Large eddy simulation study of the kinetic energy entrainment by energetic turbulent flow structures in large wind farms

Abstract

In this study, we address the question of how kinetic energy is entrained into large wind turbine arrays and, in particular, how large-scale flow structures contribute to such entrainment. Previous research has shown this entrainment to be an important limiting factor in the performance of very large arrays where the flow becomes fully developed and there is a balance between the forcing of the atmospheric boundary layer and the resistance of the wind turbines. Given the high Reynolds numbers and domain sizes on the order of kilometers, we rely on wall-modeled large eddy simulation (LES) to simulate turbulent flow within the wind farm. Three-dimensional proper orthogonal decomposition (POD) analysis is then used to identify the most energetic flow structures present in the LES data. We quantify the contribution of each POD mode to the kinetic energy entrainment and its dependence on the layout of the wind turbine array. The primary large-scale structures are found to be streamwise, counter-rotating vortices located above the height of the wind turbines. While the flow is periodic, the geometry is not invariant to all horizontal translations due to the presence of the wind turbines and thus POD modes need not be Fourier modes. Differences of the obtained modes with Fourier modes are documented. Some of the modes are responsible for a large fraction of the kinetic energy flux to the wind turbine region. Surprisingly, more flow structures (POD modes) are needed to capture at least 40% of the turbulent kinetic energy, for which the POD analysis is optimal, than are needed to capture at least 40% of the kinetic energy flux to the turbines. For comparison, we consider the cases of aligned and staggered wind turbine arrays in a neutral atmospheric boundary layer as well as a reference case without wind turbines. While the general characteristics of the flow structures are robust, the net kinetic energy entrainment to the turbines depends on the presence and relative arrangement of the wind turbines in the domain.

Stochastic Wake Modelling Based on POD Analysis

“…The most detailed dynamical simulations which can be computed in reasonable times are large eddy simulations (LES) [14] combined with simplified turbine models, such as actuator disk or actuator line models [15][16][17][18][19][20][21][22][23][24]. Even though these simulations have proven to be an efficient tool for the investigation of specific research questions, LES are still too time-consuming for most practical applications.…”

“…Another dynamic approach, also followed in this work, is to analyse and model wind turbine wakes using modal decompositions [21,[35][36][37][38][39][40][41][42][43][44][45][46][47] which describe the velocity field as a linear superposition of spatial modes with time-dependent weighting coefficients. It has been shown that a few spatial modes can already capture important features of the wake flow [35][36][37][38][39]41,43,47].…”

Altering Kinetic Energy Entrainment in Large Eddy Simulations of Large Wind Farms Using Unconventional Wind Turbine Actuator Forcing

“…The details of the code can be found in prior publications [17,21,23,24], so here, we mention only the most relevant features of the atmospheric modeling and wind turbine modeling in Sections 2.1 and 2.2, respectively.…”

“…Turbulent transfer of kinetic energy from above replenishes energy extracted by the turbine wakes, and this kinetic energy entrainment becomes the limiting factor in wind farm performance for very large wind farms [12,[17][18][19][20][21]. The entrainment of kinetic energy, and the means to modify it, is the focus of the present study.…”

Stochastic Wake Modeling Based on POD Analysis

“…Another dynamic approach, also followed in this work, is to analyze and model wind turbine wakes using modal decompositions (Andersen et al, 2012(Andersen et al, , 2013Bastine et al, 2014Bastine et al, , 2015bHamilton et al, 2015Hamilton et al, , 2016Iungo et al, 2015;Sarmast 20 et al, 2014;VerHulst and Meneveau, 2014) which describe the velocity field as a linear superposition of spatial modes with time-dependent weighting coefficients. It has been shown that a few spatial modes can already capture important features of the wake flow (Andersen et al, 2012(Andersen et al, , 2013Bastine et al, 2014Bastine et al, , 2015bHamilton et al, 2015;Iungo et al, 2015).…”