Mean droplet size correlations

MEAN DROPLET SIZE CORRELATION FOR PRESSURE SWIRL ATOMIZER... 

It has been indicated 323 that for some distributions it is possible to find, at least, an empirical correlation between the mean droplet size and the standard deviation. Gretzinger and Marshall 102 have proposed such empirical equations relating the mean droplet size and the standard deviation for water-air system. Thus, once the mean droplet size is determined from a mathematical model, an empirical correlation, and/or experimental data, the entire droplet size distribution can be then predicted quantitatively. 

In many atomization processes, physical phenomena involved have not yet been understood to such an extent that mean droplet size could be expressed with equations derived directly from first principles, although some attempts have been made to predict droplet size and velocity distributions in sprays through maximum entropy principle.I252 432] Therefore, the correlations proposed by numerous studies on droplet size distributions are mainly empirical in nature. However, the empirical correlations prove to be a practical way to determine droplet sizes from process parameters and relevant physical properties of liquid and gas involved. In addition, these previous studies have provided insightful information about the effects of process parameters and material properties on droplet sizes. 

Various correlations for mean droplet size generated using pressure-swirl and fan spray atomizers are summarized in Tables 4.4 and 4.5, respectively. In the correlations for pressure-swirl data, FN is the Flow number defined as FN = ml/APlpl) )5, l0 and d0 are the length and diameter of final orifice, respectively, ls and ds are the length and diameter of swirl chamber, respectively, Ap is the total inlet ports area, /yds the film thickness in final orifice, 6 is the half of spray cone angle, and Weyis the Weber number estimated with film... 

Table 4.4. Correlations for Mean Droplet Size Generated by Pressure-Swirl Atomizers...

As ambient air pressure is increased, the mean droplet size increases 455 " 458] up to a maximum and then turns to decline with further increase in ambient air pressure. ] The initial rise in the mean droplet size with ambient pressure is attributed to the reduction of sheet breakup length and spray cone angle. The former leads to droplet formation from a thicker liquid sheet, and the latter results in an increase in the opportunity for droplet coalescence and a decrease in the relative velocity between droplets and ambient air due to rapid acceleration. At low pressures, these effects prevail. Since the mean droplet size is proportional to the square root of liquid sheet thickness and inversely proportional to the relative velocity, the initial rise in the mean droplet size can be readily explained. With increasing ambient pressure, its effect on spray cone angle diminishes, allowing disintegration forces become dominant. Consequently, the mean droplet size turns to decline. Since ambient air pressure is directly related to air density, most correlations include air density as a variable to facilitate applications. Some experiments 452] revealed that ambient air temperature has essentially no effect on the mean droplet size. 

Various correlations for mean droplet sizes generated by air-assist atomizers are given in Table 4.6. In these correlations, mA is the mass flow rate of air, h is the height of air annulus, tf0 is the initial film thickness defined as tj ) = dQw/dan, d0 is the outer diameter of pressure nozzle, dan is the diameter of annular gas nozzle, w is the slot width of pressure nozzle, C is a constant related to nozzle design, UA is the velocity of air, and MMDC is the modified mean droplet diameter for the conditions of droplet coalescence. Distinguishing air-assist and air-blast atomizers is often difficult. Moreover, many... 

Various correlations for mean droplet size generated by plain-jet, prefilming, and miscellaneous air-blast atomizers using air as atomization gas are listed in Tables 4.7, 4.8, 4.9, and 4.10, respectively. In these correlations, ALR is the mass flow rate ratio of air to liquid, ALR = mAlmL, Dp is the prefilmer diameter, Dh is the hydraulic mean diameter of air exit duct, vr is the kinematic viscosity ratio relative to water, a is the radial distance from cup lip, DL is the diameter of cup at lip, Up is the cup peripheral velocity, Ur is the air to liquid velocity ratio defined as U=UAIUp, Lw is the diameter of wetted periphery between air and liquid streams, Aa is the flow area of atomizing air stream, m is a power index, PA is the pressure of air, and B is a composite numerical factor. The important parameters influencing the mean droplet size include relative velocity between atomization air/gas and liquid, mass flow rate ratio of air to liquid, physical properties of liquid (viscosity, density, surface tension) and air (density), and atomizer geometry as described by nozzle diameter, prefilmer diameter, etc. 

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

Very few experimental data of droplet sizes in electrostatic atomization are available in published literature. Mori et al. 4XI I proposed the following correlation for the mean droplet size generated in electrostatic atomization ... 

Analytical and empirical correlations for droplet sizes generated by ultrasonic atomization are listed in Table 4.14 for an overview. In these correlations, Dm is the median droplet diameter, X is the wavelength of capillary waves, co0 is the operating frequency, a is the amplitude, UL0 is the liquid velocity at the nozzle exit in USWA, /Jmax is the maximum sound pressure, and Us is the speed of sound in gas. Most of the analytical correlations are derived on the basis of the capillary wave theory. Experimental observations revealed that the mean droplet size generated from thin liquid films on... 

