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Chapter 7—Asynchronous Loads 7–7 P m = 0.1886Q gh η p W = 2.529 × 10−4 Q g h hp (5) η p The second expression yields power in horsepower rather than watts. Both expressions are strictly valid only for water with a density of 1 kg/L and may need a correction if warm water or other liquids are to be pumped. Proper operation of the water pumping system requires that the pump size and turbine size be matched to the total head. The multiblade turbines are typically sold in diameters of 6, 8, 10, 12, 14, and 16 ft. Pump diameters are available in quarter inch increments from 1.75 to 5 inches and in one inch increments above 5 inches. If we put a large diameter pump on a small turbine over a deep well, the turbine will not be able to develop sufficient torque to raise the water column to the discharge level. The pump acts like a brake up to some very high wind speed where torque becomes adequate for pumping to occur. On the other hand, if we put a small diameter pump on a large turbine we may get only a small fraction of the possible capacity. There is an adjustment on the torque arm of many water pumpers which can help optimize a given system to a particular pumping level. By shortening the torque arm, the length of stroke is shortened and less water is lifted per revolution of the turbine. At the same time the force available to the piston rod increases so that a greater head can be pumped. A system designed for a given head at maximum stroke can be adjusted to satisfactorily pump smaller amounts of water if the water table should become lower. This cannot be done dynamically on these simple machines, but once per season should be adequate to compensate for changes in the water table and in the seasonal wind speeds. We see in Eq. 3 that the required pump power is directly proportional to the capacity. The capacity is directly proportional to the number of pump cycles per unit time and, therefore, to the turbine rotational speed in r/min. The turbine output then varies as the turbine rotational speed while the turbine input, the power in the wind P w , varies as the cube of the wind speed. We learned in Chapter 4 that the best match of turbine to load occurs when the load input power varies as the cube of the rotational speed. This allows the turbine to stay at the peak of its coefficient of performance curve over a wide range of wind speeds. The piston pump is not an optimum load for a wind turbine since it presents a relatively heavy load at light wind speeds and a light load at strong wind speeds. The inherent speed regulation is poor in that the pump speed theoretically changes by a factor of eight while the wind speed changes by a factor of two. The speed regulation will not actually be that bad because the slip, mechanical efficiency, and turbine coefficient of performance all deteriorate with increasing turbine speed, but there will still be substantial changes in the turbine speed. Speed is regulated by turning the turbine sideways to the wind in strong winds. The dual Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001
Chapter 7—Asynchronous Loads 7–8 task of turning the turbine into the wind in light winds and out of the wind in strong winds is accomplished by some rather ingenious mechanisms which we shall not discuss in detail. These have been perfected over many years of experimentation and work very reliably. A picture of the vane mechanism for the Dempster, another well-known water pumper, is shown in Fig. 3. Figure 3: Dempster water pumper. (Courtesy of Dempster Industries, Beatrice, Nebraska.) We now return to the matter of selecting turbine size and pump size for a given application. Manufacturers data sheets are essential at this point. A typical data sheet for the Dempster water pumper is shown in Table 7.1. This table presents data for five turbine diameters and five cylinder sizes. The original table gave head in feet and capacity in gallons per hour, but these have been converted to meters and liters per second in this table. We note in the table that the product of head and capacity is almost constant for any given diameter turbine, as would be expected from Eq. 3. The rated wind speed of the Dempster is 15 mi/h (6.7 m/s) so the capacities shown will not be exceeded greatly in stronger winds, due to the speed control mechanism on the turbine. Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001
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