Drop Size Distributions in Liquid Sprays

Abstract

A comparative study was carried out on the applicability of different distribution func tions to express the drop size distributions in liquid sprays. Six different distribution functions were compared; they were the upper-limit, log-normal, Nukiyama-Tanasawa, Rosin-Rammler, log-hyperbolic and three-parameter log-hyperbolic distribution func tions. The comparison was based on experimental data consisting of twenty-two data sets from seven different experimental studies. The chi-square statistical test was used as a criterion for the goodness-of-fit.The results show 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 threeparameter log-hyperbolic distribution functions did poorly in this study.The Nukiyama-Tanasawa and log-hyperbolic distribution functions are mathema tically 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.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.

Statistical analysis of the uniformity of sprays of tire pyrolysis oil-diesel oil blends

“…There are several empirical mathematical expressions for describing the droplet size distribution in a spray, such as the equations of Rosin-Ramler, Nukiyama-Tanasawa, Log-Normal, Log-Hyperbolic and Upper Limit [28][29][30][31][32]. Paloposki [33] showed by means of a statistical analysis of 2 tests that the Log-Normal distribution functions provided a good fit to the experimental data on the droplet size distribution of liquid sprays, although lower compared to the Nukiyama-Tanasawa and Log-Hyperbolic distribution, but their distribution parameters showed greater mathematical stability and less complexity in determining their values. As described above, in was decided in this work to apply the Log-Normal density function (f), Eq.…”