Ohnesorge number modified

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. 

Typically, the Weber and Ohnesorge numbers are dimensioifless measures of the relative strength of the inertia to the surface tension in a fluid and the viscosity to the surface tension of a fluid, respectively. Here the Weber number is modified (with a hat. We) to craisider the inertia of the surrounding atmosphere in comparison to the surface tension of the fluid extending from the nozzle. 

Figure 2.11 illustrates the extended spray regime as a function of the modified Ohnesorge number Oh and the Reynolds number. Spray formation is significantly... 

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