1 IWPC 2015 – Istanbul (Turkey)

Considering Thermal Stratification

in CFD modelling

for Wind Resource Assessment

Didier DELAUNAY1, Ru LI1, Soner HARNUBOĞLU2

1 METEODYN, France

2 UCYEL ENERJI, Turkey

www.meteodyn.com

www.ucyel.com.tr

Meteodyn WT

UrbaWind Mdyn Forecast

Meteodyn software suite

3 Meteodyn WT User Meeting

Content

Introduction: Some definitions about stability

The current turbulence model in meteodyn WT

Why new developments in stability modelling?

The extended Meteodyn stability model

Calibration on Cabauw (NL) and Rödeser Berg (D) data

Conclusion

DD 13/02/2014 4

Introduction: Definitions

2/

/

zV

zgRi v

v

Obukhov Length (Definition):

Gradient Richardson number (Definition): MOST Theory (stable stratification):

Hg

uL

v /

3

*

Lz

LzRi

/51

/

Lzzz

uV /5)/ln( 0

*

11/2013 5 Meteodyn WT User Meeting

Introduction: Turbulence modelling

Reynolds Averaged Navier Stokes equations - Steady flow:

Closure of the system (turbulence modelling):

0''

iji

i

j

j

i

jij

ijFuu

x

u

x

u

xx

P

x

uu

i

j

j

itji

x

u

x

uuu ''

TT Lk 2/1

j

j

i

j

j

iTk

T

T

jk

T

j

k

j

j

x

U

x

U

x

UP

kL

C

x

k

xP

x

kU

2

Transport equation of the turbulent kinetic energy

35.0)0(

/1/1/1

)(

0

10

f

zll

lRifLT

The current turbulence model in WT

l0 : maximum value of the turbulence scale (100 m)

WT class LT(Ri)/LT(0)

3 0.95

4 0.90

5 0.85

6 0.76

7 0.67

8 0.55

9 0.30

(Model of Yamada and Arritt)

TT Lk 2/1

7

The current turbulence model in WT

WT classes

stability Obukhov length L

(m)

Gradient Richardson

number at 10 m height

Gradient Richardson

number at 100 m height

3 Near neutral 1500 0.01 0.05

4 Slightly Stable 800 0.01 0.08

5 Stable 500 0.02 0.10

6 Stable 300 0.03 0.12

7 Stable 200 0.04 0.14

Stability introduced in the computation by the Gradient Richardson number at 10 m MOST theory makes the link with Obukhov length

Calibration of drag forces

Log–linear profiles on homogeneous terrain (MOST theory)

The current turbulence model in WT

9

For a given wind direction a CFD calculation is parameterized according to the stability (turbulence model) Which stability ?

Statistical approach: The Effective Average Stability is the thermal stability class which reproduces at best the observed average flow in the considered wind direction: (vertical profiles, masts comparisons…)

Drawback: The fact that the average flow is well reproduced does not guarantee that the whole wind distribution is well transferred.

Solution Considering wind statistics of the wind sorted according direction and stability class Considering time series

NB: More restrictive the cases are, greater the probability to get very stable meso cases

Notion of « Effective Average Stability »

10

Stability classes for time series

0

10

20

30

40

50

60

70

80

90

0 1 2 3 4 5 6 7 8 9

Win

d e

ner

gy [W

/m2]

WT stability class

WM Cabauw 2009-2012: Wind energy distribution

WM Cabauw 80/10

ConWx 100/2

Vortex 100/50

(Albrecht C., Delaunay D., Grötzner A., Kohlert M., Pauscher L. EWEA 2014 )

11

Objective Handling strong stability cases (time series approach)

Extrapolate to higher levels ( 200 m, Ri>0.2)

Methodology Multi-layer model for turbulent viscosity (Zilitinkevich, Grachev…)

Calibration on a flat terrain

Validation on a complex terrain

New developments

Does a Critical Richardson Number exists? Can be the turbulence maintained at large Ri? Where is MOST applicable? Which laws when Ri> 0.20 ? The nature of turbulence at Ri ~ 0.25?

