Sauter’s diameter

Surface Diameter, Volume Diameter, and Sauter s Diameter The surface diameter, ds, volume diameter, d, and Sauter s diameter, d, are defined such that each of them reflects a three-dimensional geometric characteristic of an individual particle. A surface diameter is given as the diameter of a sphere having the same surface area as the particle, which is expressed by... 

The volume diameter of a particle may be useful in applications where equivalent volume is of primary interest, such as in the estimation of solids holdup in a fluidized bed or in the calculation of buoyancy forces of the particles. The volume of a particle can be determined by using the weighing method. Sauter s diameter is widely used in the field of reacting gas-solid flows such as in studies of pulverized coal combustion, where the specific surface area is of most interest. 

It is noted that in the evaluation of the particle surface diameter and Sauter s diameter, as discussed in 1.2.1.3, only the external surface area of the particle is considered. 

Note that Sauter s mean diameter in Eq. (1.39) is defined for a range of particle size, which is different from Sauter s diameter in Eq. (1.4), defined for a single particle size. 

S. Aureus Sausage Sausage casing Sausage casing material Sausages Sauter diameter Sauter mean diameter N.S. Savannah Savard-Lee injectors Savin ase... 

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. 

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 ... 

Sauter mean diameter, 11 795, 13 135, 23 186, 188, 189, 190-191 Sauter mean drop diameter, 10 755, 756 Savannah River production reactors, 17 583 Savard/Lee gas-shielded tuyere, 16 151 Savard-Lee injectors, 14 741 Savory, 23 171 Saybolt color scale, 7 310 Saybolt Universal Seconds (SUS), 15 207 Saytex HP-7010, 11 474 S-B-S block copolymers, 24 706 S-B-S polymers, 24 713-714, 715 SC9... 

For a given size distribution, various averaged diameters can be calculated, depending on the forms of weighing factors. The selection of an appropriate averaged diameter of a particle system depends on the specific needs of the application. For instance, in a pulverized coal combustion process, the surface area per unit volume may be important. In this case, Sauter s averaged diameter should be chosen. 

Sauter s mean diameter d32 is the diameter of a hypothetical particle having the same averaged specific surface area per unit volume as that of the given sample d is defined by... 

Table 1 Experimental results with a pressure-jet nozzle. S.M.D. is the Sauter mean diameter, X the Rosin-Rammler mean diameter.

The Sauter mean diameter has been found to be the most useful of the above definitions for characterizing the spray produced by a nozzle. It is a good indicator of a spray s performance in complex interactions with a droplet s surface and volume. Applications include spray drying, evaporative cooling, dry scrubbing, gas quenching, and gas absorption (Stavis, 1991). 

A dished head tank of diameter DT = 1.22 m is filled with water to an operating level equal to the tank diameter. The tank is equipped with four equally spaced baffles whose width is one-tenth of the tank diameter. The tank is agitated with a 0.36-m-diameter, flat, six-blade disk turbine. The impeller rotational speed is 2.8 rev/s. The sparging air enters through an open-ended tube situated below the impeller, and its volumetric flow, Q, is 0.00416 m3/s at 25°C. Calculate the following the impeller power requirement, Pm gas holdup (the volume fraction of gas phase in the dispersion), H and Sauter mean diameter of the dispersed bubbles. The viscosity of the water, //, is 8.904 x 10 4 kg/(m-s), the density, p, is 997.08 kg/m3, and, therefore, the kinematic viscosity, v, is 8.93 x 10 7 m2/s. The interfacial tension for the air-water interface, a, is 0.07197 kg/s2. Assume that the air bubbles are in the range of 2-5 mm diameter. 

Consistent performance of the ACR during scale-up depends upon thermal and kinematic similarity throughout, but with a dynamic influence on kinematic similarity in the throat and chemical similarity in the diffuser. As a result of the above considerations, it was felt that the ACR process could be scaled in a geometrically similar reactor based on matching Mach numbers, S F ratio, and residence time in the reaction section, provided two critical conditions could be met. When scaled, the sprayed particle size distributions would have to be approximately equal (i.e., equality of Sauter mean diameter) while a kinematically similar oil-particle trajectory also would be required. 

