Optimization of wind turbine rotors - using advanced aerodynamic and aeroelastic models and numerical optimization

A comprehensive investigation of the Blade Element Momentum (BEM) model using detailed numerical simulations with an axis symmetric actuator disc (AD) model has been carried out. The present implementation of the BEM model is in a version where exactly the same input in the form of non-dimensional axial and tangential load coeffi cients can be used for the BEM model as for the numerical AD model. At a rotor disc loading corresponding to maximum power coeffi cient, we found close correlation between the AD and BEM model as concerns the integral value of the power coeffi cient. However, locally along the blade radius, we found considerable deviations with the general tendency, that the BEM model underestimates the power coeffi cient on the inboard part of the rotor and overestimates the coeffi cient on the outboard part. A closer investigation of the deviations showed that underestimation of the power coeffi cient on the inboard part could be ascribed to the pressure variation in the rotating wake not taken into account in the BEM model. We further found that the overestimation of the power coeffi cient on the outboard part of the rotor is due to the expansion of the fl ow causing a non-uniform induction although the loading is uniform. Based on the fi ndings we derived two small engi- neering sub-models to be included in the BEM model to account for the physical mechanisms causing the deviations. Finally, the infl uence of using the corrected BEM model, BEMcor on two rotor designs is presented. Copyright © 2009 John Wiley & Sons, Ltd. KEYWORDS rotor aerodynamics; BEM theory; induction; swirl; wake expansion; actuator disc model; wind turbine; energy conversion Correspondence Helge Aa. Madsen, Research Specialist, Programme of Aeroelastic Design, Wind Energy Division, Riso DTU, Denmark. E-mail: hama@risoe.dtu.dk Received 22 December 2008; Revised 5 June 2009; Accepted 29 June 2009 WIND ENERGY Wind Energ. 2010; 13:373–389 Published online 25 August 2009. DOI: 10.1002/we.359 NOTATIONS a axial induction factor acor1 axial induction factor after correction for wake rotation a` tangential induction factor c chord length (m) Cd drag coeffi cient Cl lift coeffi cient CPav average power coeffi cient Cpa power coeffi cient for axial loading Cps power coeffi cient based on shaft power 373 Copyright © 2009 John Wiley & Sons, Ltd. Cpt power coeffi cient for tangential loading Cptot power coeffi cient for total energy conversion at rotor disc CQ local torque coeffi cient—tangential loading on actuator disc CT local thrust coeffi cient—axial loading on actuator disc Cx projection of lift and drag coeffi cients on tangential direction Cy projection of lift and drag coeffi cients on axial direction RESEARCH ARTICLE

[1]  O de Vries,et al.  Fluid dynamic aspects of wind energy conversion , 1979 .

[2]  P. B. S. Lissaman,et al.  Applied Aerodynamics of Wind Power Machines , 1974, Renewable Energy.

[3]  Design of a 21 m Blade with Risø-A1 Airfoils for Active Stall Controlled Wind Turbines , 2002 .

[4]  S. Suresh.  Fatigue of materials , 1991 .

[5]  D. Sharpe.  A general momentum theory applied to an energy‐extracting actuator disc , 2004 .

[6]  J. Jonkman,et al.  Definition of a 5-MW Reference Wind Turbine for Offshore System Development , 2009 .

[7]  Niels N. Sørensen,et al.  3D Navier-Stokes Simulations of a rotor designed for Maximum Aerodynamic Efficiency , 2007 .

[8]  Peter Fuglsang,et al.  Site-Specific Design Optimization of 1.5–2.0 MW Wind Turbines , 2001 .

[9]  Peter Fuglsang,et al.  Aerodynamic design guidelines for wind turbine rotors , 2002 .

[10]  J. Anderson,et al.  Fundamentals of Aerodynamics , 1984 .

[11]  M. Drela.  XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils , 1989 .

[12]  G. Bir,et al.  Preliminary Structural Design of Composite Blades for Two- and Three-Blade Rotors , 2004 .

[13]  Christian Bak,et al.  Validation and modification of the Blade Element Momentum theory based on comparisons with actuator disc simulations , 2010 .

[14]  Ya-Xiang Yuan,et al.  Optimization Theory and Methods: Nonlinear Programming , 2010 .

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

[16]  G. S. Bir,et al.  User's Guide to PreComp (Pre-Processor for Computing Composite Blade Properties) , 2006 .

[17]  J. R. Connell.  Turbulence spectrum observed by a fast-rotating wind-turbine blade , 1980 .

[18]  Morten Hartvig Hansen,et al.  Aeroelastic stability analysis of wind turbines using an eigenvalue approach , 2004 .

[19]  Vasilis Riziotis,et al.  Aeroelastic stability of wind turbines: the problem, the methods and the issues , 2004 .

[20]  Helge Aagaard Madsen,et al.  Optimization method for wind turbine rotors , 1999 .

[21]  Jeppe Johansen,et al.  Can CB be Increased by the Use of Winglets? - or - A Theoretical and Numerical Investigation of the Maximum Aerodynamic Efficiency of Wind Turbine Rotors with Winglets , 2008 .

