High efficient numerical method for limit cycle flutter analysis based on nonlinear aerodynamic reduced order model

Non-linearities can be present in an aeroelastic system due to some aerodynamic factors that occur in transonic flight regime or at large angle of attack. The sources are motions of shock wave and separated flow. By using high-fidelity CFD codes, complex aeroelastic problem due to the aerodynamic nonlinearity can be studies. However, the computational cost of this method is very high. It is convenient to solve this kind of problem by constructing a proper unsteady aerodynamic model previously. Many research works are carried out in reduced order modeling (ROM) for aeroelastic analysis. Most of the reduced order aerodynamic models are dynamic linear models and in proportion to the structural motions. By using Radial Basis Function (RBF) neural network model, the nonlinear unsteady reduced order aerodynamic model is constructed. ROM is used to analyze LCOs behaviors for two linear structural models with large shock motion in transonic flow. Different from the traditional design method of the input signals, signals of self-excited vibration of the aeroelastic system are designed as the input signals in this paper. Coupling the structural equations of motion and nonlinear aerodynamic ROM, the system responses are determined by time marching of the governing equations using a kind of hybrid linear multi-step algorithm and the limit cycle behaviors changing with velocities (dynamic pressure) can be analyzed. Two transonic aeroelastic examples show that both the structural responses and the limit cycle oscillation (LCO) characteristics simulated by ROM are agree well with those obtained by direct CFD method while the computational efficiency of ROM based method is improved 1-2 orders of magnitude comparing with the direct CFD method.