Abstract
We use large-eddy simulations (LES) to investigate the impact of stable stratification on gravity-wave excitation and energy extraction in a large wind farm. To this end, the development of an equilibrium conventionally neutral boundary layer into a stable boundary layer over a period of 8 h is considered, using two different cooling rates. We find that turbulence decay has considerable influence on the energy extraction at the beginning of the boundary-layer transition, but afterwards, energy extraction is dominated by geometrical and jet effects induced by an inertial oscillation. It is further shown that the inertial oscillation enhances gravity-wave excitation. By comparing LES results with a simple one-dimensional model, we show that this is related to an interplay between wind-farm drag, variations in the Froude number and the dispersive effects of vertically-propagating gravity waves. We further find that the pressure gradients induced by gravity waves lead to significant upstream flow deceleration, reducing the average turbine output compared to a turbine in isolated operation. This leads us to the definition of a non-local wind-farm efficiency, next to a more standard wind-farm wake efficiency, and we show that both can be of the same order of magnitude. Finally, an energy flux analysis is performed to further elucidate the effect of gravity waves on the flow in the wind farm.
Highlights
It is well-known that the superposition of turbine wakes in a wind farm reduces the wind speed and increases the turbulence intensity inside and above the farm, and in past years, many studies have focused on simulations and measurements of wake interactions in wind farms
We find that turbulence decay has considerable influence on the energy extraction at the beginning of the boundary-layer transition, but afterwards, energy extraction is dominated by geometrical and jet effects induced by an inertial oscillation
The objective of the current study is to investigate the impact of stable stratification on wind-farm performance and boundary-layer flow, with a particular interest in gravity waves
Summary
It is well-known that the superposition of turbine wakes in a wind farm reduces the wind speed and increases the turbulence intensity inside and above the farm, and in past years, many studies have focused on simulations and measurements of wake interactions in wind farms (see, e.g., Frandsen et al 2006; Barthelmie et al 2009; Calaf et al 2010; Wu and Porté-Agel 2013). The objective of the current study is to investigate the impact of stable stratification on wind-farm performance and boundary-layer flow, with a particular interest in gravity waves. Over the past few years, a considerable amount of literature has been published on the interaction between wind farms and the atmospheric boundary layer (ABL); see Stevens and Meneveau (2017) for a recent review Many of these studies use large-eddy simulations in conjunction with field measurements and wind-tunnel experiments to understand the complex flow behaviour. The simulations performed in this work consider an equilibrium, onshore, conventionally neutral boundary layer (CNBL) developing into a stable boundary layer due to a prescribed surface cooling rate This situation represents part of the diurnal cycle, similar to a lateafternoon ABL transition into a nocturnal boundary layer.
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