Weber number correlations

This correlation is valid when turbulent conditions exist in an agitated vessel, drop diameter is significantly bigger than the Kohnogoroff eddy length, and at low dispersed phase holdup. The most commonly reported correlation is based on the Weber number ... 

The Weber number becomes important at conditions of high relative velocity between the injected Hquid and surrounding gas. Other dimensionless parameters, such as the Ohnesorge ((We /Re), Euler (AP/Pj y i)y and Taylor (Re/ We) numbers, have also been used to correlate spray characteristics. These parameters, however, are not used as often as the Reynolds and Weber numbers. 

Correlating factor for turbulent flow power Weber number... 

Clark and Vermeulen (C8) measured gas holdup in three different liquids —isopropyl alcohol, ethylene glycol, and water. They measured the increase in holdup with agitation as compared to no agitation, and correlated their results as a function of the volumetric gas velocity, Weber number, P/P0, and a geometric factor. Typical volumetric gas holdup values reported in the literature vary from about 2% to 40% of the total dispersion volume (Cl, C2, C8, F2, G10). 

Clark and Vermeulen (C8) later reported an extensive experimental study of power requirements in agitated gas-liquid systems. They correlated their data in dimensionless form as a function of fractional gas holdup, Weber number, and a geometrical factor. Their correlation is shown in Fig. 5. 

The 1 (0) correlation corresponding to various Weber numbers is shown in Fig. 8.5. The shape of the interface surface in a capillary flow with phase change is presented in Fig. 8.6. As the calculations show, the curvature of the meniscus is not constant and grows toward the periphery. 

Senda et al)335 415 also derived equations describing the thickness and diameter of the radial film formed on a hot surface as a function of the Weber number, and correlated the mean diameter of droplets resulted from the breakup of the radial film with the thickness of the radial film and the Weber number. 

To determine if a droplet experiences spreading or splashing when it impinges onto a liquid film on a solid surface, the correlation between the Weber number and Ohnesorge number derived by Walzel[398] may be used ... 

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... 

The values of the Weber number pertinent to this correlation were suggested to be sufficiently small so that viscous and solidification effects can be neglected. Another analytical expression, derived from Madej ski s full model after simplification under the conditions... 

Out of these, six, viz. Weber number, Reynolds number, volume fraction X, viscosity ratios, density ratios, and length ratios were finally used for correlation. The other four were used but found not to improve the correlation. 

A range of correlations is available from the literature, usually relating the Sauter mean diameter to the Weber number, which is the ratio of shear forces to surface tension forces ... 

Most correlations show that di2 is proportional to the Weber number raised to the power of -0.6, which is consistent with the theory of drop breakup by turbulent shear forces. Strictly, these correlations should be applied only where the drop size is in the inertial subrange of turbulence, i.e.,... 

A useful generalization noted in the previous section is the widespread applicability of impeller Reynolds number for correlating performance data from different-scale operations in geometrically similar systems. In some heterogeneous systems, it may be necessary to modify the definitions of density and viscosity for use in this Reynolds number, and to introduce groups like the Weber number to account for interfacial forces (see Section V). The main point is that it requires experiment to establish finally the form of the controlling groups. 

Here Sh is the modified Sherwood number defined as Sh = /Csnsdp/fl,D and We is the modified Weber number defined as We = UoLpi.dr/hlci. A graphical illustration of the above correlation is shown in Fig. 6-20. The predictions of Eq. (6-67) also agree fairly well with the data of Lemay el al.so Specchia et al.9i showed that, in a trickle-flow reactor, KLaL and Ksas are essentially of the same order of the magnitudes. They also evaluated the conditions under which the mass-transfer (gas-liquid and liquid-solid) influences significantly the performance of a trickle-bed reactor. 

The liquid-phase holdup data in the three-phase systems were correlated in terms of Froude, Reynolds, and Weber numbers as... 

According to equation 1, the surface tension between the continuous and the disperse phase, the ratio of their respective viscosities (Weber number) and the amount of energy employed play a role. Although, in practice it is sometimes difficult to correlate an observed effect to measurable properties, the principle meaning of these relations is important to be kept in mind. 

Governing equations are the continuity equation, the chemical reactions and their thermodynamic relationships, and the heat, mass, and momentum equations. Elastic behavior of an expanding bed of particles sometimes must be included. These equations can be many and complex because we are dealing with both multiphase and multicomponent systems. Correlations are often in terms of phase-based dimensionless groups such as Reynolds numbers, Froude numbers, and Weber numbers. 

Multiphase reactor types are highly varied. The simplest approach to analyzing and predicting their behavior is to focus on the rate limiting steps or segment the reactor and model each segment and its contributions separately. Correlations are invariably a function of phase-based Reynolds and Froude numbers. Fractional volumes and properties of the solids are factors. Where interfacial tension is an important factor, the Weber number can be added. 

A typical example for a stirred two-phase system with a volume fraction of 30 vol.% organic phase dispersed in water, an interfacial tension of 25 mN m-1 and a specific power input of 0.5 W L 1 shows a droplet diameter in the range of 250 pun and a specific interface of about 10 m2 L 1. These dimensions maybe estimated from simple empirical correlations between the Sauter mean diameter of the dispersed phase (zf2.3) and the characteristic Weber number (We). In case of turbulent mixing the following correlation is proposed in the literature for calculation of the mean diameter of dispersed droplets [24]... 

The constants C i and Ci depend on chemical and physical properties of the system used. Typical values for water and hydrocarbons are 0.5 and 5, respectively. This correlation must be used with caution since at larger Weber numbers deviations are reported in literature. If the factor (1 + C2< m) is neglected, the following correlation between droplet diameter... 

Weber number We = N D pla Ratio of inertia to surface/interfacial forces for gas-liquid and immiscible L-L systems used to correlate bubble/drop size... 

Qi et al. [11, 12] have measured eiyogenie CHF data for saturated liquid nitrogen for 0.531, 0.834, 1.042 and 1.931 mm eireular microchannels. The tests were done for mass velocities from about 400 to 2,800 kg/m s at saturation pressures of about 6.8 bar. They found that the macroscale correlation of Katto and Ohno [2] and that of Zhang et al. [10] for water and extrapolated to liquid nitrogen, tended to severely under predict their data by 65-80%. Therefore, they proposed a new correlation based on the Weber number and the Confinement number as follows for CHF of liquid nitrogen ... 

A semiempirical analysis of heat transfer to impacting sprays has been developed by considering the major components of spray heat transfer to consist of (1) contact heat transfer to impacting droplets, (2) convective heat transfer to gas, and (3) thermal radiation heat transfer [142], The model further assumes that the droplet interference is negligible (i.e., dilute sprays), and the three heat transfer components are independent of each other. The heat transfer data to a single impacting droplet have been correlated by the Weber number, surface temperature superheat, and thermophysical properties. 

High Weber numbers give small droplets and high interfacial areas. Gnanasundaram et al. (1979) recommended the following correlations ... 

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