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On the Maximum of Wind Power Efficiency

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DOI: 10.4236/jpee.2016.41001    3,772 Downloads   4,910 Views   Citations

ABSTRACT

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.

Conflicts of Interest

The authors declare no conflicts of interest.

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Kramm, G. , Sellhorst, G. , Ross, H. , Cooney, J. , Dlugi, R. and Mölders, N. (2016) On the Maximum of Wind Power Efficiency. Journal of Power and Energy Engineering, 4, 1-39. doi: 10.4236/jpee.2016.41001.

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