Anisotropy stress invariants of thermally stratified wind turbine array boundary layers using large eddy simulations

Abstract

In the interest of understanding the dynamics and energy transfer between the atmospheric boundary layer and large wind turbine arrays, a description of the turbulence anisotropy in the wake region of wind turbines is necessary. Flux of high momentum flow into the wind turbine array by anisotropic turbulence is a dominant factor of mean kinetic energy resupply for the wind farm. Under thermal stratification, the behavior of the turbulence field, and the energy flux, is significantly altered. Here, a thermally stratified wind turbine array boundary layer is studied in detail using a combination of Lumley and barycentric maps together with the recently introduced spheroid and color maps. The atmospheric flow is modelled using a large eddy simulation driven by a constant geostrophic wind and a time-varying ground surface temperature, obtained from a selected period of the Cooperative Atmosphere-Surface Exchange Study-99 field experiment. The wind farm is modelled using the traditional actuator-disk with rotation and yaw-alignment. The results show that turbulence under unstable stratification tends to be more isotropic than that under neutral and stable stratification. The turbulent mixing attributed to positive buoyancy in unstable regimes determines the energy distribution between flow layers, directly affecting the vertical distribution of anisotropy. Contrarily, in the stably stratified flow, negative buoyancy damps the turbulent fluctuations, hence affecting the evolution of the Reynolds stress, leading to an increase of flow anisotropy. In both thermal stratification regimes, wind turbines alter the structure of the turbulence within the atmospheric boundary layer by creating regions of greater anisotropy and expanding the boundary layer vertically. For the modeling community, it is important to note that the wind turbine wakes display a larger degree of anisotropy that is related well to the production of turbulent kinetic energy and mean kinetic energy entrainment, and hence, it is important to model correctly for accurate power forecasting. Leveraging the new insights into wind turbine/atmospheric boundary layer interaction found here will benefit the formulation of a new generation of efficient low order models for commercial application.