270 Science and Engineering of Droplets

liquids of high viscosities, the second term becomes more significant, and thus the mean droplet size is less sensitive to variations in air velocity and density, but instead more dependent on liquid properties, particularly liquid viscosity. Some modified versions of this equation have been proposed accommodating the effect of liquid to air density ratio, liquid Reynolds number and air Mach number, as detailed in Table 4.8.

Some variant air-blast atomizer designs[102][259][429][465]-[467] have been developed and employed in certain important applications. These designs could not be fit into either of the two primary types of air-blast atomizers, i.e., plain-jet and prefilming configurations. Thus, they are considered as miscellaneous types of air-blast atomizers. The related correlations are given in Tables 4.9 and 4.10, respectively. These experimental observations showed general trends consistent with the findings in previous studies using the plain-jet and prefilming air-blast atomizers in terms of the beneficial effects of increasing the air to liquid ratio, air velocity, and air density. Typically, increasing the air to liquid ratio ALR and/or the dynamic force ρAUR2 can reduce the mean droplet size. However, with increasing air to liquid ratio, the mean droplet size approaches an asymptotic value.[272][273][429] Various studies recommended that the operation range for the air to liquid ratio ALR be from 0.1 to 10,[429] or 2 to ~5,[84]-[86] whereas Fraser et al.[73] suggested an upper limit of 1.5. Below the lower limit, the atomization quality deteriorates; above the upper limit, some portion of the air energy may be wasted so that the atomization efficiency may be lowered.

4.2.5Rotary Atomization

Various correlations for mean and maximum droplet sizes generated by smooth flat vaneless disks, vaneless disks, and wheels are listed in Tables 4.11, 4.12 and 4.13, respectively. In these corre-

lations, d is the diameter of disk/cup, ω and ω rps are the rotational speed of disk/cup in radians/s and rps, respectively, θ is the semicone

Empirical and Analytical Correlations 271

angle of rotating cup, n is the number of vanes, h is the vane height, w is the vane opening, and K is a constant. These correlations may be used for prediction purposes because each of them was derived from data involving only one well-defined mechanism of droplet formation. The important parameters influencing the mean droplet size include liquid flow rate, physical properties of liquid (viscosity, density, and surface tension), and rotational speed and diameter of disk. For disks or wheels fitted with vanes, the height, opening, and number of vanes are some additional geometry parameters of importance.

Table 4.11a. Correlations for Mean and Maximum Droplet Sizes Generated by Smooth Flat Vaneless Disks in Direct Droplet Formation Regime

272 Science and Engineering of Droplets

Table 4.11b. Correlations for Mean and Maximum Droplet Sizes Generated by Smooth Flat Vaneless Disks in Ligament Formation Regime

Table 4.11c. Correlations for Mean Droplet Sizes Generated by Smooth Flat Vaneless Disks in Sheet Formation Regime

Empirical and Analytical Correlations 273

Table 4.12. Correlations for Mean Droplet Size Generated by Vaneless Disks in Three Droplet Formation Regimes

Table 4.13. Correlations for Mean Droplet Size Generated by Wheels Fitted with Vanes

274 Science and Engineering of Droplets

A number of theoretical and experimental studies on centrifugal atomization[16][73][110]-[112][424][470]-[480] have been conducted in an effort to ascertain atomization mechanisms and establish correlations between droplet sizes and process parameters. The results of these studies suggested that, generally, the mean droplet size decreases with increasing rotational speed, liquid density, disk diameter, air density, and/or air velocity if exposed to an air flow. In contrast, an increase in liquid flow rate, viscosity, and/or surface tension generally increases the mean droplet size. The liquid flow rate appears to exert less influence on the droplet size than the rotational speed, suggesting the relative importance of controlling the rotational speed to obtain droplets with reproducible size characteristics. Uniform droplets can be produced in the range of

2.67 < ω D(dρ L/σ )1/2

Several research groups[73][112][470][480] presented experimental and semi-empirical equations for the transitional conditions from Direct Droplet Formation regime to Ligament Formation regime, or from Ligament Formation regime to Film/Sheet Formation regime. Matsumoto et al.[470] conducted a theoretical analysis and related three dimensionless parameters to the two transitions based on two simple models. The three dimensionless parameters are the Reynolds

Matsumoto et al. derived correlations for the transition flow rates from their experimental results in terms of these dimensionless parameters.

Accordingly, for the transition from Direct Droplet to Ligament Formation regime and the reverse transition, the dimensionless transition flow rates are Q+1 = 0.096 Re0.95/We1.15 and Q¯ +1 = 0.073 Re0.95/We1.15, respectively.[470]

For the transition from Ligament to Film/Sheet Formation regime or the reverse transition, the equation of Hinze and Milborn,[112] Q2+ = 0.340 Re2/3/We0.883, may be used to predict the dimensionless transition flow rate for liquids of low viscosities (less than a few poises). For more viscous liquids, the equation derived by Tanasawa et al.,[480] Q2+ = 0.297 Re6/5/We, is applicable for the calculation of the dimensionless transition flow rate.