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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