6th OpenFOAMR⃝ WorkshopPennState University, USA13-16 June 2011

Towards Simulating the

Atmospheric Boundary Layer and Wind Farm Flows

Matthew J. Churchfield∗†1 and Patrick J. Moriarty1

1National Renewable Energy Laboratory

March 15, 2011

atmospheric, turbine, wind-farm, LES.

The purpose of this work is to perform large-eddy simulations (LES) of wind farm flows tobetter understand the physical interactions of wind turbine wakes with turbulence in the at-mospheric boundary layer (ABL). At the present, there is a lack of knowledge concerningwake–ABL interaction. This is reflected by the fact that currently-used engineering tools areoverpredicting the performance of wind farms. The effect of atmospheric stability on turbinewakes is significant. For example, it has been shown by Jensen [1] that the Horns Rev windfarm off the Danish coast performs roughly 6% more efficiently under unstable atmosphericconditions as compared to stable conditions. This wake–ABL interaction needs to be betterunderstood so that it can be modeled and incorporated into lower-order wind farm perfor-mance tools. LES is able to capture relevant turbulent length scales and has successful historyof application to ABL flows.

In this work, a substantially-modified version of the incompressiblebuoyantBoussinesqPisoFoam solver is used. The solver accounts for buoyancy, and henceatmospheric stability, using the Boussinesq approximation. After performing a precursorsimulation to develop a turbulent ABL, a single full flow field and subsequent boundary fieldsare saved and used as the initial field and time-varying boundary conditions for wind farmsimulations. Surface roughness and temperature flux are specified and dictate the stability andturbulence intensity of the simulated ABL. We have attempted to follow the high-quality ABLLES work of Moeng and Sullivan [2] as much as possible. Isosurfaces of velocity fluctuationsare shown in Figure 1 and highlight the differences in turbulent structures generated in theABL depending upon stability conditions.

The actuator line method of Sørensen and Shen [3] is used to model the effect of the turbine onthe flow field. This method projects forces equal and opposite to the lift and drag created bydiscrete rotating blade elements onto the flow field. Figure 2 (a) shows the flow field throughan actuator line model of a 126 m rotor diameter turbine subject to uniform 8 m/s flow. Bycombining the data saved from the ABL precursor with the actuator line method, we are able

†Corresponding Author: Matthew J. Churchfield (Matt.Churchfield@nrel.gov)

to create turbine wakes within atmospheric flow and examine power being produced by theturbines as shown in Figure 2 (b), which shows how increasing the separation distance of twoin-line turbines increases power production of the downstream turbine.

Due to its free, open-source nature, OpenFOAM R⃝ is proving to be an essential tool in this studyin which many custom aspects of the solver, such as the actuator line model and atmospheric-style boundary conditions, are necessary. We are currently working toward studying, in detail,the effect of atmospheric stability on turbine performance.

(a) (b)

Figure 1: (a) Isosurfaces of 1.5 m/s horizontal velocity fluctuations in blue and of 0.6 m/svertical velocity fluctuations in red for a neutral atmospheric boundary layer. (b) Isosurfacesof 0.88 m/s vertical velocity fluctuations in red for an unstable atmospheric boundary layer.The domain extents are 3 km horizontally and 1 km vertically.

(a) (b)

Figure 2: (a) Contours of streamwise velocity in a horizontal plane through an actuator linemodel of a turbine and isosurfaces of the Q-criterion in red indicating tip and root vortices. (b)Power produced by a waked turbine relative to the unwaked case versus separation distance ofthe two turbines.

References

[1] L. E. Jensen, Array efficiency at Horns Rev and the effect of atmospheric stability, pre-sentation by Dong Energy (2007).

[2] C.-H. Moeng and P. P. Sullivan, A comparison of shear- and buoyancy-driven planetaryboundary layer flows, Journal of the Atmospheric Sciences, 51, 999–1022 (1994).

[3] J. N. Sørensen and W. Z. Shen, Numerical modeling of wind turbine wakes, Journal ofFluids Engineering, 124, 393–399 (2002).