WIND ENERGY SYSTEMS - Cd3wd

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