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Wind Energy Handbook. Michael Barton Graham
Читать онлайн.Название Wind Energy Handbook
Год выпуска 0
isbn 9781119451167
Автор произведения Michael Barton Graham
Жанр Физика
Издательство John Wiley & Sons Limited
Snel et al. (1993) have proposed a simple, empirical modification to the usually available 2‐D, static aerofoil lift coefficient data that fits the measured lift coefficients by Ronsten (1991) and the computed results given by 3‐D RANS CFD.
If the linear part of the static, 2‐D, Cl − α curve is extended beyond the stall, then let ΔCl be the difference between the two curves. Then the correction to the 2‐D curve to account for the rotational, 3‐D, effects is
Table 3.1 compares the measured static
Table 3.1 Summary of Ronsten's measurements of lift coefficient and lift coefficients corrected to rotating conditions using Eq. (3.94).
| r/R*100 | 30% | 55% | 75% |
|---|---|---|---|
| c/r | 0.374 | 0.161 | 0.093 |
| Angle of attack α | 30.41° | 18.12° | 12.94° |
| Cl static (measured) | 0.8 | 0.74 | 1.3 |
| Cl rotating (measured) | 1.83 | 0.93 | 1.3 |
| Cl rotating (Snel) | 1.87 | 0.84 | 1.3 |
Figure 3.43 A comparison of measured and Snel's predicted power curves for a NORDTANK 300 kW turbine.
3.11 Calculated results for an actual turbine
The blade design of a turbine operating at constant uniform rotational speed and fixed pitch is given in Table 3.2, and the aerofoil characteristics are shown in Figure 3.44.
The complete CP– λ curve for the design is given in Figure 3.15.
Using the above data the results shown in Figure 3.45 are obtained.
The blade is designed for optimum performance at a tip speed ratio of about 6 and, ideally, the angle of attack, uniform along the span at the level for which the lift/drag ratio is a maximum, is about 7° for the aerofoil concerned. At the lowest tip speed ratio shown in Figure 3.45, the entire blade is stalled, and for a rotational speed of 60 rpm, the corresponding wind speed will be 26 m/s, which is the cut‐out speed. For the highest tip speed ratio shown, the corresponding wind speed will be 4.5 m/s, the cut‐in speed. Maximum power is developed at a tip speed ratio of 4.0 in a wind speed of 13 m/s and, clearly, much of the blade is stalled.
The axial flow induction factor is not uniform along the span at any tip speed ratio, indicating that the blade design is an engineering compromise, but at the tip speed ratio of 6.0 there is a range where the value is a little higher than 1/3. The flow factors shown in Figure 3.46 are those local to the blade, and so the average value of axial flow factor will be close to 1/3 at a tip speed ratio of 6.
Generally, the axial flow factor increases with tip speed ratio while the tangential flow factor decreases with tip speed ratio. The angular velocity of the wake increases sharply with decreasing radius because it is mainly determined by the root vortex, the angular velocity about a straight line vortex being inversely proportional to distance.
Table 3.2 Blade design of a 17 m diameter rotor.
| Radius r mm |
|
Chord c mm | Pitch β deg | Thickness/chord ratio of blade % |
|---|---|---|---|---|
| 1700 | 0.20 | 1085 | 15.0 | 24.6 |
| 2125 | 0.25 | 1045 | 12.1 | 22.5 |
| 2150 |