WindSim Forest Model
A pragmatic search for useful parameter values
REpower Systems AG
Tomas Blodau-Konick Peter Lazarev
Tonsberg 16.06.2008
Contents
• Background
– Description
– Setup
– Issues
• Study Results
– Height
– Porosity
– C2
• Next Steps
Background
Project Description
Use flat plate CFD Model to find plausible
parameters for Forest Model
Forest Model Parameters
•
•
•
•
•
Forest Height
Z-Cells
P- Porosity
C1 – resistance proportional to wind speed
C2 – resistance proportional to square of
wind speed
The Model
Initial setup
• Artificial Terrain Model (flat plate)
– 24 km x 6 km
– Height: 1 km
• Forest Model
– 7 km x 2 km
– Height: Typically 10 or 25 m
• Seven fixed analysis points
Initial Setup continued…
• Total cells: 700,000
• 30 cells in z-direction
• Resolution:
– Horizontal: 80 m
– Vertical: 1.2 m at base (Height distribution factor 0.05)
• Forest: 10 cells in z-direction
• Top Boundary Condition: frictionless wall
• One sector 270 at 10 m/s
Wind speed (f80)
Height: 80 Meters
Wind Profile at 7 analysis points
Windspeed Vertical Profiles [f45]
190
1:1700m up wind
170
2: 200 m up wind
150
3: 200 m into forest
4: 5000m into forest
130
5: 300 m down wind
110
6: 2300m down wind
90
7: 7500m down wind
70
50
30
10
2.5
-10
3.5
4.5
5.5
6.5
7.5
8.5
Pre-Tests
• Solver/Convergence
–
–
–
–
Coupled: ca 500 iterations
Segregated: ca 6000 iterations
Similar results from Segregated and Coupled Solver
Similar time required
•
Segregated takes about 5 times more iterations than coupled, but every iteration is 5 times faster
– Crashes in particular cases
Used coupled solver with 1000 iterations (ca 4.5hrs)
• Upper BC
– wall or pressure?
used wall to avoid “leakage”
Encountered Problems
• Profile changes throughout the empty model
(standard inlet profile needs to adapt itself)
• Diverging profiles (~3% deviation)
• Convergence problems with very long model
• Some WindSim crashes (apparently linked to forest height cell
Heights or low Z-cell Numbers etc) Forest models appears to promote
divergence – reduces stability)
• Are real world measurements comparable
Profile changes without forest
Windspeed over flat plate [f06a]
190
1:1700m up wind
2: 200 m up wind
170
3: 200 m into forest
150
4: 5000m into forest
130
5: 300 m down wind
110
6: 2300m down wind
90
7: 7500m down wind
70
50
30
10
2.5
-10
3.5
4.5
5.5
6.5
7.5
8.5
Poor Convergence of long Model
after 1000 iterations (f66)
Artefacts in Plain Terrain of a Long
Model (f66)
Artefacts in Long Model (Plain)
WindSpeed:Plain Terrain (f66)
1b:1700m up wind
2b: 200 m up wind
100
3b: 200 m into forest
4b: 5000m into forest
5b: 300 m down wind
6b: 2300m down wind
80
7b: 7500m down wind
8a: 25 km down wind
8b: 17 km down wind
60
9a: 30 km down wind
9b: 34 km down wind
9c: 37 km down wind
9d: 40 km down wind
40
20
0
0
1
2
3
4
5
6
7
8
9
10
Questions
• Reason for diverging profiles
• Options for adjusting inflow conditions
Until these questions are answered
uncertainties in model performance remain,
limiting our potential for accurate results.
Revised Aims
• Understand parameters
• Find plausible ranges
Study Results
The Model
What should it look like
What should profile look like?
