BEM (Bladed Element Momentum) models have shown to be inaccurate in predicting loads in the case of yawed flow [1-3]. Actuator disk momentum theory is the basis for BEM codes, following Glauert’s auto-gyro theory [4]. Therefore, a first step to improve BEM in yawed flow is to assess momentum models for the actuator disk in yaw and investigate possibilities for improvement. In the past, several models have been developed for an actuator disc under yawed conditions, but they are subject to various assumptions. In this paper, different yaw models for the actuator disk will be reviewed and compared against higher fidelity models: fixed and free [5] wake vortex models so that the earlier made assumptions can be assessed. The comparison considers the case of a uniformly loaded actuator disk at varying yaw angle (0°~90°) and thrust coefficient (0.1~0.9). From the models which have been assessed, Øye’s correction [6] performs best, however, this model too suffers from deficiencies. This indicates that an improved momentum model for yawed flow is necessary. @en

A PhD project is being carried out on the topic of far-wake aerodynamics of Horizontal Axis Wind Turbines (HAWTs) in yawed conditions, which has a large relevance for wind farm design and optimization. Characteristic for a turbine in yaw are the inherent unsteady and non-uniform rotor loading, and the typical wake deflection and strong three-dimensional deformation effects under influence of self-induction (see figure 1). Investigation of HAWTs in yaw is important, as the larce-scale eddies of the turbulent atmosphere dictate that a wind turbine is in practise always operating in unsteady yaw, while the resulting wake effects are already significant for small yaw angles. Despite this relevance, research into the far-wake of yawed wind turbines has been very limited and the symmetry assumptions on which common wake engineering models are based conflict with the physics of the skewed wake of a yawed turbine. Nevertheless, there is an increasing interest into this topic, as it is recognized that the effect of wake deflection can be exploited as a way to optimize the overall wind farm power production through active yaw control. For this purpose, simple two-dimensional models are applied for approximating the wake deflection, but which are unable to capture the typical three-dimensional deformation effects. In summary, there is a large gap of fundamental knowledge on wake physics in yawed conditions, and what the relevance of these phenomena is on the development and issues like the re-energization process of the far-wake. To bridge this gap, the PhD project aims at improving our understanding of the wake physics of HAWTs in yaw and to draft guidelines for reduced-order models that can be applied for wind farm design and optimization. In support of this aim, the objective is to analyze the different physical “modes” that play a role in the yawed wake, through a numerial and experimental investigation of the skewed wakes aft of HAWTs and actuator discs. The results from these investigations are collected (along with results from third parties) into a high-fidelity benchmark database for model validation purposes and to be able to derive the reduced-order models. For the current conference, results will be presented of both two- and three-dimensional free-wake vortex simulations of an actuator disc in yaw. The focus is put on the crescent or kidney shaped convective wake deformation (figure 1), which is naturally not present in a two-dimensional simulation. The magnitude of this phenomenon is investigated as function of the yaw angle and thrust coefficient, and the effect on global wake parameters is assessed such as the wake deflection and velocity profile. The outcomes of this investigation are relevant for assessing the validity of two-dimensional assumptions made in current yaw models regarding the wake deflection, definition of the wake center and width, and the wake profile. @en

The application of a 3-dimensional Lagrangian vortex particle method has been assessed for modelling the near-wake of an axisymmetrical actuator disc and 3-bladed horizontal axis wind turbine with prescribed circulation from the MEXICO (Model EXperiments In COntrolled conditions) experiment. The method was developed in the framework of the open- source Parallel Particle-Mesh library for handling the efficient data-parallelism on a CPU (Central Processing Unit) cluster, and utilized a O(N log N)-type fast multipole method for computational acceleration. Simulations with the actuator disc resulted in a wake expansion, velocity deficit profile, and induction factor that showed a close agreement with theoretical, numerical, and experimental results from literature. Also the shear layer expansion was present; the Kelvin-Helmholtz instability in the shear layer was triggered due to the round-off limitations of a numerical method, but this instability was delayed to beyond 1 diameter downstream due to the particle smoothing. Simulations with the 3-bladed turbine demonstrated that a purely 3-dimensional flow representation is challenging to model with particles. The manifestation of local complex flow structures of highly stretched vortices made the simulation unstable, but this was successfully counteracted by the application of a particle strength exchange scheme. The axial and radial velocity profile over the near wake have been compared to that of the original MEXICO experiment, which showed close agreement between results.@en

In the current paper, a method for deriving the analytical expressions for the velocity and vortex stretching terms as a function of the spherical multipole expansion approximation of the vector potential is presented. These terms are essential in the context of 3D Lagrangian vortex particle methods combined with fast summation techniques. The convergence and computational efficiency of this approach is assessed in the framework of an O(N log N)-type Fast Multipole Method (FMM), by using vorticity particles to simulate a system of coaxial vortex rings for which also the exact results are known. It is found that the current implementation converges rapidly to the exact solution with increasing expansion order and acceptance factor. An investigation into the computational efficiency demonstrated that the O(N log N)-type FMM is already viable for a particle size of only several thousands and that this speedup increases significantly with the number of particles. Finally, it is shown that the implementation of the FMM with the current analytical expressions is at least twice as fast as when opting for using even the simplest implementation of finite differences instead.@en