The behavior of fixed point iteration and Newton-Raphson methods in solving the blade element momentum equations

Wind Engineering

Volumn 35, Issue 1, 2011, Pages 17-32

  McWilliam, Michael ^a   Crawford, Curran ^a  

^a UNIVERSITY OF VICTORIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

BLADE-ELEMENT MOMENTUMS; DESIGN VARIABLES; FIXED POINT FUNCTION; FIXED POINT ITERATION; MULTIPLE SOLUTIONS; NEWTON-RAPHSON; WIND TURBINE ROTORS;

AIRFOILS; BOUNDARY ELEMENT METHOD; NEWTON-RAPHSON METHOD; TURBOMACHINE BLADES; WIND POWER;

NUMERICAL METHODS;

CONFERENCE PROCEEDING; MOMENTUM; NUMERICAL METHOD; WIND TURBINE;

EID: 79953854776     PISSN: 0309524X     EISSN: None     Source Type: Journal    
DOI: 10.1260/0309-524X.35.1.17     Document Type: Conference Paper

References (31)

1. R. Lanzafame and M. Messina. Design and performance of a double-pitch wind turbine with non-twisted blades. Renewable Energy, 34:1413-1420, 2009.
2. Zhaohui Du and Michael S. Selig. A 3-D Stall-Delay Model for Horizontal Axis Wind Turbine Performance Prediction. In AIAA 36th Aerospace Sciences Meeting and Exhibit, 1998.
3. James L. Tangler and Michael S. Selig. An Evaluation of an Empirical Model for Stall Delay due to Rotation for HAWTs. In WINDPOWER '97 Conference Austin, Texas, June 15-18, 1997, 1997.
4. Wen Zhong Shen, Robert Mikkelsen, and Jens Norkaer Sorensen. Tip Loss Corrections for Wind Turbine Computations. Wind Energy, 8:457-475, 2005. (Pubitemid 41788615)
5. K. Chaney and A. J. Eggers Jr. Expanding Wake Induction Effect on Thrust Distribution on a Rotor Disc. Wind Energy, 5:213-226, 2002.
6. Helge Aa. Madsen, Christian Bak, Mads Dossing, Robert Mikkelsen, and Stig Oye. Validation and modification of the Blade Element Momentum theory based on comparisons with actuator disc simulations. Wind Energy, 13:373-389, August 2009.
7. Wouter Haans, Tonio Sant, and Gijs Van Kuik Gerard van Bussel. Stall in Yawed Flow Conditions: A Correlation of Blade Element Momentum Predictions With Experiments. Journal of Solar Energy Engineering, 128:472-480, 2006. (Pubitemid 44935613)
8. Curran Crawford. Re-examining the Precepts of the Blade Element Momentum Theory for Coning Rotors. Wind Energy, 9:457-478, 2006. (Pubitemid 44372432)
9. D. J. Sharpe. A General Momentum Theory Applied to an Energy-extracting Actuator Disc. Wind Energy, 7:177-188, 2004. (Pubitemid 40290412)
10. Tony Burton, David Sharpe, Nick Jenkins, and Ervin Bossanyi. Wind Energy Handbook. John Wiley and Sons, Chichester, England, 2001.
11. Jaime Martinez, Luca Bernabini, Oliver Probst, and Ciro Rodriguez. An Improved BEM Model for the Power Curve Prediction of Stall-regulated Wind Turbines. Wind Energy, 8:385-402, 2004. (Pubitemid 41788611)
12. Wang Xudong, Wen Zhong Shen, Wei Jun Zhu, Jens Norkaer Sorensen, and Chen Jin. Shape Optimization of Wind Turbine Blades. Wind Engineering, 12:781-803, 2009
13. P. Fuglsang and H. A. Madsen. Optimization method for wind turbine rotors. Journal of Wind Engineering and Industrial Aerodynamics, 80:191-206, 1999. (Pubitemid 30024263)
14. M. J. Clifton-Smith and D. H. Wood. Further dual purpose evolutionary optimization of small wind turbine blades. Journal of Physics: Conference Series, 75, 2007.
15. M. J. Clifton-Smith. Wind Turbine Blade Optimization with Tip Loss Corrections. Wind Engineering, 33:477-496, 2009.
16. Ernesto Benini and Andrea Toffolo. Optimal Design of Horizontal-Axis Wind Turbines Using Blade-Element Theory and Evolutionary Computation. Journal of Solar Energy Engineering, 124:357-363, 2002. (Pubitemid 46059441)
