雾状水幕2种常用分布函数的近似转换

Approximate conversion between two conventional distribution functions for water spray

上限对数正态分布(LN分布)和Rosin-Rammler分布(R-R分布)经常同时用于拟合同一种雾状水幕水滴粒径分布。该文研究这2种分布函数之间能否等价、能否近似相互转换以及转换的条件,为雾状水幕粒度试验数据分析和相关数值计算中的分布函数选择、使用和转换的进一步研究提供参考。在推导上限LN分布函数的累积体积百分比公式和粒子体积粒径分布公式的基础上,利用Euclidean空间距离评价2种函数近似程度。分析结果表明:液滴直径上限对LN分布累积体积百分数比曲线形状影响较大;虽然2种分布函数不等价,但是存在着近似转换关系;实现最优近似的转换时,LN分布的直径上限总是对应R-R分布累积体积百分比为94%时的直径。

Upper limit lognormal（LN） distribution and Rosin-Rammler（R-R） distribution functions are often used to simultaneously describe the droplet diameter distribution of the same water spray.This paper investigates the equivalence,approximation and conversion conditions of the two functions for the choice and application of these functions and the data transformation between the two functions in the data analysis and calculation.The Euclidean space distance was used to evaluate the optimum approximation of the two functions based on the derivation of LN＇s cumulative volume percent and volume diameter distribution.The results show that the LN distribution upper diameter limit dominates the cumulative volume curve shape and that an approximate conversion exists between the two functions with the two not being exactly equivalent.The results also show that the best approximation appears at the diameter at which the R-R distribution volume cumulative ratio is 94%.