Prediction of droplet size and spreading parameter by rotary cup atomisation using dimensional analysis

Abstract

This study experimentally investigated the atomisation performance of a rotary cup atomiser, and atomisation parameters (volume median diameter and spreading parameter) were modelled using dimensional analysis. Two types of dimensional correlations were identified from the 126 experimental points for the training dataset. The first type employed multiple linear regression to derive a monomial (power) form equation, while the second used symbolic regression to establish a non-monomial form. The latter more effectively captured the nonlinear characteristics of droplet formation, resulting in higher prediction accuracy, with droplet sizes across the test dataset falling within a ±15 % relative error range. The droplet size distribution was modelled using the two-parameter Rosin-Rammler distribution function, and the spreading parameter was correlated to the main dimensionless parameters through multiple linear regression and symbolic regression. The non-monomial form demonstrated superior accuracy compared to the monomial form. Thus, the combination of dimensional analysis and symbolic regression provided a physically sound and user-friendly approach for the accurate prediction of droplet size and its distribution.