Large eddy simulation study of fully developed wind-turbine array boundary layers

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.

Study of a Fully Developed Wind Turbine Array Boundary Layer

Marc Calaf Bracons

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.

EPFL2011

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

Marc Calaf Bracons, Varun Sharma

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.

Amer Physical Soc2017

Large-eddy simulation of a diurnal cycle of the atmospheric boundary layer: Atmospheric stability and scaling issues

Charles Vivant Ignacio Meneveau, Marc Parlange

A simulation of a diurnal cycle of atmospheric boundary layer (ABL) flow over a homogeneous terrain is performed using large-eddy simulation (LES) with the Lagrangian scale-dependent dynamic subgrid-scale model. The surface boundary condition is derived from the field observations of surface heat flux from the HATS experiment (Horst et al., 2004; Kleissl et al., 2004). The simulation results display good general agreement with previous modeling and experimental studies with regard to characteristic features such as growth of the convective boundary layer by entrainment, nocturnal jet, and multilayered flow structure of the nocturnal regime. To gain a better understanding of the physical parameters affecting the statistics of the flow, we study the dependence of a subgrid parameter (dynamic Smagorinsky coefficient), resolved turbulent kinetic energy, and resolved vertical velocity variance upon atmospheric stability. The profiles of these turbulent variables plotted as a function of Obukhov length show “hysteretic” behavior that implies nonunique dependence. The subsequent use of local Richardson number as the scaling parameter shows a decrease in this “hysteresis,” but there is an increased scatter in the profiles with increasing height. Conversely, profiles plotted as a function of local Obukhov length (based on the fluxes at the local vertical level) show almost no hysteresis, confirming the validity of Nieuwstadt's local scaling hypothesis. Although the local scaling hypothesis was formulated for the stable boundary layer, we find that it applies to the entire stability range of the diurnal cycle.

American Geophysical Union2006

Study of a Fully Developed Wind Turbine Array Boundary Layer

Marc Calaf Bracons

EPFL2011