September 2011

ECN-M--11-086

Turbulence and Wind TurbinesArno J. Brand

Joachim Peinke Jakob Mann

Presented at: 13th European Turbulence Conference, Warsaw, Poland, 12-15 September 2011

Turbulence and wind turbines

Arno J. Brand ECN Wind Energy, Petten, Netherlands E-mail: brand@ecn.nl Joachim Peinke ForWind, Institute of Physics, University of Oldenburg, Oldenburg, Germany E-mail: peinke@uni-oldenburg.de Jakob Mann Risø Nat. Lab. for Sust. Energy, Techn. Univ. of Denmark, Wind En. Div., Roskilde, Denmark E-mail: jmsq@risoe.dtu.dk Abstract. The nature of turbulent flow towards, near and behind a wind turbine, the effect of turbulence on the electricity production and the mechanical loading of individual and clustered wind turbines, and some future issues are discussed.

1. Wind energy conversion and turbulence A wind energy conversion system extracts energy from the turbulent wind and while doing so creates extra turbulence. Wind energy conversion systems include horizontal axis wind turbines, vertical axis wind turbines, and other devices like kites or ladders, but in this paper the focus is on horizontal axis wind turbines. In the following these devices are referred to as wind turbines. Wind is motion of air in the planetary boundary layer. As shown in figure 1 it is a process at various time and space scales (Orlanski, 1975). This paper addresses small scale turbulence, which is all variation in time of wind speed and wind direction with periods less than ten minutes. In this paper an overview is given of the effect of wind turbines on turbulence, and the effect of turbulence on wind turbines. In addition various modeling approaches are presented. First, in section 2 descriptions are presented of the turbulent flow towards, near and behind a wind turbine. Next, in section 3 the electricity production and the mechanical loading under turbulent conditions are addressed. Finally, in section 4 some future issues are presented. 2. Turbulent flow towards, near and behind a wind turbine 2.1. The flow towards a wind turbine The flow towards a wind turbine is essentially turbulent, with wind speed variations originating from production of turbulent kinetic energy due to surface roughness in combination with production or destruction of turbulent kinetic energy due to atmospheric stability. The modeling of the flow towards a wind turbine is based on classical assumptions on the time variation of wind speed (van der Hoven, 1957), the type of the probability density function of wind speed variations within ten-minute periods (Wyngaard, 1992), and the shape of the wind speed profiles under various atmospheric stability conditions (Businger et al., 1971). These assumptions are shown in the figures 2, 3 and 4. Recent insights challenge these assumptions: the spectral gap in the Van der Hoven spectrum is absent over land (Courtney and Troen, 1990) and under unstable maritime conditions (Gjerstad et al., 1994), the distribution of wind speed variation is non-Gaussian (Böttcher et al., 2006), and wind speed profiles under maritime conditions differ from the Businger-Dyer profiles (Gryning et al., 2007).

Space Scale

Time Scale

second minute hour day week month year years

1000 km

100 km

10 km

1 km

100 m

10 m

1 m

10000 km trade winds

westerlies polar winds fronts

huricanes cyclones

thunderstorms mountain winds

tornadoes

gusts turbulence

Figure 1. Processes in the planetary boundary layer according to the classification by Orlanski, 1975

1.E-041.E-031.E-021.E-011.E+001.E+011.E+021.E+031.E+041.E+05

Time Scale [Hour]

Am

plitu

de [m

2 /s2 ]

Figure 2. The classical assumption on the time variation of the wind speed. The spectrum of wind

speed variation has a gap allowing for a separation of scales (van der Hoven, 1957) The turbulence in the flow towards a wind turbine is modeled on basis of similarity theory in combination with computational fluid dynamics methods (Satoh, 2004; chapter 11). The computational fluid dynamics approaches employ closure models in order to threat the effect of scales smaller than the resolution of the numerical model. These closure models include the classic zero, one and two-equation turbulence sub-models as well as the modern Smagorinsky and Mellor-Yamada sub-models. The closure models are implemented in atmospheric models like the HiRLAM (Undén et al., 2002), the WRF (Skamarock et al., 2008) or EllipSys3D (Bechman et al., 2007).

f(u)

μu + σuμu – σu μuu

Figure 3. Sketch of the classical assumption of the probability density function f(u) of the wind speed u within ten-minute periods. This distribution is Gaussian and is characterized by the

average value μU and the standard deviation σU (Wyngaard, 1992)

