Non-equilibrium scaling applied to the wake evolution of a model scale wind turbine

Abstract

The present paper addresses the evolution of turbulence characteristics in wind turbine wakes immersed in a turbulent boundary layer. The study thereby focuses on finding physically consistent scaling laws for the wake width, the velocity deficit, and the Reynolds stresses in the far wake region. For this purpose, the concept of an added wake is derived which allows to analyse the self-similarity of the added flow quantities and the applicability of the non-equilibrium dissipation theory. The investigation is based on wind tunnel measurements in the wake of a three-bladed horizontal axis wind turbine model (HAWT) immersed in two neutrally-stratified turbulent boundary layers of different aerodynamic roughness length. The dataset also includes wake measurements for various yaw angles. A high degree of self-similarity is found in the lateral profiles of the velocity deficit and of the added Reynolds stress components. It is shown that these can be described by combined Gaussian shape functions. In the vertical, self-similarity can just be shown in the upper part of the wake. Moreover, it is observed that the degree of self-similarity is affected by the ground roughness. Results suggest an approximately constant anisotropy of the added turbulent stresses in the far wake, and the axial scaling of the added Reynolds stress components is found to be in accordance with non-equilibrium dissipation theory. It predicts a x−1 decay of the added turbulent intensity I+, and a x−2 evolution of the added Reynolds shear stresses ∆ui0u0j and the velocity deficit ∆u. Based on these findings a semi-empirical model is proposed for predicting the Reynolds stresses in the far wake region which can easily be coupled with existing analytical wake models. The proposed model is found to be in good agreement with the measurement results.