Abstract
The classical blade-element/momentum (BE/M) method, which is used together with different types of corrections (e.g. the Prandtl or Glauert tip correction), is today the most basic tool in the design of wind turbine rotors. However, there are other classical techniques based on a combination of the blade-element approach and lifting-line (BE/LL) methods, which are less used by the wind turbine community. The BE/LL method involves different interpretations for rotors with finite or infinite numbers of blades and different assumptions with respect to the optimum circulation distribution. In the present study we compare the performance and the resulting design of the BE/M method by Glauert [1] and the BE/LL method by Betz [2] for finite as well as for infinite-bladed rotors, corrected for finiteness through the tip correction.In the first part of the paper, expressions are given for the optimum design, including blade plan forms and local pitch distributions. The comparison shows that the resulting geometry of the rotor depends on the method used, but that the differences mainly exist in the inner part of the blade and at relatively small tip speed ratios (TSR<5). An important conclusion is that an infinite-bladed approach combined with a tip correction results in a geometry which is nearly identical to a geometry generated from a finite-bladed approach.Next, the results from an experimental investigation on the influence on rotor performances of the tip correction on two different rotors are presented. Employing BE/M without the tip correction (“Glauert rotor”) and BE/LL with the Goldstein's circulation (“Betz rotor”) two different 3-bladed rotors were designed and manufactured. The two rotors were investigated experimentally in a water flume to compare their performance at different tip speed ratios and pitch angles. As a result of the comparison it was found that the Betz rotor had the best performance.
Highlights
Today almost all aerodynamic designs of wind turbine rotors rely on the blade-element/momentum theory as it was formulated in the 1930th by Glauert [1]
Including a tip correction makes it possible to employ the theory to design practical finite-bladed rotors. There exists another class of methods, based on a combination of the blade-element approach and lifting-line (BE/LL) theory, which are less used by the wind turbine community
2.2 The tip correction Since the equations forming the optimum Glauert rotor are based on axial momentum theory, they are only valid for rotors with infinitely many blades
Summary
Today almost all aerodynamic designs of wind turbine rotors rely on the blade-element/momentum theory as it was formulated in the 1930th by Glauert [1]. 2.2 The tip correction Since the equations forming the optimum Glauert rotor are based on axial momentum theory, they are only valid for rotors with infinitely many blades. 2.3 Design of optimum Betz rotor For a rotor with a finite number of blades, Betz [2] showed that the ideal efficiency is obtained when the distribution of circulation along the blade produces a rigidly moving helicoidal vortex sheet with constant pitch, h , that moves in the direction of the undisturbed flow (in the case of a propeller) or against it (in the case of a wind turbine) with a constant velocity w (see Figure 2). The last equality in eq (18) is not obvious, and we refer the reader to [8] for a formal proof
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