A simple unsteady blade element analysis is used to account for the effect of the trailing wake on the induced velocity of a wind turbine rotor undergoing fast changes in pitch angle. At sufficiently high tip speed ratio, the equation describing the thrust of the element reduces to a first order, nonlinear Riccti's equation which is solved in a closed form for a ramp change in pitch followed by a constant pitch. Finite tip speed ratio results in a first order, nonlinear Abel's equation. The unsteady aerodynamic forces on the NREL VI wind turbine are analyzed at different pitch rates and tip speed ratio, and it is found that the overshoot in the forces increases as the tip speed ratio and/or the pitch angle increase. The analytical solution of the Riccati's equation and numerical solution of Abel's equation gave very similar results at high tip speed ratio but the solutions differ as the tip speed ratio reduces, partly because the Abel's equation was found to magnify the error of assuming linear lift at low tip speed ratio. The unsteady tangential induction factor is expressed in the form of first order differential equation with the time constant estimated using Jowkowsky's vortex model and it was found that it is negligible for large tip speed ratio operation.
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October 2016
Research-Article
Development of an Analytical Unsteady Model for Wind Turbine Aerodynamic Response to Linear Pitch Changes
Mohamed M. Hammam,
Mohamed M. Hammam
Department of Mechanical and
Manufacturing Engineering,
University of Calgary,
Calgary, AB T2N 1N4, Canada
e-mail: mmahamma@ucalgary.ca
Manufacturing Engineering,
University of Calgary,
Calgary, AB T2N 1N4, Canada
e-mail: mmahamma@ucalgary.ca
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David H. Wood,
David H. Wood
Professor
Department of Mechanical and
Manufacturing Engineering,
University of Calgary,
Calgary, AB T2N 1N4, Canada
e-mail: dhwood@ucalgary.ca
Department of Mechanical and
Manufacturing Engineering,
University of Calgary,
Calgary, AB T2N 1N4, Canada
e-mail: dhwood@ucalgary.ca
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Curran Crawford
Curran Crawford
Associate Professor
Department of Mechanical Engineering,
University of Victoria,
Victoria, BC V8W 2Y2, Canada
e-mail: curranc@uvic.ca
Department of Mechanical Engineering,
University of Victoria,
Victoria, BC V8W 2Y2, Canada
e-mail: curranc@uvic.ca
Search for other works by this author on:
Mohamed M. Hammam
Department of Mechanical and
Manufacturing Engineering,
University of Calgary,
Calgary, AB T2N 1N4, Canada
e-mail: mmahamma@ucalgary.ca
Manufacturing Engineering,
University of Calgary,
Calgary, AB T2N 1N4, Canada
e-mail: mmahamma@ucalgary.ca
David H. Wood
Professor
Department of Mechanical and
Manufacturing Engineering,
University of Calgary,
Calgary, AB T2N 1N4, Canada
e-mail: dhwood@ucalgary.ca
Department of Mechanical and
Manufacturing Engineering,
University of Calgary,
Calgary, AB T2N 1N4, Canada
e-mail: dhwood@ucalgary.ca
Curran Crawford
Associate Professor
Department of Mechanical Engineering,
University of Victoria,
Victoria, BC V8W 2Y2, Canada
e-mail: curranc@uvic.ca
Department of Mechanical Engineering,
University of Victoria,
Victoria, BC V8W 2Y2, Canada
e-mail: curranc@uvic.ca
1Corresponding author.
Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING: INCLUDING WIND ENERGY AND BUILDING ENERGY CONSERVATION. Manuscript received June 5, 2015; final manuscript received April 28, 2016; published online June 14, 2016. Assoc. Editor: Yves Gagnon.
J. Sol. Energy Eng. Oct 2016, 138(5): 051001 (9 pages)
Published Online: June 14, 2016
Article history
Received:
June 5, 2015
Revised:
April 28, 2016
Citation
Hammam, M. M., Wood, D. H., and Crawford, C. (June 14, 2016). "Development of an Analytical Unsteady Model for Wind Turbine Aerodynamic Response to Linear Pitch Changes." ASME. J. Sol. Energy Eng. October 2016; 138(5): 051001. https://doi.org/10.1115/1.4033592
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