Michael Graham - Wind Energy Handbook

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 3.45are 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 3.46are 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	0.30	1005	9.5	20.7
2975	0.35	965	7.6	19.5
3400	0.40	925	6.1	18.7
3825	0.45	885	4.9	18.1
4250	0.50	845	3.9	17.6
4675	0.55	805	3.1	17.1
5100	0.60	765	2.4	16.6
5525	0.65	725	1.9	16.1
5950	0.70	685	1.5	15.6
6375	0.75	645	1.2	15.1
6800	0.80	605	0.9	14.6
6375	0.85	565	0.6	14.1
7225	0.90	525	0.4	13.6
8075	0.95	485	0.2	13.1
8500	1.00	445	0.0	12.6

Figure 3.44 The aerodynamic characteristics of the NACA632XX aerofoil series. (XX corresponding to the percentage thickness ratio of each section indicated.)

Figure 3.45 Angle of attack distribution for a range of tip speed ratios.

The importance of the outboard section of the blade is clearly demonstrated in Figure 3.47. The dramatic effect of stall is shown in the difference in torque distribution between the tip speed ratio of 4 and the tip speed ratio of 2. Note, also, the flat distribution of torque at the high tip speed ratio of 12; this is caused by the effect of drag, which reduces torque as the square of the local speed ratio and with the low angle of attack at λ = 12 drag causes a significant loss of power.

Figure 3.46 Distribution of the flow induction factors for a range of tip speed ratios (lines and symbols as for Figure 3.45).

Figure 3.47 Distribution of blade loads for a range of tip speed ratios (lines and symbols as for Figure 3.45).

Although the blade thrust coefficient increases with tip speed ratio as shown in Figure 3.48, it must be remembered that the actual thrust force increases with wind speed, as is demonstrated in Figure 3.49.

Figure 3.48 Variation of thrust coefficient with tip speed ratio.

Figure 3.49 Variation of the actual force with wind speed.

The performance of a wind turbine can be characterised by the manner in which the three main indicators, power, torque, and thrust, vary with wind speed. The power determines the amount of energy captured by the rotor, and the torque developed determines the size of the gearbox and must be matched by whatever generator is being driven by the rotor. The rotor thrust has great influence on the structural design of the tower. It is usually convenient to express the performance by means of non‐dimensional, characteristic performance curves from which the actual performance can be determined regardless of how the turbine is operated, e.g. at constant rotational speed or some regime of variable rotor speed. Assuming that the aerodynamic performance of the rotor blades does not deteriorate, the non‐dimensional aerodynamic performance of the rotor will depend upon the tip speed ratio and, if appropriate, the pitch setting of the blades. It is usual, therefore, to display the power, torque, and thrust coefficients as functions of tip speed ratio.

The theory described earlier in this chapter gives the wind turbine designer a means of examining how the power developed by a turbine is governed by the various design parameters. The usual method of presenting power performance is the non‐dimensional C P– λ curve, and the performance curve under fixed‐pitch conditions for a typical three bladed turbine of the type used for large‐scale generation of electrical power is shown in Figure 3.50.

The first point to notice is that the maximum value of C Pis only 0.47, achieved at a tip speed ratio of 7, which is much less than the Betz limit for that tip speed ratio. The discrepancy is caused, in this case, by drag and tip‐losses, but the stall also reduces the C Pat low values of the tip speed ratio.