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Chapter 7—Asynchronous Loads 7–21 design the pump and wind turbine together in order to get the best match. There are a number of large scale irrigation projects under study around the world which could use such machines in very large quantities if the cost was acceptable. 3 PADDLE WHEEL WATER HEATERS A significant amount of energy is used to heat water for the needs of homes, farms, and industry. Wind electric generators can be used to produce electricity for operating resistance heaters, as we have seen. If the only use of the wind generated electricity is to heat water, however, it may be more economical to heat the water directly by mechanical means. A paddle wheel water heater which can be used for this purpose is shown in Fig. 8. It is basically a cylindrical insulated tank with baffles around the perimeter and paddles on a rotating impeller. This particular design is geometrically simple, has good strength characteristics, and is simple to build[5, 13]. The power input to such a water heater has been found experimentally to be[5] P =4.69ρL 1.09 w 0.62 b 0.88 D −1.07 H 0.64 d 2.84 ω 3 m W (17) where ρ is the density of water in kg/m 3 , L is the length of the agitator blades, w is the width of the agitator blades, b is the width of the baffles, D is the tank diameter, H is the tank height, d is the diameter of the agitator disks, and ω m is the angular velocity in rad/s. All dimensions are in meters. We notice immediately that the power input is proportional to ω 3 m or n 3 , the desired variation to properly match or load a wind turbine over a range of speeds. We also notice that when we add up the exponents of the length terms in Eq. 17, the resultant exponent is 5. That is, the power absorbing ability of this heater increases as the fifth power of any one linear dimension if all dimensions are scaled up equally. This compares very favorably with the power rating of an electrical generator, which increases as the volume or the cube of any one linear dimension. Another advantage of this type of load is the lack of a well defined power limit. Electrical generators are limited by conductor and insulation properties at high temperatures, but the highest temperature of the water heater would be that of boiling water. A simple control valve could dump hot water when wind speeds were high, to maintain non boiling conditions. This means that a wider range of wind speeds between cut-in and rated may be possible with such a load. This could increase the average power output by a significant amount. Example A 100 liter paddle wheel water heater has dimensions L = w =0.11m,b = 0.089 m, D =0.61m, H = 0.394 m, and d = 0.305 m. What is the power input for a speed of 115 r/min? What is the rate of temperature rise in the tank in o C per hour, assuming no transfer of water into or out of the tank and no heat loss through the sides of the tank? Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001
Chapter 7—Asynchronous Loads 7–22 Figure 8: Paddle wheel water heater: (a) side view; (b) top view. We first compute the angular velocity, ω m =2πn/60 = (2π)(115)/60 = 12.04 rad/s. Then from Eq. 17, we find, for water with a density of 1000 kg/m 3 , P = 4.69(1000)(0.11) 1.09 (0.11) 0.62 (0.089) 0.88 (0.61) −1.07 (0.394) 0.64 (0.305) 2.84 (12.04) 3 = 717 W For the temperature rise, we know that 1 kcal or 4184 J will raise the temperature of 1 kg of water 1 o C. The application of 717 W = 717 J/s yields a total input of 717(3600) = 2,581,200 J in one hour, Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001
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