Wind turbine wake aerodynamics
Introduction
The conversion of wind energy to useful energy involves two processes: the primary process of extracting kinetic energy from wind and conversion to mechanical energy at the rotor axis, and the secondary process of the conversion into useful energy (mostly electrical, but also mechanical for water pumps or chemical for water desalination or hydrolyses). This paper concerns the primary process: the extraction of kinetic energy from the wind. The major field of science involved in this process is aerodynamics, but it needs meteorology (wind description) as input, and system dynamics for the interaction with the structure. The latter is important since all movement of the rotor blades, including bending of the blades out of their plane of rotation, induces apparent velocities that can influence or even destabilize the energy conversion process. Aerodynamics is the oldest science in wind energy: in 1915, Lanchester [1] was the first to predict the maximum power output of an ideal wind turbine. A major break-through was achieved by Glauert [2], by formulating the blade element momentum (BEM) method. This method, extended with many ‘engineering rules’ is still the basis for all rotor design codes. Recently, first results of complete Navier–Stokes calculations for the most simple wind turbine operational mode have been reported. Progress is significant in the 30-year history of modern wind energy. To name one example: a better understanding of the aerodynamics improved the efficiency of the primary process from 0.4 to 0.5 (out of a maximum of 0.592). Nevertheless, many phenomena are still not fully understood or quantified. This is due to several aspects that are unique for wind turbine aerodynamics:
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Although at present wind turbines are the biggest rotating machines on earth (up to 110 m diameter so each blade has approximately the size of the span of a Boeing 777) they operate in the lowest part of the earth boundary layer. Most aircraft try to fly high enough to avoid turbulence and extreme wind events, but for wind turbines steady wind is an off-design condition. All aerodynamic phenomena are essentially unsteady, which, however, is still beyond the scope of current design knowledge.
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The very successful ‘Danish concept’ for wind turbines relies on stall for aerodynamic power limitation in high wind speeds: the increase in drag due to stall limits the torque produced at the rotor axis. All other aerodynamic objects (except military aircraft) avoid stall as much as possible because of the associated high loads and the possible loss of aerodynamic damping. Since many wind turbines rely on stall, a thorough understanding of unsteady (deep) stall is necessary.
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The flow in the blade tip- and root region is three-dimensional: for example, due to centrifugal and coriolis forces the flow in the boundary layer at the root is in spanwise direction, while the flow just outside the layer is chordwise. This effect delays stall, by which much higher lift is achieved compared to two-dimensional data. The relevance of two-dimensional data for wind turbine performance prediction is very limited.
The aerodynamic research for wind turbines has contributed significantly to the success of modern wind energy. For most unsolved problems, engineering rules have been developed and verified. All of these rules have a limited applicability, and the need to replace these rules by physical understanding and modelling is increasing. This is one of the reasons that the worldwide aerodynamic research on wind energy shows a shift towards a more fundamental approach. ‘Back to basics’, based on experiments in controlled conditions, is governing most research programs. This paper contributes to this by surveying all previous experiments and analyses on the flow through the rotor. For an overview on the technology development of wind turbines, see [3]. For a survey of the future R&D needs for wind energy, see [4].
Section snippets
Overview
Wind turbine wakes have been a topic of research from the early start of the renewed interest in wind energy utilisation in the late 1970s. From an outsider's point of view, aerodynamics of wind turbines may seem quite simple. However, the description is complicated, by the fact that the inflow always is subject to stochastic wind fields and that, for machines that are not pitch-regulated, stall is an intrinsic part of the operational envelope. Indeed, in spite of the wind turbine being one of
Near wake experiments
In sharp contrast to the helicopter research (see [8]), good near wake experiments are hard to find in wind energy research. And also, unlike in helicopter industry, there are only few financial resources available for experiments, but the need for experimental data is nevertheless well recognized (see also [9]).
Since the start of the wind energy revival, effort has been put into experiments, both for single turbines and wind farms. During the literature survey for this article, a number of
Near wake computations
Although there exists a large variety of methods for predicting performance and loadings of wind turbines, the only approach used today by wind turbine manufacturers is based on the blade element/momentum (BEM) theory. A basic assumption in the BEM theory is that the flow takes place in independent stream tubes and that the loading is determined from two-dimensional sectional aerofoil characteristics. The advantage of the model is that it is easy to implement and use on a computer, it contains
Far wake experiments
The far wake is the region located downstream of the near wake previously studied. As explained before, in the near wake region, immediately downstream of the rotor, vortex sheets, associated with the radial variation in circulation along the blades, are shed from their trailing edge, and roll up in a short downstream distance forming tip vortices that describe helical trajectories, as can be seen in Fig. 4, Fig. 5, Fig. 6, Fig. 7, Fig. 8, Fig. 32. When the inclination angle of the helix is
Far wake modelling
In this section the numerical research on the far wake will be presented. Much of it has already been reviewed by Crespo et al. [203], so that previous contributions in this field will not be examined in much detail. The first subsection will be dedicated to individual wakes in flat terrain, that are easy to characterize with few parameters, and provide information of basic interest that can be easily arranged. However, the usual situation of practical interest, that will be discussed next, is
Velocity deficit
In many cases it is of interest for the designer to have, as an alternative to numerical models, analytical expressions which can estimate the order of magnitude and the tendencies of the most important parameters characterising wake evolution. Regressions or correlations of this type were obtained by different authors to describe single wake behaviour, [226], [224], [159], [266], [215], for the velocity deficit and the width of the wake. For the velocity deficit in the far wake, these
Concluding remarks
At a time when it is realised that the matter of interest is really complicated, it is worthwhile to review the work that has been done. Hopefully, this overview will provide a point of departure for ‘plunging’ into the subject.
Acknowledgements
Thanks to everyone who has contributed to this article: Gijs van Kuik for writing the introduction on wind energy and proof-reading, Gerard van Bussel for proof-reading and “restructuring advice”, and Gustave Corten for his help with the stall-flag pictures.
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