Two improvements to the dynamic wake meandering model: including the effects of atmospheric shear on wake turbulence and incorporating turbulence build‐up in a row of wind turbines

Abstract

The dynamic wake meandering (DWM) model is an engineering wake model designed to physically model the wake deficit evolution and the unsteady meandering that occurs in wind turbine wakes. The present study aims at improving two features of the model: The effect of the atmospheric boundary layer shear on the wake deficit evolution by including a strain‐rate contribution in the wake turbulence calculation.The method to account for the increased turbulence at a wake‐affected turbine by basing the wake‐added turbulence directly on the Reynolds stresses of the oncoming wake. This also allows the model to simulate the build‐up of turbulence over a row of turbines in a physically consistent manner. The performance of the modified model is validated against actuator line (AL) model results and field data from the Lillgrund offshore wind farm. Qualitatively, the modified DWM model is in fair agreement with the reference data. A quantitative comparison between the mean flow field of the DWM model with and without the suggested improvements, to that of the AL model, shows that the root‐mean‐square difference in terms of wind speed and turbulence intensity is reduced on the order of 30% and 40%, respectively, by including the proposed corrections for a row of eight turbines. Furthermore, it is found that the root‐mean‐square difference between the AL model and the modified DWM model in terms of wind speed and turbulence intensity does not increase over a row of turbines compared with the root‐mean‐square difference of a single turbine. Copyright © 2013 John Wiley & Sons, Ltd.

Stochastic Wake Modelling Based on POD Analysis

“…Thus, another possible improvement of our model could be the inclusion of the meandering motion through an additional model, such as the DWM [28][29][30][31]. In the DWM, the meandering caused by large atmospheric structures is the only large-scale effect which is modeled explicitly and thus a POD-based approach is a promising extension.…”

“…In this section, we examine a different approach, describing the large-scale and small-scale dynamics of the wake separately by combining the spectral model including a few modes with an additional homogeneous turbulent field. Similar approaches have been used in [28][29][30][31]39]. We start by illustrating the basic idea and underlying hypothesis of our approach in Section 6.1.…”

“…Such a single quantity, however, can obviously not describe all relevant dynamical features of a wake flow. One possible approach to a more precise description is given by the dynamic wake meandering model (DWM) [28][29][30][31]. It consists of three major elements, namely a model for a steady velocity deficit, a model describing large-scale movement of the wake caused by large atmospheric structures and a model for the added turbulence caused by the rotor.…”

“…Furthermore, we investigate the problem of missing turbulent kinetic energy in the modeled wake flow, which is a principle shortcoming of reduced order models based on modal decompositions. Inspired by similar approaches in [28][29][30][31]39], we illustrate that it is possible to capture the small-scale properties of the flow by adding a homogeneous turbulent field to the wake structure, which is modeled by the POD-based approach.…”

Stochastic Wake Modeling Based on POD Analysis

“…Such a single quantity, however, can obviously not describe all relevant dynamical features of a wake flow. One possible approach to a more precise description is 10 given by the dynamic wake meandering model (DWM) (Larsen et al, 2007b(Larsen et al, , 2008Madsen et al, 2010;Keck et al, 2015). It consists of three major elements, namely a model for a steady velocity deficit, a model describing large-scale movement of the wake caused by large atmospheric structures and a model for the added turbulence caused by the rotor.…”