Dynamic Stall Model for Wind Turbine Airfoils

Abstract A model is presented for aerodynamic lift of wind turbine profiles under dynamic stall. The model combines memory delay effects under attached flow with reduced lift due to flow separation under dynamic stall conditions. The model is based on a backbone curve in the form of the static lift as a function of the angle of attack. The static lift is described by two parameters, the lift at fully attached flow and the degree of attachment. A relationship between these parameters and the static lift is available from a thin plate approximation. Assuming the parameters to be known during static conditions, nonstationary effects are included by three mechanisms: a delay of the lift coefficient of fully attached flow via a second-order filter, a delay of the development of separation represented via a first-order filter, and a lift contribution due to leading edge separation also represented via a first-order filter. The latter is likely to occur during active pitch control of vibrations. It is shown that all included effects can be important when considering wind turbine blades. The proposed model is validated against test data from two load cases, one at fully attached flow conditions and one during dynamic stall conditions. The proposed model is compared with five other dynamic stall models including, among others, the Beddoes–Leishman model and the ONERA model. It is demonstrated that the proposed model performs equally well or even better than more complicated models and that the included nonstationary effects are essential for obtaining satisfactory results. Finally, the influence of camber and thickness distribution on the backbone curve are analysed. It is shown that both of these effects are adequately accounted for via the static input data.

[1]  Christian Bak,et al.  Observations and hypothesis of double stall , 1999 .

[2]  M. Raffel,et al.  Experimental and numerical investigations of dynamic stall on a pitching airfoil , 1996 .

[3]  Jaan Liiva,et al.  Unsteady aerodynamic and stall effects on helicopter rotor blade airfoil sections. , 1969 .

[4]  R. A. McD. Galbraith,et al.  Measurements of the dynamic stall vortex convection speed , 1992, The Aeronautical Journal (1968).

[5]  T. S. Beddoes,et al.  A Generalised Model for Airfoil Unsteady Aerodynamic Behaviour and Dynamic Stall Using the Indicial Method , 1986 .

[6]  Franklin D. Harris,et al.  Prediction Of Inflight Stalled Airloads From Oscillating Airfoil Data , 1969 .

[7]  I. H. Abbott,et al.  Theory of Wing Sections , 1959 .

[8]  H. Madsen,et al.  A Beddoes-Leishman type dynamic stall model in state-space and indicial formulations , 2004 .

[9]  J. Leishman.  Validation of approximate indicial aerodynamic functions for two-dimensional subsonic flow , 1988 .

[10]  R. T. Jones.  The unsteady lift of a wing of finite aspect ratio , 1940 .

[11]  M. Selig,et al.  A 3-D stall-delay model for horizontal axis wind turbine performance prediction , 1998 .

[12]  J. G. Leishman,et al.  A Semi-Empirical Model for Dynamic Stall , 1989 .

[13]  F. J. Tarzanin,et al.  Prediction of Control Loads Due to Blade Stall , 1972 .

[14]  Sundaram Suresh,et al.  Lift coefficient prediction at high angle of attack using recurrent neural network , 2003 .

[15]  Michael S. Selig,et al.  The effect of rotation on the boundary layer of a wind turbine blade , 2000 .

[16]  J. Gordon Leishman,et al.  Principles of Helicopter Aerodynamics , 2000 .

[17]  Yuan-Cheng Fung,et al.  An introduction to the theory of aeroelasticity , 1955 .

[18]  John A. Ekaterinaris,et al.  Evaluation of turbulence models for unsteady flows of an oscillating airfoil , 1995 .

[19]  M. Akbari,et al.  Simulation of dynamic stall for a NACA 0012 airfoil using a vortex method , 2003 .