μu

z

Uh

h

stable

unstable

neutral

z0

Figure 4. Sketch of the classical assumption on the shape of the wind speed profiles under various atmospheric stability conditions but for the same wind speed Uh at the top h of the atmospheric boundary layer. The average wind speed μU depends on the height z; z0 is the surface roughness

length where the wind speed is zero (Businger et al., 1971) 2.2. The flow near a wind turbine Upon approaching a wind turbine, the wind speed decreases and the turbulence increases in anticipation of the flow disturbing and energy extracting object. The flow near a wind turbine is modeled by using a rotor disk which contains the rotor blades. The flow through the rotor disk traditionally is modeled homogeneously under the assumption that the wind speed and the turbulence do not depend on the position in the rotor disk, although it is not unusual to include some inhomogeneity in the form of a horizontal or vertical

wind gradient in order to model wind shear respectively yaw misalignment. The turbulence in a point in the rotor disk is modeled on basis of a spectrum, usually Kaimal (Kaimal et al., 1972), in combination with inverse Fourier transforms (Veers, 1984), or an approach based on rapid distortion theory (Mann, 1998). A rotating rotor blade meets the incoming wind, and as a result feels an effective wind speed and an effective angle of attack (figure 5). Turbulent structures in the incoming wind are rotationally sampled by the rotor blade. The flow past a rotor blade is modeled by using blade-element/momentum theory and employing sectional airfoil data (Sørensen, 2011). The airfoil data have been found to depend heavily on unsteadiness (Devinant et al., 2002); for example a turbulent intensity of a percent considerably reduces the lift force and increases the drag force which effectively spoils rotor performance. The airfoil data traditionally originate from wind tunnel experiments but to date also from computationally fluid dynamics methods or aerodynamic design methods. If the computationally fluid dynamics method is based on the Reynolds-averaged Navier-Stokes equations, usually a kε or kω sub-model is used in order to calculate the flow over the airfoil section beyond transition. In the case of a Large Eddy Simulation method, the Smagorinsky-Lilly sub-grid model is used for this purpose. Aerodynamic design codes employ integral boundary layer formulations. 2.3. The flow behind a wind turbine The flow behind a wind turbine is sub-divided in three regions, each requiring distinct modeling approaches (Vermeer et al., 2003). This is shown in the figures 6 and 7. In the near wake the flow is dominated by the velocity deficit due to the energy extraction and the vortices created at the tip of the rotor blades, resulting in a wind speed deficit and extra turbulence. In this region the flow structure essentially depends on the aerodynamics of the rotor blades. On basis of solutions of this flow problem and empirical information the resulting flow is assumed to have a top-hat shaped wind speed profile and edge-concentrated turbulence. In the intermediate wake the tip vortices gradually lose identity, and the undisturbed flow mixes with the core flow. As a result the wind speed deficit and the extra turbulence begin to decay. In the far wake equilibrium is assumed between the convective forces and the gradients of the turbulent momentum fluxes. On basis of analytical solutions of the governing equations the profiles of the wind speed deficit are assumed to be Gaussian. On basis of empirical information the profiles of the extra turbulence are assumed to be Gaussian too, but with different values of the decay parameters. Both the velocity deficit and the extra turbulence decay with the streamwise and the spanwise distance until the limit situation of the upstream wind speed and the ambient turbulence is reached. Depending of the atmospheric stability, this takes a distance of 10 to 20 rotor diameters. The mechanism here is redistribution of energy between the mean and the turbulent wind field in combination with feed-in of undisturbed flow. A wind turbine wake does not have a fixed position even if the mean wind direction is constant: it has been found to move in horizontal as well as vertical direction. This effect is known as wake meandering. A meandering wake smears the velocity deficit and the extra turbulence over a much larger volume than a fixed wake does. To date the process is not completely understood; hypotheses include stochastic wind direction variation (Bingöl et al., 2010), an analogy with bluff body vortex shedding (Medici & Alfredsson, 2006), and motion due to a spanwise wind speed component (Larsen et al., 2008). May this be as it is, a small number of empirical wake meandering models exist.

u(1–a)

α

w

ωr(1+a')

