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On the Maximum of Wind Power Efficiency

Journal of Power and Energy Engineering 2016年第1期4卷 1-39页

作者： Gerhard Kramm Gary sellhorst Hannah K. Ross John Cooney Ralph Dlugi Nicole Mölders Engineering Meteorology Consulting Fairbanks USA Geophysical Institute University of Alaska Fairbanks Fairbanks USA Department of Mechanical Engineering University of Washington Seattle USA Department of Atmospheric sciences Texas A & M University College Station USA Arbeitsgruppe Atmosphärische Prozesse (AGAP) Munich Germany College of Natural science and Mathematics and Geophysical Institute University of Alaska Fairbanks Fairbanks USA

In our paper we demonstrate that the filtration equation used by Gorban’ et al. for determining the maximum efficiency of plane propellers of about 30 percent for free fluids plays no role in describing the flows in the atmospheric boundary layer (ABL) because the ABL is mainly governed by turbulent motions. We also demonstrate that the stream tube model customarily applied to derive the Rankine-Froude theorem must be corrected in the sense of Glauert to provide an appropriate value for the axial velocity at the rotor area. Including this correction leads to the Betz-Joukowsky limit, the maximum efficiency of 59.3 percent. Thus, Gorban’ et al.’s 30% value may be valid in water, but it has to be discarded for the atmosphere. We also show that Joukowsky’s constant circulation model leads to values of the maximum efficiency which are higher than the Betz-Jow-kowsky limit if the tip speed ratio is very low. some of these values, however, have to be rejected for physical reasons. Based on Glauert’s optimum actuator disk, and the results of the blade-element analysis by Okulov and sørensen we also illustrate that the maximum efficiency of propeller-type wind turbines depends on tip-speed ratio and the number of blades.

关键词： Wind Power Power Efficiency General Momentum Theory Axial Momentum Theory Blade Element Analysis Betz-Joukowsky Limit Joukowsky’s Constant Circulation Model Glauert’s Optimum Actuator Disk Balance Equation for Momentum Equation of Continuity Balance Equation for Kinetic Energy Reynolds’ average Hesselberg’s average favre’s average Bernoulli’s Equation Integral Equations

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