Real Life Turbulence and Model Simplifications. Jørgen Højstrup Wind Solutions/Højstrup Wind Energy VindKraftNet 28 May 2015

Transcription

1 Real Life Turbulence and Model Simplifications Jørgen Højstrup Wind Solutions/Højstrup Wind Energy VindKraftNet 28 May 2015

2 Contents What is turbulence? Description of turbulence Modelling spectra. Wake turbulence near and far Measured turbulence Distributions and gusts

3 What is turbulence? May 2015 Wind Solutions 3

4 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

5 Not turbulence May 2015 Wind Solutions 5

6 Turbulence May 2015 Wind Solutions 6

7 Turbulence May 2015 Wind Solutions 7

8 Generating turbulence Turbulence is generated by mechanical forces along the wind (Ucomponent). Turbulent eddies are generated (or destroyed) by thermal forces in the vertical component. May 2015 Wind Solutions 8

9 Height [m] Surface friction decreases wind speed Windspeed [m/s] May 2015 Wind Solutions 9

10 Height [m] Windspeed [m/s] May 2015 Wind Solutions 10

11 Height [m] Mixing of air with different speeds Windspeed [m/s] May 2015 Wind Solutions 11

12 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

13 Description of turbulence May 2015 Wind Solutions 13

14 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

15 Distribution Time [sec] 180 Distribution: We count how many times we have a value in a certain interval

16 Standard deviation Time [sec] Variance = ([a 1 M] 2 +[a 2 M] [a n M] 2 )/n =1.0 Standard deviation = Variance (also called RMS) Turbulence intensity = std.dev./mean = 10% May 2015 Wind Solutions 16

17 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

18 Spectra

19 Coherence Correlation of spectra measured at separate points

20 Modelling Spectra May 2015 Wind Solutions 20

21 Spectra - models Kaimal measurements up to 32 m. Fits neutral data. Modified Kaimal (IEC ), 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

22 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

23 Thermal turbulence 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. Højstrup: Journal of the Atmospheric Sciences, 1982, 39, pp

24 Spectra length scales

25 Length scales (measurements Vindeby 48m) Large range of scales IEC ed.2 specifies the length scale as constant 600m, independent of height (Kaimal spectrum fixed at 30m height) IEC ed.3 specifies length scale as constant 1200 above 60 m

26 High wind speed data Additional energy at 3000m length scale. Can be modelled, but gets complicated. Højstrup, Larsen, Madsen: AMS 9 th symposium on turbulence and diffusion, 1990, pp

27 Wake turbulence near and far May 2015 Wind Solutions 27

28 Turbulence in wakes Strong shear in upper part of wake creates large amount of turbulence

29 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.

30 Turbulence in wakes

31 Turbulence has a long memory The turbulence remembers upstream conditions much longer than the average wind speed. Low turbulence Here exemplified by the island of Gotland, but might just as well be an offshore wind farm. High turbulence Low turbulence Measurements by RAF C130.

32 Measured turbulence May 2015 Wind Solutions 33

33 Quick and dirty turbulence intensity Scaling velocity u * Along wind: σ u /u * = 2.5 Lateral: σ v /u * = 2 Vertical: σ w /u * = 1.5 Log profile: U = u * /k * ln(z/z 0 ), k=0.4 => Turbulence intensity: σ u /U = 1/ln(z/z 0 ) Correlation coefficient <uw>/(σ u σ w ) = -0.3 May 2015 Wind Solutions 34

34 Quick and dirty turbulence intensity Land, height 70m, grass surface, roughness length = 0.03 m => Turbulence intensity: 13% Offshore, height 70m, roughness length = m => Turbulence intensity: 7% Forest, height 70m, grass surface, roughness length = 1 m => Turbulence intensity: 24% May 2015 Wind Solutions 35

35 Offshore turb. Intensities. Fetch 100km Turb.int Horns Rev 62m Vertical bars denote +-1 std.err.on mean value Wind speed [m/s] May 2015 Wind Solutions 36

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

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

38 Nice graph showing connection May 2015 Wind Solutions 39

39 Distributions and gusts May 2015 Wind Solutions 40

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

41 Gust from turbulence intensity Simulation Measured Theory:

42 Gust from turbulence intensity hour minutes Gust factor: (U max -U avg )/ u Height 50m Solid line: Kaimal spectrum Dashed line: JH spectrum 1 minute Wind speed [m/s]

43 Thank you for your attention Højstrup Wind Energy & Wind Solutions