Atomizers droplet size correlation

MEAN DROPLET SIZE CORRELATION FOR PRESSURE SWIRL ATOMIZER... 

Abstract This chapter discusses several other types of atomizers that were not considered in the previous chapters. This includes swirl nozzles, T-jet nozzles, and vibrating mesh nebulizers. The droplet size correlations for different types of nozzles is provided in Chap. 24. 

FtoZXldPfeed Pressure nozzle preferred for most applications. Very small particles (e.g., for inhalation powders), feeds with large suspended particles and very viscous feeds, may require other atomization systems, namely two-fluid nozzle. Use droplet size correlations to select the most suited nozzle and atomization conditions... 

In practical fan sheet breakup processes, sheet thickness diminishes as the sheet expands away from the atomizer orifice, and liquid viscosity affects the breakup and the resultant droplet size. Dombrowski and Johns[238] considered these realistic factors and derived an analytical correlation for the mean droplet diameter on the basis of an analysis of the aerodynamic instability and disintegration of viscous sheets with particular reference to those generated by fan spray atomizers ... 

Atomization, or generally speaking droplet generation, is an extremely complex process that cannot yet be precisely predicted theoretically. The lack of general theoretical treatment of droplet processes has led to the development of numerous empirical correlations for droplet properties as a function of process parameters and material properties. In this chapter, empirical and analytical correlations for the prediction of droplet properties, such as droplet size distribution and droplet deformation characteristics will be summarized from experimental observations and theoretical analyses in available literature. 

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. 

In the following sections, the correlations for droplet sizes generated by different types of atomizers will be summarized, and the effects of process parameters and material properties on droplet sizes will be discussed on the basis of the analytical and experimental studies available in published literature. 

Table 4.3. Correlations for Mean, Minimum and Maximum Droplet Sizes Generated in Pressure Jet Atomization by Plain-Orifice Atomizers... 

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...

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. 

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... 

Table 4.14. Analytical and Empirical Correlations for Droplet Sizes Generated by Ultrasonic Atomization...

As described above, a number of empirical and analytical correlations for droplet sizes have been established for normal liquids. These correlations are applicable mainly to atomizer designs, and operation conditions under which they were derived, and hold for fairly narrow variations of geometry and process parameters. In contrast, correlations for droplet sizes of liquid metals/alloys available in published literature 318]f323ff328]- 3311 [485]-[487] are relatively limited, and most of these correlations fail to provide quantitative information on mechanisms of droplet formation. Many of the empirical correlations for metal droplet sizes have been derived from off-line measurements of solidified particles (powders), mainly sieve analysis. In addition, the validity of the published correlations needs to be examined for a wide range of process conditions in different applications. Reviews of mathematical models and correlations for... 

Table 4.15. Empirical Correlations for Droplet Sizes of Liquid Metals in Gas Atomization Jet Breakup...

Table 4.16. Analytical and Experimental Correlations for Metal Droplet Sizes in Gas Atomization via Film or Sheet Breakup...

Dunkley14871 analyzed droplet size data for gas-atomized Al, Fe, Cu-Al and Sn-Sb, and developed an empirical correlation between the specific gas consumption, SGC, and mass median diameter of droplets for various atomization gases, pressures, and atomizers ... 

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 ... 

A limited number of empirical correlations have been developed for metal droplet sizes generated by water atomization, as listed in Table 4.18. In these correlations p is a system-specific constant, is the atomizing angle, i.e., angle between water nozzle axis and metal delivery nozzle axis, A is a proportional constant specific to atomizer type, melt type and melt temperature, n is a parameter depending on atomizer type, APw is the water pressure, Uw is the water velocity, and mw is the mass flow rate of water. 

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 4.19. 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. 

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