A methodology to obtain the performance curves of windmills associated with piston pumps: application in water desalination systems by reverse osmosis

Abstract

The use of windmills for the pumping of well water has appeared economically feasible in regions with average winds above 5 m/s, and when the water is used for human consumption and irrigation in arid rural zones, the importance of extracting the water from these wells efficiently and sustainably becomes more evident. However, concerning the state of Ceará/Brazil, only 18% of the drilled wells are freshwater wells, thus requiring additional energy for the utilization of desalination systems such as reverse osmosis. For that, the correct sizing of the pumping system associated with water desalination systems is essential, bearing in mind that the knowledge of the performance curves of the windmills, usually associated with piston pumps, is the "key factor" of the project. A brief analysis of the literature and websites of windmill suppliers shows that the performance curves of windmills associated with piston pumps are scarce, and the procedure to obtain them is not clear. This work's novelty is to use the windmill's power coefficient curve in association with the piston pumps to obtain the windpump performance curves, as pressure head versus volumetric flow rate in different wind conditions and sizes of windmills. The obtained curves were compared with other two curves found in the literature: one in a supplier's catalog and another from the "rule of thumb". The results showed a considerable divergence when calculating the root mean square deviation: 43.73% in relation to the supplier data average, and 125.76% in relation to the rule of thumb average results; however, the model proposed herein presented a limited operational range, which was not verified in the other two curves, which reproduced unlimited machines in terms of provided pressure head and flow rate. The unreal and asymptotic characteristics are more evident in the curves obtained by the rule of thumb, where the differences are also greater (125.76%) in relation to the proposed model. In terms of freshwater production, the model proposed herein reached, with an average wind speed of 6.5 m/s, and with a windmill of 6.1 m in diameter, a flow rate of up to 9.1 m 3 /day, after going through the reverse osmosis system. The same condition with the rule of thumb's model reached a flow rate of up to 11.3 m 3 /day. Finally, the model proposed herein for obtaining windmill's performance curves proved to be easy to implement and with realistic results, becoming an important design tool.