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Gas volume fraction

For the simulations we use a 2D TFM as described in the previous sections. The simulation conditions are specified in Table V. The gas flow enters at the bottom through a porous distributor. The initial gas volume fraction in each fluid cell is set to an average value of 0.4 and with a random variation of + 5%. Also for the boundary condition at the bottom, we use a uniform gas velocity with a superimposed random component (10%), following Goldschmidt et al. (2004). [Pg.128]

The Reynolds-average gas volume fraction (xg) is found from... [Pg.297]

Liquid-phase mass transfer coefficient Gas-liquid interfacial area per unit volume of dispersion Gas volume fraction in dispersion Diffusivity of cyanogen in solution Henry law coefficient... [Pg.287]

The proposed catalyst loading, that is the ratio by volume of catalyst to aniline, is to be 0.03. Under the conditions of agitation to be used, it is estimated that the gas volume fraction in the three-phase system will be 0.15 and that the volumetric gas-liquid mass transfer coefficient (also with respect to unit volume of the whole three-phase system) kLa, 0.20 s-1. The liquid-solid mass transfer coefficient is estimated to be 2.2 x 10-3 m/s and the Henry s law coefficient M = PA/CA for hydrogen in aniline at 403 K (130°C) = 2240 barm3/kmol where PA is the partial pressure in the gas phase and CA is the equilibrium concentration in the liquid. [Pg.294]

Most current multidimensional spray simulations have adopted the thin or very thin spray assumptions,[55°1 i.e., the volume occupied by the dispersed phase is assumed to be small. This can be justified if a simulation starts some distance downstream of the nozzle exit, where the gas volume fraction is large enough, or if the computational cells are relatively large. Accordingly, two major classes of models have been used in spray modeling locally homogeneous flow (LHF) models and two-phase-flow or separated-flow (SF) models. [Pg.342]

When one refers to the in situ gas-volume fraction, Rq, the term void fraction is commonly used. The holdup ratio, Hb), is a related quantity, and is defined as the ratio of the gas-liquid volume ratio in the feed to the gas-liquid volume ratio in the flow section. Analogous to these... [Pg.201]

Incorporating these latter two expressions in Eq. (46), the gas volume-fraction in slug flow can be obtained. [Pg.234]

Considering a section of a vertical pipe through the base of a gas slug where the liquid film thickness is constant, and calling the gas volume fraction at this point Ro and the true point gas flow Qo, we find from Eq. (46) that... [Pg.239]

If now the definitions of the average gas volume-fraction and of the mass-flow rates, Wl and Wq, are written, and Eq. (65) and (66) are substituted in them together with the definition of the quality, x = + Wo), then integration gives... [Pg.243]

In a later study [56], the effect of gas volume fraction (foam rheology was investigated. Two models were considered one in which the liquid was confined to the Plateau borders, with thin films of negligible thickness and the second, which involves a finite (strain-dependent) film thickness. For small deformations, no differences were observed in the stress/strain results for the two cases. This was attributed to the film thickness being very much smaller than the cell size. Thus, it was possible to neglect the effect of finite film thickness on stress/strain behaviour, for small strains. [Pg.174]

Diffusivity of 02 in liquid xylene Da = 1.4 x 10 9 m2/s Equipment performance characteristics Gas volume fraction in the dispersion (1 - eg) = 0.34 Mean diameter of the bubbles present in the dispersion = 1.0 mm Liquid-phase mass transfer coefficient kL = 4.1 x 10 4 m/s... [Pg.209]

In order to substitute numerical values, the interfacial area per unit volume of dispersion a needs to be calculated from the mean bubble diameter volume fraction to = (1 - eL) = 0.34. Let there be nt bubbles per unit volume of the dispersion, all of the same size. [Pg.211]

The size of the bubbles produced in the reactor and the gas volume fraction will depend on the agitation conditions, and the rate at which fresh hydrogen is fed to the impeller, as shown in Fig. 4.20. (Some hydrogenation reactors use gas-inducing impellers to recirculate gas from the head-space above the liquid while others use an external compressor.) For the purposes of the present example, the typical values, db = 0.8 mm and eg m 0.20, will be taken. Also dependent to some extent on the agitation conditions are the values of the transfer coefficients kL and k, although these will depend mainly on the physical properties of the system such as the viscosity of the liquid and the diffusivity of the dissolved gas. The values taken here will be kL = 1.23 x 10 5 m/s and k, = 0.54x 10"3 m/s. [Pg.238]

