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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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Wind Power Potential in Interior Alaska from a Micrometeorological Perspective

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Atmospheric and Climate sciences 2014年第1期4卷 100-121页

作者： Hannah K.Ross John Cooney Megan Hinzman samuel smock Gary sellhorst Ralph Dlugi Nicole Molders Gerhard Kramm Department of Mechanical Engineering Tennessee Tech UniversityCookevilleUSA Department of Atmospheric sciences College of GeosciencesTexas A&M UniversityCollege StationUSA College of Arts and sciences University of WashingtonSeattleUSA Fu Foundation school of Engineering and Applied science Columbia UniversityNew YorkUSA Geophysical Institute University of Alaska FairbanksFairbanksUSA Arbeitgruppe Atmospharische Prozesse(AGAP) MunichGermany Department of Atmospheric sciences College of Natural Science and MathematicsUniversity of Alaska FairbanksFairbanksUSA

The wind power potential in Interior Alaska is evaluated from a micrometeorological perspective. Based on the local balance equation of momentum and the equation of continuity we derive the local balance equation of kinetic energy for macroscopic and turbulent systems, and in a further step, bernoulli’s equation and integral equations that customarily serve as the key equations in momentum theory and blade-element analysis, where the Lanchester-Betz-Joukowsky limit, Glauert’s optimum actuator disk, and the results of the blade-element analysis by Okulov and sorensen are exemplarily illustrated. The wind power potential at three different sites in Interior Alaska (Delta Junction, Eva Creek, and Poker Flat) is assessed by considering the results of wind field predictions for the winter period from October 1, 2008, to April 1, 2009 provided by the Weather Research and Forecasting (WRF) model to avoid time-consuming and expensive tall-tower observations in Interior Alaska which is characterized by a relatively low degree of infrastructure outside of the city of Fairbanks. To predict the average power output we use the Weibull distributions derived from the predicted wind fields for these three different sites and the power curves of five different propeller-type wind turbines with rated powers ranging from 2 MW to 2.5 MW. These power curves are represented by general logistic functions. The predicted power capacity for the Eva Creek site is compared with that of the Eva Creek wind farm established in 2012. The results of our predictions for the winter period 2008/2009 are nearly 20 percent lower than those of the Eva Creek wind farm for the period from January to september 2013.

关键词： Wind Power Power Efficiency Wind Power Potential Wind Power Prediction WRF/Chem Micrometeorology Momentum Theory Blade Element Analysis Betz Limit Glauert’s Optimum Rotor Balance equation for Momentum equation of Continuity Balance equation for Kinetic Energy Reynolds’Average Hesselberg’s Average bernoulli’s equation Integral equations Weibull Distribution General Logistic Function Eva Creek Wind Farm

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