Nonlinear Aeroelastic Study of Stall Induced Oscillation in a Symmetric Airfoil

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Abstract

In this paper the aeroelastic stability of a wind turbine rotor in the dynamic stall regime is investigated. Increased flexibility of modern turbine blades makes them more susceptible to aeroelastic instabilities. Complex oscillation modes like flap/lead-lag are of particular concern, which give way to potential structural damage, see Chaviaropoulos (1999), Chaviaropoulos et.al. (2003). We study the stall induced oscillations in pitching direction and in combined flapwise, lead-lag wise directions. The aerodynamic loads acting on the rotor body in the stall regime are nonlinear. We consider a wide ranging parametric variation and underline their effect on the aeroelastic instability and overall nonlinear dynamical behavior of the system. A common engineering dynamic stall model (Onera) has been used to calculate the aerodynamic loads, (see Tran and Petot (1981), Dunn and Dugundji (1992). The aerodynamic loads are captured well by this model in the dynamic stall regime and are subsequently used to predict the bifurcation behavior and the chaotic routes of the aeroelastic system under study are . The aerodynamic loads are given in terms of differential equations which are combined with the governing equations of the aeroelastic system; the resulting system of equations are solved by a 4th order variable step Runge-Kutta method. In the pitching oscillation study we consider the following parameters: nondimensional airspeed (U), mean angle of attack, initial condition, structural nonlinearity and reduced frequency (k) and amplitude of external forcing. The self excited and forced system reveal existence of quasi-periodic and chaotic response. For different mean angle of attack, quasi-periodic response have been obtained with different initial conditions. A cubic structural nonlinearity has been seen to alter the bifurcation pattern of the above system. Varying k as a bifurcation parameter in the forced system shows presence of period-3 orbits near chaos. The second case of flap/edgewise oscillation in the stall regime identifies nondimensional rotational speed of the rotor along with structural stiffnesses and nonlinearity as most important parameters of the self excited system. However, no chaotic response has been obtained. External forcing shows presence of higher harmonics and quasi-harmonics in the response. Once again, no chaotic attractor has been found.

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