Study of a Fully Developed Wind Turbine Array Boundary Layer

Wind harvesting is fast becoming an important alternative source of energy. As wind farms become larger, they begin to attain scales at which two-way interactions with the atmospheric boundary layer (ABL) must be taken into account. Several studies (Baidya-Roy et al. (2004); Baidya-Roy and Traiteur (2010)) have shown that there is a quantifiable effect of wind farms on the local meteorology, mainly through changes in the land-atmosphere fluxes of heat and moisture. Also, 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 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 stream-wise 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. Now, a suite of Large Eddy Simulations (LES), in which wind turbines are modeled using the classical "drag disk" concept, are performed for various wind turbine arrangements, turbine loading factors, and surface roughness values. Further, simulations including scalar transport from the ground surface without stratification, are also performed. 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. Results from the LES are compared with several existing models for effective roughness lengths. Based on the observed trends, a modified model is proposed showing improvement in predicted effective roughness length. Results also show an overall increase in the scalar fluxes of about 10-15% when wind turbines are present in the ABL, and that the increase does not strongly depend upon wind farm loading as described by the turbines' thrust coefficient and the wind turbines spacings. Similiarly as for the effective roughness length scales, a single-column analysis including now scalar transport, confirms that the presence of wind farms can be expected to increase slightly the scalar transport from the bottom surface. This slight increase is due to a delicate balance between two strong opposing trends: an increase of the friction velocity above the wind turbines, together with a decrease underneath.