Mathematical modeling of the droplet flow of a spraying device

Abstract

The paper presents the results of mathematical modeling, numerical and laboratory experiments aimed at developing an optical method for estimating the size distribution of droplets in a spray. The optical method is based on analyzing the brightness of light reflected by drops of a liquid. The object of study was a spray of a transparent liquid (distilled water) produced by a centrifugal axisymmetric nozzle. It is known that the intensity (brightness) of light reflected by a drop is proportional to the surface area of the drop, and for spherical drops, accordingly, to the square of the drop’s diameter (hereinafter, the terms intensity and brightness are used as synonyms). For a more detailed representation of the patterns of this dependence in the case of a flow of droplets, we considered a mathematical model representing the spray as a flow of spherical particles with parameterization of almost all significant properties: arbitrary distribution of droplets in size and speed as well as changes in these characteristics over time during the movement of drops along the flow. We obtained formulas and tested a mathematical model of nozzle spray that takes into account the change in droplet density due to the scattering of droplets in the spray cone and the inhomogeneity of velocity fields. The zone of possible cessation of droplet fission was determined.