Prediction of Aeroelastic Limit-Cycle Oscillations Based on Harmonic Forced-Motion Oscillations

Abstract

Aeroelastic limit-cycle oscillations (LCO) due to aerodynamic non-linearities are usually investigated using coupled fluid-structure interaction simulations in the time domain. These simulations are computationally expensive, especially if a large number of LCO solutions must be computed to study the Hopf bifurcation behaviour in the immediate surrounding of the flutter point. To facilitate such bifurcation parameter studies an adaptation of the well-known p-k flutter analysis method is proposed in this paper. In this frequency domain method, the first harmonic of the motion-induced unsteady aerodynamic forces is no longer assumed to be solely determined by constantcoefficient frequency response functions. Instead, the non-linear dependence on the oscillation amplitudes and the phase angle between the input degrees of freedom is additionally taken into account. Therefore, the first harmonic Fourier components of the aerodynamic forces are sampled and interpolated in advance. The LCO solution is then found iteratively. The proposed amplitude-dependent p-k method (ADePK) is applied to a classic two-degree-of-freedom spring-mounted airfoil system where the non-linear aerodynamic forces are computed from Euler simulations. Fluid-structure

Bifurcations of limit-cycle oscillations of a two degree-of-freedom airfoil caused by aerodynamic non-linearities

“…Furthermore, unstable LCOs as well as multiple nested LCOs cannot be found directly from coupled fluid-structure interaction simulations. Therefore, the well-known p-k method, used in classical (linear) flutter analysis, has been extended for the prediction of limit-cycle oscillations, see van Rooij et al [1][2][3] This method allows one to extensively study the Hopf bifurcation behaviour of limit-cycle oscillation solutions, due to the reduced computational time once the aerodynamic response is known as a function of the frequencies, amplitudes and phase differences of the degrees of freedom. Figure 1 shows a sketch of the LCO amplitude as a function of the airspeed (after Dowell et al 4 ).…”

“…This results in a total of 1280 sample points for the viscous flow test case and 1120 sample points for the inviscid flow test cases. Is is noted here that the response surface is set up at a certain reference velocity and hence the results obtained with ADePK are non-matched, see van Rooij et al 3 Interpolation of the response surface is applied using cubic spline interpolation. …”