Shear, turbulence, stability, and veer - Vindmølleindustrien · (formerly Risø) Shear,...
Transcript of Shear, turbulence, stability, and veer - Vindmølleindustrien · (formerly Risø) Shear,...
(formerly Risø)
Shear, turbulence, stability, and veer...
from observations and theory, toward application
(or, from simple measures, to turbulence, to loads...)
Mark Kelly
MET group, Wind Energy Dept.
Danish Technical University
May 2015
DTU Wind Energy, Technical University of Denmark, Risø campus
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Shear Exponent (α)
Mark Kelly May 2015
α depends on site (z0,eff), height (z), rotor size (Δz), wind speed (U)...
dU dz
U z
hub hub( ) ( )U z U z z z
2
DTU Wind Energy, Technical University of Denmark, Risø campus
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Shear Exponent (α) distributions: at different sites
Mark Kelly May 2015
α depends on site (z0,eff), height (z), rotor size (Δz)
3
DTU Wind Energy, Technical University of Denmark, Risø campus
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Shear Exponent (α) distributions: at different sites
Mark Kelly May 2015
α depends on site (z0,eff), height (z), rotor size (Δz), wind speed (U)
(+ stability, ABL depth...)
z/z0,eff
U=14-16 m/s
4
DTU Wind Energy, Technical University of Denmark, Risø campus
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Effective roughness, shear above ASL
• above ASL, surface roughness not applicable
– Stability, terrain/inhomogeneity & transport effects
via P(α) over all U; P(α,TI) over all U; P(α,U) over all TI
Mark Kelly May 2015
00
0 0
1
ln( / )
dU dz
U z z z 0,eff exp 1/z z
5
DTU Wind Energy, Technical University of Denmark, Risø campus
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Mean Shear Exponent <α|U > , with site (z/z0) :
• increase from cut-in; • peak at moderate U, then constant section;
lower z/z0,eff larger αpeak
filter out low TI :
• Reach αpeak , ~constant at higher U (not shown)
Mark Kelly May 2015 6
DTU Wind Energy, Technical University of Denmark, Risø campus
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systematic behavior:
σα (U) ~ 1/U (+minor z/z0,eff dependence)
Variability in shear : σα | U
Mark Kelly May 2015 7
DTU Wind Energy, Technical University of Denmark, Risø campus
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Stability and shear
ASL (10-40m)
• Can map stability to shear in ASL
11 1 5
( )5 | |
( )1
zP
L
zP L
Mark Kelly May 2015
P(L-1)
8
DTU Wind Energy, Technical University of Denmark, Risø campus
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Stability and shear
ASL (10-40m) above ASL (60-160m)
• Can map stability to shear in ASL; NOT at current hub heights ...
Mark Kelly May 2015 9
DTU Wind Energy, Technical University of Denmark, Risø campus
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A “decomposition” of the problem
Turbulent Kinetic Energy balance
• Surface-layer limit
where
using
Mark Kelly May 2015
*0 0
2 2
0 *0 *0
( )
/
u gz w T
U u U u U z
0de dU
uw B Tdt dz
( )z B T
U uw
0( / )B g w
1U
z TI
L
*02.5U u
2*0
0u uw
10
where
DTU Wind Energy, Technical University of Denmark, Risø campus
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(mean) TI ↔ shear
Mark Kelly May 2015
Extended ASL theory (stability-modified profile, TKE): where
0
01 ( )
II
c
0 0 * 0( / )u UI a u
11
DTU Wind Energy, Technical University of Denmark, Risø campus
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IEC 61400-12 Extended Rotor Equiv. Wind Speed:
Wind Shear + Wind Veer Effects
• Combined shear and veer effect is described by:
• Normalisation to reference shear and veer conditions possible as in case of just normalising shear effects
3
1n
1i
i3
iieqA
Acosvv
D l u veer fr
[m] [-] [-] [°/m] [%]
60 0 0 0.0 1.000
60 0 0 0.2 0.999
60 0 0 0.4 0.995
120 0 0 0.0 1.000
120 0 0 0.2 0.995
120 0 0 0.4 0.979
180 0 0 0.0 1.000
180 0 0 0.2 0.988
180 0 0 0.4 0.954
Mark Kelly May 2015
DTU Wind Energy, Technical University of Denmark, Risø campus
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Shear-veer connection/theory
• Ekman does not really work (“duh”, at left)
• Modified-Ekman not so bad (at right)
– currently testing; modification for “tall” regime
Mark Kelly May 2015 13
DTU Wind Energy, Technical University of Denmark, Risø campus
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Shear-veer behavior/stats:
Mark Kelly May 2015 14
DTU Wind Energy, Technical University of Denmark, Risø campus
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Summary
• Above ASL, can get <I> estimate from <α>, with IEC Iref
– Depends on effective roughness (z0 + hills); stability
• Variability: σα ~ 1/U ;
• TI is more important for input to loads (Dimitrov et al 2014)
– P(α) significant for fatigue loads in low-TI conditions
– P(α) can drive blade-tip deflection for extreme-TI
• P(α) power curve modification
Working towards completion:
• Monte-Carlo (HAWC2) -- loads distributions [G.Larsen, D.Verelst]:
– “2-D”: P(α, veer), and 1-D veer(α) parameterization
– “2-D” TI + (combined) shear/veer distributions
• Effective roughness (upwind terrain: elevation+roughness)
– z/z0,eff dependence for TI, α
• Modified power curve via P(α)
Mark Kelly May 2015 15
(formerly Risø)
Buoyant RDT
“Mann”-turbulence model, plus buoyancy...
Abhijit Chougule, Mark Kelly, Jakob Mann
MET group
DTU Wind Energy, Technical University of Denmark, Risø campus
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Rapid Distortion Theory (RDT)
• + model for eddy lifetime = “Mann Model”
get anisotropy, per wavenumber (eddy size)
Mark Kelly Tall-Wind, Århus 17 29 Jan 2013
DTU Wind Energy, Technical University of Denmark, Risø campus
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Rapid Distortion Theory (RDT)
• + model for eddy lifetime = “Mann Model”
get anisotropy, per wavenumber (eddy size)
Mark Kelly Tall-Wind, Århus 18 29 Jan 2013
DTU Wind Energy, Technical University of Denmark, Risø campus
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Anisotropy – it’s real...especially due to stability
Lumley triangle : invariants of motion...stress tensor
Mark Kelly Tall-Wind, Århus 19 29 Jan 2013
DTU Wind Energy, Technical University of Denmark, Risø campus
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‘old’ vs. buoyant Mann-model: unstable conditions
Mark Kelly Tall-Wind, Århus 20 29 Jan 2013
DTU Wind Energy, Technical University of Denmark, Risø campus
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buoyant Mann-model: unstable conditions
TT, wT, uT spectra
Mark Kelly Tall-Wind, Århus 21 29 Jan 2013
DTU Wind Energy, Technical University of Denmark, Risø campus
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buoyant Mann-model: stable conditions
uu, vv, ww, uw spectra TT, wT, uT spectra
Mark Kelly Tall-Wind, Århus 22 29 Jan 2013
DTU Wind Energy, Technical University of Denmark, Risø campus
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ongoing work, for spectral tensor+stability
• Automated fitting of parameters (done)
• Confirm relation: ‘model’ and measured stability, heat flux
– comparison to surface-layer theory (done)
• Inclusion of ground: blocked buoyant spectral tensor
– corrects for (very) unstable conditions
– confirm/adjust eddy lifetime model
• Inclusion in WEng
23 Mark Kelly May 2015