Measuring Higher-Order Moments with a Cup Anemometer

L. Kristensen Risø National Laboratory, Roskilde, Denmark

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Abstract

Modern, fast cup anemometers are very useful for measuring the mean-wind speed. The calibration is linear and its operation is well described as a linear, first-order filter. Discussion in the literature about the importance of the response asymmetry to increases and decreases in the streamwise turbulent wind-velocity component seems to have ended at the conclusion that there is no detectable influence on the mean-wind determination from this source, that is, the part of “overspeeding” due to response asymmetry can be neglected. However, a bias on the mean-wind speed from wind-direction fluctuations cannot always be excluded. Here the author addresses the problem of whether higher-order moments are influenced by the asymmetry and the direction fluctuations. Based on a theoretical analysis—a straightforward perturbation calculation—and an experimental test, the author finds that moments up to and including the fourth order are unaffected by the asymmetry as well as wind-direction fluctuations. The author suspects that this is true even for higher-order moments. It is argued that the cup anemometer together with a wind vane is well suited for measuring the horizontal components of the turbulent wind velocity.

Corresponding author address: Dr. Leif Kristensen, Risø National Laboratory, Wind Energy and Atmospheric Physics Department Building 125, P.O. Box 49, DK-4000 Roskilde, Denmark.

Email: leif.kristensen@risoe.dk

Abstract

Modern, fast cup anemometers are very useful for measuring the mean-wind speed. The calibration is linear and its operation is well described as a linear, first-order filter. Discussion in the literature about the importance of the response asymmetry to increases and decreases in the streamwise turbulent wind-velocity component seems to have ended at the conclusion that there is no detectable influence on the mean-wind determination from this source, that is, the part of “overspeeding” due to response asymmetry can be neglected. However, a bias on the mean-wind speed from wind-direction fluctuations cannot always be excluded. Here the author addresses the problem of whether higher-order moments are influenced by the asymmetry and the direction fluctuations. Based on a theoretical analysis—a straightforward perturbation calculation—and an experimental test, the author finds that moments up to and including the fourth order are unaffected by the asymmetry as well as wind-direction fluctuations. The author suspects that this is true even for higher-order moments. It is argued that the cup anemometer together with a wind vane is well suited for measuring the horizontal components of the turbulent wind velocity.

Corresponding author address: Dr. Leif Kristensen, Risø National Laboratory, Wind Energy and Atmospheric Physics Department Building 125, P.O. Box 49, DK-4000 Roskilde, Denmark.

Email: leif.kristensen@risoe.dk

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