Simulating droplet distribution characteristics in sprinkler irrigation using a modified ballistic model under multifactor coupling

Abstract

External factors affecting the processes of sprinkler irrigation water flow generation, flight, and landing have not been thoroughly considered in existing ballistic models. This result indicates that ballistic models with better prediction effects under specific conditions are not sufficient for extension to multi-factor coupled scenarios in large-scale farmlands. Therefore, wind, evaporation, surface slope, and tilted sprinkler riser factors were comprehensively considered in this study. Differential equations for jet and droplet motion under the influence of wind, differential equations of droplet evaporation, sprinkler riser deflection angle matrix, and surface slope angle matrix were constructed to establish a droplet distribution model for sprinkler irrigation considering multifactor coupling using MATLAB 2018a software. The results showed that, under different working conditions, the data points of the droplet landing diameter, velocity, and angle were distributed near the 1:1 line. The Nash efficiency coefficients (NSE) for the droplet landing diameter, velocity, and angle varied from 0.821 to 0.932, 0.616 to 0.931, and 0.770 to 0.911, respectively. The increase in slope resulted in droplets with diameters larger than 4.63 mm concentrating on the land in the reverse slope direction. When the ambient temperature increases from 10 to 45 °C and the total evaporation rate increases from 0.45 to 4.37 %, the larger droplets have a larger area of contact with the air, and the higher the temperature, the greater the energy loss to the larger droplet diameters. The higher the wind speed, the more droplets in the downwind direction fall to the ground at a smaller landing angle, which can easily increase the risk of soil shear damage. If the sprinkler riser was tilted east, the droplets on both the east and west sides tended to be distributed centrally; the maximum droplet landing velocity occurred on the east side (tilted side), and the maximum droplet landing angle occurred on the west side. This study considers various factors that may affect the motion of sprinkler irrigation water flow, extends the application scenarios of the theoretical model, and improves the applicability of the theoretical model for sprinkler irrigation droplet motion in more complex and practical agricultural environments.