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A Review of Wind Turbine Wake Models and Future Directions

2013 North American Wind Energy Academy (NAWEA) Symposium

Matthew J. Churchfield

Boulder, Colorado August 6, 2013 NREL/PR-5200-60208

2

Why Are Wind Turbine Wakes Important?

• Wake effects impact: o Power production o Mechanical loads

• High importance in wind-plant-level control strategies

• Having a good wake model is a necessity in predicting plant performance and understanding fatigue loads

Wind speed (m/s)

Contours of instantaneous wind speed in simulated flow through the Lillgrund wind plant

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Flow field generated from large-eddy simulation (velocity field minus mean shear)

What Does a Wake Look Like?

Characteristics: • Velocity deficit • Low-frequency meandering • Intermittent edge • Shear-layer-generated turbulence

Notice how many of the characteristics describe some sort of unsteadiness

top view

view from downstream

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Differing Needs in Wake Modeling

• Power Prediction and Annual Energy Production (AEP) o Steady, time-averaged

• Loads

o Unsteady, time-accurate

• Control Strategies o Steady and unsteady may both be needed

• Basic Physics

o As much fidelity as possible

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Hierarchy of Wake Models

Empirical

Linearized Reynolds-averaged Navier-Stokes (RANS)

Nonlinear RANS

Large-eddy simulation (LES)

Other

-Jensen (1983)/Katíc (1986) (Park)

-Ainslie (1985) (Eddy-viscosity)

-Ott et al. (2011) (Fuga)

-Larsen et al. (2007) (Dynamic Wake Meandering)

-stochastic

-k-ω closure with actuator disk, line, fully resolved

-Dynamic Smagorinsky with actuator disk, line

Type Example

increasing cost/fidelity

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Wake Models for Power Production

• There are many models • Two of the more popular:

o Jensen (1983)/Katíc (1986) – Park model o Ainslie (1985) – Eddy-viscosity model

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u=

Uh

ub

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LES snapshot of full unsteady wake

x=D

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Park Eddy-Viscosity x/D

y/D

u/U

hub

x/D x/D

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Wake Models for Power Production

Park k = 0.06 Park k = 0.04 LES

Full wind farm example: Lillgrund (48 turbines)

Source: Smith et al. (2012)

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Wake Models for Power Production

• Fuga: o Linearized RANS based on simple turbulence closure κu*z o Uses spectral solution with reference tables that provide fast, accurate solution o Latest version incorporates atmospheric stability and wake meandering effects o Included in Wind Atlas Analysis and Application Program (WAsP) o Shown to work as well as full computational fluid dynamics (CFD) at 10-5 to 10-8 the cost o Designed for offshore wind plants

Fuga computed wakes (view from above) in the Nysted and Rødsand wind plants – Source: Ott (2013)

Fuga computed Horns Rev wind plant efficiency – Source: Ott (2013)

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Deep Array Correction

• Theory: A large wind farm that is many rows deep acts as an increased surface roughness that creates an internal boundary layer of slower flow

• Deep array correction can be applied to standard models, like Park

• See Schlez et al. (2009), Johnson et al. (2009), Brower and Robinson (2009)

Source: Schlez et al. (2009)/Johnson et al. (2009)

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How Well Do Reduced-Order Models Work?

• Overall, CFD (LES, DES, RANS) and vortex method seem to have less error than reduced-order models, but there are exceptions o Two cases computed with LES and one

computed with a RANS code were less accurate than those computed with the much more computationally efficient Fuga, Larsen, and Jensen models

decreasing simulation fidelity

Simulation Type

Wake prediction error from IEA Task 31 Wakebench, Sexbierum single wake benchmark

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How Well Do Reduced-Order Models Work?

Comparison of reduced-order models and data from Horns Rev wind plant (down the row case)

Source: Gaumond et al. (2012)

• The reduced-order models perform better for wider direction-bins • Gaumond et al. (2012) say the directional uncertainty is larger than

the bin width causing the observations to appear falsely high

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Wake Models For Mechanical Loads

• Fatigue loads are damaging o Such loads are cyclic o Can be caused by

intermittent/partial waking

• Need to model wake unsteadiness

lateral wake meandering

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Wake Models for Mechanical Loads

• Standard IEC 61400-1 says: “The increase in loading generally assumed to result from wake effects may be accounted for by the use of an effective turbulence intensity, which shall include adequate representation of the effect on loading of ambient turbulence and discrete and turbulent wake effects. For fatigue calculations, the effective turbulence intensity, Ieff, may be derived according to Annex D. For ultimate loads, Ieff, may be assumed to be the maximum of the wake turbulence intensity from neighbouring wind turbines as defined in Annex D.”

