High efficient numerical method for lco analysis in transonic flow

Non-linearities can be present in an aeroelastic systemdue to some aerodynamic phenomena that occur in transonic flight regime orat large angles of attack. The candidate sources are motions of shock waveand separated flow. With the recently well-developed software and hardwaretechnologies, numerical simulation of complex aeroelasticity phenomenabecomes possible, such as limit cycle oscillations (LCOs) due to theaerodynamic nonlinearity. However, the computational cost of solvingaeroelastic problem in nonlinear flow field is very high, so it is aconvenient method to solve this kind of problem by constructing a properunsteady aerodynamic model previously. Many research works are carried outin reduced order modeling (ROM) for aeroelastic analysis. Most of thereduced order aerodynamic models are dynamic linear models and in proportionto the structural motions. In this study, by using Radial Basis Function(RBF) neural network model, the nonlinear unsteady reduced order aerodynamicmodel is constructed. The ROM is used to analyze LCOs behaviors for twolinear structural models with large shock motion in transonic flow.Different from the traditional design method of the input signals, signalsof self-excited vibration of the aeroelastic system are designed as theinput signals in this paper. Coupled the structural equations of motion andnonlinear aerodynamic ROM, the system responses are determined by timemarching of the governing equations using a kind of hybrid linear multi-stepalgorithm and the limit cycle behaviors changing with velocities (dynamicpressure) can be analyzed. Two transonic aeroelastic examples show that boththe structural responses and the limit cycle oscillation (LCO)characteristics simulated by ROM agree well with those obtained by directCFD method, and the computational efficiency of ROM based method can beimproved by 1-2 orders of magnitude compared with the direct CFD method.