NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by 

Adding Complex Terrai

Atmospheric Condition 

the Simulator for On/O

Farm Applications (SOW

First Symposium on OpenFOAM 

Oldenburg, GermanyMatthew J. ChurchfieldMarch 20, 2013

NREL/PR‐5000‐58397
OutlineI. What is SOWFA?

II. The Stably Stratified Atmospheric Boundary Layer

III. TerrainIV. Conclusions
OutlineI. What is SOWFA?

II. The Stably Stratified Atmospheric Boundary Layer

III. TerrainIV. Conclusions
• The Simulator for On/Offshore Wind Farm Applications (SOWFA

• Meant for understanding:

o Atmospheric stability affects on wakes, power production, and mechanico Wake‐wake interaction, wake meanderingo Advanced control strategies

• Available at http://wind.nrel.gov/designcodes/simulators/sowfWhat is SOWFA?

Mesoscale weather modeling

(WRF)

Microscale/wind plant scale large‐eddy

simulation (LES) (OpenFOAM)

Photo by Iberdrola Renewables, Inc., NREL 15177

Photo by NASA, NREL 03565

The focus of this talk is on this component of SOWFA
What is SOWFA?

“Precursor” atmospheric large‐eddy simulation (LES)

Save planes of data

every N time steps

Use saved precursordata as inflow

boundary conditions

Actua

aerod

(coup

turbi

Initialize windfarm domainwith precursorvolume field

3 km 3 km

1 km

Wind f
Use of SOWFA: Power Production

Top view of contours of instantaneous velocity normalized b

speed at hub height (black lines represent turbine ro

Simulation of 48‐turbine Lillgrund wind plant [1]
Use of SOWFA: Power Production

Simulation of 48‐turbine Lillgrund wind plant [1]

Fractional contribution of each turbine’s

time‐averaged power output to total power

Average powe
Use of SOWFA: Mechanical Loads

3 km

3 km

neutralunstable Damage E

Equivalent faamplitude cysame amounactual loadinSecond turbdamaging ya

Simulation of two turbines subject to four different atmospheric inflows

each with low and high surface roughness [2,3]

Instantaneous isosurfacesin atmospheric boundarylayer viewed from aboveBlue: low speed structuresRed: updraftsSignificant updrafts inunstable case

turbine 1

turbine 2

turbine 1

turbine 2
Limitations of SOWFA• Could not handle complex terrain

o Wall shear stress model

• Unsure about simulation of stable

stratification

o Our custom subgrid‐scale (SGS) model

implementation limited solver to stand

Smagorinsky model; could not use Ope

standard SGS models
OutlineI. What is SOWFA?

II. The Stably Stratified Atmospheric Boundary Layer

III. TerrainIV. Conclusions
Uniqueness of the Stable Atmospheric Boun

• The stable atmospheric boundary la

o Cooling of air at lower surfaceo Positive vertical gradient of potential teo Common at night, warm air over cool wo Characterized by:

– Low/intermittent turbulence

– Strong vertical wind speed and direction s

– Formation of a low‐level jet

o Known to be particularly damaging to t

– See the work of Neil Kelley of NREL [4]
Uniqueness of the Stable Atmospheric Bou

LLJ max

12 m/s

Midwestern U.S. low‐level 

Windcube LIDAR [6,7]

Low‐level jet (LLJ) formation after sunset

observed with scanning light detectionand ranging (LIDAR) (velocity along beam)

[5]

Figure courtesy of R. M. Banta, Y. L. Pichugina, and W. A. Brewer,NOAA/ESRL

Figure courtesy of Julie K. Lundquist, Univ. of Colo. Bo
Subgrid‐Scale Modeling• Smaller scales and low/intermittent turbulence mak

atmospheric boundary layer LES sensitive to SGS mo

o SGS model has larger role than in neutral/unstable atm

boundary layer LES

• Simpler models like standard Smagorinsky or one‐eq

kinetic energy models:

o Are only dissipative (large‐ to small‐scale energy flow)o Include an SGS stress linearly related straino Contain “tunable” model constants

• However, the following is true:

o Backscatter is important (small‐ to large‐scale energy fo In regions of strong shear, SGS stresses become anisoto Ideal model constant value is problem‐specific
Subgrid‐Scale Modeling• Modified SGS Models

o United Kingdom Met Office Smagorinsky m

– Sensitized to flux Richardson number– Backscatter through random number accelera

fluxes

o One‐equation anisotropic [9]

– Contains an “isotropy” factor

– Reduces dissipation near surface in high shear

o Nonlinear one‐equation [10]

– Anisotropy through nonlinear stress/strain rel

– Accounts for backscatter
Subgrid‐Scale Modeling• Dynamic SGS Models

o Model determines model “constants” based o

and test‐filtered flow

o Model constants vary in space/time causing in

averaging is necessary

– Over homogeneous directions (plane in flat ABL)

– Backward along streamline (Lagrangian)

– About cell/grid point of interest (local)

Resolved Test‐filtered
Subgrid‐Scale Modeling• Dynamic SGS Models

o Two variants:

– Scale‐invariant

 Assumes the ideal model constant is the same at 

and test‐filtered scale

 Found to be under dissipative in ABL application

– Scale‐dependent [11,12,13]

 Assumes the ideal model constant is a function o

 Better level of dissipation

o Lagrangian‐averaged scale‐independent (L

dynamic Smagorinsky model [14]

– Included in OpenFOAM

– Dynamically solves for model constant, Cs
• Global Energy and Water Cycle Experiment Atmospheric 

Study (GABLS) model intercomparison case [15]

