DROP SIZE DISTRIBUTIONS IN LIQUID SPRAYS

Abstract

A comparative study was carried out on the applicability of various distribution functions to describe drop size distributions in sprays. Six different distribution functions were compared; they were the upper-limit, log-normal, Nukiyama-Tanasawa, Rosm-Rammler, log-hyperbolic and three-parameter log-hyperbolic distribution functions. The comparison was based on experimental data consisting of twenty-two data sets from seven different experimental studies. The x²statistical test was employed as a criterion for the goodness-of-fit. <br><br> It was found that the best fit to the experimental data was provided by the Nukiyama-Tanasawa and log-hyperbolic distribution functions. The upper-limit and log-normal distribution functions were reasonable but clearly inferior to the Nukiyama-Tanasawa and log-hyperbolic distribution functions. The Rosin-Rammler and three-parameter log-hyperbolic distribution functions did poorly in this study. <br><br> The Nukiyama-Tanasawa and log-hyperbolic distribution functions are mathematically rather complex and problems occurred in the determination of the best-fit values of the parameters. The log-normal distribution function is particularly simple and easy to use and can perhaps be used in applications where the accuracy requirements are less stringent. <br><br> It is not clear why the Nukiyama-Tanasawa and log-hyperbolic distribution functions were the best. Further work is needed to develop drop size distribution functions based on theoretical understanding of the break-up of bulk liquid into drops. <br><br> Some problems were encountered when the x² test was applied to experimental drop size distribution data and the interpretation of the test results is therefore difficult. A more advanced statistical theory would be rather useful.