Large eddy simulation study of fully developed windturbine array boundary layers
Abstract
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 windturbine 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 windturbine 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 windturbine 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 windturbine 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.
 Publication:

Physics of Fluids
 Pub Date:
 January 2010
 DOI:
 10.1063/1.3291077
 Bibcode:
 2010PhFl...22a5110C
 Keywords:

 atmospheric boundary layer;
 boundary layer turbulence;
 drag;
 flow simulation;
 surface roughness;
 wind turbines;
 47.27.nb;
 47.50.Cd;
 89.20.Kk;
 92.60.Fm;
 47.11.j;
 47.85.g;
 Boundary layer turbulence;
 Modeling;
 Engineering;
 Boundary layer structure and processes;
 Computational methods in fluid dynamics;
 Applied fluid mechanics