Analytical Study of Wind Influence on In-Flight Sprinkler Droplets
AbstractAn analytical model to describe the dynamics of in-flight droplets is presented in this paper to augment information on wind influence on travel distance of in-flight sprinkler droplets. The model is ballistic-theory based. It employs a relatively simple, wide-range empirical relationship between drag coefficient and Reynolds' number to replace the several sets of relations for a specified range of Reynolds numbers. The fourth-order Runge-Kutta numerical integration techniques were used to solve the trajectory equations. A modified exponential model for droplet size distribution was used during the simulation. Comparative analysis showed that agreement exists between the predictions of this model and that of earlier models. Droplets with a diameter smaller than 0.1 mm travelled farthest. Within the droplet range of 0.5 mm to 4.5 mm, as droplet diameter increased, travelled distance increased with increasing wind speed. The extent of drift increased sharply within the droplet range of 0.5 mm to 0.05 mm and increased mildly for droplet diameters greater than 0.5 mm. The model also attempts to identify droplets that are likely to contribute to drift loss and those that have a high probability of contributing only to distortion of the distribution pattern.
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