Fig. 4.21. Estimated bubble sizes in a-methyl styrene with catalyst particles in a three-phase fluidised bed particle volume fraction f.p = 0.5, gas volume fraction ec = 0.2... Fig. 4.21. Estimated bubble sizes in a-methyl styrene with catalyst particles in a three-phase fluidised bed particle volume fraction f.p = 0.5, gas volume fraction ec = 0.2...
The frequency of collision relates to the flow pattern and gas volume fraction The more random the flow pattern or the higher the gas volume fraction, the higher the frequency. The efficiency of coalescence relates to physical properties of the gas-liquid system. Some systems, such as air-water, have a high efficiency of coalescence and are often called coalescing systems. Other systems, such as gas-alcohol or gas-salt solution, have a low efficiency of coalescence and are called noncoalescing systems. ... [Pg.261]

The same considerations apply to the making of a foam by dispersion of gas bubbles into water, assuming constant gas volume fraction. When dispersing particles by subdivision energy is still required, but the situation is somewhat different in that particles fracture rather than deforming and pinching off, as is the case with droplets and bubbles. [Pg.61]

The gas volume fraction in a foam. Expressed as a percentage this fraction is sometimes referred to as the Mitchell foam quality . In three-phase systems, other measures are used. For example, when foams are formulated to contain solid particles as well, the slurry quality, Qs, which gives the volume fraction of gas plus solid, can be used Qs = (Vg + Vs)/(Vg + Vs + Vi), where Vg, Vs, and Vi denote the volumes of gas, solid, and liquid phases, respectively. [Pg.373]

The maximum separation efficiency of the cyclone was determined to be 98 % by entraining a 2 % gas volume fraction with the liquid phase. In countercurrent flow in the multistage plant these 2 % of gas volume fraction and the not separated liquid in the gas phase will reduce the efficiency of the apparatus because of back mixing. [Pg.613]

Fig. 1.2. Dependence of collective velocity of bubble rise on gas volume fraction in a liquid-gas... Fig. 1.2. Dependence of collective velocity of bubble rise on gas volume fraction in a liquid-gas...
The increase in expansion ratio (respectively, gas volume fraction polydisperse emulsions the total increase in specific surface area eG in the process of transformation to polyhedral structure (from spherical drops to polyhedron) represents 8.3%, i.e. A 1.083 [84]. [Pg.23]

As mentioned above, at low gas volume fraction the shape of bubbles in a gas emulsion is close to spherical and the excess pressure in them (compared with pressure in the bulk liquid) equals 2a/R. [Pg.31]

The dependence expressed in Eq. (1.35) is strictly fulfilled only when V> = Vc, i.e. when the gas volume fraction (p — 1. In order to calculate the excess (internal) pressure in bubbles of a fully polyhedral foam it is necessary to introduce two correction [84] ... [Pg.32]

The second term in Eq. (1.36) accounts for the non-isomorphic change of cell shape in the process of its transformation into a polyhedron. The value of this term does not exceed 2.8% of the main equation term and equals zero when volume fraction in close-packed spheres). [Pg.32]

In [84] the corrections are expressed by the gas volume fraction and the osmotic pressure in the foam (see below). [Pg.32]

Princen and Kiss [13] have divided the profile of the dependence of gas volume fraction in a foam (or volume fraction of the disperse phase in emulsion) on foam column height into three regions, giving the respective analytical expressions for each one of them. [Pg.350]

If the gas volume fraction is larger than 70%, the foam behaves as a solid body and possesses a shear stress. This means that at low stresses the foam moves as a solid body,... [Pg.576]

Calculations of the elastic constants and yield stress of disordered two-dimensional foams as a function of the gas volume fraction have been reported by Weaire et al. [26-28]. [Pg.579]


See other pages where Gas volume fraction is mentioned: [Pg.97]    [Pg.166]    [Pg.350]    [Pg.48]    [Pg.294]    [Pg.648]    [Pg.216]    [Pg.455]    [Pg.242]    [Pg.243]    [Pg.214]    [Pg.238]    [Pg.742]    [Pg.197]    [Pg.357]    [Pg.526]    [Pg.8]    [Pg.5]    [Pg.350]    [Pg.350]    [Pg.578]    [Pg.582]   
See also in sourсe #XX -- [ Pg.5 ]

See also in sourсe #XX -- [ Pg.107 ]

See also in sourсe #XX -- [ Pg.286 ]




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