Thus, both the mean droplet size and the size distribution may be predicted using these correlations [Eqs. (26), (27), (28), or (29) and Eqs. (30), (31)] for given process parameters and material properties. For a given atomizer design, the standard deviation of droplet size distribution has been found to increase with the melt flow rate, but appears to be less sensitive to the gas flow rated5 Moreover, the variation of the standard deviation is very atomizer- and melt-specific. An empirical correlation which fits with a wide range of atomization data has the following form ... 

In the empirical correlation proposed by Kato et al.,[503] the mean droplet size is inversely proportional to the water pressure, with a power index of 0.5 for conical shaped annular-jet atomizers, and 0.7-1.0 for V-shaped flat-jet atomizers. This suggests a lower efficiency of the annular-jet atomizers in terms of spray fineness at high water pressures. The data of Kato et al.15031 were obtained for water pressures lower than 10 MPa. Seki et al.15021 observed the similar trend in the water atomization of nickel and various steels at higher water pressures (>10 MPa). Since k is dependent on both... 

Table 4.18. Empirical Correlations for Mean Droplet Size of Liquid Metals in Water Atomization via Jet Breakup...

Table 4.19. Correlations for Mean Droplet Sizes of Liquid Metals in Centrifugal Atomization...

This approximate relationship is similar to those for centrifugal atomization of normal liquids in both Direct Droplet and Ligament regimes. However, it is uncertain how accurately the model for K developed for normal liquid atomization could be applied to the estimation of droplet sizes of liquid metals Tombergl486 derived a semi-empirical correlation for rotating disk atomization or REP of liquid metals with the proportionality between the mean droplet size, rotational speed, and electrode or disk diameter similar to the above equation. Tornberg also presented the values of the constants in the correlation for some given operation conditions and material properties. 

Droplet Size Correlations. The majority of correlations found in the Hterature deal with mean droplet diameters. A usefiil equation for Sauter... 

Viscosity adjustment factors for droplet size distribution may be determined by a correlation such as that shown in Figure 4. Mean droplet size is defined on a volume basis. Dispersity is an index of wideness of the droplet size distribution. It is defined for this purpose as the ratio of volume-mean droplet size to population-mean droplet size. 

List of Previously Published Correlations Reported for the Mean Droplet Size Produced by Spinning Disk Atomization... 

Lefebvre [1] has compiled droplet size correlations for variety of spray nozzles. The present chapter extends the same compilation to include more recent correlations. The correlations provided are by no means exhaustive, yet they provide commonly used correlations. These correlations are provided in Tables 24.1-24.12 at the end of this chapter. The correlations are mainly based on the (i) fluid properties (mainly density, viscosity, and surface tension), (ii) nozzle geometry, such as the exit orifice diameter, impinging angle of the air on the liquid, etc., and (iii) operational parameters such as the flow rates of the liquid or gas. While some experiments have been conducted to consider the effects of all these three types of variables, many simply choose only to deal with a handful of them, and neglect the effects of others. Obviously, the more the experimental variables, the more difficult it is to obtain an accurate correlation for the droplet size. 

Correlations for the mean droplet sizes produced by prefilming airblast nozzles are summarized in Table 24.1. In general, the similar correlations are grouped together. The first few equations are the ones derived using experimental data, whereas the ones at the end of the table were derived from theory. All tables presented at the end of this chapter follow this format. For convenience, each equation is given a reference number. 

The last major type of rotary nozzles is the twin-fluid rotary nozzle. Its main application is combustion for various devices. The air (or another gas) is supplied with a spinning fan, at a flow rate much greater than that of the liquid. Once the air comes in contact with the liquid, the droplets produced become smaller and the spray is finer. This type of atomization is also very good for high viscosity liquids. Table 24.11 shows some mean drop size correlations for twin fluid rotary nozzles. 

A review of the past literature on the available correlations on the mean droplet size produced by splash plate nozzles shows that there are large discrepancies between the results. The prediction of the droplet sizes generated by splash plate nozzles is based on the Kelvin-Helmholtz (K-H) instability theory for a liquid sheet. Dombrowski and Johns [14], Dombrowski and Hooper [18] and Fraser et al. [13] developed such a theoretical model to predict droplet sizes from the breakup of a liquid sheet. They considered effects of liquid inertia, shear viscosity, surface tension and aerodynamic forces on the sheet breakup and ligament formation. Dombrowski and Johns [14] obtained the following equation for droplets produced by a viscous liquid sheet ... 

These relationships are based on theoretical reasoning and experiments. In 32.4 /(e/eo) is a numerical function that has been tabulated and for liquids whose dielectric constant is e/eq > 40, /(e/eq) 80 [10]. These relations are valid when the electrospray is operated in the cone-jet mode [10] which is a particular mode of electrospray operation which will be discussed in a following section. Figure 32.3 shows experimental results that correlate well with the above relations for electrospray mean droplet size. 

Figure 13.16 gives the voltage signal obtained from the pulse laser photometer against the Sauter diameter measured by the Coulter LS 230. The peaks between the different pressures are due to air bubbles and for this reason they are neglected. It depicts the good correlation between mean droplet size and optical density of an emulsion. 

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