WIND SPEED
• available real
measurements
• change of profile in
forest
• similar to roughness
profile far behind
forest
TURBULENCE
• real world
measurements for
(turbulence profiles)
• real measurements –
typically don’t go into
canopy
Turbulence assessment
Default values: turbulence
Turbulence: Default Values (P=0.5 C1&C2=0.01 Z-Cells 3 to 10)
Lower: 5 Meters (f62): 5000m into forest
190
Lower: 5 Meters (f62): 7500m down wind
Higher: 25 Meters (f63): 5000m into forest
170
Higher: 25 Meters (f63): 7500m down wind
Original: 10 Meters (f64): 5000m into forest
Original: 10 Meters (f64): 7500m down wind
150
Roughness (f08a): 5000m into forest
Roughness (f08a): 7500m down wind
130
Real world turbulence range in forest
Real world turbulence range w/o forest
110
90
70
50
30
10
0
-10
10
20
30
40
50
60
70
80
90
100
Comparison Graphs
•
Height (10m 25m) P=0.5 C2 = 0.0001
– Turbulence
– Speed
•
Porosity (0.25 0.5) H=25m C2 = 0.0001
– Turbulence
– Speed
•
C2 (0.0001, 0.00025, 0.0005) P= 0.25 H=25m
– Turbulence
– Speed
•
C2 (0.0001, 0.00025, 0.0005) P= 0.5 H=25m
– Turbulence
– Speed
C1 always 0.0001
Forest height change
Windspeed: 10 vs 25 Meters ( p=0.5 C1&c2=0.0001)
190
Plain (f06a): 5000m into forest
Plain (f06a): 7500m down wind
170
25 Meters (f45): 5000m into forest
150
25 Meters (f45): 7500m down wind
10 Meters (f40): 5000m into forest
130
10 Meters (f40): 7500m down wind
110
90
70
50
30
10
2.5
-10
3.5
4.5
5.5
6.5
7.5
8.5
Forest height change
Turbulence: 10 vs 25 Meters ( p=0.5 C1&c2=0.0001)
25 Meters (f45): 5000m into
forest
25 Meters (f45): 7500m down
wind
100
10 Meters (f40): 5000m into
forest
10 Meters (f40): 7500m down
wind
80
Plain (f06a): 5000m into forest
Plain (f06a): 7500m down wind
60
Real World Turbulence Range
Real World Turbulence Range
40
20
0
0
10
20
30
40
50
60
Porosity changes
Windspeed: P=0.5 vs P=0.25 (25 Meters, c1&c2=0.0001 )
190
P=0.5 (f45): 5000m into forest
P=0.5 (f45): 7500m down wind
170
P=0.25 (f51): 5000m into forest
150
P=0.25 (f51): 7500m down wind
Roughness (f08a): 5000m into forest
130
Roughness (f08a): 7500m down wind
110
90
70
50
30
10
2.5
-10
3.5
4.5
5.5
6.5
7.5
8.5
Porosity changes
Turbulence: P=0.5 vs P=0.25 (25 Meters, c1&c2=0.0001 )
P=0.5 (f45): 5000m into forest
P=0.5 (f45): 7500m down wind
100
P=0.25 (f51): 5000m into forest
P=0.25 (f51): 7500m down wind
80
Roughness (f08a): 5000m into
forest
Roughness (f08a): 7500m
down wind
60
Real World Turbulence Range
Real World Turbulence Range
40
20
0
0
10
20
30
40
50
60
C2 Changes at high porosity P=0.5
Wind speed: P=0.5 (C1=0.0001 Height: 25 Meters)
Original C2=0.0001 (f45): 5000m into forest
190
Higher C2=0.00025 (f46): 5000m into forest
Even higher C2=0.0005 (f47): 5000m into forest
170
Roughness (f08a): 5000m into forest
150
Original C2=0.0001 (f45): 7500m down wind
Higher C2=0.00025 (f46): 7500m down wind
130
Even higher C2=0.0005 (f47): 7500m down wind
110
Roughness (f08a): 7500m down wind
90
70
50
30
10
2.5
-10
3.5
4.5
5.5
6.5
7.5
8.5
C2 Changes at low porosity P=0.25
Wind speed: P=0.25 (C1=0.0001 Height: 25 Meters)
Original C2=0.0001 (f51): 5000m into forest
190
Original C2=0.0001 (f51): 7500m down wind
170
Higher C2=0.00025 (f52): 5000m into forest
Higher C2=0.00025 (f52): 7500m down wind
150
Even higher C2=0.0005 (f53): 5000m into forest
130
