The Fluid Dynamic Basis for Actuator Disc and Rotor Theories

The first rotor performance predictions were published by Joukowsky exactly 100 years ago. Although a century of research has expanded the knowledge of rotor aerodynamics enormously, and modern computer power and measurement techniques now enable detailed analyses that were previously out of reach, the concepts proposed by Froude, Betz, Joukowsky and Glauert for modelling a rotor in performance calculations are still in use today, albeit with modifications and expansions. This book is the result of the author’s curiosity as to whether a return to these models with a combination of mathematics, dedicated computations and wind tunnel experiments could yield more physical insight and answer some of the old questions still waiting to be resolved. Although most of the work included here has been published previously, the book connects the various topics, linking them in a coherent storyline. “The Fluid Dynamic Basis for Actuator Disc and Rotor Theories” was first published in 2018. This Revised Second Edition (2022) will be of interest to those working in all branches of rotor aerodynamics – wind turbines, propellers, ship screws and helicopter rotors. It has been written for proficient students and researchers, and reading it will demand a good knowledge of inviscid (fluid) mechanics

Estimating the angle of attack from blade pressure measurements on the National Renewable Energy Laboratory phase VI rotor using a free wake vortex model : yawed conditions

Wind turbine design codes for calculating blade loads are usually based on a blade element momentum (BEM) approach. Since wind turbine rotors often operate in off-design conditions, such as yawed flow, several engineering methods have been developed to take into account such conditions. An essential feature of a BEM code is the coupling of local blade element loads with an external (induced) velocity field determined with momentum theory through the angle of attack. Local blade loads follow directly from blade pressure measurements as performed in the National Renewable Energy Laboratory (NREL) phase IV campaign, but corresponding angles of attack cannot (on principle) be measured. By developing a free wake vortex method using measured local blade loads, time-dependent angle of attack and induced velocity distributions are reconstructed. In a previous paper, a method was described for deriving such distributions in conjunction with blade pressure measurements for the NREL phase VI wind turbine in axial (non-yawed) conditions. In this paper, the same method is applied to investigate yawed conditions on the same turbine. The study considered different operating conditions in yaw in both attached and separated flows over the blades. The derived free wake geometry solutions are used to determine induced velocity distributions at the rotor blade. These are then used to determine the local (azimuth time dependent) angle of attack, as well as the corresponding lift and drag for each blade section. The derived results are helpful to develop better engineering models for wind turbine design codes.peer-reviewe

HAWT near-wake aerodynamics, part I : axial flow conditions

An improved physical understanding of the rotor aerodynamics of a horizontal axis wind turbine (HAWT) is required to reduce the uncertainties associated with today’s design codes. Wind tunnel experiments contribute to increased knowledge and enable valida- tion and construction of models. The present study focuses on the near-wake of a model HAWT in both axial and yawed flow conditions. At three downstream planes parallel to the rotor plane, single-sensor hot-film traverses are made. The phase-locked unsteady three- dimensional flow velocity vector is determined by a novel data reduction method. A series of two papers discusses the near-wake aerodynamics of a model HAWT. The main goals are to obtain a detailed understanding of the near-wake development and to arrive at a base for model construction and validation. The first paper presents the experimental setup, data reduction and the results for the baseline case (axial flow conditions). In the second paper, the results for the yawed flow cases are presented and the effect of yaw misalignment on the near-wake development is discussed. Copyrightpeer-reviewe

Velocity measurements in the near wake of a horizontal axis wind turbine

Single film hot-film measurements in the near wake of a horizontal axis wind turbine are performed in the Delft University of Technology Open Jet Facility in order to capture the blade azimuth dependent velocity vectors. A novel approach to determine the average, blade azimuth dependent, velocity vector is proposed. It makes use of the asymmetric response of hot-films that have the film parallel to its probe. Contrary to the traditional approach in which the direction of velocity components cannot be determined and which poorly predicts relatively small velocity components, the proposed method yields velocity direction as part of the solution and consistently predicts relatively small velocity components. An uncertainty analysis is performed on the velocity magnitude and flow angle, quantifying the data quality. Furthermore, comparisons with previously published data on the same rotor, in the same wind tunnel are made. The comparisons increase confidence in the data and reveal the advantages of the proposed velocity determination method. Qualitatively, the velocity signals derived with the proposed approach are in agreement with expectations from a general vortex wake model, also the relatively small tangential and radial velocity components.peer-reviewe

An approach for the verification and validation of rotor aerodynamics codes based on free-wake vortex methods

This paper presents an approach to verify and validate a newly developed free-wake lifting line vortex code to model the wake generated by a wind turbine in axial flow conditions. Although the code is intended to simulate wind turbine wakes, it may be readily applied to propellers and helicopter rotors. The Delft University of Technology model wind turbine is used for this case study. Detailed hot-film inflow measurements in the near wake and smoke visualizations of tip vortex cores are used as a basis for validating the free-wake model. A parametric analysis was carried out to investigate how different levels of blade/wake descretizations and viscous modeling influence the accuracy of the inflow results. The tip vortex locations were compared with those predicted by the vortex model. In general very good agreement was obtained. It was found that the middle sections of the blades are rather insensitive to the choice of the viscous modeling parameters. However, high sensitivity to these parameters was observed at the blade tip and root regions.peer-reviewe

Validation of four LES and a vortex model against stereo-PIV measurements in the near wake of an actuator disc and a wind turbine

In this paper we report the results of a workshop organised by the Delft University of Technology in 2014, aiming at the comparison between different state-of-the-art numerical models for the simulation of wind turbine wakes. The chosen benchmark case is a wind tunnel measurement, where stereoscopic Particle Image Velocimetry was employed to obtain the velocity field and turbulence statistics in the near wake of a two-bladed wind turbine model and of a porous disc, which mimics the numerical actuator used in the simulations. Researchers have been invited to simulate the experimental case based on the disc drag coefficient and the inflow characteristics. Four large eddy simulation (LES) codes from different institutions and a vortex model are part of the comparison. The purpose of this benchmark is to validate the numerical predictions of the flow field statistics in the near wake of an actuator disc, a case that is highly relevant for full wind farm applications. The comparison has shown that, despite its extreme simplicity, the vortex model is capable of reproducing the wake expansion and the centreline velocity with very high accuracy. Also all tested LES models are able to predict the velocity deficit in the very near wake well, contrary to what was expected from previous literature. However, the resolved velocity fluctuations in the LES are below the experimentally measured values