Figure 5. The effective wind speed w and the effective angle of attack α of a section of a wind turbine rotor blade is a function of the upstream wind speed u, the rotor speed ω and the radial

position r. The induction factors a and a' represent the effect of the rotor blade on the flow

y

x

μ0

μw

σw

y

x

σ0

near wake intermediate wake

far wake

Figure 6. Top view of the average μ (top) and the standard deviation σ (bottom) of the wind speed at hub height near a wind turbine. The upstream values are μ0 and σ0, and the downstream values

are μw and σw. The streamwise and the spanwise directions are x and y, respectively

z

x

μ0 μw μw μw

σ0

z

x

σw

near wake intermediate wake

far wake

σw σw

Figure 7. Side view of the average μ (top) and the standard deviation σ (bottom) of the wind speed near a wind turbine as a function of the height. The upstream values are μ0 and σ0, and the

downstream values are μw and σw. The streamwise and the vertical directions are x and z, respectively

3. Effect of turbulence on electricity production and mechanical loading 3.1. Individual wind turbine The wind exerts forces on the rotor blades of a wind turbine. When rotating, the in-plane components of the aerodynamic force on the rotor blades cause torque about the rotor axis. Similarly, the out-of-plane components cause thrust on the rotor. Turbulence now leads to time variations in the rotor shaft torque and the rotor thrust. The aerodynamic power is the product of the rotor shaft torque and the rotor speed. Turbulence therefore gives rise to variations in the power and consequently the electricity production. In fact, turbulence is believed to be essential in assessing energy yield (Gottschall & Peinke, 2008). The mechanical loading of the components of a wind turbine, like the blades or the shaft, originates from the aerodynamic force on the rotor blades. Turbulence therefore causes variations in the mechanical loading; in other words: it causes fatigue loading. To date fatigue loading is

considered the primary factor which determines the life time of a wind turbine, and several methods for designing for a given life time exist. Understanding and characterizing turbulence before and behind a wind turbine is believed to be essential here (Mücke et al., 2010). 3.2. Cluster of wind turbines In a cluster of wind turbines the flow towards a given wind turbine is affected by the velocity deficit and the extra turbulence due to any upstream wind turbine. Such a cluster usually is referred to as a wind farm. In general, this interaction leads to a complex structure of the flow in and behind the wind farm. For example, depending on the wind direction and the layout of the wind farm, regions with multiple velocity wakes and multiple turbulence wakes may be identified. In this section of the paper the focus is on the relatively simple case where the wind direction is parallel to a row of wind turbines. The limit situation of the upstream wind speed and the ambient turbulence only is reached after the most downstream turbine of a row of wind turbines. In the row a different limit situation is reached (Barthelmie et al., 2004). If the separation distance between the turbines is smaller than a critical value, the power deficit at the second turbine is the largest in the row and the power deficits in the subsequent turbines are constant. In this case beyond the second turbine equilibrium is reached between the mean kinetic energy extracted by a wind turbine and the vertical fluxes of the turbulent kinetic energy (Cal et al., 2010). On the other hand, for separation distances larger than the critical value, the power deficit smoothly increases with position in the row and a constant power deficit is not obtained. The mechanism in this case is superposition of the individual values of the velocity deficit and the added turbulence, without replacement from above. The consequences for the mechanical loading of the turbine components are less clear, but in general the loading has been found to increase with the position in the row. 4. Future issues In the preceding sections of this paper it has been shown that a wind turbine produces turbulence at a scale of the rotor size (diameter as well as chord) and the corresponding frequency (rotor speed) and induced velocity, and that this turbulence decays to smaller scales when traveling in downstream direction and eventually dissipates to a level which can not be discriminated from the background turbulence. In addition it has been shown that a wind turbine adds turbulence to the inhomogeneous turbulence in the atmospheric boundary layer, which turbulence is created by the always present roughness of the surface but usually also by the thermal structure of the atmospheric boundary layer. In the remainder we address three outstanding issues. First, the classic turbulence sub-models that were addressed in the section 2 have been found to perform poorly in validations on basis of full-scale data. This has to do with the limitations of the experimental techniques (usually point measurements), but it also points to a limited understanding of the complex structure of the flow towards, near and behind a wind turbine. Second, as already explained in section 2.1, the modeling of the flow towards a wind turbine is based on classical assumptions on the variability of wind speed which have been challenged by recent insights. The third issue is the assumed homogeneity of the wind field in the rotor plane (section 2.2). This assumption has been found to be reasonable for wind turbines which are small compared to the length scales of the coherent motions in the atmospheric boundary layer. (These coherent motions include – but are not limited to – flow induced by thermal instability, low-frequency/large-scale structures due to weather systems, and short-lived and local bursts.) Since the scales of larger rotors are of the same order as those of the coherent motions, the wind field in the rotor plane of such a wind turbine is expected to be inhomogeneous.

