Random flutter of a 2-DOF nonlinear airfoil in pitch and plunge with freeplay in pitch

Abstract

The two-degree-of-freedom (2-DOF) airfoil system with freeplay nonlinearity in pitch is investigated numerically. The relation between eigenvalues and flutter speed has been analyzed. The effect of parameters of the freeplay nonlinearity on the system responses is obtained. The probability density function (PDF) and phase plane of the deterministic system have been studied and the results show that the amplitude of limit cycle oscillation (LCO) grows with mean airspeeds increasing. Marginal PDFs, bidimensional PDFs, random bifurcation, and the largest Lyapunov exponent are used in investigation of the random system. The results show that, for low and intermediate level turbulences, the marginal PDFs of system exhibit different characters at different airspeed ranges. However, for high level turbulence the marginal PDFs are similar in the whole airspeed region. The bidimensional PDF has different shapes in low level turbulence at pre-and post-flutter speeds, but the PDF keeps similar shape in high level turbulence. The random bifurcation analysis indicates the P-bifurcation can happen at both pre-and post-flutter speeds but the D-bifurcation never occurs. Numerical simulations approve the results.

Manifestation of additional frequencies in vortex induced vibrations in the presence of noise

“…Waugh et al [13] have reported that the intensity of noise has a major role in deciding the practical stability limits. Poirel et al [15], [16] and Zhao et al [17] have addressed that aerofoils undergoing flutter with cubic and freeplay nonlinearities are subjected to major qualitative changes when subjected to turbulence in the environment. The number of studies pertaining to discussions on stochastic uncertainties which can be inherently present or externally induced on VIV system are limited.…”

Numerical Simulation of Airfoil Vibrations Induced by Turbulent Flow

“…The algebraic model of turbulence was applied to the numerical simulation of turbulent flow-induced vibrations of an airfoil with two degrees of freedom (2-DOF) by Dubcova et al [11] and [12]. Random flutter of the 2-DOF airfoil with freeplay nonlinearity in pitch was investigated numerically by Zhao et al [53], [54] for low, intermediate and high level of turbulence. Poirel et al [39] studied the low amplitude self-sustained pitch airfoil oscillations in incompressible flow by 2D numerical simulations in the Reynolds number range from 5.0·10 4 to 1.5·10 5 .…”

Parallel numerical simulation of oscillating airfoil NACA0015 in the channel due to flutter instability

“…The paper by Wang and Zha [9] investigates the NLR7301 airfoil limit cycle oscillation (LCO) in transonic flow caused by the flow nonlinearity using Detached Eddy Simulation (DES) of turbulence. The 2-DOF airfoil with freeplay nonlinearity in pitch was investigated numerically by Zhao et al [11] for low, intermediate and high level of turbulence. Poirel et al [6] studied the low amplitude self-sustained pitch airfoil oscillations in incompressible flow by 2D numerical simulations for Reynolds numbers between 50,000 and 150,000.…”