Reduced-Order Modeling for Nonlinear Aeroelasticity with Varying Mach Numbers

Abstract

This paper proposes a nonlinear aerodynamic reduced-order model robust to different Mach numbers based on a recursive neural network. To model the nonlinear features with varying flow parameters, the Mach number is adopted as an additional input variable. The training case is a weighted filtered Gaussian white noise with wide ranges of frequency and amplitude. For a better generalization capability, proper orthogonal decomposition and partial particle swarm optimization algorithm are introduced to the training process. The approach is tested by predicting the unsteady aerodynamic forces and nonlinear aeroelastic behaviors of a NACA 64A1 airfoil in transonic flow across multiple flow conditions. Comparisons of harmonic aerodynamic responses in the time domain and the frequency domain demonstrate that the model accurately captures the main flow characteristics in a range of transonic flows. After coupling the structural equations of motion and the nonlinear reduced-order model, the proposed method precisely predicts the limit-cycle oscillation trends changing with Mach numbers or structural parameters. The computational time of the present approach is only about 4% of the total time cost of full-order simulations based on a computational fluid dynamics solver. Moreover, as the Mach number range is extended, the resulting model can still account for the parameter-varying linear dynamics, providing a good flutter behavior approximation.