Turbulent and Deterministic Stresses in the Near Wake of a Wind Turbine Array

Abstract

A wind tunnel experiment was conducted to investigate the evolution of the stress field in the wake of a wind turbine array boundary layer. Phase-locked stereo particle image velocimetry measurements were taken in planes parallel to the turbine rotor and progressing throughout the near wake. Turbulent stresses vary significantly as a function of phase angle of the turbine rotor blades in the near wake. The resupply of kinetic energy to the momentum-deficit area of the wake is accomplished largely through the flux term in the mean kinetic energy equation. Phase-dependent contributions to the total flux into the wake indicate that turbulent structures impart periodic increases in entrainment of high-momentum flow. Deviations of phase-averaged velocities from total mean values are used to formulate deterministic stresses, which provide relatively decreased overall contributions to the flux of kinetic energy into the wake. Contributions of deterministic stresses are redudeced in the wake due to turbulent mixing in the wind turbine canopy. Based on the observable dependence of the Reynolds stresses on the phase orientation of the rotor blades, decomposition analogous to that of the deterministic stresses is applied directly to the Reynolds stress tensor. Termed the tertiary decomposition, root-mean-square deviations of the phase-averaged from the time-averaged turbulent stress tensor, and associated contributions to the flux of kinetic energy are shown to be of the same order of magnitude as the turbulence and greater than deterministic contributions.