WindSim Forest Model

WindSim Forest ModelA pragmatic search for useful parameter valuesREpower Systems AGTomas Blodau-Konick Peter LazarevTonsberg 16.06.2008

• Background– Description– Setup– Issues• Study Results– Height– Porosity– C2• Next StepsContents

Background

Project DescriptionUse flat plate CFD Model to find plausibleparameters for Forest Model

Forest Model Parameters• Forest Height• Z-Cells• P- Porosity• C1 – resistance proportional to wind speed• C2 – resistance proportional to square ofwind 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 pointsWindspeed Vertical Profiles [f45]1901:1700m up wind1702: 200 m up wind1503: 200 m into forest1304: 5000m into forest5: 300 m down wind1106: 2300m down wind907: 7500m down wind705030102.5 3.5 4.5 5.5 6.5 7.5 8.5-10

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 casesUsed 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 cellHeights or low Z-cell Numbers etc) Forest models appears to promotedivergence – reduces stability)• Are real world measurements comparable

Profile changes without forestWindspeed over flat plate [f06a]1901:1700m up wind1702: 200 m up wind1503: 200 m into forest4: 5000m into forest1305: 300 m down wind1106: 2300m down wind907: 7500m down wind705030102.5 3.5 4.5 5.5 6.5 7.5 8.5-10

Poor Convergence of long Modelafter 1000 iterations (f66)

Artefacts in Plain Terrain of a LongModel (f66)

Artefacts in Long Model (Plain)WindSpeed:Plain Terrain (f66)1b:1700m up wind2b: 200 m up wind1003b: 200 m into forest4b: 5000m into forest5b: 300 m down wind80606b: 2300m down wind7b: 7500m down wind8a: 25 km down wind8b: 17 km down wind9a: 30 km down wind9b: 34 km down wind9c: 37 km down wind409d: 40 km down wind2000 1 2 3 4 5 6 7 8 9 10

Questions• Reason for diverging profiles• Options for adjusting inflow conditionsUntil these questions are answereduncertainties 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 realmeasurements• change of profile inforest• similar to roughnessprofile far behindforestTURBULENCE• real worldmeasurements for(turbulence profiles)• real measurements –typically don’t go intocanopy

Turbulence assessment

Default values: turbulenceTurbulence: Default Values (P=0.5 C1&C2=0.01 Z-Cells 3 to 10)190170150130110Lower: 5 Meters (f62): 5000m into forestLower: 5 Meters (f62): 7500m down windHigher: 25 Meters (f63): 5000m into forestHigher: 25 Meters (f63): 7500m down windOriginal: 10 Meters (f64): 5000m into forestOriginal: 10 Meters (f64): 7500m down windRoughness (f08a): 5000m into forestRoughness (f08a): 7500m down windReal world turbulence range in forestReal world turbulence range w/o forest9070503010-100 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– SpeedC1 always 0.0001

Forest height changeWindspeed: 10 vs 25 Meters ( p=0.5 C1&c2=0.0001)190Plain (f06a): 5000m into forest170150Plain (f06a): 7500m down wind25 Meters (f45): 5000m into forest25 Meters (f45): 7500m down wind13010 Meters (f40): 5000m into forest10 Meters (f40): 7500m down wind11090705030102.5 3.5 4.5 5.5 6.5 7.5 8.5-10

Forest height changeTurbulence: 10 vs 25 Meters ( p=0.5 C1&c2=0.0001)25 Meters (f45): 5000m intoforest10025 Meters (f45): 7500m downwind10 Meters (f40): 5000m intoforest8010 Meters (f40): 7500m downwindPlain (f06a): 5000m into forestPlain (f06a): 7500m down wind60Real World Turbulence RangeReal World Turbulence Range402000 10 20 30 40 50 60

Porosity changesWindspeed: P=0.5 vs P=0.25 (25 Meters, c1&c2=0.0001 )190P=0.5 (f45): 5000m into forest170P=0.5 (f45): 7500m down windP=0.25 (f51): 5000m into forest150P=0.25 (f51): 7500m down wind130Roughness (f08a): 5000m into forestRoughness (f08a): 7500m down wind1109070503010-102.5 3.5 4.5 5.5 6.5 7.5 8.5

