On the Maximum of Wind Power Efficiency

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 S&oslashrensen we also illustrate that the maximum efficiency of propeller-type wind turbines depends on tip-speed ratio and the number of blades.

Wind Power Potential in Interior Alaska from a Micrometeorological Perspective

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.