Focused-based multifractal analysis of the wake in a wind turbine array utilizing proper orthogonal decomposition

Abstract

Hot-wire anemometry measurements have been performed in a 3 × 3 wind turbine array to study the multifractality of the turbulent kinetic energy dissipation. A multifractal spectrum and Hurst exponents are determined at nine locations downstream of the hub height, bottom and top tips. Higher multifractality is found at 0.5D and 1D downstream of the bottom tip and hub height. The second order of the Hurst exponent and combination factor shows the ability to predict the flow state in terms of its development. Snapshot proper orthogonal decomposition (POD) is used to identify the coherent and incoherent structures and to reconstruct the stochastic velocity signal using a specific number of the POD eigenfunctions. The accumulation of the turbulence kinetic energy in the top tip location exhibits fast convergence compared with the bottom tip and hub height. The dissipation of the large and small scales is determined using the reconstructed stochastic velocities. The higher multifractality is shown in the dissipation of the large scale compared with small scale dissipation showing consistency with the behavior of the original signals. Multifractality of turbulent kinetic energy dissipation in the wind farm is examined and the effect of the reconstructed flow field via proper orthogonal decomposition on the multifractality behavior is investigated. Findings are relevant in wind energy as multifractal parameters identify the variation between the near- and far-wake regions.