Porosity changesTurbulence: P=0.5 vs P=0.25 (25 Meters, c1&c2=0.0001 )P=0.5 (f45): 5000m into forest100P=0.5 (f45): 7500m down windP=0.25 (f51): 5000m into forest80P=0.25 (f51): 7500m down windRoughness (f08a): 5000m intoforest60Roughness (f08a): 7500mdown windReal World Turbulence Range40Real World Turbulence Range2000 10 20 30 40 50 60

C2 Changes at high porosity P=0.5Original C2=0.0001 (f45): 5000m into forestWind speed: P=0.5 (C1=0.0001 Height: 25 Meters)190170Higher C2=0.00025 (f46): 5000m into forestEven higher C2=0.0005 (f47): 5000m into forestRoughness (f08a): 5000m into forest150130Original C2=0.0001 (f45): 7500m down windHigher C2=0.00025 (f46): 7500m down windEven higher C2=0.0005 (f47): 7500m down wind110Roughness (f08a): 7500m down wind90705030102.5 3.5 4.5 5.5 6.5 7.5 8.5-10

C2 Changes at low porosity P=0.25Wind speed: P=0.25 (C1=0.0001 Height: 25 Meters)190170150130110Original C2=0.0001 (f51): 5000m into forestOriginal C2=0.0001 (f51): 7500m down windHigher C2=0.00025 (f52): 5000m into forestHigher C2=0.00025 (f52): 7500m down windEven higher C2=0.0005 (f53): 5000m into forestEven higher C2=0.0005 (f53): 7500m down windRoughness (f08a): 5000m into forestRoughness (f08a): 7500m down wind90705030102.5 3.5 4.5 5.5 6.5 7.5 8.5-10

C2 Changes at high porosity P=0.5Turbulence: P=0.5 (C1=0.0001 Height: 25 Meters)Original C2=0.0001 (f45): 5000m into forestOriginal C2=0.0001 (f45): 7500m down wind100Higher C2=0.00025 (f46): 5000m into forestHigher C2=0.00025 (f46): 7500m down windEven higher C2=0.0005 (f47): 5000m into forest80Even higher C2=0.0005 (f47): 7500m down windRoughness (f08a): 5000m into forestRoughness (f08a): 7500m down windReal World Turbulence Range60Real World Turbulence Range402000 10 20 30 40 50 60

C2 Changes at low porosity P=0.25Turbulence: P=0.25 (C1=0.0001 Height: 25 Meters)Original C2=0.0001 (f51)_4: 5000m into forestOriginal C2=0.0001 (f51)_7: 7500m down wind1008060Higher C2=0.00025 (f52)_4: 5000m into forestHigher C2=0.00025 (f52)_7: 7500m down windEven higher C2=0.0005 (f53)_4: 5000m into forestEven higher C2=0.0005 (f53)_7: 7500m down windRoughness (f08a)_4: 5000m into forestRoughness (f08a)_7: 7500m down windReal World Turbulence RangeReal World Turbulence Range402000 10 20 30 40 50 60

Summary Porosity vs. C2 ChangesWind speed: (p=0.5, c1 & c2=0.0001 height: 25 Meters)190Original (f45): 5000m into forest170Original (f45): 7500m down windHigher c2=0.0005 (f47): 5000m into forest150Higher c2=0.0005 (f47): 7500m down windLower P=0.25 (f51): 5000m into forest130Lower P=0.25 (f51): 7500m down wind110Roughness (f08a): 5000m into forestRoughness (f08a): 7500m down wind9070503010-102.5 3.5 4.5 5.5 6.5 7.5 8.5

Summary Porosity vs. C2 ChangesTurbulence: (p=0.5, c1 & c2=0.0001 height: 25 Meters)Original (f45): 5000m into forest100Original (f45): 7500m down windHigher c2=0.0005 (f47): 5000m into forestHigher c2=0.0005 (f47): 7500m down windLower P=0.25 (f51): 5000m into forest80Lower P=0.25 (f51): 7500m down windRoughness (f08a): 5000m into forestRoughness (f08a): 7500m down wind60Real World Turbulence RangeReal World Turbulence Range402000 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 0.5for 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

SuggestionsIncrease flexibility: allow vertical profiles based on anynumber of available sector resultsAllow yield calculation based on combinations of sectorsizes eg 10°and 30°Terrain:Rectangle Selections with the mouse(Extension/Refinement/etc) show coordinates onMouseoverOption of showing Objects or their coordinates in Terrainview eg for extension area selectionBetter support for parallel Windsim calculations (conflictingangle 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 asconvergence criteria• Nearest vs best modelled mast….