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Research Papers

# Relevant Criteria for Testing the Quality of Models for Turbulent Wind Speed Fluctuations

[+] Author and Article Information
Sten Frandsen

Risø National Laboratory, Frederksborgvej 399, Roskilde 4000, Denmarksten.frandsen@risoe.dk

Hans E. Jørgensen

Risø National Laboratory, Frederksborgvej 399, Roskilde 4000, Denmarkhans.e.joergensen@risoe.dk

John Dalsgaard Sørensen

Aalborg University, Fredrik Bajers Vej 5, P.O.Box 159, DK-9100 Aalborg, Denmarkjds@civil.aau.dk

In practical data analysis, block averaging or running-average filters are applied.

Kenneth Thomsen, personal communication.

The length scale of the Kaimal spectrum is linked—not equal—to the integral of the autocorrelation function of wind speed fluctuations. The integration gives rise to the term “integral scale.”

J. Sol. Energy Eng 130(3), 031016 (Jul 16, 2008) (7 pages) doi:10.1115/1.2931511 History: Received May 24, 2007; Revised September 03, 2007; Published July 16, 2008

## Abstract

Seeking relevant criteria for testing the quality of turbulence models, the scale of turbulence and the gust factor have been estimated from data and compared with predictions from first-order models of these two quantities. It is found that the mean of the measured length scales is approximately 10% smaller than the IEC model for wind turbine hub height levels. The mean is only marginally dependent on trends in time series. It is also found that the coefficient of variation of the measured length scales is about 50%. $3s$ and $10s$ preaveraging of wind speed data are relevant for megawatt-size wind turbines when seeking wind characteristics that correspond to one blade and the entire rotor, respectively. For heights exceeding $50–60m$, the gust factor increases with wind speed. For heights larger than $60–80m$, present assumptions on the value of the gust factor are significantly conservative, both for $3s$ and $10s$ preaverages. The usually applied value of $kp≈3$ should probably be reduced.

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## Figures

Figure 1

Zero-crossing frequency as function of preaveraging time for different time scales of turbulence Tu. The lines with (m) correspond to the truncated expressions 11,12.

Figure 2

Wind spectrum filter functions

Figure 3

Overview of the test site at Høvsøre. Five wind turbines may be tested simultaneously; met mast are erected to the west of all machine. South of the most southern wind turbine location, the 116m met tower is located.

Figure 4

The spectrum of each 10min time series is fitted to the Kaimal spectrum 6 and the scale of turbulence deduced

Figure 5

Høvsøre. Scale of turbulence as function of height. Wind speed at H=100m: 10m∕s<U<12m∕s. The “error bars” represent the standard deviation of the observations.

Figure 6

Høvsøre; same as Fig. 5, but with logarithmic ordinate

Figure 7

Høvsøre. Scale of turbulence as function of wind speed for five different heights, neutral stratification. The wind speed bins contain between 70 and 260 time series.

Figure 8

Høvsøre; gust factor as function of preaveraging time ΔT measurement height 100m and wind speed 10m∕s<U<12m∕s

Figure 9

Høvsøre. Gust factor as function of height for different wind speeds. Sinc-filter frequency is 1∕3Hz. Based on the same time series as in Fig. 5.

Figure 10

Høvsøre. Gust factor as function of height for different wind speeds. Sinc-filter frequency is 1∕10Hz. Based on same time series as in Fig. 5.

Figure 11

Høvsøre. Measurement and model of normalized wind gust kp as function of height for preaveraging times of 3s and 10s, respectively. 10m∕s<U<12m∕s.

Figure 12

Density function for gust factor kp based on 10s averaging data for 80m height (201 data points)

Figure 13

Return period for gust factor kp based on 10s averaging data for 80m height (50 largest data)

Figure 14

Høvsøre. Fitting of measured spectrum measured at height 100m in signal tower approximately 100m from nearest wind turbine; wind direction 355deg between tower and wind turbine, which is approximately center-wake conditions.

Figure 15

Høvsøre; turbulence length scale estimated from measurements as function of wind direction; 7m∕s<U<8m∕s

Figure 16

Høvsøre; gust factor estimated from measurements as function of wind direction; 7m∕s<U<8m∕s

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