter the “curse of dimensionality,” making them computationally intensive as the number of variable increases. This study tackles these challenges by employing a deep learning strategy with a convolutional neural network (CNN) model to predict film cooling effectiveness efficiently, reducing computational loads compared to traditional computational fluid dynamics (CFD) simulations. It enables the CNN model to act as a surrogate for the CFD simulation and provides gradient information for subsequent analyses. Additionally, this study employs active subspace (AS) analysis for dimensionality reduction, identifying dominant parameters based on the trained CNN model. This approach not only enhances the speed of simulations but also provides an effective way to analyze dominant parameters and carry out optimizations. Results demonstrate a strong correlation between the CNN predictions and detailed CFD simulations, with all the mean absolute errors below 0.08, validating the model's efficacy in capturing complex cooling dynamics. The dominant analysis based on the AS method gives the blowing ratio as the most important factors, and the subsequent parameter dimension reduction and suggested optimization region are also explored by applying the low-dimensional active variable. The tested optimal factors yield higher spatially averaged cooling effectiveness above 0.35 and show reasonable pattern changes compared to the maximum and minimum results in the sample.