In order to resolve these issues and to identify the consequences for the design of wind turbines, there is a need to describe the physical processes which are relevant to the production, the transport and the dissipation of the turbulence due to the wind turbine and their interaction with the turbulence in the atmospheric boundary layer. New experiments will play an important role in this research (Knebel et al., 2010). In addition there is a need to develop a comprehensive model of this kind of turbulence for application in wind turbine and wind farm design. References BARTHELMIE R., LARSEN G., PRYOR S., JØRGENSEN H., BERGSTRÖM H., SCHLEZ W., RADOS K., LANGE B., VØLUND P., NECKELMANN S., MOGENSEN S., SCHEPERS G., HEGBERG T., FOLKERTS L., & MAGNUSSON M. 2004 Efficient development of offshore wind farms – Modeling wake and boundary layer interactions. Wind Energy, Vol. 7, Iss. 3, pp. 225-245 BECHMANN A., SØRENSEN N. & JOHANSEN J. 2007 Atmospheric flow over terrain using hybrid RANS/LES. In: Proceedings of EWEC 2007. European Wind Energy Association, pp. 64-67 BINGÖL F., MANN J. & LARSEN G.C. 2010 Light detection and ranging measurements of wake dynamics - Part I: One-dimensional scanning. Wind Energy, Vol. 13, Iss. 1, pp. 51-61 BÖTTCHER F., BARTH ST. & PEINKE J. 2006 Small and large-scale fluctuations in atmospheric wind speeds. Stoch. Env. Res. and Risk Ass., Vol. 21, No. 3, pp. 299-308 BUSINGER J.A., WYNGAARD J.C., IZUMI Y. & BRADLEY E.F. 1971 Flux-profile relationship in the atmospheric surface layer. J. Atmos. Sci., Vol. 28, pp. 181-189 CAL R.B., LEBRÓN J., CASTILLO L., KANG H.S. & MENEVEAU C. 2010 Experimental study of the horizontally averaged flow structure in a model wind-turbine array boundary layer. J. Renewable Sustainable Energy, Vol. 2, 013106, 25 pp COURTNEY M. & TROEN I. 1990 Wind speed spectrum from one year of continuous 8 Hz measurements. In: Ninth Symposium of Turbulence and Diffusion, pp. 301-304 DEVINANT PH., LAVERNE T., & HUREAU J. 2002 Experimental study of wind turbine airfoil aerodynamics in high turbulence. J. Wind Eng. Ind. Aerodyn., Vol. 90, Iss. 6, pp. 689-707 GJERSTAD J., AASEN S.E., ANDERSSON H.I., BREVIK I., & LØVSETH J. 1994 An analysis of low-frequency maritime atmospheric turbulence. J. Atmos. Sci., Vol. 52, pp. 2663-2669 GOTTSCHALL J. & PEINKE J. 2008 How to improve the estimation of power curves for wind turbines. Environ. Res. Lett., Vol. 3, 015005, 7 pp GRYNING S.E., BATCHVAVORA E., BRÜMMER B., JØRGENSEN H. & LARSEN S. 2007 On the extension of the wind profile over homogeneous terrain beyond the surface layer. Bound. Layer Meteor., Vol. 124, pp. 251-268 VAN DER HOVEN I. 1957 Power spectrum of horizontal wind speed in the frequency range from 0.0007 to 900 cycles per hour. J. Meteorology, Vol. 14, pp. 160-164 KAIMAL J.C., WYNGAARD J.C., IZUMI Y. & COTÉ O.R. 1972 Spectral characteristics of surface layer turbulence. Q. Journal Roy. Met. Soc., Vol. 98, Iss. 417, pp. 563-589 KNEBEL P., KITTEL A. & PEINKE J. 2010. Atmospheric wind field conditions generated by active grids. Exps. Fluids, Submitted LARSEN G.C., MADSEN H.A., THOMSEN K. & LARSEN T.J. 2010 Wake meandering: A pragmatic approach. Wind Energy, Vol. 11, Iss. 4, pp. 377-395 MANN J. 1998 Wind field simulation. Prob. Mech. Engng., Vol. 13, No. 4, pp. 269-282 MEDICI D. & ALFREDSSON P.H. 2006 Measurements on a wind turbine wake – 3D effects and bluff body vortex shedding. Wind Energy, Vol. 9, Iss. 3, pp. 219-236

