Deep active subspace method for dominant factor exploration and optimization in fan-shaped film cooling

•Introduce the Deep Active Subspace method to analyze and optimize the dominant factors influencing shaped-hole film cooling performance.•A convolutional neural network is utilized as a surrogate model, achieving a mean absolute error of less than 0.02 and efficient gradients propagation.•The blowing ratio, expansion angle, and density ratio are identified as the dominant factors influencing cooling effectiveness, and their sensitivity evolution is analyzed.•The optimal fan-shaped hole geometry corresponds to a specific angle of 20° without scaling and 14° with scaling, demonstrating superior performance. This study introduces a novel algorithm that combines deep learning with active subspace method to address the challenge of quantitatively analyzing the effects of various geometrical and freestream factors on the performance of fan-shaped film cooling, which is critical for protecting surfaces exposed to high temperatures. Leveraging neural networks, the algorithm constructs a high-performance surrogate model that efficiently propagates gradients and utilizes active subspace method for sensitivity analysis and dimensionality reduction. The well-trained convolutional neural network accurately predicts the cooling plate's effectiveness distribution within milliseconds, achieving a mean absolute error of less than 0.02 compared to computational fluid dynamics results. Sensitivity analysis reveals that blowing ratio, expansion angle, and density ratio are the dominant factors affecting cooling effectiveness, while inclination angle, mainstream turbulence intensity, and Mach number have lesser impacts. Notably, the study finds that an expansion angle of 20∘ provides optimal performance without scaling by breakout width, whereas an angle of 14∘ is optimal when scaling is applied. These findings underscore the algorithm's potential to enhance the design and efficiency of fan-shaped film cooling systems and open new avenues for improving cooling performance metrics.