Physics-informed neural network for predicting multi-row film cooling superposition using Fourier transform and attention mechanism

Film cooling superposition prediction is a critical technique in cooling system design and plays a vital role in the thermal protection of aero-engine nozzles and turbines. This study develops a physics-informed neural network to address the Sellers prediction deviation in film cooling superposition, which is primarily caused by flow and diffusion effects. The proposed model comprises three main branches. The first branch, the time-domain branch, extracts input features from multiple perspectives using successive convolution operations. The second branch, the frequency-domain branch, employs the discrete Fourier transform to identify error-prone regions in the frequency domain and integrates an attention mechanism to enhance learning and focus on key information. The third branch, the residual branch, processes parameters related to hole type, hole-row structure, and aerodynamics through a multi-layer fully connected network, serving as a residual correction term to improve the prediction accuracy of the spanwise-averaged film cooling effectiveness ( η ¯ ). Furthermore, to address the larger prediction errors observed in the downstream region of Sellers superposition prediction, a loss function is designed with increased weighting in the downstream region. The trained model exhibits strong extrapolation capability, with prediction deviations of η ¯ within 5% at most locations. The maximum local error reaches up to 8% for the fan-shaped hole in the downstream region when the blowing ratio is 2.0, while the deviation of the area-averaged η remains below 3%.