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Real Life Turbulence and Model
Simplifications
Jørgen Højstrup
Wind Solutions/Højstrup Wind Energy
VindKraftNet
28 May 2015
Contents
• What is turbulence?
• Description of turbulence
• Modelling spectra.
• Wake turbulence – near and far
• Measured turbulence
• Distributions and gusts
What is turbulence?
May 2015 Wind Solutions 3
What is turbulence?
• In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic, stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time.
May 2015 Wind Solutions 4
Not turbulence
May 2015 Wind Solutions 5
Turbulence
May 2015 Wind Solutions 6
Turbulence
May 2015 Wind Solutions 7
Generating turbulence
• Turbulence is generated by mechanical forces along the wind (U-component).
• Turbulent eddies are generated (or destroyed) by thermal forces in the vertical component.
May 2015 Wind Solutions 8
Surface friction decreases wind speed
He
ight
[m]
Windspeed [m/s]May 2015 Wind Solutions 9
He
ight
[m]
Windspeed [m/s]May 2015 Wind Solutions 10
Mixing of air with different speeds
He
ight
[m]
Windspeed [m/s]May 2015 Wind Solutions 11
Wind shear and turbulence?
• Assume increasing wind speed with height • Assume that we have vertical turbulent
fluctuations • A positive vertical fluctuation will bring an
air parcel to height “2” where the speed is higher – therefore we get a negative variation on the u-component, or in other words the product uw will be negative
• A negative vertical fluctuation will bring an air parcel to height “3” where the speed is lower – therefore we get a positive variation on the u-component, or in other words again the product uw will be negative.
• The higher the wind shear, the larger the absolute value of uw
Description of turbulence
May 2015 Wind Solutions 13
Taylor Hypothesis
• FROZEN TURBULENCE
• Turbulent structures are advected past your observation point.
• Frequency = propagation speed/wave length
• You always see turbulence described as time series, but you should think of turbulence as spatial structures
May 2015 Wind Solutions 14
0 200 400 600 800 1000
6
8
10
12
14
Time [sec]
Distribution: We count how many times we have a value in a certain interval
7 8 9 10 11 12 13
0
20
40
60
80
100
120
140
160
180
Distribution
0 200 400 600 800 1000
6
8
10
12
14
Time [sec]
Variance = ([a1 – M]2+[a2 – M]2 +.. [an – M]2)/n =1.0 Standard deviation = (also called RMS)
Turbulence intensity = std.dev./mean = 10%
Variance
Standard deviation
May 2015 Wind Solutions 16
Spectra
• Definition: Decomposition of variance on different frequencies (scales) • Length scale = U*f • We plot frequency*power spectra (area preserving in loglin plot) • Area under graph equals the variance
Spectra
Coherence
• “Correlation” of spectra measured at separate points
Modelling Spectra
May 2015 Wind Solutions 20
Spectra - models
• Kaimal – measurements up to 32 m. Fits neutral data. • Modified Kaimal (IEC 61400-1), to work higher up than 32m • Von Karmann – Analytical autocorrelation and coherence functions
(Mann model). • Does not fit data (shape more pointed than Kaimal)
• Unstable/stable spectra • High windspeed spectra
Kaimal Spectra
• Definition: Decomposition of variance on different frequencies (scales) • Length scale = U*f • We plot frequency*power spectra (area preserving in loglin plot) • Area under graph equals the variance
Thermal turbulence
Højstrup: Journal of the Atmospheric Sciences, 1982, 39, pp. 2239-2248
Thermally generated turbulence appear at scales comparable to the height of the boundary layer. Daytime: 1-5 km We see the opposite effect in stable conditions (cooling from the ground) where turbulence with large length scales are being suppressed, i.e. the peak moves towards higher frequencies.
