Wind Energy Handbook. Michael Barton Graham
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Название: Wind Energy Handbook
Автор: Michael Barton Graham
Издательство: John Wiley & Sons Limited
Жанр: Физика
isbn: 9781119451167
isbn:
substituting for sinϕ gives
The value of the lift coefficient Cl in the above equation is an input, and it is commonly included as above on the left side of Eq. (3.70) with a ‘chord solidity’ parameter representing blade geometry. The lift coefficient can be chosen as that value that corresponds to the maximum lift/drag ratio
Hence
Introducing the optimum conditions of Eq. (3.67),
The parameter λμ is the local speed ratio λr and is equal to the tip speed ratio where μ = 1.
If, for a given design, Cl is held constant, then Figure 3.17 shows the blade plan‐form for increasing tip speed ratio. A high design tip speed ratio would require a long, slender blade (high aspect ratio) whilst a low design tip speed ratio would need a short, fat blade. The design tip speed ratio is that at which optimum performance is achieved. Operating a rotor at other than the design tip speed ratio gives a less than optimum performance even in ideal drag‐free conditions.
In off‐optimum operation, the axial inflow factor is not uniformly equal to 1/3; in fact, it is not uniform at all.
The local inflow angle ϕ at each blade station also varies along the blade span, as shown in Eq. (3.73) and Figure 3.18:
Figure 3.17 Variation of blade geometry parameter with local speed ratio.
Figure 3.18 Variation of inflow angle with local speed ratio.
which, for optimum operation, is
Close to the blade root the inflow angle is large, which could cause the blade to stall in that region. If the lift coefficient is to be held constant such that drag is minimised everywhere, then the angle of attack α also needs to be uniform at the appropriate value. For a prescribed angle of attack variation, the design pitch angle β = ϕ − α of the blade must vary accordingly.
As an example, suppose that the blade aerofoil is National Advisory Committee for Aeronautics (NACA) 4412, popular for hand‐built wind turbines because the bottom (high‐pressure) side of the profile is almost flat, which facilitates manufacture. At a Reynolds number of about 5 ⋅ 105, the maximum lift/drag ratio occurs at a lift coefficient of about 0.7 and an angle of attack of about 3°. Assuming that both Cl and α are to be held constant along each blade and there are to be three blades operating at a tip speed ratio of 6, then the blade design in pitch (twist) and plan‐form variation are shown in Figures 3.19a and b, respectively. This blade solidity becomes very large at the root but can be accommodated to around r/R = 0.1 depending on the location of the blade axis.
3.8.3 A simple blade design
The blade design of Figure 3.19 is efficient but complex to build and therefore costly. Suppose the plan‐form was prescribed to have a uniform taper such that the outer part of the blade corresponds closely to Figure 3.19b. The straight line given by Eq. (3.75) and shown as the solid line in Figure СКАЧАТЬ