Empirical and Analytical Correlations 275

4.2.6Effervescent Atomization

The studies on the performance of effervescent atomizer have been very limited as compared to those described above. However, the results of droplet size measurements made by Lefebvre et al.[87] for the effervescent atomizer provided insightful information about the effects of process parameters on droplet size. Their analysis of the experimental data suggested that the atomization quality by the effervescent atomizer is generally quite high. Better atomization may be achieved by generating small bubbles. Droplet size distribution may follow the Rosin-Rammler distribution pattern with the parameter q ranging from 1 to 2 for a gas to liquid ratio up to 0.2, and a liquid injection pressure from 34.5 to 345 kPa. The mean droplet size decreases with an increase in the gas to liquid ratio and/or liquid injection pressure. Any factor that tends to impair atomization quality, and increase the mean droplet size (for example, decreasing gas to liquid ratio and/or injection pressure) also leads to a more monodisperse spray.

For a constant gas flow rate, a decrease in gas density leads to an increase in mean gas velocity and/or average gas flow area. The increases in both these quantities prove to be beneficial to atomization quality. In the former case, it accelerates the liquid flow through the injector orifice so that the liquid is discharged at a higher velocity. In the latter case, it reduces the area available for the liquid flow so that the liquid is squeezed into thinner films and ligaments as it flows through the injector orifice.

The decrease in the mean droplet size with increasing liquid injection pressure may be attributed to two effects. First, the high pressure-drop across the exit orifice makes the process more like a pressure atomization at high pressure. Second, the liquid is squeezed into fine ligaments as it flows through the injector orifice, and the ligaments are shattered into small droplets by the explosion downstream of the nozzle exit.

The experimental results of Lefebvre et al.[87] also revealed that the mean droplet size is virtually independent of injector orifice diameter. This is a desirable feature for spray combustion applications.

276Science and Engineering of Droplets

4.2.7Electrostatic Atomization

Very few experimental data of droplet sizes in electrostatic atomization are available in published literature. Mori et al.[481] proposed the following correlation for the mean droplet size generated in electrostatic atomization:

Eq. (25)

SMD = 5.39d 0

E

−0.255V

0.277

Re−0.124

with

= E 2 d

/ σ ,

=ρ V& 2

/(σ d 3 ) ,

Re= ρ

V&

/(μ

d

)

E

0

V

L

L

0

L L

0

L

where d0 is the outer diameter of liquid supply tube, is the dielectric constant, and E is the intensity of electric field. Clearly, the mean droplet size decreases with increasing electric field intensity, dielectric constant, and/or liquid surface tension, but increases with increasing liquid flow rate, liquid density, liquid viscosity, and/or liquid supply tube diameter. The effects of liquid surface tension and liquid supply tube diameter appear less significant in electrostatic atomization.

Some researchers have suggested correlations based on theoretical analyses, as reviewed by Lee et al.[88] However, the equations have not been experimentally verified.

4.2.8Ultrasonic 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, λ is the wavelength of capillary waves, ω 0 is the operating frequency, a is the amplitude, UL0 is the liquid velocity at the nozzle exit in USWA, Pmax 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

Empirical and Analytical Correlations 277

an ultrasonically excited plate is proportional to the theoretical wavelength of capillary waves excited by the ultrasonic vibrations on the liquid surface. Lang[127] suggested D = 0.34λ , and Lobdell[484] derived a theoretical value of 0.36λ based on considerations of droplet formation from high-amplitude capillary waves, whereas Mizutani et al.[482] proposed 0.53λ for low flow rates, at which a thin liquid film forms before atomization. The wavelength of the capillary waves is controlled by the vibration frequency. Thus, the mean droplet size can be related to the operating frequency of the ultrasonic atomizer. In addition, the mean droplet size may be influenced by several other parameters, (such as flow rate and vibration amplitude) and physical properties of liquid (density, surface tension and viscosity), as suggested by many researchers on the basis of the Taylor instability[483] or experiments.[130][482]

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

	Correlations								Process Characteristics &	References
									Remarks
Dm ≈ 0.34 λ = 0.34 (8πσ / ρ L ω					2	1 / 3			Derived on the basis of	Lang
					0 )				capillary wave theory (semi-	[127]
									empirical)
SMD ≈ 0.53λ = 0.53(8πσ					2		1 / 3		Derived on the basis of	Mizutani
				/ ρ Lω0 )					capillary wave theory, for	[482]
									low flow rates	et al.
Dm = (4π 3σ / ρ Lω02 )1/ 3									Derived on the basis of	Peskin
Dm = 0.42πa ,									capillary wave theory in	& Raco
					2		3	/ 2σ	terms of Taylor instability,
		for large ρLω0 a							for thick films	[483]
									For water-glycerin
									(methanol) solutions and
æ	σ	ö	0.354						distilled water with a horn	Mochida
ç		÷	0.303 & 0.139
SMD = 0.158ç		÷	μ L	VL					type of ultrasonic atomizer at	[130]
	ρ L
è		ø							V&
									ω0=26 kHz, L ≤50 l/h
MMD = 0.53d0Z −0.48 Re−0.69									Ultrasonic standing wave
									atomization of Drivanil
Re = ρLU L0d0 / μL									250/25:	Bauckhage
		,							0.01≤Re≤1,
2	2		2							et al.[143]
Z = Pmax / ρGU s ρLUL0									0.01≤MMD/d0≤0.3,
									2.5Z-0.5≤Re≤100Z-0.7,
									10≤Z≤10000