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WIND ENERGY-RELATED ATMOSPHERIC BOUNDARY LAYER LARGE-EDDY SIMULATION USING Openfoam Conference Paper Wind Energy-Related Atmospheric NREL/CP-500-48905 Boundary Layer Large-Eddy August 2010 Simulation Using OpenFOAM Preprint M.J. Churchfield and P.J. Moriarty National Renewable Energy Laboratory G. Vijayakumar and J.G. Brasseur The Pennsylvania State University Presented at 19th Symposium on Boundary Layers and Turbulence Keystone, Colorado August 2-6, 2010 NOTICE The submitted manuscript has been offered by an employee of the Alliance for Sustainable Energy, LLC (ASE), a contractor of the US Government under Contract No. DE-AC36-08-GO28308. Accordingly, the US Government and ASE retain a nonexclusive royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for US Government purposes. This report was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or any agency thereof. Available electronically at http://www.osti.gov/bridge Available for a processing fee to U.S. Department of Energy and its contractors, in paper, from: U.S. Department of Energy Office of Scientific and Technical Information P.O. Box 62 Oak Ridge, TN 37831-0062 phone: 865.576.8401 fax: 865.576.5728 email: mailto:[email protected] Available for sale to the public, in paper, from: U.S. Department of Commerce National Technical Information Service 5285 Port Royal Road Springfield, VA 22161 phone: 800.553.6847 fax: 703.605.6900 email: [email protected] online ordering: http://www.ntis.gov/ordering.htm Printed on paper containing at least 50% wastepaper, including 20% postconsumer waste 1B.6 WIND ENERGY-RELATED ATMOSPHERIC BOUNDARY LAYER LARGE-EDDY SIMULATION USING OpenFOAM Matthew J. Churchfield∗ National Wind Technology Center, National Renewable Energy Laboratory, Golden, Colorado Ganesh Vijayakumar Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, Pennsylvania James G. Brasseur Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, Pennsylvania Patrick J. Moriarty National Wind Technology Center, National Renewable Energy Laboratory, Golden, Colorado 1. INTRODUCTION pare energy spectra and isosurfaces depicting ABL structure to the LESs of Khanna and Brasseur (1998), The purpose of the current work is to develop and which were also computed using the algorithm of Mo- evaluate the performance of a large-eddy simulation eng (1984). In developing and testing our LES code, (LES) solver in computing the atmospheric boundary we will make use of a recent analysis (Brasseur and layer (ABL) over flat terrain under a variety of sta- Wei 2010) that explains the well-known inability for bility conditions, ranging from shear driven (neutral LES to properly predict law-of-the-wall scaling and pro- stratification) to moderately convective (unstable strat- vides a design methodology to avoid this pathology. ification). This colocated, unstructured, finite-volume solver is developed using the OpenFOAM framework. Only a few researchers have performed LESs of Although, to our knowledge, OpenFOAM has never wind farm flows. Examples include the work of Ivanell been used to perform LESs, its flexible, open source, (2009), Calaf et al. (2010), and Stovall et al. (2010) and parallel nature combined with its availability at no (Stovall used an OpenFOAM-based solver), but all of cost, make it an ideal choice for this application. Data these works are limited to neutrally-stratified condi- from our ABL simulations, like those presented in this tions. The wind farm LES framework of Porté-Angel work, will be used in our future work as precursors for et al. (Porté-Agel et al. 2010; Conzemius et al. 2010) LESs of flow through wind farms consisting of multi- is clearly capable of simulation in a variety of stability megawatt wind turbines. conditions, though. Over the past four decades, the atmospheric com- The eventual goal of our work is to perform wind- munity has done much work using LES (in many cases farm LESs that will provide a better understanding of with a pseudo-spectral solver) to accurately simulate both the interactions of wind turbine wakes with one the ABL. A few examples include the work of Dear- another and with the surrounding ABL. Current utility- dorff (1972), Moeng and Sullivan (1994), Mason and scale wind turbines have tower heights of 80 m to Brown (1999), Khanna and Brasseur (1998), and Cui- 100 m and rotor diameters of 70 m to 120 m. At jpers and Duynkerke (1993). An objective of our work these tower heights and with such large rotor diam- is to use that knowledge to create an