• This refers to the model of Frandsen (2005)

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Wake Models for Mechanical Loads

• Standard IEC 61400-1 says:

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0.1

0.12

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rotor diameters (D)

effe

ctiv

e co

mbi

ned

ambi

ent &

wak

e tu

rb. i

nten

sity

0 1 2 3 4 5 6 7 8 9 100.1

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rotor diameters (D)

max

. wak

e ce

nter

hub

hei

ght t

urb.

inte

nsity

increasing Wöhler constant from 1 to 12

ambient turb. intensity = 0.1

for fatigue loads for ultimate loads

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Wake Models for Mechanical Loads

• Dynamic Wake Meandering (DWM) model, Larsen et al. (2007) • Theory: The wake is a passive tracer in a turbulent atmospheric flow field • Advantages:

o Can inherently include atmospheric stability effects through turbulent field o Turbulent field can be stochastically generated using spectra/coherence from

model spectrum or field measurements • Procedure:

o Create a base wake with eddy-viscosity model o Obtain a turbulent field with smallest scales on order of rotor diameter o Use turbulent field to meander base wake

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Turbulence DWM (snapshot) LES (for comparison) x/D x/D x/D

y/D

y/D

u/U

hub

u/U

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u/U

hub

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Wake Models for Mechanical Loads

Loads calculations using DWM model for 7D separation case in Egmond aan Zee (OWEZ) offshore wind plant in Netherlands composed of Vestas V90 turbines (see Larsen et al. (2012))

Loads predictions compare remarkably well to measurements

Source: Larsen

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Wake Models for Mechanical Loads

• Theory: stochastic wake model using wake spectral characteristics o With mean field, power spectral density (PSD), and coherence measurements or LES of

wake field, model spectra and coherence could be made to stochastically generate wake o Similar to stochastic generation of atmospheric turbulence, except that wake is not

homogeneous in horizontal o This idea is currently being investigated by a group led by L. Manuel (University of Texas,

Austin) and P. Veers (NREL)

frequency

S(f)

Coh

separation wake time history mean flow

PSD

Coherence

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Conclusions

• Wakes are very complex due to their unsteadiness, interaction with atmospheric turbulence, and interaction with each other o This is difficult to model in a computationally inexpensive way

• Range of wake models are needed, but right now there is lack of

computationally-inexpensive models suitable for wake-induced loads analysis o Dynamic wake meandering model shows promise

• Although simplistic, wake models for power production like Park and eddy-viscosity models can be highly effective if used by an informed/experienced user

• Wake models of varying fidelity should not be viewed as competitors. High fidelity, expensive models should be used to inform faster, reduced-order models

• There is still much work to be done on modeling wake-wake interaction, wake-terrain interaction, and understanding atmospheric stability impacts

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References

Ainslie, J. F. , “Calculating the Flowfield in the Wake of Turbines,” Journal of Wind Engineering and Industrial Aerodynamics, Vol. 27, pp. 213 – 224, 1985. Brower, M. C., Robinson, N. M., “The Openwind Deep-Array Model—Development and Validation,” AWS Truepower Report, 2012. Frandsen, S., “Turbulence and Turbulence-Generated Structural Loading in Wind Turbine Clusters,” Risø National Laboratory, Report R-1188(EN), 2005. Gaumond, M., Réthoré, P.-E., Bechmann, A., Ott, S., Larsen, G. C., Peña, A. and Hansen, K. S., “Benchmarking of Wind Turbine Wake Models in Large

Offshore Wind Farms,” Proceedings of The science of Making Torque from Wind, Oldenburg, Germany, 2012. Jensen, N.O., “A Note on Wind Generator Interaction,” Risø National Laboratory, Report M-2411, 1983. Johnson, C., Graves, A.-M., Tindal, A., Cox, S., Schlez, W., and Neubert, A., “New Developments in Wake Models for Large Wind Farms,” 2009 American

Wind Energy Association Windpower Conference, Chicago, 2009. Katíc, I., Højstrup, J., Jensen, N. O., “A Simple Model for Cluster Efficiency,” European Wind Energy Association Conference and Exhibition, Rome, Italy, 1986. Larsen, G. C., Madsen, H. A., Bingöl, F., Mann, J., Ott, S., Sørensen, J. N., Okulov, V., Troldborg, N., Nielsen, M., Thomsen, K., Larsen, T. J., and Mikkelsen, R.,

“Dynamic Wake Meandering Modeling,” Risø National Laboratory, Report R-1607(EN), 2007. Larsen, T. J., Madsen, H. A., Larsen, G. C., and Hansen, K. S., “Validation of the Dynamic Wake Meander Model for Loads and Power Production in the

Egmond aan Zee Wind Farm,” Wind Energy, 2012. Ott, S., Berg, J., and Nielsen, M., “Linearized CFD Models for Wakes,” Risø National Laboratory, Report R-1772(EN), 2011. Ott, S, Nielsen, M., and Hansen, K. S., “Fuga – Validating a Wake Model for Offshore Wind Farms,” European Wind Energy Association meeting, Dublin,

Ireland, 2013. Schlez, W. and Neubert A., “New Developments in Large Wind Farm Modelling,” European Wind Energy Conference, Marseille, France, 2009. Smith, C. M., Barthelmie, R. J., Churchfield M. J., and Moriarty P. J., “Complex Wake Merging Phenomena in Large Offshore Wind Farms,” American

Meteorological Society 20th Symposium on Boundary Layers and Turbulence, Boston, Massachussetts, Aug. 2012.

Contact Information: Matthew J. Churchfield Senior Engineer National Renewable Energy Laboratory Matt.Churchfield@nrel.gov 1-303-384-7080