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Publication# Wind farm density and harvested power in very large wind farms: A low-order model

Résumé

In this work we create new understanding of wind turbine wakes recovery process as a function of wind farm density using large-eddy simulations of an atmospheric boundary layer diurnal cycle. Simulations are forced with a constant geostrophic wind and a time varying surface temperature extracted from a selected period of the Cooperative Atmospheric Surface Exchange Study field experiment. Wind turbines are represented using the actuator disk model with rotation and yaw alignment. A control volume analysis around each turbine has been used to evaluate wind turbine wake recovery and corresponding harvested power. Results confirm the existence of two dominant recovery mechanisms, advection and flux of mean kinetic energy, which are modulated by the background thermal stratification. For the low-density arrangements advection dominates, while for the highly loaded wind farms the mean kinetic energy recovers through fluxes of mean kinetic energy. For those cases in between, a smooth balance of bothmechanisms exists. From the results, a low-order model for the wind farms' harvested power as a function of thermal stratification and wind farm density has been developed, which has the potential to be used as an order-of-magnitude assessment tool.

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Marc Calaf Bracons, Charles Vivant Ignacio Meneveau

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.

2010Wind 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.

Hao Lu, Fernando Porté Agel, Yu-Ting Wu

Accurate prediction of atmospheric boundary layer (ABL) flow and its interactions with wind turbines and wind farms is critical for optimizing the design (turbine siting) of wind energy projects. Large-eddy simulation (LES) can potentially provide the kind of high-resolution spatial and temporal information needed to maximize wind energy production and minimize fatigue loads in wind farms. However, the accuracy of LESs of ABL flow with wind turbines hinges on our ability to parameterize subgrid-scale (SGS) turbulent fluxes as well as turbine-induced forces. This paper focuses on recent research efforts to develop and validate an LES framework for wind energy applications. SGS fluxes are parameterized using tuning-free Lagrangian scale-dependent dynamic models. These models optimize the local value of the model coefficients based on the dynamics of the resolved scales. The turbine-induced forces (e.g., thrust, lift and drag) are parameterized using two types of models: actuator-disk models that distribute the force loading over the rotor disk, and actuator-line models that distribute the forces along lines that follow the position of the blades. Simulation results are compared to wind-tunnel measurements collected with hot-wire anemometry in the wake of a miniature three-blade wind turbine placed in a boundary layer flow. In general, the characteristics of the turbine wakes simulated with the proposed LES framework are in good agreement with the measurements in the far-wake region. Near the turbine, up to about five rotor diameters downwind, the best performance is obtained with turbine models that induce wake-flow rotation and account for the non-uniformity of the turbine-induced forces. Finally, the LES framework is used to simulate atmospheric boundary-layer flow through an operational wind farm. (C) 2011 Elsevier Ltd. All rights reserved.