MÜCKE T., KLEINHANS D. & PEINKE J. 2010 Atmospheric turbulence and its influence on the alternating loads on wind turbines. Wind Energy, Vol. 14, Iss. 2, pp. 301-316 ORLANSKI I. 1975 A rational subdivsion of scales for atmospheric processes. Bull. Am. Met. Soc., Vol. 56, No. 5, pp. 527-530 SATOH M. 2004 Atmospheric circulation dynamics and general circulation models. Springer. ISBN 3-540-42638-8 SKAMAROCK W.C., KLEMP J.B., DUDHIA J., GILL D.O., BARKER D.M., DUDA M.G., HUANG X.-Y., WANG W. & POWERS J.G. 2008 A description of the Advanced Research WRF Version 3. NCAR Technical Note NCAR/TN–475+STR SØRENSEN J.N. 2011 Aerodynamic aspects of wind energy conversion. Ann. Rev. Fluid Mech., Vol. 43, pp. 427-448 UNDÉN P. et al. 2002. HiRLAM-5 scientific documentation. Online: www.hirlam.org, accessed 31 May 2011 VEERS P.S. 1984 Three-dimensional wind simulation. Technical report SAND88-0152, Sandia National Laboratories VERMEER L.J., SØRENSEN J.N. & CRESPO A. 2003 Wind turbine wake aerodynamics. Prog. Aerosp. Sci., Vol. 39, pp. 467-510 WYNGAARD J.C. 1992 Atmospheric turbulence. Ann. Rev. Fluid Mech., Vol. 24, pp. 205-234

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deVi

ewW

ind

Spee

d St

anda

rd D

evia

tion

–Si

de V

iew

z

σ 0

σ w

σ w

σ w

x

near

wak

e in

term

edia

te w

ake

far w

ake

16O

utlin

e -M

otiv

atio

n -F

low

-Ef

fect

s -I

ssue

s -S

umm

ary

17

Effe

ct o

f Tur

bule

nce

Win

dTu

rbin

eR

otor

Win

d Tu

rbin

e R

otor

Sou

rce:

Tom

Obd

am

17O

utlin

e -M

otiv

atio

n -F

low

-Ef

fect

s -I

ssue

s -S

umm

ary

18

Effe

ct o

f Tur

bule

nce

Clu

ster

ofW

ind

Turb

ines

Clu

ster

of W

ind

Turb

ines

W

ind

Spee

d hi

gh

low

Uno

m

Ust

op

very

hig

h

low

nom

Ust

art

med

ium

WT1

WT2

y

W

WT3

x W

T4

18O

utlin

e -M

otiv

atio

n -F

low

-Ef

fect

s -I

ssue

s -S

umm

ary

19

Effe

ct o

f Tur

bule

nce

Clu

ster

ofW

ind

Turb

ines

Clu

ster

of W

ind

Turb

ines

C

apac

ity

full

zero

zero

zero

100%

0%

part

ial

WT1

WT2

y

W

WT3

WT1

+WT2

+WT3

+WT4

x W

T4

19O

utlin

e -M

otiv

atio

n -F

low

-Ef

fect

s -I

ssue

s -S

umm

ary

20

Rot

oran

dW

ind

Scal

es

The

Hom

ogen

eity

Issu

e

1000

k

1000

0 km

tra

de w

inds

w

este

rlies

Rot

or a

nd W

ind

Scal

es

1000

km

100

km

10km

pola

r w

inds

fr

onts

hu

rican

es

cycl

ones

Spa

ce S

cale

10 k

m

1 km

100

m

yth

unde

rsto

rms

mou

ntai

n w

inds

to

rnad

oes

100

m

10 m

1m

gu

sts

turb

ulen

ce

Sca

les

of R

otor

≈S

cale

s of

Coh

eren

t Mot

ions

Tim

e S

cale

seco

nd m

inut

e ho

ur

day

wee

k m

onth

ye

ar

year

s

1 m

Sou

rce:

