EWEA RA2013 Dublin 4 2 Soren Ott DTU Wind Energy

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28-06-2013

Fuga- Validating a wake model foroffshore wind farms

Sren Ott, Morten Nielsen & Kurt Shaldemose Hansen


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Danmarks Tekniske Universitet

Outline

What is Fuga?

Model validation: which assumptions are tested?

Met data interpretation: Is it important?

Simple models for the impact of large scales

Illustrated with Fuga tests

Conclusions

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Fuga features*

Solves linearized RANS equations

Latest version incorporates: atmosphericstability, meandering, effects of non-stationarity and spatial de-correlation ofthe flow field.

No computational grid, no numericaldiffusion, no spurious pressure gradients

Integration with WAsP: import of windclimate and turbine data.

Fast, mixed-spectral solver:

106times faster than conventional

RANS! 108to 1010times faster than LES! Fuga development

partly sponsored by

*Sren Ott, Jacob Berg and Morten Nielsen: Linearised CFD Models for Wakes, Risoe-R-1772(EN), 2011


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Variable atmospheric stability horizontalprofiles

4


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Variable atmospheric stability verticalprofiles

5


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Model testing and assumptions

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Measurements

Met mast

SCADA

PredictionsReal world

4D fields

Weather

Model world

Idealized flow

Homogeneous

Stationary

Two layers of assumptions:

1) interpretation of data interms of an idealizedmodel world

2) Flow model assumptions

Controlled experiments test onlyone assumption at a time!

Is data

interpretationimportant?


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Two different interpretations of met data

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Wind direction time series

Wind direction measurements

Interpretation 1: each ten minutes period can be regarded asa piece of a stationary time series with mean = ten minutes

average. We only need to simulate the measured meandirection.

Interpretation 2: the mean value changes following the redcurve. The deviation from the red curve is statistically stationary.We need to simulate a range of directions for each measuremean direction.

Ten minutes average wind direction


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EERA-DTOC:17/1-2013/ksh

Flow cases part 1- wide inflow sector

Thanks

to

K

urtS.Hansen

f

orthis

slide

Interpretation 1


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Flow cases part 1 narrow inflow sector

Thanks

to

K

urtS.Hansen

f

orthis

slide

Interpretation 1


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Flow cases part 1 narrow inflow sector

Thanks

to

K

urtS.Hansen

f

orthis

slide

Interpretation 2

Fuga + 5deg filter


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Effect of drifting winddirection can beestimated from data

Dqa= Difference of twoconsecutive ten minutesaverages of the wind direction

Width sDqa= (Dqa)2

sDqa can be obtained from 10

minutes averages.

Horns Rev 1 met mast data

Exponential pdf

Dqa


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Spatial de-correlations of wind direction

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Wind dir. dif. between M6 and M7

Pdf at M7

Predicted

pdf at M6

Data

Problem: wind direction at met mast wind directions at the turbines.

This uncertainty can be estimated using Taylors hypothesis:

Delay=Dx/U

M6 M7


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Technical University of Denmark

Spectral regimes

Courtney & Troen 1990

Larsn, Vincent & Larsen 2011

2D 3D


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Meandering

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Measurements with SgurrEnergys

Galion Lidar.

C

reech

etal.(2013):High-

resolutionCFD

m

odellingofLillgrundWind

farm,

RE&PQJ,

11

LES


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Lillgrund wind farm

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B8

B7

B1

B6

B5

B4

B3

B2

Photo by Kurts wife

D8

D7

D1

D6

D4

D3

D2


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D7 being shadowed by D8

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Fuga

SCADA

median

SCADA

LES*

*Creech et al.(2013): High-resolution CFD modelling of Lillgrund Wind farm, RE&PQJ, 11

CPU time:

Fuga: < 1 minute

LES: 105000 hours


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Stochastic meandering

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But something like this is more realistic:

The model says:


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Meandering model

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1) Make spectra of the differencebetween the green and the redcurves.

2) Fit to the Mann model spectra*

3) Make tracer particle diffusion inMann turbulence field using thespectra

4) Compute Lagrangian velocity auto-correlation function

5) Fit a model to it

* Pea, Gryning & Mann (2010):On the length-scale of the wind profile, Q. J. R. Meteorol. Soc. 136: 21192131

Simulating U-U


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A model for turbulent diffusion in Mann turbulence

Fitting the Lagrangian velocity auto-correlation function:

v(t+t)v(t) = s2(1 + lt)lt

This model says: the acceleration is an Ornstein-Uhlenbeck process.

Analytical solution in terms of stochastic numbers.

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0 50 100 150 200 250

0.1

0.0

0.1

0.2

0.3


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Validation Horns Rev 1

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Fuga 2.5

bin

Measurements


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21 28 June2013

Fuga 2.5

bin, meandering

Measurements


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22 28 June2013

Fuga 2.5

bin, meandering, decorrelation

Measurements


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Horns Rev 1. Efficiency for individual turbines

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Conclusions

The interpretation of met data can have a profound impact on the resultsof validation exercises for offshore turbine wake models.

The interpretation of met data can and should be backed up by on-siteobservations.

Data for narrow bins around down-the-rows wind directions are the mostuncertain.

Sampling in very small wind direction bins introduces a large uncertaintybecause we dont really know what true wind direction we should feedthe models with.

We need to know more about spatial and temporal wind field correlationsacross wind farms. The Doppler lidar is the key instrument.

Fuga is fast and yields good results. It is a useful tool.

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EWEA RA2013 Dublin 4 2 Soren Ott DTU Wind Energy