École Nationale Supérieure de
Techniques Avancées

Abstract

As wind energy becomes more and more ubiquitous as a source of renewable energy, the need to develop accurate and reliable numerical models to predict power production becomes more pressing. In this work we explore an array of turbulence models, in order to assess their effectiveness at modelling the wake behind a wind turbine. More specifically, we are interested in determining the capabilities of turbulence models to capture the wake downstream of a turbine. Indeed, as wake interactions significantly contribute to power losses within a wind farm, their accurate modeling is critical for reliable power production estimations. In this report, first-order two-equation models such as k − ε as well as second-order models are investigated. The k − ε models we will study are the following. First the standard k − ε model [1][16], then a modified version of this model presented by Duynkerke[4] , which was proposed in order to model the neutral and stable ABL (Atmospheric boundary Layer). Additionally we explore the k−ε−LP model of Guimet[6] where the TKE (Turbulent Kinetic Energy) production term is linearized, next the k − ε − LL model from Apsley [2] where the turbulent mixing length is limited by a specified value, and then we examine a model proposed by Van der Laan[18] where the eddy viscosity coefficient is variable over space and not a constant. At first we chose to restrain our scope to k − ε models (section 3), but after consideration we also investigated second-order Rij − ε models (see section 3.6), such as the LRR-IP model from Launder [9] and the model from Rotta [14]. The purpose of this work is to apply each of these models to compute the velocity deficit in the wake of a wind turbine, and discuss the outcome of these simulations. We were unfortunately unable to produce satisfying results for several of the models mentioned above. More specifically, we will show no results for the k − ε − fP , k − ε − LL and LRR-IP models. We managed to use the Rotta model only to represent the ABL (Atmospheric boundary Layer) and not the wind turbine wake. Our simulations show the weaknesses of the standard k−ε model, which proves the need for better models, and indicate that linearizing the TKE production term, and using the Duynkerke model yields better results.