Stall Flutter Prediction Based on Energy Map by Operator-Network Aerodynamic Modeling

Dynamic stall modeling is essential to stall flutter due to the flow separation in large-amplitude pitching motion. This paper presents the Energy map by velocity operator network (VONet) architecture for predicting the stall flutter of a pitching airfoil. The VONet is modeled by two subnetworks: motion net and velocity net, with aerodynamic forces computed by their dot product. First, the aerodynamic moment coefficient is calculated by solving Navier–Stokes equations at Reynolds numbers of 1000. The swept frequency strategy with constant amplitude is established to train the VONet model. With reduced velocity calibration, the VONet with U* model achieves aerodynamic interpolation errors within 3% and maintains errors within 10% for extrapolations up to 20% beyond the training range. Then, the VONet demonstrates physical interpretability similar to the classic model. To predict the bifurcation velocity and limit-cycle oscillation amplitudes of stall flutter, the swept amplitude strategy is developed for training the VONet with A (A-VONet) model. The energy maps based on A-VONet predict stall flutter responses with under 2% relative error as compared to fluid–structure interaction while requiring significantly less computational cost. Finally, the influence of the damping ratio is investigated, demonstrating the potential of the proposed method to capture the stall flutter phenomenon.