It is well known that when wind turbines are deployed in large arrays, their efficiency decreases due to complex interactions among themselves and with the atmospheric boundary layer (ABL). For wind farms whose length exceeds the height of the ABL by over an order of magnitude, a “fully developed” flow regime can be established. In this asymptotic regime, changes in the streamwise direction can be neglected and the relevant exchanges occur in the vertical direction. Such a fully developed wind-turbine array boundary layer (WTABL) has not been studied systematically before. A suite of large eddy simulations (LES), in which wind turbines are modeled using the classical “drag disk” concept, is performed for various wind-turbine arrangements, turbine loading factors, and surface roughness values. The results are used to quantify the vertical transport of momentum and kinetic energy across the boundary layer. It is shown that the vertical fluxes of kinetic energy are of the same order of magnitude as the power extracted by the forces modeling the wind turbines. In the fully developed WTABL, the kinetic energy extracted by the wind turbines is transported into the wind-turbine region by vertical fluxes associated with turbulence. The results are also used to develop improved models for effective roughness length scales experienced by the ABL. The effective roughness scale is often used to model wind-turbine arrays in simulations of atmospheric dynamics at larger (regional and global) scales. The results from the LES are compared to several existing models for effective roughness lengths. Based on the observed trends, a modified model is proposed, showing improvement in the predicted effective roughness length.
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January 2010
Research Article|
January 25 2010
Large eddy simulation study of fully developed wind-turbine array boundary layers
Marc Calaf;
Marc Calaf
a)
1Laboratory of Environmental Fluid Mechanics and Hydrology,
École Polytechnique Fédérale de Lausanne
, 1015 Lausanne, Switzerland
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Charles Meneveau;
Charles Meneveau
b)
2Department of Mechanical Engineering,
Johns Hopkins University
, 3400 North Charles Street, Baltimore, Maryland 21218, USA
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Johan Meyers
Johan Meyers
c)
3Department of Mechanical Engineering,
Katholieke Universiteit Leuven
, Celestijnenlaan 300A-Bus 2421, B3001 Leuven, Belgium
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a)
Visiting student at the Department of Mechanical Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA. Electronic mail: [email protected].
b)
Electronic mail: [email protected].
c)
Electronic mail: [email protected].
Physics of Fluids 22, 015110 (2010)
Article history
Received:
August 13 2009
Accepted:
December 15 2009
Citation
Marc Calaf, Charles Meneveau, Johan Meyers; Large eddy simulation study of fully developed wind-turbine array boundary layers. Physics of Fluids 1 January 2010; 22 (1): 015110. https://doi.org/10.1063/1.3291077
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