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 Δ u i ′ u j ′ ¯ and the velocity deficit Δ u . Based on these findingsa 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.

Application of the Townsend–George theory for free shear flows to single and double wind turbine wakes – a wind tunnel study

“…It should be noted that the axisymmetry may be influenced by the presence of the ground and an ABL profile when investigating the wake of a wind turbine in the field. However, as the mean far wake evolving downstream a turbine exposed to an ABL inflow is often described as the superposition of an ABL profile with an axisymmetric wake, it can be assumed that the requirement also holds for these cases (Bastankhah and Porté-Agel, 2014;Stein and Kaltenbach, 2019).…”

“…However, Okulov et al (2015) applied the standard equilibrium bluff body wake scalings derived from the Richardson-Kolmogorov phenomenology to experimental data to justify the presence of power law decays for U and δ. In addition, Stein and Kaltenbach (2019) performed a systematic study on the nature of the dissipation scaling, testing also the non-equilibrium scaling, but with neither measuring nor taking C ε into account in the discussion. Furthermore, for the latter, the turbine studied was within a turbulent boundary layer background flow, which means that the turbulence evolution was additionally influenced by the turbulent background flow.…”

Validation of a Large-Eddy Simulation Approach for Prediction of the Ground Roughness Influence on Wind Turbine Wakes

“…1.0 m [13]. Wind tunnel experiments on the wake evolution over rough ground have been carried out by Stein [14,15] using a scale model of a 3-bladed wind-turbine with a rotor radius of R = 225 mm. Turbulent boundary layers of thickness δ ≈ 1.5 m were generated over surfaces with homogeneous roughness using a combination of vertical fins and castellated horizontal barriers proposed by Counihan [16].…”

“…The main goal of the present paper is an assessment of the capability of a high-fidelity simulation approach to describe the influence of ground-roughness on the evolution of a wind-turbine wake. For that purpose an investigation is carried out that matches as closely as possible the conditions of a reference experiment documented in [14,15,53].…”

Wind Tunnel Study on the Tip Speed Ratio’s Impact on a Wind Turbine Wake Development

“…However, the main difference lies in the presence of a virtual origin. It has been shown that the wake of a wind turbine fulfills the requirements necessary to apply the Townsend-George model [27], and several works that apply this phenomenology to wind turbine wakes found a better fit compared to engineering wind turbine wake models [27][28][29][30][31].…”