High efficient numerical method for LCO analysis in transonic flow

Non-linearities can be present in an aeroelastic system due to some aerodynamic phenomena that occur in transonic flight regime or at large angles of attack. The candidate sources are motions of shock wave and separated flow. With the recently well-developed software and hardware technologies, numerical simulation of complex aeroelasticity phenomena becomes possible, such as limit cycle oscillations (LCOs) due to the aerodynamic nonlinearity. However, the computational cost of solving aeroelastic problem in nonlinear flow field is very high, so it is a convenient method 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. In this study, by using Radial Basis Function (RBF) neural network model, the nonlinear unsteady reduced order aerodynamic model is constructed. The 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. Coupled 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 agree well with those obtained by direct CFD method, and the computational efficiency of ROM based method can be improved by 1-2 orders of magnitude compared with the direct CFD method.