Even higher C2=0.0005 (f53): 7500m down wind
Roughness (f08a): 5000m into forest
110
Roughness (f08a): 7500m down wind
90
70
50
30
10
2.5
-10
3.5
4.5
5.5
6.5
7.5
8.5
C2 Changes at high porosity P=0.5
Turbulence: P=0.5 (C1=0.0001 Height: 25 Meters)
Original C2=0.0001 (f45): 5000m into forest
Original C2=0.0001 (f45): 7500m down wind
Higher C2=0.00025 (f46): 5000m into forest
100
Higher C2=0.00025 (f46): 7500m down wind
Even higher C2=0.0005 (f47): 5000m into forest
Even higher C2=0.0005 (f47): 7500m down wind
80
Roughness (f08a): 5000m into forest
Roughness (f08a): 7500m down wind
Real World Turbulence Range
60
Real World Turbulence Range
40
20
0
0
10
20
30
40
50
60
C2 Changes at low porosity P=0.25
Turbulence: P=0.25 (C1=0.0001 Height: 25 Meters)
Original C2=0.0001 (f51)_4: 5000m into forest
Original C2=0.0001 (f51)_7: 7500m down wind
Higher C2=0.00025 (f52)_4: 5000m into forest
100
Higher C2=0.00025 (f52)_7: 7500m down wind
Even higher C2=0.0005 (f53)_4: 5000m into forest
Even higher C2=0.0005 (f53)_7: 7500m down wind
80
Roughness (f08a)_4: 5000m into forest
Roughness (f08a)_7: 7500m down wind
Real World Turbulence Range
Real World Turbulence Range
60
40
20
0
0
10
20
30
40
50
60
Summary Porosity vs. C2 Changes
Wind speed: (p=0.5, c1 & c2=0.0001 height: 25 Meters)
Original (f45): 5000m into forest
190
Original (f45): 7500m down wind
170
Higher c2=0.0005 (f47): 5000m into forest
Higher c2=0.0005 (f47): 7500m down wind
150
Lower P=0.25 (f51): 5000m into forest
130
Lower P=0.25 (f51): 7500m down wind
Roughness (f08a): 5000m into forest
110
Roughness (f08a): 7500m down wind
90
70
50
30
10
2.5
-10
3.5
4.5
5.5
6.5
7.5
8.5
Summary Porosity vs. C2 Changes
Turbulence: (p=0.5, c1 & c2=0.0001 height: 25 Meters)
Original (f45): 5000m into forest
Original (f45): 7500m down wind
100
Higher c2=0.0005 (f47): 5000m into forest
Higher c2=0.0005 (f47): 7500m down wind
Lower P=0.25 (f51): 5000m into forest
80
Lower P=0.25 (f51): 7500m down wind
Roughness (f08a): 5000m into forest
Roughness (f08a): 7500m down wind
60
Real World Turbulence Range
Real World Turbulence Range
40
20
0
0
10
20
30
40
50
60
Summary: Parameter Ranges
• C1 and C2 have similar effects
• C2 ~ 0.0001 to 0.001
• P ~ 0.25 to 0.5
for 25m forest and C1= 0.0001
Next Steps
Next steps
• Answer flow model questions…
• Further refinement of parameters…
– Comparison to normalised wind speeds
– Just behind forest (100m to 3 km)
– Simple real forest cases in simple terrain
– Extend forest database
– Refine forest database for different conditions
– … study forest in complex terrain
• Additional measurements
Thank You
Suggestions
Increase flexibility: allow vertical profiles based on any
number of available sector results
Allow yield calculation based on combinations of sector
sizes eg 10°and 30°
Terrain:Rectangle Selections with the mouse
(Extension/Refinement/etc) show coordinates on
Mouseover
Option of showing Objects or their coordinates in Terrain
view eg for extension area selection
Better support for parallel Windsim calculations (conflicting
angle lists)
General Questions
• Reason for diverging profiles
• Options for adjusting inflow conditions
• Coupled solver crashes with large models
~6mio cells
• How to use residuals or spot values as
convergence criteria
• Nearest vs best modelled mast….