WIND SYSTEM PERFORMANCE Comparing Different Types of Wind Machines
Figure 5-3 shows a farm windmill, and Figure 5-4, a Savon-ious rotor. While these two types of wind systems are very different, both windwheels present a large surface area to the. wind in relation to the width and height on the machine. Notice thdt almost the entire disk area of the farm windmill is covered by blade surface; this presents a solid appearance to the wind. The appropriate term for this is solidity, which is the ratio of blade or windwheel surface area to rotor swept area, the area inside the perimeter of the spinning blades. Thus, solidity for the two machines illustrated in Figures 5-3 and 5-4 is nearly 1.0.
Solidity = blade surface area -s- windwheel swept area.
To calculate windwheel swept area, look at Figures 5-7 an J 5-8. Swept area for a vertical-axis machine like the Savonious rotor is simply height times width. Swept area for disk-shaped windwheels is calculated from:
A = swept area, in square feet or square meters, and
D = diameter in feet or meters
For example, the swept area of a 16-foot diameter windwheel is calculated as follows:
Mechanical drive applications, such as pumping water, demand very high starting torque« from the windwheel. The pump may have a load of water it is trying to lift from a deep well at the same time the windwheel is starting to turn. Further, high rpm operation (high revolution rates from the windwheel) is not required because it is generally better to pump a large quantity of water slowly than it is to pump a small quantity rapidly. This reduces resistance to water flow in the pipes. Larger-diameter, slower-moving pumps require slow-turning, high-torque windwheels, such as shown in Figure 5-3-
Electric generators operate by moving magnets past coils of wire. Two methods are available to get the required power from a generator:
• Large coils and strong magnets
• High-speed motion of magnet past coil
Most generators are actually a balance of these two design methods. However, to get, say, 2 kW out of a generator that turns at 200 rpm, the large magnets and coils might weigh as much as 300 pounds (135
• See discussion on torque in Chapter 2.
kg). The same 2 kW can be generated by a smaller generator, which weighs about 50 pounds (22.5 kg), by spinning that generator at about 2000 rpm.
From this, we can see that a lightweight, low-cost wind turbine requires a fast-turning windwheel with much lower solidity, as shown in Figure 5-6.
One further relationship is needed to complete the discussion of solidity: tip speed ratio, the speed at which the windwheel perimeter is moving divided by the wind speed. If the wind is blowing at, say, 20 mph (9 m/s), and a windwheel is turning so that the cuter tip of the blade is also moving at 20 mph around its circular path, tip speed ratio equals 1. Windwheels such as that in Figure 5-3 operate at tip speed ratios of about 1.
Suppose the tip were moving at 200 mph. With a wind speed of 20 mph the tip speed ratio would equal 10. Low-solidity wind-wheels operate at tip speed ratios much greater than 1, usually between 5 ana 10. We can now see a relationship between tip speed ratio, which is a measure of rpm, and solidity. High solidity windwheels spin slowly compared to low solidity windwheels.
Figure 5-9 shows how the relative torque of various wind turbines decreases with increasing tip speed ratio. As we noted previously, high torque requires a high solidity, and that type of wind turbine works best at low tip speed ratios. Figure 5-10 shows how the best operating tip speed ratio changes with solidity.
A wide variety of wind machines are sketched in Figures 5-11 and 5-12. Lest you get th immediate impression that there are more types of wind systems available than you might care to choose from, be assured that many of the types shown are only interesting historically. Some of the others are presently the subject of advanced concept studies.
The relative efficiencies of the types of wind turbines in which you might have an interest are illustrated in Figure 5-13-Notice that the efficiency is also related to tip speed ratio, as is starting torque. As stated in Chapter 2, the maximum amount of power a simple windwheel (without a shroud or tip vanes) can extract from the wind is 59.3 percent of the wind power that would pass through that windwheel. From Figure 5-13, you can see that no windwheel actually extracts 59.3 percent.
Solidity affects design appearance in its relation to the number of blades a machine has. High solidity wind turbines have many blades; low solidity machines have few, usually four or less. Figure 5-14 illustrates a wind turbine of intermediate solidity used for electric power generation.
tip speed ratio
FIGURE 5-9: Relative starting torque.
tip speed ratio
FIGURE 5-9: Relative starting torque.
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