Orla

nski

, 197

5

20O

utlin

e -M

otiv

atio

n -F

low

-Ef

fect

s -I

ssue

s -S

umm

ary

21

Win

dSp

eed

Spec

trum

The

Varia

bilit

y Is

sue

2]

Win

d Sp

eed

Spec

trum

Mod

est D

epth

tude [m2/s

2Amplit

1.E

-04

1.E

-03

1.E

-02

1.E

-01

1.E

+00

1.E

+01

1.E

+02

1.E

+03

1.E

+04

1.E

+05

Tim

e S

cale

[Hou

r]

It

Al

It

Al

Di

lI

tM

it

It

Mi

t

10+5

1

0+4

10

+3

10+2

10+1

100

1

0-1

1

0-2

10

-3

1

0-4

Int

er-A

nnua

l In

tra-A

nnua

l

Diu

rnal

Inte

r-M

inut

e

I

ntra

-Min

ute

Sour

ce: C

ourtn

ey a

nd T

roen

, 199

0; G

jers

tad

et a

l., 1

994

21O

utlin

e -M

otiv

atio

n -F

low

-Ef

fect

s -I

ssue

s -S

umm

ary

22

Dis

trib

utio

nof

Win

dSp

eed

Varia

tion

The

Varia

bilit

y Is

sue

f(

u)

Dis

trib

utio

n of

Win

d Sp

eed

Varia

tion

Hea

vier

Tai

ls

uμ u

+ σ

uμ u

– σ

uμ u

u

Sou

rce:

Böt

tche

r et a

l., 2

006

22O

utlin

e -M

otiv

atio

n -F

low

-Ef

fect

s -I

ssue

s -S

umm

ary

23

Win

dSp

eed

Prof

ile

The

Varia

bilit

y Is

sue

z

Win

d Sp

eed

Prof

ile

Hig

her W

ind

Spe

eds

h

stab

le

neut

ral

μ

unst

able

z 0

μ uU

h S

ourc

e: G

ryni

ng e

t al.,

200

7

23O

utlin

e -M

otiv

atio

n -F

low

-Ef

fect

s -I

ssue

s -S

umm

ary

24

The

Sub-

Mod

els

Issu

e

kεm

odel

sve

rsus

mea

sure

men

ts

1

1.2

Obs

erva

tions

kε-m

odel

s ve

rsus

mea

sure

men

ts

0.81

Obs

erva

tions

Wak

eFar

mF

arm

Flo

w

0.4

0.6

Pi/P1

0

0.2

01

23

45

6

orde

r in

row

Sou

rce:

Edw

in B

otN

ear W

ake:

Red

uced

turb

ulen

t mix

ing

Inte

rmed

iate

Wak

e:Tu

rbul

entm

ixin

gco

ncen

trate

d

24O

utlin

e -M

otiv

atio

n -F

low

-Ef

fect

s -I

ssue

s -S

umm

ary

Inte

rmed

iate

Wak

e: T

urbu

lent

mix

ing

conc

entra

ted

in a

nnul

ar s

hear

laye

r

25

Sum

mar

y

Win

d en

ergy

con

vers

ion

Flow

tow

ards

, nea

r and

beh

ind

a w

ind

turb

ine

Effe

cts

of tu

rbul

ence

Mod

ellin

g is

sues

25O

utlin

e -M

otiv

atio

n -F

low

-Ef

fect

s -I

ssue

s -S

umm

ary

26

Arn

o J.

Bra

nd

EC

N W

ind

Ene

rgy

Win

d tu

rbin

e ro

tor a

nd W

ind

farm

Aer

odyn

amic

s

M: P

.O. B

ox 1

, NL

1755

ZG

Pet

ten,

Net

herla

nds

E: b

rand

@ec

n.nl

T: +

31 2

24 5

6 47

75F:

+31

224

56

8214

I: nl

.link

edin

.com

/in/a

rnob

rand

26O

utlin

e -M

otiv

atio

n -F

low

-Ef

fect

s -I

ssue

s -S

umm

ary