Sauter mean diameter empirical equation

Recently, Razumovskid441 studied the shape of drops, and satellite droplets formed by forced capillary breakup of a liquid jet. On the basis of an instability analysis, Teng et al.[442] derived a simple equation for the prediction of droplet size from the breakup of cylindrical liquid jets at low-velocities. The equation correlates droplet size to a modified Ohnesorge number, and is applicable to both liquid-in-liquid, and liquid-in-gas jets of Newtonian or non-Newtonian fluids. Yamane et al.[439] measured Sauter mean diameter, and air-entrainment characteristics of non-evaporating unsteady dense sprays by means of an image analysis technique which uses an instantaneous shadow picture of the spray and amount of injected fuel. Influences of injection pressure and ambient gas density on the Sauter mean diameter and air entrainment were investigated parametrically. An empirical equation for the Sauter mean diameter was proposed based on a dimensionless analysis of the experimental results. It was indicated that the Sauter mean diameter decreases with an increase in injection pressure and a decrease in ambient gas density. It was also shown that the air-entrainment characteristics can be predicted from the quasi-steady jet theory. 

Empirical relations such as the Schwarz-Bezemer equation, given by eq. (12-11), are nsed to relate the Sauter mean diameter, ds2, to the maximnm drop size, d ax- a is an empirical constant. 

Semi empirical equations and numerical approaches are developed to describe the drop size of an atomization at different spraying parameters and material properties. Most of the empirical equations calculate the Sauter mean diameter (SMD) xi 2 representing the mean diameter of an area-based DSD Q2. Compared to a distribution of a certain number n of drops it is the one drop, of which diameter is Xi-2 and having the same surface area multiplied with n like the whole DSD. For most processes like spray drying, where the drying rate is directly proportional to the surface area, a parameter like the SMD is of great importance. 

Most of the investigators have assumed the effective drop size of the spray to be the Sauter (surface-mean) diameter and have used the empirical equation of Nuldyama and Tanasawa [Trons. Soc. Mech. Eng., Japan, 5, 63 (1939)] to estimate the Sauter diameter ... 

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