Influence of Rotational Effects on Droplet Trajectories and Sprinkler Spray Uniformity

A three-dimensional droplet motion model considering the rotational effect of the sprinkler tray was established in a fixed reference frame for low-pressure rotary sprinklers to reveal the effects of tray rotation of a rotary sprinkler on the flight trajectories of water droplets and spray uniformity. Conventional ballistic models for fixed sprinklers only incorporate radial and vertical ejection velocities and neglect the circumferential velocity generated by tray rotation, which cannot describe the circumferential deflection behavior of water droplets. The circumferential velocity induced by tray rotation was introduced as the initial boundary condition of the droplets, and an initial velocity model of the droplets leaving the tray, including radial, circumferential and vertical components, was constructed. Meanwhile, influences of air drag, gravity, buoyancy, ambient wind speed and evaporation on the droplet flight process were comprehensively considered. The fitting performance of Rosin–Rammler, Upper-Limit Log-Normal and Gamma distributions for droplet size was evaluated based on laser disdrometer measured data, showing that the Gamma distribution performed best and can serve as the droplet size input for trajectory and spray uniformity calculations. With droplet sizes and initial velocities defined, the Runge–Kutta fourth-order (RK4) method was adopted to solve three-dimensional trajectories, obtaining droplet distributions and uniformity coefficient through landing-point interpolation and grid statistics. Model validation results show that the simulated ranges of single water droplets agree well with the measured values, with relative errors all controlled within 6%. Further comparison of the spray characteristics between fixed and rotary sprinklers reveals that the circumferential initial velocity imparted to droplets by the rotational effect can significantly alter their spatial flight trajectories and landing point distributions, enabling droplets to complement each other in the circumferential direction and thereby enhancing the continuity of spray coverage. The single-sprinkler application uniformity coefficient was increased from 54.6% in the fixed state to 76.9% in the rotating state under the identical operating conditions. The findings can provide a theoretical basis and computational tools for analyzing the spraying mechanism, structural optimization and application uniformity improvement of low-pressure rotary sprinklers. Experiments in this study had no external wind speed criteria, but model development includes wind speed if relevant.