Mathematical modelling and simulation of irrigation sprinklers

Abstract

A set of equations suitable for describing the dynamics of a liquid droplet - gas mixture (spray) have been developed. The equations are arrived at by considering the spray as a multiphase continuum within which the gas and droplets of different sizes constitute individual phases. By ignoring droplet-droplet interactions and considering the gas phase as an inviscid fluid a simplified form of the equations of motion has been arrived at. The equations are considered in one dimension and used to describe the dynamics of the interior of spray produced by a large or medium scale irrigation sprinkler. When combined with data representing the distribution of droplet diameters within the spray this model can be used to predict the water application produced by a sprinkler operating in windy conditions. Such simulations have been undertaken to predict the water application from static sprinklers and the results validated by comparison with data obtained experimentally. A simulation methodology is used to determine the uniformity of water application produced by a travelling sprinkler. By considering the results of large number of simulations produced using meteorological data spanning several years the manner in which the simulation can be used for determining optimum irrigation practice is demonstrated. A simple model has been developed for predicting the water application from a travelling sprinkler operating in still air. The model can be used for obtaining first approximations to optimum operating conditions and provides a means for easily quantifying the performance of a given sprinkler. Further use of the model may be made for aiding in the design and control of irrigation sprinklers.