Effects of self-induced gravity waves on finite wind-farm operations using a large-eddy simulation framework

Abstract

In the present study, we use large-eddy simulation (LES) to investigate how a capping inversion in combination with a stable free atmosphere influences the flow development and energy extraction in a large finite wind farm with a staggered and aligned layout. In the conventionally neutral boundary layer (CNBL), we find that gravity waves induce an unfavourable pressure gradient in the induction region of the farm which contributes to the upstream blockage, decreasing the available energy for first-row turbines. However, a favourable pressure gradient establishes through the farm in such conditions, which redistributes the energy and enhances wake recovery. These results are compared with a farm operating in the neutral boundary layer (NBL). Here, we find that only hydrodynamic effects induced by the turbines drag play a role, which cause minor pressure perturbations across the domain. For the selected atmospheric conditions, the power losses generated by the upstream blockage are balanced by the enhanced wake recovery promoted by the favourable pressure gradient throughout the farm. Consequently, the staggered farm efficiency in the CNBL is 8.8% higher than in the NBL. We note that this difference in efficiency is slightly enhanced by the 0.5? difference in wind direction at the location of the first-row turbines between the CNBL and NBL cases, which is caused by the presence of flow blockage. Since both simulations are forced with an equal turbulent velocity profile, the variation in performance is solely caused by the different vertical temperature profiles in the main domain. Finally, the staggered layout leads to a slightly stronger flow blockage than the aligned one when both farms operate in the CNBL.

An analytical model of momentum availability for predicting large wind farm power

“…This is a strong assumption, and in reality, this would depend on the atmospheric conditions. The LES results of Wu & Porté-Agel (2017) and Lanzilao & Meyers (2022) show approximately equal and opposite pressure changes at the front and rear of the farm, suggesting that this approximation is valid. However, the LES of Allaerts & Meyers (2017) and Lanzilao & Meyers (2023) suggest that this assumption is likely to be valid only for certain atmospheric stratifications.…”

“…The LES results in the literature have shown that large wind farms can induce additional pressure gradients across them (e.g. Allaerts & Meyers 2017; Wu & Porté-Agel 2017; Lanzilao & Meyers 2022). When farms induce additional pressure gradients, commonly a velocity reduction at the front of the farm is observed.…”

“…We compared the predictions against finite wind farm LES results from Wu & Porté-Agel (2017), Allaerts & Meyers (2017) and Lanzilao & Meyers (2022). We selected these studies because they simulated large wind farms (longer than 15 km in the streamwise direction).…”

“…. Allaerts & Meyers (2017) and Lanzilao & Meyers (2022) used an actuator disc no-rotation model for the turbines, with . For these studies, we used from the actuator disc theory (4.2) as an upper limit for in (4.4), and then used the expression .…”

Large-eddy simulation of a 15 GW wind farm: Flow effects, energy budgets and comparison with wake models

“…With LES all relevant processes such as turbulent entrainment of energy or Coriolis effects are modeled. Many wind farm LES studies have been performed in recent years, e.g., Allaerts and Meyers (2017), Wu and Porté-Agel (2017), Zhang et al (2019), Centurelli et al (2021), Lanzilao and Meyers (2022) and Maas and Raasch (2022). They show that complex flow phenomenon like inversion layer displacement, gravity wave induced pressure gradients, flow blockage and Coriolis force related wind direction changes can occur for large wind farms.…”