• Flat terrain

• 400 m400 m 400 m

• 643 (6.25 m) and 1283 (3.125 m) cells

• Initial temperature profile constant up to 100 m, capped 

• Surface cooling rate 0.25 K/hr

• Periodic• Geostrophic wind 8 m/s

• 73 N latitude• z0 0.1 m

• SGS models

o Standard Smagorinsky

– Used various values of model constant, Cs

o LASI dynamic Smagorinsky

– Model solves for model constant, Cs

Stable Stratification Test Case
Results

Standard Smagorinsky

results in general

agreement with GABLS

intercomparisonresultsLASI dynamicSmagorinksy greatly

overpredicts height of

low‐level jet—increasing resolutioncauses lower jet

Standard Smagorinsky

results for total wind

turning angle in

agreement with GABLS

intercomparisonLASI dynamicSmagorinskyoverpredicts totalturning angle
Results

Standard Smagorinsky

generally overpredictshorizontal velocity

variance and greatly

overpredicts verticalAs model constant is

increased, peakpredicted variance is

reducedLASI dynamicSmagorinsky far

overpredicts variances,

hinting at not enough

dissipation
Results

Vertical profiles of mean Cs from LASI

dynamic Smagorinsky simulation

• Cs increases as the surface is approached from low‐level jet height

reduces near the surface

• Instantaneous Cs is very noisy (values range from 0.0035 to 4.6 in 

• The noise possibly acts like excessive backscatter

Instantaneous Cs in a p

above surface from 64

Smagorinsky simulatio
OutlineI. What is SOWFA?

II. The Stably Stratified Atmospheric Boundary Layer

III. TerrainIV. Conclusions
Issues with Modeling Flow Over T• Difficult to model with computation

tools needed by wind plant designe

• Often unsteady effects, like separat

side of hills
Wall‐Modeled LES• LES is meant to capture larger energy‐cont

scales

• As the wall is approached, energy‐containi

get smaller

o Requires increasingly higher resolution

• There are roughness elements near the wa

affect the flow

o Grass, rock, shrubs, and so on

Commonly, the above effects are dealt with b

surface shear stress and temperature flux mo
Surface Shear Stress Model• At surface,• Surface stress is caused by viscosity,

roughness drag, and SGS turbulence

s

nU s  0

  

00 0013 23 

s s 

 

ττ

z0z1

SGS turbulence surface rough
Surface Shear Stress ModelWith the following definitions/relationships:

o Friction velocityo Monin‐Obukhov ABL

similarity laws (angle

brackets denote planar average)

o Obukhov length

• Implicitly solve (using an iterative technique) for

friction velocity in the Monin‐Obukhov similarity law usin

velocity information at the wall‐adjacent cell centers (z1)

• Then apply Schumann’s surface stress model

that uses friction velocity and velocity

at surface‐adjacent cell centers

• Constraints

o Relies on planar averages (angle brackets)o Mathematically valid only for flow over flat terrain

  

13 2* u , yx 

s 

  

  

 

  

u z 

* 

1 log 

 U

L 

  

3 

, 

uyx 

i s 

 
Surface Shear Stress Model• Terrain

o Apply local Monin‐Obukhov (no planar averago In a terrain‐local coordinate system (primes d

coordinates)

   2 23 2 13 2* , , , yxyxyxu s s     

              Lz zzyxu zyx m 1 0 * 1 1 log , ,,   U

   1 2 1 3 * ,, ),,( ,, zyx U x y z yxuyx i i s     U 

x 

 flow direction

orthogonal to x’ and surface normal direct

y



z



τ  

s 

L


Surface Shear Stress Model• Does it make sense to apply Monin‐Ob

o Locally?o Over complex terrain?

• Alternatives

o Include a Reynolds‐averaged Navier‐Stoke

layer to replace wall shear stress model

o Include a curvature correction to Monin‐O

• Surface temperature flux model faces 

issues
Terrain Test Case• Simple, hilly terrain

• 3 km3 km 1 km

• 125125 50 cells

• Neutral stability

capped by inversion

• Periodic• Geostrophic wind 15 m/s

• 45 N latitude• z0 0.16 m

• Mesh generated with moveDynamicMes
Results

separatnon‐ortneeded

Mean resolved‐scale velocity field
Results

separat

View from above 

directed velocity i

adjacent to surfacBlack lines are con

stress acting in x‐d

Mean resolved‐scale turbulent kinetic energy field
OutlineI. What is SOWFA?

II. The Stably Stratified Atmospheric Boundary Layer

III. TerrainIV. Conclusions
Conclusions• LES of stably stratified ABL

o Standard Smagorinsky model within range of predictions of GABLS interc

but overpredicts velocity variances

o LASI dynamic Smagorinksy model significantly overpredicts the height of 

peak values of velocity variance

– It appears not dissipative enough

o Need to examine velocity/temperature spectra

– Try LASD [13], Kosović nonlinear [10], and Sullivan et al. anisotropic model [9]

– Remember, even the dynamic Smagorinsky model relies on linear stress/strai

• Terrain

o Terrain‐local surface stress model using local Monin‐Obukhov scaling see

qualitatively correctly

o Does local Monin‐Obukhov make sense?o Does Monin‐Obukhov over complex terrain make sense?o An alternative is to have a near‐surface RANS layer

• The wind plant computational fluid dynamics part of SOWFA is 

o Can use any OpenFOAM turbulence modelo Although not tested, could run in RANS or detached‐eddy simulation (DEo ABL‐specific boundary conditions now separated from solver code as cla
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Contact Information

Matthew J. Churchfield

Research Engineer | National Wind Technology Cente

National Renewable Energy Laboratory (NREL

Golden, Colorado, USA

Matt.Churchfield@nrel.gov

1‐303‐384‐7080