A Mathematical Model for Predicting the Sauter Mean Diameter of Liquid-Medium Ultrasonic Atomizing Nozzle Based on Orthogonal Design

Abstract

As a new type of atomizing nozzle with superior atomizing performance, the liquid-medium ultrasonic atomization nozzle has been widely applied in the field of spray dust reduction. In this study, in order to establish a mathematical model for predicting the Sauter mean diameter (SMD) of such nozzles, the interaction between the SMD of the nozzle and the three influencing factors, i.e., air pressure, water pressure, and outlet diameter were investigated based on the custom-designed spraying experiment platform and orthogonal design methods. Through range analysis, it was obtained that the three parameters affecting the SMD of the nozzle are in the order of air pressure > water pressure > outlet diameter. On this basis, using the multivariate nonlinear regression method, the mathematical model for predicting the SMD of the nozzle was constructed. Comparison of the experimental results with the predicted values of the SMD of the nozzle by the multivariate nonlinear regression mathematical model, showed strong similarity with an average relative error of only about 5%. Therefore, the established mathematical model in this paper can be used to predict and calculate the droplet size for liquid-medium ultrasonic atomizing nozzles.