Sauter equation

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

Using equations 11 and 12, the estimated Sauter mean diameters agree quite weU with experimental data obtained for a wide range of atomizer designs. Note that the two constants in equation 11 differ from those shown in Lefebvre s equation (32). These constants have been changed to fit a wide range of experimental data. 

For airblast-type atomizers, it has been speculated (33) that the Sauter mean diameter is governed by two factors, one controlled by air velocity and density, the other by Hquid viscosity. Equation 13 has been proposed for the estimation of equation 13, and B are constants whose values depend... 

AP is the pressure drop, cm of water p and Pg are the density of the scrubbing liquid and gas respectively, g/cm L/g is the velocity of the gas at the throat inlet, cm/s QtIQg is the volumetric ratio of liquid to gas at the throat inlet, dimensionless It is the length of the throat, cm Coi is the drag coefficient, dimensionless, for the mean liquid diameter, evaluated at the throat inlet and d[ is the Sauter mean diameter, cm, for the atomized liquid. The atomized-liquid mean diameter must be evaluated by the Nuldyama and Tanasawa [Trans. Soc Mech Eng (Japan), 4, 5, 6 (1937-1940)] equation ... 

Most of the investigators have assumed the effective drop size of the spray to be the Sauter (surface-mean) diameter and have used the empirical equation of Nuldyama and Tanasawa [Trons. Soc. Mech. Eng., Japan, 5, 63 (1939)] to estimate the Sauter diameter ... 

Recent data by Calabrese indicates that the sauter mean drop diameter can be correlated by equation and is useful to compare with other predictions indicated previously. 

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. 

Calderbank and Rennie (C4) and Rennie and Evans (R5) have found Sauter mean bubble diameters both photographically and from foam densities by y-ray absorption technique. Their bubble size could be predicted by the equation of Leibson et al. (L2) with a frothing system, for orifice Reynolds numbers between 2000 and 10,000. Thus,... 

For non-spherical particles, the Sauter mean diameter ds should be used in place of d. This is given in Chapter 1, equation 1.15. 

In these equations, a is the specific interfacial area for a significant degree of surface aeration (m2/m3), I is the agitator power per unit volume of vessel (W/m3), pL is the liquid density, o is the surface tension (N/m), us is the superficial gas velocity (m/s), u0 is the terminal bubble-rise velocity (m/s), N is the impeller speed (Hz), d, is the impeller diameter (m), dt is the tank diameter (m), pi is the liquid viscosity (Ns/m2) and d0 is the Sauter mean bubble diameter defined in Chapter 1, Section 1.2.4. 

In order to estimate the specific surface area of the dispersed organic droplets, the mean droplet size (Sauter diameter 32) has to be determined, which can be calculated according to the Okufi equation (Eq. 5) ... 

From experiments, equations have been derived that enable calculation of the minimum velocity in the nozzle, the nozzle velocity, and the Sauter diameter at the drop size minimum. They provide the basis for the correct design of a sieve tray [3,4]. Figure 9.4a shows the geometric design of sieve trays and their arrangement in an extraction column. Let us again consider toluene-phenol-water as the liquid system. The water continuous phase flows across the tray and down to the lower tray through a downcomer. The toluene must coalesce into a continuous layer below each tray and reaches... 

Influenced by interfacial tension and centrifugal forces, spherical drops of various diameters originate at the holes. If we again assume the Sauter diameter, according to Eq. (9.1), as the mean diameter of the spectrum of particles, the following equation for heavy and light phases results from theoretical and experimental results [10] ... 

B) have found excellent correlation between the measured sizes of drops atomized by high-velocity gas streams with the equations developed by Nukiyama and Tanasawa (6L), so long as conditions are held within certain limits. The behavior of sprays of 7i-heptane, benzene, toluene, and other fuels has been studied by Garner and Henny (SB) by use of a small air-blast atomizer under reduced pressures. A marked increase in the Sauter mean diameter was obtained for benzene and toluene as compared with n-heptane, which parallels their poor performance in gas turbines. Duffie and Marshall (2B) give a theoretical analysis of the breakup characteristics of a viscous-jet atomizer and show high-speed photographs of the process. 

For a given value of O and y in the log-normal distribution function, the mean and variance of the distribution function were computed and compared with the mean and variance of the measured bubble lengths. A regula falsi technique was used to minimize the difference between observed and calculated mean and variance. The values of O and y that minimized the difference between observed and calculated mean and variance were then employed in Equation (1) to describe the local bubble diameter distribution. The Sauter mean bubble diameter was evaluated from the second and third moments of Equation (4). 

The regression coefficient, r, was 0.985 for the use of the above equation to predict Sauter mean bubble size. 

The radial distribution of interfacial area for a two-phase system is shown in Figure 11. As discussed earlier, the gas holdup fraction is a strong function of radial position, but the Sauter mean bubble size is a less pronounced function of radial position. Consequently, the radial distribution of interfacial area has a shape similar to the gas holdup radial profile. Therefore, the inter facial area is well described with a third order polynominal equation. 

Using a multivariate regression approach based upon a modified El-Shanawany and Lefebvre equation (32) yields for following predictive relation of Sauter mean droplet size (SMD) for a twin-fluid type atomizer (33) utilizing the non-dimensional parameters of ALR, Weop and Ohj>p ... 

The optimization of pneumatic nebulizers is aimed in particular at selecting the working conditions that give the optimum droplet size and efficieny. The so-called Sauter diameter do, i.e. the diameter for which the volume to surface ratio equals that of the complete aerosol, is given by the Nukuyama-Tanasawa equation (see Ref. [137]) ... 

The coupled equations had been solved by numerical computation using an implicit finite difference technique [34]. While solving the above equations, the emulsion globule size J32 (sauter mean diameter) was calculated by using the following correlation [35] ... 

The Sauter mean drop diameter, d M or (32, defined by Equation (9.45), is most commonly used to characterize drop size because it relates to the volume fraction of the dispersed phase, O, and the interfacial area, a. The Sauter mean drop diameter is also known as the volume-to-surface average drop diameter. The interfacial area, a, in Equation (9.45) is also used to deal with mass transfer, such as ki a. Other commonly used terms are d o, dgo, and d They represent the midsize, the 90th percentile, and the largest size in the drop size distribution, respectively, on a volume basis. The... 

The maximum surviving drop diameter, is approximately 1.6 times d M- The Sauter mean drop diameter can be calculated using Equation (9.45) from a population of n drops of different sizes, 4. 4+1 4- The drop size distribution often becomes self-preserving (similar shape distri-... 

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