Sprinkler Irrigation Droplet Dynamics. II: Numerical Solution and Model Evaluation

Abstract

A system of equations, with strong physical basis, was derived for sprinkler irrigation droplet dynamics in the companion paper. Numerical solution of these equations and model evaluation is discussed in this paper. With the aim of enhancing computational efficiency and robustness, the droplet dynamics equations were scaled using four characteristic variables: characteristic time, length, velocity, and density. The characteristic time, length, and velocity are derived based on consideration of the motion of a droplet falling freely, starting from rest, through a quiescent ambient air, to an eventual steady-state condition. The characteristic density was set to the density of water at standard conditions. The dimensionless system of equations was then solved numerically with a fourth-fifth order pair Runge-Kutta method capable of local error estimation and time-step size control. The numerical model was first evaluated through successful comparisons with simplified solutions derived based on more limiting assumptions. Computations were then made for more realistic scenarios of droplet motion, considering the interactive effects of wind velocity, droplet diameter, and nozzle angular setting. The simulated patterns of droplet motion concur with expectations stemming from physical and intuitive reasoning.