On the interaction of very-large-scale motions in a neutral atmospheric boundary layer with a row of wind turbines

Abstract

Recent experiments have revealed the existence of very long streamwise features, denoted as very-large-scale motions (VLSMs), in the thermally neutral atmospheric boundary layer (ABL) (Hutchins et al., Boundary-Layer Meteorol., vol. 145(2), 2012, pp. 273–306). The aim of our study is to elaborate the role of these large-scale anisotropic patterns in wind-energy harvesting with special emphasis on the organization of turbulent fields around wind turbines. To this end, we perform large-eddy simulation (LES) of a turbine row operating under neutral conditions. The ABL data are produced separately in a very long domain of $240\unicode[STIX]{x1D6FF}$, where $\unicode[STIX]{x1D6FF}$ is the ABL thickness, to ensure a realistic representation for very large scales of $O(10\unicode[STIX]{x1D6FF})$. VLSMs are extracted from the LES database using a cutoff at streamwise wavelength $\unicode[STIX]{x1D706}_{x}=5\unicode[STIX]{x1D6FF}$, or $\unicode[STIX]{x1D706}_{x}=50D$ in terms of turbine diameter. Reynolds averaging of low-pass filtered fields shows that the interaction of VLSMs and turbines produce very-long-wavelength motions in the wake region, which contain approximately $20\,\%$ of the resolved Reynolds shear stress, and $30\,\%$ of the resolved streamwise kinetic energy in the shear layers. To further elucidate these statistics, we conduct a geometrical analysis using conditional averaging based on large-scale low- and high-velocity events. The conditional eddies provide evidence for very long (${\sim}10\unicode[STIX]{x1D6FF}$) and wide (${\sim}\unicode[STIX]{x1D6FF}$) streak–roller structures around the turbine row. Although all of these eddies share the same streak–roller topology, there are remarkable modifications in the morphology of the conditional eddies whose cores are located sideways to the turbines. In these cases, the turbine row pushes the whole low- or high-momentum streak aside, and prevails as a sharp boundary to the low–high-momentum streak pair. In this process, accompanying rollers remain relatively unaffected. This creates a two-way flux towards the turbine row. These observations provide some insights about the high lateral spreading observed in the large-scale Reynolds stress fields.

Dynamics of Large Scale Turbulence in Finite-sized Wind Farm Canopy using Proper Orthogonal Decomposition and a Novel Fourier-POD Framework

“…Additionally, the grid counts and the average normalized grid sizes for the farm layout as well as neutral ABL ( turbulent scales fed to the inflow) can be found in Table 2. This illustrates that the smallest resolved length scales is an order of magnitude smaller than the turbine rotor size, d. Note, here that the definition of lengthscales or wavelength resolved is 4 based on the Nyquist limit of the coarsest grid size ( twice the coarsest grid size). For more details of how the grid sizes were defined, See [5,43].…”

“…Wind farms in atmospheric boundary layer (ABL) pose a complex dynamical system with turbulent phenomenology occurring at multiple length scales, mainly due the interaction of atmospheric boundary layer turbulent eddies [1] and the turbulence generated by the wind turbine wakes [2][3][4]. These interactions are manifested not only in the small scale structures (of the order or smaller than the turbine rotor diameter) but also in the large scale structures (one or two orders of magnitude larger than the turbine rotor diameter) [5].…”

“…These interactions are manifested not only in the small scale structures (of the order or smaller than the turbine rotor diameter) but also in the large scale structures (one or two orders of magnitude larger than the turbine rotor diameter) [5]. In the current paper, we are concerned towards the understanding of these large turbulent structures which arguably can serve as mediators to the generation of large scale motions or very large scale motions [6] (LSM's or VLSM's) which has significant contribution to wind farm power [4,7]. Several researchers have shown before that large scale counter-rotating roll cell structures are formed in atmospheric boundary layer [8][9][10][11], and wind farms in ABL modulate such structures in and around the turbine rotors [12][13][14].…”

Dynamics of Large Scale Turbulence in Finite-Sized Wind Farm Canopy Using Proper Orthogonal Decomposition and a Novel Fourier-POD Framework

“…Wind farms in the atmospheric boundary layer (ABL) pose a complex dynamical system with turbulent phenomenology occurring at multiple length scales, mainly due to the interaction of atmospheric boundary layer turbulent eddies [1] and the turbulence generated by the wind turbine wakes [2][3][4]. These interactions are manifested not only in the small scale structures (of the order or smaller than the turbine rotor diameter) but also in the large scale structures (one or two orders of magnitude larger than the turbine rotor diameter) [5].…”

“…These interactions are manifested not only in the small scale structures (of the order or smaller than the turbine rotor diameter) but also in the large scale structures (one or two orders of magnitude larger than the turbine rotor diameter) [5]. In the current paper, we are concerned with the understanding of these large turbulent structures which arguably can serve as mediators to the generation of large scale motions or very large scale motions [6] (LSMs or VLSMs) which has significant contribution to wind farm power [4,7]. Several researchers have shown before that large scale counter-rotating roll cell structures are formed in the atmospheric boundary layer [8,9].…”