Relevant criteria for testing the quality of turbulence models

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Relevant criteria for testing the quality of
turbulence models

• Sten Frandsen
• Hans E. Jørgensen, John Dalsgaard Sørensen
• Risø/DTU and AUC
• EWEC2007
• Session DS2 paper 56 May 10, 2007

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Problem

• A simulator of atmospheric turbulence is a
  crucial part of any wind turbine response
  simulation code
• The IEC standards turbulence models for
  aeroelastic codes give divergent results
• Extrapolation of loads for identification of
  lifetime extreme is presently a big issue, but we
  have a chain of models

• the result is not better than what is put in
  (turbulence)
• Thus, IEC61400-1 gives specific models
• it should rather specify how turbulence models
  shall/must work to emulate the atmospheric flow.

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Mission

• Devise requirements that will make sure that
  when followed different turbulence models will
  yield the same response with any particular
  aerodynamic/structural model

• Candidate characteristics to be evaluated
• scale of turbulence
• gust factor
• (extreme) distribution of gusts
• coherence function factor

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How is turbulence characteristics identified?

• By full scale measurements

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The Risø/DTU wind turbine test site overview

• 5 Wind Turbines
• 5 Wind Turbine Masts (70-116m)
• 2 Obstruction Lighting masts (165m)
• Meteorological Mast (116m)

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Instrumentation

• Wind shear and turbulence
• Sonic anemometers in 6 levels
• Wind speed in 7 levels
• Wind direction in 3 levels
• Absolute temperature in 2 levels
• Temperature difference in 5 levels
• Also, a 160 m tower with measuring levels at 160,
  100 and 60 m

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Scale of turbulence

• IEC61400-1 - Kaimal

Fitting data to Kaimal
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Scale of turbulence height-dependency

• In average IEC
• fits quite well
• COV is 50

Scale of turbulence as function of height. Wind
speed at H100m 10m/sltUlt12m/s. The error bars
represent the standard deviation of the
observations.
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Scale of turbulence wind speed and wake
dependency
Lu under wake conditions
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Gust factor kp
CartwrightLonguet-Higgins (1956)
For Kaimal spectrum, the up-crossing frequency is
T is the time duration of each considered period
typical 10min
fC is the structural cut-off frequency the
rotor/blade filter frequency
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Gust factor kp pre-averaging time

• Most often, a 3-sec running average of recorded
  wind speed is performed, assuming that this time
  averaging represents the spatial averaging of the
  structure.
• By integrating the coherence function of the
  wind, the rotor filter may be found

Comparison of the filters
This way it is found that the wind speed data
should be pre-average over 5 to 20 sec to emulate
the rotor filter
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Gust factor kp pre-averaging time
Model works qualitatively but estimates10 too
high
Gust factor as function of pre-averaging time,
measurement height 100m and wind speed
10m/sltUlt12m/s.
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Gust factor kp height-dependency
Gust factor as function of height for different
wind speeds. Sinc-filter frequency is 1/3 Hz.
Gust factor as function of height for different
wind speeds. Sinc-filter frequency is 1/10 Hz.
IEC61400-1 For relevant averaging times, kp is
set 25 too high
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Gust factor kp wake effects
Gust factor only marginally different under wake
conditions
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Distribution of extreme gusts
Return period for Gust factor based on 10 sec
averaging data for 80m height (50 largest data).
Density function for Gust factor based on 10 sec
averaging data for 80m height (201 data points).
Gumbel distribution fits the data well,
especially at higher kp values
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Coherence of turbulence
IEC coherence
where b 12, but should rather be of order 5 to
fit Mann model

• In near-future experimental determination of b
• Directly from wind speed measurements
• Indirectly from tower bending moments
• Also previous work will be included

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Conclusion

• IEC scale of turbulence qualitatively good though
  10 too high
• Scale of turbulence is function of wind speed,
  for heights relevant for MW wts
• IEC gust factor approx. 25 too high approx. 1
  std
• Distribution of gust factor should be Gumbel
• Proposal for amendment to IEC61400-1
• specify that selected turbulence model shall
  yield (output) a flow field where
• mean and std. of Lu ,kp and b are within given
  limits
• distribution of (extreme) gusts must be Gumbel,
  with given values of scale and shape parameters