Real Life Turbulence and Model Simplifications · What is turbulence? •In fluid dynamics,...

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.

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Not turbulence

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Turbulence

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Turbulence

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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.

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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

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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

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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

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Distribution

0 200 400 600 800 1000

6

8

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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

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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

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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

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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

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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

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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%

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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.

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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).

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Nice graph showing connection

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Distributions and gusts

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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 Jorgen@hojstrup.eu