Pena, Gryning, Hasager, Courtney 2010 – Hovsore data

Model parameters: Obukhov lenght L Height of MOST layer Height of local MOST layer Minimum length scale Lo Thermal stability in the « free layer »

New developments

11/2013 13

Calibration flat terrain: Cabauw data

14

Cabauw data

21212

1212

1 )/())()((

)/())()((

zzzVzV

zzzzgSI

S03 S04 S05 S06 S07 S08 S09 S10 S11 S12 S13 S14SI range 0.00 - 0.01 0.01-0.05 0.05-0.10 0.10-0.15 0.15-0.20 0.20-0.25 0.25-0.32 0.32-0.40 0.40-0.50 0.50-0.70 0.70-1.00 > 1.00

frequency 7.3% 9.4% 14.4% 11.2% 9.0% 6.9% 6.7% 4.5% 3.4% 3.1% 1.6% 1.9%

power contribution 9.1% 24.1% 21.4% 9.6% 6.0% 4.0% 3.5% 2.1% 1.4% 1.0% 0.4% 0.2%

(V80+V140)/2 (m/s) 8.1 11.3 9.5 8.0 7.4 7.1 6.8 6.5 6.2 5.8 5.2 4.3

11/2013 15

Model calibration: Cabauw data

Mean wind vertical profiles according to stability classes

16

erreur k1/2 S03 S04 S05 S06 S07

40 0% -5% -8% 10% 21%

80 2% -3% -7% 9% 16%

140 14% 9% -7% 4% 5%

200 17% 6% -29% -21% -23%

Model calibration: Cabauw data

Turbulent Kinectic Energy vertical profiles according to stability classes

17

new model S03 S04 S05 S06 S07 S08 S09 S10 S11 S12 S13 S14

Obukhov length L 1000 280 160 150 130 140 140 100 80 52 40 25

L0 80 60 38 35 35 30 30 30 30 25 20 20

Hn 8 8 8 15 8 8 8 8 8 8 8 8

Hmost/L 0.8 0.8 0.8 0.8 0.7 0.5 0.5 0.5 0.8 0.9 1 1

Hout/L 1.5 1.5 1.5 1.2 1.0 1.2 1.2 1.2 1.2 1.35 1.5 1.5

Sout 0.10 0.10 0.10 0.14 0.14 0.27 0.27 0.20 0.13 0.07 0.05 0.30

WT 4.6.1 model WT-4 WT-7

L 800 200

L0 100 100

Hn 0 0

Hmost/L infinite infinite

Model parameters

Rödeser Berg site

Source: Google Earth and IWES Fraunhöfer

Rödeser Berg : Hilly and forested terrain;

• Dense forest in the SW and S sectors ; moderate roughness in the East sector

• 200 m height met mast + LiDAR measurements

• Sonic anemometer for flux and turbulence measurements;

• 1 year data sorted according to the Monin-Obukhov length L at 40 m height,

Measurement site

Measured vs Computed profiles

South-West winds

0

40

80

120

160

200

0,0 0,1 0,2 0,3 0,4 0,5

Heig

ht

(m)

S04_model

S05_model

measurement_100<L<400

measurement_60<L<100

measurement_20<L<60

√𝒌/𝑼_𝟒𝟎

Meteodyn WT simulations of wind profile and TKE in Rödeser Berg

(Southwest Direction)

The surface friction generated by

the tree weakens the thermal

effect for the wind speed gradient,

but the TKE is strongly affected by

stability.

0

40

80

120

160

200

0 0,2 0,4 0,6 0,8 1

Heig

ht

(m)

Normalized wind velocity (m/s)

S04_model

S05_model

measurement_100<L<400

measurement_60<L<100

measurement_20<L<60

0

40

80

120

160

200

0,0 0,2 0,4 0,6 0,8 1,0

Heig

ht

(m)

Normalized wind velocity (m/s)

S04_model

S05_model

S06_model

measurement_100<L<400

measurement_60<L<100

measurement_20<L<60

0

40

80

120

160

200

0,0 0,1 0,2 0,3 0,4 0,5

Heig

ht

(m)

S04_model

S05_model

S06_model

measurement_100<L<400

measurement_60<L<100

measurement_20<L<60

√𝒌/𝑼_𝟒𝟎

Meteodyn WT simulations of wind profile and TKE in Rödeser Berg (East winds)

The wind speed gradients increase according

to the thermal stability (L decrease),

The TKE is less dependent on stability than

expected in the computations. Calibrations on

the dissipation terms in the TKE equation will

have to reduce this discrepancy.

Measured vs Computed profiles

East winds

21

Conclusion

Present stability model in Meteodyn WT validated up to stability class 7

Classes 0-7 useful in the statistical approach (Effective Average Stability)

Stronger stability cases in the time series approach

New model elaborated for strongly stable cases (class > 7)

This new model calibrated with Cabauw data an

The new model validated on a complex terrain (Rödeser Berg)

Implementation in Meteodyn WT 5.3

Thank you for your attention!

For more information on Meteodyn WT: Ucyel Enerji www.ucyel.com.tr