Liquid volume fraction

Figure 10-114. Design chart for liquid volume fraction using parameter defined in equation 10-168. (Used by permission Fair, J. R. Petroleum Refiner, Feb. 1960, p. 105. Gulf Publishing Company. All rights reserved.)...

Rl Liquid volume fraction based on one-third of outlet fractional vaporization Figure 10-114 forSE = x /S ... 

Figure 3.41 The in-situ liquid volume fraction as a function of dimensionless liquid flow rate W and dimensionless tube size parameter R+. (From Cheremisinoff and Davis, 1979. Copyright 1979 by American Institute of Chemical Engineers, New York. Reprinted with permission.)... 

Cravarolo, L., and A. Hassid, 1965, Liquid Volume Fraction in Two-Phase Adiabatic Systems, Exeter Symposium, England. (3)... 

Wu, Ruff and Faeth12491 studied the breakup of liquid jets with holography. Their measurements showed that the liquid volume fraction on the spray centerline starts to decrease from unit atZ/<70=150 for non-turbulent flows, whereas the decrease starts at aboutZ/<70=10 for fully developed turbulent flows. Their measurements of the primary breakup also showed that the classical linear wave growth theories were not effective, plausibly due to the non-linear nature of liquid breakup processes. 

Superficial gas velocity (m/s) Average liquid volume fraction Sav... 

This correlation (C3) is intended to apply for turbulent-turbulent horizontal flow in pipes, and was developed to give better pressure-drop prediction for higher pressures and larger-diameter pipes. On an entirely empirical basis, the quantity APtp/aPl is given as a function of liquid volume-fraction of the feed, with a quantity >Pq pl/ l po as a parameter. For this correlation aP l is evaluated as the pressure-drop based on the total mass-flow using the liquid-phase properties. The parameter po ph/ Lpo is defined as... 

In the region of slug flow, Chenoweth and Martin s correlation of superficial liquid volume fraction against a pressure-drop ratio can be represented by an expression... 

Hughmark (Hll) has extended this approach to obtain an empirical correlation covering wide ranges of data for the air-water systems in vertical flow. Basically the correlation consists of using Eq. (70) with a variable value of the coefficient K. This coefficient was expressed by Hughmark as a function of the mixture Reynolds number, Froude number, and liquid volume-fraction. Hughmark s approach gives... 

Individuals of multicomponent mixtures compete for the limited space on the adsorbent. Equilibrium curves of binary mixtures, when plotted as x vs. y diagrams, resemble those of vapor-liquid mixtures, either for gases (Fig. 15.5) or liquids (Fig. 15.6). The shapes of adsorption curves of binary mixtures, Figure 15.7, are varied the total adsorptions of the components of the pairs of Figure 15.7 would be more nearly constant over the whole range of compositions in terms of liquid volume fractions rather than the mol fractions shown. 

For fully developed incompressible horizontal gas/liquid flow, a quick estimate for RL may be obtained from Fig. 6-27, as a function of the Lockhart-Martinelli parameter X defined by Eq. (6-131). Indications are that liquid volume fractions may be overpredicted for liquids more viscous than water (Alves, Chem. Eng. Prog., 50, 449-456 [1954]), and underpredicted for pipes larger than 25 mm diameter (Baker, Oil Gas]., 53[12], 185-190, 192-195 [1954]). 

FIG. 6-27 Liquid volume fraction in liquid/gas flow through horizontal pipes. (From Lockhart and Martinelli, Eng. Prog., 45, 39 [1949].)... 

The foam expansion ratio or its reciprocal value the foam liquid volume fraction, called also relative or volume density of a foam, is used as a basic parameter characterizing the liquid to gas ratio in the foam. 

The liquid volume fraction cpL can be expressed as a sum of the volume fractions of films, Plateau borders and vertexes... 

When h r a the contribution of vertexes to the liquid volume fraction of a foam estimated from Eq. (4.4) is smaller compared to that of films, Eq. (4.2) and borders, Eq. (4.3). The relative contribution of borders and films depends on capillary and disjoining pressures. In a foam with thin (black) films at capillary pressures up to 5.103 Pa the border volume is... 

Sharovamikov and Tsap [66] have proposed another way to measure the liquid distribution in a foam based on the evaluation of the geometric coefficient B. The dependence of the film liquid volume fraction on the total foam liquid volume (ft = cp/( +(p) can be expressed by two almost equivalent formulae (see Section 8.3.)... 

In the process of foam evaporation the films on the exterior protect those in the interior from rupturing until they themselves reach the exterior. That is why the rate of foam column destruction vh caused by evaporation would depend on the rate of film evaporation and the liquid volume fraction in films tp /, i. e. 

Number density Liquid volume fraction Liquid velocity Enthalpy... 

First a steady turbulent two-phase flame is calculated. The 15 pm droplet motion follows the carrier phase dynamics so that the Centered Recirculation Zones (CRZ) are similar for gas and liquid, as illustrated on Fig. 10.4, showing the instantaneous backflow lines of both phases, plotted in the vertical central cutting plane. Maintained by this CRZ, the droplets accumulate and the droplet number density, presented with the liquid volume fraction field on Fig. 10.4, rises above its initial value a zone where the droplet number density n is larger than 2n j j (where is its value... 

An alternate description of the derivation of this equation, given by Brinker and Scherer [3], describes the driving force, VC, in terms of the pressure, VP, and then relates this pressure gradient to the liquid volume fraction, <))i [= 1 - d>]. 

This minimviin liquid volume fraction should be built into the ceramic green body to take maximum advantage of liquid phase densification. 

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