Abstract

We study large-eddy simulations of coherent structures within and above different wind-farm configurations in a neutral atmospheric boundary layer (ABL) using proper orthogonal decomposition (POD) to improve understanding of the flow structures in both physical and spectral space. We find that the spanwise extent of elongated streamwise counter-rotating rolls is constrained by the spanwise turbine spacings. The very large streamwise extent of the observed POD flow structures in physical space indicates that the interaction between the wind turbines and the ABL also causes large-scale flow organization. Using a spectral POD analysis to characterize the coherent structures at a certain frequency, we find that the flow dynamics for the frequency corresponding to the time a fluid parcel takes to traverse one streamwise turbine spacing is dominated by the wind-turbine wakes. The first POD mode at this frequency indicates that the wakes are spatially correlated. However, the flow dynamics at lower frequencies, corresponding to the longer time a fluid parcel takes to traverse the entire wind farm, are dominated by large flow structures originating from the ABL dynamics. We find that hundreds of POD modes are required to accurately describe the full three-dimensional flow profiles in large wind farms, while even more POD modes are required to accurately describe the Reynolds stresses that are important to describe the momentum exchange between the wind farm and the ABL. This indicates that wind-farm dynamics in the ABL are very complex.

Highlights

  • Wind energy is a very promising renewable-energy source and in recent years the industry has grown tremendously

  • We study large-eddy simulations of coherent structures within and above different windfarm configurations in a neutral atmospheric boundary layer (ABL) using proper orthogonal decomposition (POD) to improve understanding of the flow structures in both physical and spectral space

  • We find that the POD modes for both the aligned and staggered wind-farm geometry display similar characteristics, which indicates that the large-scale interaction between the turbines and the atmospheric flow is mostly determined by the number of turbines, and not by their exact configuration

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Summary

Introduction

Wind energy is a very promising renewable-energy source and in recent years the industry has grown tremendously. By analyzing the velocity and stress fields, Hamilton et al (2015, 2016) demonstrated that the streamwise development can be taken into account in the double POD analysis because it collectively evaluates the flow field spanning the rows of the measurement locations They showed that the double POD analysis significantly reduces the number of modes required to capture the wind-turbine wakes. Bastine et al (2018) found that, even though large-scale structures contain the most kinetic energy, the small-scale turbulence plays an important role in the wind-farm dynamics Another promising area of research is the use of the POD technique for flow control. By using dynamic mode decomposition, which is related to the POD technique, Iungo et al (2015a) constructed a reduced-order model of the wind-turbine wakes embedded in a Kalman filter, and demonstrated the potential of this tool for real-time flow control in large-scale wind farms.

Proper Orthogonal Decomposition
Large-Eddy-Simulation Method
Averaged Wind-Farm Flow Field
Convergence Test
Proper Orthogonal Decomposition Modes
Proper-Orthogonal-Decomposition Modes of the Reynolds Stress
10-10 Staggered developing wind farm
Discussion and Conclusions
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