Wind Energy Handbook. Michael Barton Graham

Wind Energy Handbook

of attack, so stall appears to be greatly delayed, and the low adverse pressure gradient shown by the reduced slope of the pressure recovery may be a reason for the delay. At 30% span the ratio StartFraction c Over r EndFraction equals 0.374

StartFraction c Over r EndFraction equals 0.374

StartFraction c Over r EndFraction equals 0.161

at 55% span, and at the 75% location StartFraction c Over r EndFraction equals 0.093

. The increased lift also occurs in the post‐stall region and is attributed to the radial flow in the separated flow regions.

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, C_l − α curve is extended beyond the stall, then let ΔC_l be the difference between the two curves. Then the correction to the 2‐D curve to account for the rotational, 3‐D, effects is 3 left-parenthesis StartFraction c Over r EndFraction right-parenthesis squared normal upper Delta upper C Subscript l :

(3.94) upper C Subscript l Baseline .3 upper D Baseline equals upper C Subscript l Baseline .2 upper D Baseline plus 3 left-parenthesis StartFraction c Over r EndFraction right-parenthesis squared normal upper Delta upper C Subscript l

Table 3.1 compares the measured static left-parenthesis upper C Subscript l Baseline .2 upper D Baseline right-parenthesis and rotating (C_l.3D) lift coefficients with the calculated values for the rotating values using Snel's correction of Eq. (3.94). The correction is quite good and is very simple to apply. An example of the correction is given by Snel in (1993) and is shown in Figure 3.43.

Table 3.1 Summary of Ronsten's measurements of lift coefficient and lift coefficients corrected to rotating conditions using Eq. (3.94).

r/R100*	30%	55%	75%
c/r	0.374	0.161	0.093
Angle of attack α	30.41°	18.12°	12.94°
C_l static (measured)	0.8	0.74	1.3
C_l rotating (measured)	1.83	0.93	1.3
C_l rotating (Snel)	1.87	0.84	1.3

Graph depicts a comparison of measured and Snel's predicted power curves for a NORTANK 300 kW turbine.

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 C_P– 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.

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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