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



Shear Exponent (α) distributions: at different sites

Mark Kelly May 2015

α depends on site (z0,eff), height (z), rotor size (Δz)

3



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



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



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



systematic behavior:

σα (U) ~ 1/U (+minor z/z0,eff dependence)

Variability in shear : σα | U




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



Stability and shear

ASL (10-40m) above ASL (60-160m)

• Can map stability to shear in ASL; NOT at current hub heights ...




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



(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



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



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




Shear-veer behavior/stats:




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)


(formerly Risø)

Buoyant RDT

“Mann”-turbulence model, plus buoyancy...

Abhijit Chougule, Mark Kelly, Jakob Mann

MET group



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



Rapid Distortion Theory (RDT)

• + model for eddy lifetime = “Mann Model”

get anisotropy, per wavenumber (eddy size)




Anisotropy – it’s real...especially due to stability

Lumley triangle : invariants of motion...stress tensor




‘old’ vs. buoyant Mann-model: unstable conditions




buoyant Mann-model: unstable conditions

TT, wT, uT spectra




buoyant Mann-model: stable conditions

uu, vv, ww, uw spectra TT, wT, uT spectra




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

shear, turbulence, stability, and veer - vindmølleindustrien · (formerly risø) shear,...

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