Sauter mean diameter equation

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 ... 

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. 

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. 

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. 

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] ... 

Equation 5.27 has the disadvantage that it ignores the viscous forces inside the polymerizing droplet. Calabrese et al. [41 ] proposed the following relation for the calculation of the Sauter mean diameter for a viscous dispersion system ... 

Equation 5.28 can be used as a scale-up criterion in order to produce polymer particles with the same Sauter mean diameter. In this case, the criterion that can be derived is ... 

The appropriate apparent viscosity is estimated at the effective shear rate, = 5,000 Nakanoh and Yoshida found it necessary to introduce another correction in case of viscoelastic liquids [61]. The right hand side of Equation 35 must be divided by (1 +0.13 De ) where De, Deborah number, is defined as XWJ d j, with Vg the bubble swarm velocity and d is the sauter mean diameters K is the fluid relaxation time, which was arbitrarily defined as the reciprocal of the shear rate at which the apparent viscosity of the solution had dropped to (2/3) of its zero shear viscosity. 

There are multiple spray measurements used to quantify an injectors spray quality. Some of these measurements include DIO (arithmetic mean), D32 (Sauter mean diameter), D31 (evaporative mean diameter), DvO.9, and droplet distribution curve. Figure 15.9 provides a description and equation used to calculate SMD, DIO, and D31. Figure 15.10 shows a typical droplet distribution curve with an overlay to show the DvO.9 calculation. The DvO.9 value represents the point where... 

To provide clarity when calculating Sauter mean diameter (D32), an example has been provided below. The SMD measurement represents a one number descriptor used to compare different sprays and is considered industry standard for comparing spray quality. Table 15.1 provides a truncated sampling of a hypothetical spray. For this example, whole numbers are used to signify the number of droplets counted for a given diameter measurement. This data can be used to calculate the SMD for the example outlined below. Equations 15.2-15.4 show an example of how to calculate SMD based on the data provided in Table 15.1. 

In this equation, D is orifice diameter (m), is inlet channel diameter (m), Ai is inlet channel area (m ), V1 is volumetric flow rate (mVs), and b is thickness of fluid film in the orifice. The resulting Sauter mean diameter is in j,m. 

Empirical relations such as the Schwarz-Bezemer equation, given by eq. (12-11), are nsed to relate the Sauter mean diameter, ds2, to the maximnm drop size, d ax- a is an empirical constant. 

Equations (12.1) and (12.3) are strictly valid for monodisperse systems. Eor polydisperse systems only a mean value of the particle size can be measured. According to Kerker [10] and Dobbins and Jizmagian [11], (12.1) can be modified, so that it is valid for a wide variety of monomodal size distributions. In this case, the mean diameter of the particles is close to the Sauter mean diameter Xj 2- The Sauter mean diameter is the diameter of a sphere, which has the same volume-to-surface ratio as the disperse system. But (12.1) is only used to calculate the particle concentration from the measured transmission T and the mean particle size, which is calculated by (12.3). 

Semi empirical equations and numerical approaches are developed to describe the drop size of an atomization at different spraying parameters and material properties. Most of the empirical equations calculate the Sauter mean diameter (SMD) xi 2 representing the mean diameter of an area-based DSD Q2. Compared to a distribution of a certain number n of drops it is the one drop, of which diameter is Xi-2 and having the same surface area multiplied with n like the whole DSD. For most processes like spray drying, where the drying rate is directly proportional to the surface area, a parameter like the SMD is of great importance. 

In order to find a numerical solution of the PBM the finite volume method has been applied. The investigated size domain has been discretized with equal-sized grid into 1000 intervals and partial differential equation has been represented as a system of ODE s. In Fig. 33, the time progressions of Sauter mean diameter of PSD for three different overspray rates are shown. 

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. 

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,... 

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. 

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] ... 

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