Data Driven Modal Decomposition of the Wake behind an NREL-5MW Wind Turbine

Stefania Cherubini,Giovanni De Cillis,Stefano Leonardi,Pietro De Palma,Onofrio Semeraro

doi:10.3390/ijtpp6040044

Abstract

The wake produced by a utility-scale wind turbine invested by a laminar, uniform inflow is analyzed by means of two different modal decompositions, the proper orthogonal decomposition (POD) and the dynamic mode decomposition (DMD), in its sparsity-promoting variant. The turbine considered is the NREL-5MW at tip-speed ratio λ=7 and a diameter-based Reynolds number of the order 108. The flow is simulated through large eddy simulation, where the forces exerted by the blades are modeled using the actuator line method, whereas tower and nacelle are modeled employing the immersed boundary method. The main flow structures identified by both modal decompositions are compared and some differences emerge that can be of great importance for the formulation of a reduced-order model. In particular, a high-frequency mode directly related to the tip vortices is found using both methods, but it is ranked differently. The other dominant modes are composed by large-scale low-frequency structures, but with different frequency content and spatial structure. The most energetic 200 POD modes account for ≈20% only of the flow kinetic energy. While using the same number of DMD modes, it is possible to reconstruct the flow field to within 80% accuracy. Despite the similarities between the set of modes, the comparison between these modal-decomposition techniques points out that an energy-based criterion such as that used in the POD may not be suitable for formulating a reduced-order model of wind turbine wakes, while the sparsity-promoting DMD appears able to perform well in reconstructing the flow field with only a few modes.

Highlights

Low-dimensional models based on modal decomposition of complex flows are often sought in many different fields and among those in wind energy
Andersen et al [1] applied this modal decomposition to planes perpendicular to the streamwise direction of large eddy simulations (LES) of the flow impinging on an infinite series of rows of wind turbines, each one consisting of three turbines modeled by the actuator line technique
We identify the most relevant coherent structures embedded in the turbulent wake flow developing downstream of the NREL-5MW wind turbine, using the two mentioned modal decompositions, addressing convergence, selection and physical interpretation of both proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) modes

Summary

Introduction

Low-dimensional models based on modal decomposition of complex flows are often sought in many different fields and among those in wind energy. In the wind-energy field, POD was at first applied to two-dimensional data. Andersen et al [1] applied this modal decomposition to planes perpendicular to the streamwise direction of large eddy simulations (LES) of the flow impinging on an infinite series of rows of wind turbines, each one consisting of three turbines modeled by the actuator line technique. Applied two-dimensional POD to the case of a single wind turbine, impinged by a turbulent neutrally stratified atmospheric boundary layer. POD analysis was applied to threedimensional flow fields behind a wind turbine array by VerHulst and Meneveau [3], both

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