The data indicated that droplet-size changes are primarily influenced by injection pressure and orifice size while secondary changes can be attributed to fluid properties, orifice shape, and the nozzle s internal length diameter ratio. This last point was not observed by Dombrowski and Wolfsohn (8) for more conventional swirl spray nozzles. Nevertheless, they present a useful correlation between Sauter mean diameter and operating conditions. 

In this section, we discuss the effects of solids addition on the rheology of oil-in-water emulsions, in particular, the effects of solids size (size distribution) and shape (spherical versus irregular). Because the type of the oil used to form an emulsion is important in determining the viscosity of the oil-in-water emulsion, the rheology of the emulsion-solids mixtures is also influenced by the type of oil. Thus, two distinct emulsion systems with added solids will be discussed (1) synthetic (Bayol-35) oil-in-water emulsions 21, 57) and (2) bitumen-in-water emulsions (58). The synthetic oil has a viscosity of 2.4 mPa s, whereas the bitumen has a viscosity of 306,000 mPa s at 25 C. The Sauter mean diameter of the oil droplets is 10 xm for synthetic oil, and 6 xm for bitumen-in-water emulsions. The synthetic OAV emulsions are fairly shear-thinning, whereas the bitumen OAV emulsions are fairly Newtonian. 

The specific surface area of contact for mass transfer in a gas-liquid dispersion (or in any type of gas-liquid reactor) is defined as the interfacial area of all the bubbles or drops (or phase elements such as films or rivulets) within a volume element divided by the volume of the element. It is necessary to distinguish between the overall specific contact area S for the whole reactor with volume Vr and the local specific contact area 51 for a small volume element AVi- In practice AVi is directly determined by physical methods. The main difficulty in determining overall specific area from local specific areas is that Si varies strongly with the location of AVi in the reactor—a consequence of variations in local gas holdup and in the local Sauter mean diameter [Eq. (64)]. So there is a need for a direct determination of overall interfacial area, over the entire reactor, which is possible with use of the chemical technique. 

Couto, H. S., Carvalho, J. A., and Bastos-Netto, D., Theoretical Formulation for Sauter Mean Diameter of Pressure Swirl Atomizers, J. Propul. Power, Vol. 13, No. 5, 1997,... 

In order to analyze the atomization mechanism of the air-shrouded injector, the atomization characteristics of the fabricated atomizer was investigated using a phase Doppler particle analyzer (PDPA). The Sauter mean diameter (SMD) and mean velocity distribution at 5 ms ASI are shown in Fig. 34.8. As the air pressure increases, the air velocity increases and the air dispersion area is enlarged proportionally. The maximum velocity achieved is 55 m/s when the air pressure is 50 kPa. The degree of atomization is greater at the center flow because the air velocity at the center flow is greater. Spray patterns for various air pressures are shown in Fig. 34.9. It can be seen that as the air pressure increases, the atomization process transitions from varicose wave to sinuous wave mode. Atomization at low air pressure and low fuel pressure can be seen to be affected by a twisted or sinuous mode. The spray angle... 

Operating conditions and injector properties directly influence momentum and drop size of the developing fuel spray, and are thus immediately reflected in the four global spray parameters defined in Fig. 34.22 tip penetration S, cone angle 6, equivalence ratio (j), and Sauter mean diameter SMD. 

Sauter mean diameter [m] mean particle diameter [m] dispersion coefficient [m s ] terminal double bonds [mol] impeller diameter [dm]... 

Fig. 9 Water droplet distribution at jet exit for 2.75% water addition, 3.9 tn/s. 50% of the water volume is carried by drops with a diameter greater than 55pm. Sauter mean diameter is 52pm and the mean dia. is 30pm. Half of all drops have diameters between 10 22pm and account for 13% of the water flow rate.

Test no. Feed flow rate (kgh ) Foaming gas flow rate (gh ) Sauter mean diameter (fim Bulk density (kg ) Tap density (kg ) Apparent particle density (kgm ) Angle of repose ( ) Particle porosity (%) Solubility (%) Wetting time (s)... 

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