Simulating droplet distribution characteristics for sprinkler irrigation with a modified ballistic model

Abstract

The ballistic model, with its high computational efficiency and small test workload, is an effective method to simulate the distribution of spray droplets. It can be employed to solve the problems of oversimplifying the droplet crushing process and motion shape and ignoring the droplet energy characteristics in the equivalent droplet indicator in the existing model assumptions. Based on the law of the motion of sprinkler irrigation water flow, the model assumption of continuous motion and segmental fragmentation of the jet is proposed in the current study. Ellipsoidal droplet shape parameters were introduced to construct the equations of the motion of sprinkler irrigation water flow in the jet and droplet stages, respectively. The critical conditions for large droplet separation and correction drag coefficient for small droplets are defined and solved, and the calculation formulas based on the energy-weighted equivalent droplet indicators were derived. The accuracy of the model was verified using 50PYC, ZY-2, and HY50 nozzles, and the modified model was compared with Fukui’s and Li’s models. The effects of working pressure, nozzle diameter, nozzle elevation angle, and installation height on the droplet landing distance, velocity, and angle at the end of the spray range were investigated. The results showed that: (1) The mean absolute error (MAE) and root-mean-square error (RMSE) of droplet landing distance, velocity, and angle under different working conditions simulated by the modified model were smaller than those obtained using Fukui’s and Li’s models, showing better simulation accuracy. Considering the simulated values of droplet landing distance, velocity, and angle of the 50 PYC nozzle (nozzle diameter of 22 mm and working pressure of 0.35 MPa) as an example, the accuracy of the modified model was improved by 72.86 % and 53.45 % (landing distance), 35.86 % and 70.57 % (landing velocity), 42.10 % and 67.66 % (landing angle) compared with the Fukui’s and the Li’s models, respectively. (2) Fukui’s and Li’s models demonstrate higher accuracy in simulating the droplet landing distance of the ZY-2 nozzle with a smaller nozzle diameter (7 mm) than in simulating the HY50 and 50PYC nozzles; (3) The changes in nozzle operating pressure, nozzle diameter, and nozzle elevation angle exert the greatest effect on the droplet landing distance, landing velocity, and landing angle, respectively. This study provides a novel idea for using the ballistic model to simulate the spray droplet distribution.