On the adequacy between the laser diffraction diameter distribution and the 3-parameter Generalized-Gamma function

Abstract

The determination of a universal mathematical function to represent liquid spray drop-size distribution is still debated in the literature. The ability of such a mathematical function is usually quantified by exploring its capability to represent experimental data. Since experimental diagnostics are not sensible to the same spray characteristics, we have reasons to believe that the most appropriate mathematical function to represent experimental data depends on the diagnostic used. In this paper, we investigate the adequacy between the Laser Diffraction Technique (LDT) distribution and the mathematical 3-parameter Generalized-Gamma function. LDT is a very often-used diagnostic to characterize liquid sprays and the 3-parameter Generalized-Gamma function is another form of the well-known Nukiyama–Tanasawa distribution whose competence to reproduce measured data has been often reported. It is demonstrated that the three adjustable parameters of the mathematical function allow reaching beyond the simple curve fitting exercise. Besides the volume-based distribution, which is the type of distribution reported by LDT, a correct choice of the parameters allows retrieving the mean-diameter series in the small order range as well as the fractal dimension that characterizes the small drop population. Therefore, the three parameters allow performing more complete descriptions of the measured LDT distribution as illustrated by a couple of applications. Furthermore, this finding suggests a first interpretation of these parameters to describe LDT drop-diameter distribution.