OpenFOAM- eters, utility-scale wind turbine blades can often cover based solver that can perform simulations with the the entire atmospheric surface layer, which contains same accuracy as that achieved by the atmospheric the highest levels of shear in the mean wind. This community. To assess our solvers’ performance, we means that turbine rotor blades experience substan- mainly compared our results to the LESs performed by tial cyclic loading as they rotate. Additionally, each Moeng and Sullivan (1994) because their LES code, turbine in a wind farm creates a wake that can affect which is outlined by Moeng (1984), is well proven, their the performance and mechanical loads of the wind tur- simulations are of a smaller grid size that is ideal for bines downstream. Turbine wakes interact with each this initial validation study, and the simulations are all other and are significantly affected by the stability con- windy while ranging from neutral to unstable, which dition of the surrounding ABL. For example, according is of interest in wind-farm modeling. We also com- to Jensen (2007), power output data from the Horns Rev Offshore Wind Farm, which is an 8 by 10 array of 2-MW turbines in the North Sea 14 km off the Danish ∗Corresponding author address: Matthew J. Churchfield, National coast, shows that in a stable ABL, the farm’s efficiency Renewable Energy Laboratory, 1617 Cole Boulevard, Golden, Col- is 61%; in an unstable ABL, the farm’s efficiency dra- orado 80401; e-mail: matt.churchfi[email protected]. matically increases to 74%. This is because an un- 1 stable ABL contains more turbulent kinetic energy that specified mean geostrophic wind, ¯ is the resolved vir- has a greater potential to replace the low-momentum tual potential temperature, ¯0 is the reference virtual air within a turbine’s wake with higher-momentum sur- potential temperature, ijk is the alternating symbol, rounding air through turbulent mixing. Consequently, f c is the Coriolis parameter, and the subscripts 1, 2, in the unstable condition, the downstream rows of tur- and 3 refer to the x-, y-, and z-directions, respectively. bines are fed higher-momentum air than in the sta- ¯0 is set to the initial virtual potential temperature be- ble condition, resulting in increased wind farm perfor- low the capping inversion of 300 K, gravity is set to 2 mance. However, according to Wharton and Lundquist gi = ( 9.81, 0, 0) m/s , and the Coriolis parameter (2010), in the absence of wakes, turbines perform is set to− a typical mid-latitude value of 1.028 10−4 more efficiently in stable conditions. s−1. The Boussinesq approximation for buoyancy× is Many aerodynamic and atmospheric phenomena included through the fifth term on the right-hand side occur within large wind farms that are not well under- of Equation 1. stood. This lack of understanding is reflected by the The filtered continuity equation is fact that wind farm developers consistently overpredict the performance of large modern wind farms by 5% or ∂u¯ j = 0, (2) more (Johnson 2008). This lower performance can re- ∂xj sult in millions of dollars less revenue generated than expected over the farm’s lifetime. Poor wake and at- and the filtered transport equation for virtual potential mospheric modeling is cited as one of the reasons for temperature is this overprediction. Developers currently use tools de- ¯ veloped in the 1980s and early 1990s, like that of Katic ∂ ∂ ∂Rj = u¯j ¯ , (3) et al. (1986) when wind turbines were much smaller, ∂t −∂xj − ∂xj that are simpler and less computationally-expensive than computational fluid dynamics (CFD). A clearer where Rj is the SGS potential temperature flux vec- understanding of the aerodynamics and atmospheric tor. physics within large wind farms would allow for the cre- ation of more accurate, lower-order wind farm planning 2.2 SUB-GRID-SCALE MODELING and design tools. LES has the potential to provide an accurate, highly-resolved description of the flow field The deviatoric SGS stress tensor found in the mo- through a wind farm. However, much work remains to mentum equation (Equation 1) is modeled using be done to establish a set of “best practices” for per- D SGS ¯ forming wind-farm-scale LES. This involves the ability Rij = Sij , (4) − to perform accurate LESs of canonical ABL flows, the subject of this paper. where SGS is the SGS viscosity, and 1 ∂u¯i ∂u¯j S¯ij = + (5) 2. FLOW PHYSICS EQUATIONS AND MODELING 2 ∂xj ∂xi 2.1 FILTERED GOVERNING EQUATIONS is the resolved strain-rate tensor.
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