Spectra length scales
Length scales (measurements Vindeby 48m)
• Large range of scales • IEC 61400-12-1 ed.2
specifies the length scale as constant 600m, independent of height (Kaimal spectrum fixed at 30m height)
• IEC 61400-12-1 ed.3 specifies length scale as constant 1200 above 60 m
High wind speed data
Højstrup, Larsen, Madsen: AMS 9th symposium on turbulence and diffusion, 1990, pp.305-308
Additional energy at 3000m length scale. Can be modelled, but gets complicated.
Wake turbulence – near and far
May 2015 Wind Solutions 27
Turbulence in wakes
Strong shear in upper part of wake creates large amount of turbulence
Turbulence in wakes
Hubheight wake at 2D (Nørrekær Enge II) • Wakes generate large shears at length
scales comparable with the rotor size • Consequently wake turbulence is
generated at much smaller scales than “ordinary” turbulence.
Turbulence in wakes
Turbulence has a long memory
The turbulence “remembers” upstream conditions much longer than the average wind speed. Here exemplified by the island of Gotland, but might just as well be an offshore wind farm. Measurements by RAF C130. High
turbulence
Low turbulence
Low turbulence
Measured turbulence
May 2015 Wind Solutions 33
Quick and dirty turbulence intensity
• Scaling velocity u*
• Along wind: σu/u* = 2.5
• Lateral: σv/u* = 2
• Vertical: σw/u* = 1.5
• Log profile: U = u*/k * ln(z/z0), k=0.4
=>
• Turbulence intensity: σu/U = 1/ln(z/z0)
• Correlation coefficient <uw>/(σuσw) = -0.3
May 2015 Wind Solutions 34
Quick and dirty turbulence intensity
• Land, height 70m, grass surface, roughness length = 0.03 m • => Turbulence intensity: 13%
• Offshore, height 70m, roughness length = 0.0001 m • => Turbulence intensity: 7%
• Forest, height 70m, grass surface, roughness length = 1 m • => Turbulence intensity: 24%
May 2015 Wind Solutions 35
Offshore turb. Intensities. Fetch 100km
5 10 15 20 25 300.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.11
Vertical bars denote
+-1 std.err.on mean value
Horns Rev 62m
Tu
rb.int.
Wind speed [m/s]May 2015 Wind Solutions 36
Measurement of turbulence
• Because of instrument limitations you do not measure the whole turbulence intensity.
• Lowest frequency in measurement f=1/T
• Highest frequency in measurement determined by averaging time and instrument time constant.
• For power curve fluctuations (and some loads) the relevant way to measure would be to average wind speed over the rotor area. Therefore measured turbulence will always be higher than the turbulence relevant for the rotor.
May 2015 Wind Solutions 37
Measurement of turbulence
• Cup anemometer timecst= L/U. Typical 0.2 sec (L=distance constant, 2m, U wind speed 10m/s)
• Typical timecst for 100m rotor at 10 m/s: 10 sec
At 10 m/s you would measure 93% of the total std.dev. by cupanemometer (600 sec avg.)
At 10 m/s you would measure 60% of the total std.dev. by a sensor the size of a 100m rotor (600 sec avg).
May 2015 Wind Solutions 38
Nice graph showing connection
May 2015 Wind Solutions 39
Distributions and gusts
May 2015 Wind Solutions 40
Turbulence is not Gaussian Wind speed fluctuations are nearly Gaussian Accelerations are not Gaussian
THEREFORE ATMOSPHERIC TURBULENCE IS NOT A RESULT OF A GAUSSIAN PROCESS
Gust from turbulence intensity Simulation Measured
Theory:
Gust from turbulence intensity
0 10 20 30 40 50 60
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
1 minute
10 minutes
1 hour
Gu
st fa
cto
r: (
Um
ax-U
avg)/
u
Wind speed [m/s]
Height 50m
Solid line: Kaimal spectrum
Dashed line: JH spectrum
Thank you for your attention
Højstrup Wind Energy & Wind Solutions www.wind-solutions.com [email protected]