[22]  Tim Cockerill,et al.  Site-specific design optimization of wind turbines , 1998 .

[23]  M. Matsuichi,et al.  Fatigue of metals subjected to varying stress , 1968 .

[24]  Martin Otto Laver Hansen,et al.  Aerodynamics of Wind Turbines , 2001 .

[25]  Sten Tronæs Frandsen,et al.  Model for power spectra of the blade of a wind turbine measured from the moving frame of reference , 1982 .

[26]  J. Sørensen,et al.  Analysis of wake states by a full‐field actuator disc model , 1998 .

[27]  Christian Bak,et al.  Research in aeroelasticity EFP-2005 , 2006 .

[28]  Herman Snel,et al.  Review of Aerodynamics for Wind Turbines , 2003 .

[29]  Steen Krenk,et al.  CROSS SECTION. Program Description and user manual , 1989 .

[30]  Christian Bak,et al.  Three-dimensional corrections of airfoil characteristics based on pressure distributions (paper and poster) , 2006 .

[31]  S. Frandsen.  Turbulence and turbulence-generated structural loading in wind turbine clusters , 2007 .

[32]  Niels N. Sørensen,et al.  Inboard rotor/blade aerodynamics and its influence on blade design , 2006 .

[33]  T.H.G. Megson,et al.  Aircraft structures for engineering students , 1972 .

[34]  Morten Hartvig Hansen,et al.  Improved Modal Dynamics of Wind Turbines to Avoid Stall‐induced Vibrations , 2003 .

[35]  Michael S. Selig,et al.  BLADE GEOMETRY OPTIMIZATION FOR THE DESIGN OF WIND TURBINE ROTORS , 2000 .

[36]  John D. Sørensen,et al.  Wind energy systems : optimising design and construction for safe and reliable operation , 2011 .

[37]  Thomas Buhl.  Research in Aeroelasticity EFP-2007-II , 2009 .

[38]  Mads Døssing.  Vortex lattice modelling of winglets on wind turbine blades , 2007 .

[39]  Magnus Joyce,et al.  Shrinked (1− α) ensemble Kalman filter and α particle filter , 2011 .

[40]  Dan Christian Bak.  Key parameters in aerodynamic rotor design , 2007 .

[41]  Christian Bak,et al.  A Detailed investigation of the Blade Element Momentum (BEM) model based on analytical and numerical results and proposal for modifications of the BEM model , 2007 .

[42]  Jens Nørkær Sørensen,et al.  Modelling and analysis of the flow field around a coned rotor , 2001 .

[43]  Helge Aa. Madsen,et al.  Modelling of transient wind turbine loads during pitch motion (paper and poster) , 2006 .

[44]  Christian Bak,et al.  Development of the Risø wind turbine airfoils , 2004 .

[45]  Garret N. Vanderplaats,et al.  Numerical Optimization Techniques for Engineering Design: With Applications , 1984 .

[46]  Mads Døssing.  A detailed investigation of the corrected BEM method and the potential for improving blade design , 2009 .

[47]  David Wood,et al.  Including Swirl in the Actuator Disk Analysis of Wind Turbines , 2007 .

[48]  N. I. Xiros,et al.  Remarks on wind turbine power absorption increase by including the axial force due to the radial pressure gradient in the general momentum theory , 2007 .

[49]  Mads Døssing.  High frequency microphone measurements for transition detection on airfoils. Risø B1-18 appendix report , 2008 .

[50]  Niels N. Sørensen,et al.  Yaw aerodynamics analyzed with three codes in comparison with experiment , 2003 .

[51]  Ervin Bossanyi,et al.  Wind Energy Handbook , 2001 .

[52]  Karl O. Merz,et al.  Conceptual Design of a Stall-Regulated Rotor for a Deepwater Offshore Wind Turbine , 2011 .

[53]  Helge Aagaard Madsen.  Forskning i aeroelasticitet EFP-2001 , 2002 .

[54]  C. Bak,et al.  Aerodynamic design of wind turbine rotors , 2011 .

[55]  Forskning i Aeroelasticitet EFP-2002 , 2004 .

[56]  Jeppe Johansen,et al.  Design of a Wind Turbine Rotor for Maximum Aerodynamic Efficiency , 2009 .

[57]  Mac Gaunaa,et al.  Prediction of steady aerodynamic performance of rotors with winglets using simple prescribed wake methods , 2011 .

[58]  Morten Hartvig Hansen,et al.  Aeroelastic instability problems for wind turbines , 2007 .

[59]  W. A. Timmer,et al.  Summary of the Delft University Wind Turbine Dedicated Airfoils , 2003 .

[60]  H. Madsen.  A CFD analysis of the actuator disc flow compared with momentum theory results , 1997 .

[61]  Hui Chen,et al.  A Critical Assessment of Computer Tools for Calculating Composite Wind Turbine Blade Properties , 2009 .

[62]  H. Aagaard Madsen.  Yaw simulation using a 3D actuator disc model coupled to the aeroelastic code HawC , 2000 .