17. Curran A. Crawford and Luke Stack. Optimal rotors for distributed wind turbines. In 28th ASME Wind Energy Symposium/47th AIAA Aerospace Sciences Meeting and Exhibit, Orlando, FL, January 5-8 2009.
18. Curran Crawford and Jim Platts. Updating and Optimization of a Coning Rotor Concept. Journal of Solar Energy Engineering, 130, August 2008.
19. R. Lanzafame and M. Messina. Fluid dynamics wind turbine design: Critical analysis, optimization and application of BEM theory. Renewable Energy, 32:2291-2305, 2007. (Pubitemid 46964891)
20. Sren Hjort, Kristian Dixon, Michael Gineste, and Anders S. Olsen. Fast Prototype Blade Design. Wind Engineering, 33:321-334, 2009.
21. Curran Crawford. Advanced Engineering Models for Wind Turbines with Application to the Design of a Coning Rotor Concept. PhD thesis, Trinity College, Department of Engineering, University of Cambridge, October 2006.
22. J. F. Manwell, J. G. McGowan, and A. L. Rogers. Wind Energy Explained, Theory, Design and Application. John Wiley and Sons, Chichester, England, 2002.
23. R. Reuss Ramsay, M. J. Hoffmann, and G. M. Gregorek. Effects of Grit Roughness and Pitch Oscillations on the S801 Airfoil. Technical report, National Renewable Energy Laboratories, 1617 Cole Boulevard, Golden, Colorado, United States of America, 1996.NREL/TP-442-7818.
24. R. Reuss Ramsay, M. J. Hoffmann, and G. M. Gregorek. Effects of Grit Roughness and Pitch Oscillations on the S809 Airfoil. Technical report, National Renewable Energy Laboratories, 1617 Cole Boulevard, Golden, Colorado, United States of America, 1995. NREL/TP-442-7817.
25. R. Reuss Ramsay, M. J. Hoffmann, and G. M. Gregorek. Effects of Grit Roughness and Pitch Oscillations on the S810 Airfoil. Technical report, National Renewable Energy Laboratories, 1617 Cole Boulevard, Golden, Colorado, United States of America, 1996.NREL/TP-442-7816.
26. R. Reuss Ramsay and G. M. Gregorek. Effects of Grit Roughness and Pitch Oscillations on the S812 Airfoil. Technical report, National Renewable Energy Laboratories, 1617 Cole Boulevard, Golden, Colorado, United States of America, 1998. NREL/TP-442-8167.
27. R. Reuss Ramsay and G. M. Gregorek. Effects of Grit Roughness and Pitch Oscillations on the S813 Airfoil. Technical report, National Renewable Energy Laboratories, 1617 Cole Boulevard, Golden, Colorado, United States of America, 1996. NREL/TP-442-8168.
28. J. M. Janiszewska, R. Reuss Ramsay, M. J. Hoffman, and G. M. Gregorek. Effects of Grit Roughness and Pitch Oscillations on the S814 Airfoil. Technical report, National Renewable Energy Laboratories, 1617 Cole Boulevard, Golden, Colorado, United States of America, 1996. NREL/TP-442-8161.
29. R. Reuss Ramsay, M. J. Hoffmann, and G. M. Gregorek. Effects of Grit Roughness and Pitch Oscillations on the S815 Airfoil. Technical report, National Renewable Energy Laboratories, 1617 Cole Boulevard, Golden, Colorado, United States of America, 1996. NREL/TP-442-7820.
30. R. Reuss Ramsay, J. M. Janiszewska, and G. M. Gregorek. Effects of Grit Roughness and Pitch Oscillations on the S825 Airfoil. Technical report, National Renewable Energy Laboratories, 1617 Cole Boulevard, Golden, Colorado, United States of America, 1998.
31. James Tangler and J. David Kocurek. Wind Turbine Post-Stall Airfoil Performance Characteristics Guidelines for Blade-Element Momentum Methods. Technical report, National Renewable Energy Laboratories, 1617 Cole Boulevard, Golden, Colorado, United States of America, October 2004.