Prediction of Spray Droplet Size Distribution Based on Maximum Entropy

Abstract

The spray process relies heavily on the droplet size distribution, which plays a crucial role in mass, momentum and energy transport. Currently, determining the droplet size distribution is a major scientific problem, which is represented by distribution functions classified into empirical and theoretical distribution methods. Empirical methods which derive droplet size distribution formulae from statistical analysis of experimental data lack practical physical significance and rely too heavily on empirical data. In contrast, theoretical approaches mainly use the maximum entropy approach, which originates from physical conservation laws but faces challenges in accurately predicting the droplet size distribution under complex conditions. To address these challenges, a maximum entropy model of droplet size distribution was proposed based on the maximum entropy principle, with an average diameter constraint condition used for constructing three and four-parameter maximum entropy models. The optimal model was selected based on the comparison of Akaike information criterion numbers, and the three-parameter maximum entropy model using the average diameter was found to be the best in predicting droplet number distribution. Air-blast nozzle atomization experimental data were used to optimize the proposed model, and the results showed that the correlation coefficient between predicted and experimental droplet number differential distribution values was above 0.96, with a mean square error lower than 0.135. Moreover, the three-parameter maximum entropy model accurately predicted the number and distribution of spray droplets. The proposed model was also tested against experimental data on atomized droplet size distribution from different nozzle types, yielding a good match with the experimental data. Finally, the selected model was applied to predict the particle size distribution of spray droplets from pressure nozzles manufactured by Pratt & Whitney Canada, demonstrating its accuracy in predicting the spray droplet size and quantity distribution despite the complexity of the working conditions. In conclusion, the research result can provide a significant contribution to accurately predicting droplet size distribution and quantity, and the proposed three-parameter maximum entropy model had great potential in improving spray droplet size and quantity distribution prediction accuracy.

Keywords: spray, droplet size distribution, mean diameter, maximum entropy