Ohnesorge number correlations

To determine if a droplet experiences spreading or splashing when it impinges onto a liquid film on a solid surface, the correlation between the Weber number and Ohnesorge number derived by Walzel[398] may be used ... 

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. 

Figure 35.4 shows the variation of ellipticity with respect to the Weber, Reynolds, and capillary numbers at various axial locations. As observed fi-om these figures, the droplets are big close to the injector and the Ohnesorge numbers are small. The Weber number is much larger than the critical Weber number ( 6) and the drops undergo breakup. The deformation predicted by the above correlation... 

The Weber number becomes important at conditions of high relative velocity between the injected Hquid and surrounding gas. Other dimensionless parameters, such as the Ohnesorge ((We /Re), Euler (AP/Pj y i)y and Taylor (Re/ We) numbers, have also been used to correlate spray characteristics. These parameters, however, are not used as often as the Reynolds and Weber numbers. 

Orzechowski derived two more correlations, one for kerosene 24.7.x, and the other for a water-glycerin mixture 24.7.xi. The correlations are said to be a functirm of film thickness, Weber number and Ohnesorge s number. The effect of film thickness and Weber number remains unchanged on both liquids. The difference arises in Ohnesorge s number, where the exponent is slightly lower for kerosene. Figure 24.46 shows a comparison of the two equations, using t = 0.1 nun. 

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