Bubbling velocity

Because bubbles occupy space in a bubbling fluid bed, the expansion of the bed becomes a function of both the bubble velocity and the volume of the gas entering the bed ... 

NodMOclature d -Crtuudet ameter Ug Bubble velocity Dg Bubblediameter i - Bubblespacinf 0 - Veuei, impeller or chopper tpeed Vessel radius 4 - Angle of fcdl or inclination g - Acceleration of gravity... 

Fluidization may be described as incipient buoyancy because the particles are still so close as to have essentially no mobility, whereas the usual desire in fluidization is to create bed homogeneity. Such homogeneity can be achieved only by violent mixing. This is brought about by increasing the fluid velocity to the point of blowing "bubbles" or voids into the bed, which mix the bed as they rise. The increased fluid velocity at which bubbles form first is referred to as the incipient (or minimum) bubbling velocity. 

Figure 30. Particle size effects on minimum fluidization and bubbling velocities.

Knowing the bubble rise velocity, the bed expansion can be predicted from a material balance on the bubble phase gas. Thus, total gas flow through the bubble phase equals absolute bubble velocity times the volume fraction E of bubbles in the bed. 

The flow pattern of gas within the emulsion phase surrounding a bubble depends on whether the bubble velocity Ug is less than or greater than minimum fluidization velocity U . For Ubflow lines. For Ub> U , the much different case of Figure 4(B) results. Here a gas element which leaves the bubble eap rises much more slowly than the bubble, and as the bubble passes, it remms to the base of the bubble. Thus, a cloud of captive gas surrounds a bubble as it rises. The ratio of eloud diameter to bubble diameter may be written... 

Measurements in large fluidized beds of fine particles indicate that bubble coalescence often ceases within a short distance above the gas distributor plate. Indications from density measurements or single bubble velocities are that bubble velocity Ug and diameter often reach maximum stable values, which are invariant with height or fluidizing gas velocity. 

Minimum Bubbling Velocity (Umb). The velocity at which discrete bubbles begin to form. Typical minimum bubbling velocity for an FCC catalyst is... 

Ratio of Minimum Bubbling Velocity to Minimum Fluidization Velocity (Umb/Umf). This ratio can be calculated as follows ... 

The mass transfer coefficient is expected to relate gas power per unit volume and gas terminal velocity. Measurement of gas bubble velocity is troublesome in the experimental stage of aeration. Extensive research has been conducted for an explanation of the above correlation. Gas-liquid mass transfer in low viscosity fluids in agitated vessels has been reviewed and summarised as stated in (3.5.1.7)—(3.6.2) 3... 

Hydrodynamics and mass transfer in bubble columns are dependent on the bubble size and the bubble velocity. As the bubble is released from the sparger, it comes into contact with media and microorganisms in the column. In sugar fermentation, glucose is converted to ethanol and carbon dioxide ... 

Coppock and Meiklejohn (C9) determined liquid mass-transfer coefficients for the absorption of oxygen in water. The value of k, was observed to vary markedly with variations of bubble velocity, from 0.028 to 0.055 cm/sec for a velocity range from 22 to 28 cm/sec. These results appear to be in general agreement with the results obtained by Datta et al. (D2) and by Guyer and Pfister (G9) for the absorption of carbon dioxide by water. 

Later publications have been concerned with mass transfer in systems containing no suspended solids. Calderbank measured and correlated gas-liquid interfacial areas (Cl), and evaluated the gas and liquid mass-transfer coefficients for gas-liquid contacting equipment with and without mechanical agitation (C2). It was found that gas film resistance was negligible compared to liquid film resistance, and that the latter was largely independent of bubble size and bubble velocity. He concluded that the effect of mechanical agitation on absorber performance is due to an increase of interfacial gas-liquid area corresponding to a decrease of bubble size. 

F. Flow Patterns and Bubble Velocities 1. Experimental Studies... 

In Section I, a qualitative schematic description of the main connection between increased agitation intensity and increased total mass-transfer rate was given. It can readily be seen from this description that further research in gas and liquid flow patterns and in the area of relative bubble velocities in dispersions will contribute to the basic knowledge necessary for understand ing the real mechanisms occurring in these systems. 

See also Sections IJIA and 11IB for the effect of surface-active agents on bubble velocity. 

To evaluate the effect of holdup on bubble velocity, Marrucci (M3) used a spherical cell model of radius b such that... 

The overall set of partial differential equations that can be considered as a mathematical characterization of the processing system of gas-liquid dispersions should include such environmental parameters as composition, temperature, and velocity, in addition to the equations of bubble-size and residence-time distributions that describe the dependence of bubble nucleation and growth on the bubble environmental factors. A simultaneous solution of this set of differential equations with the appropriate initial and boundary conditions is needed to evaluate the behavior of the system. Subject to the Curie principle, this set of equations should include the possibilities of coupling effects among the various fluxes involved. In dispersions, the possibilities of couplings between fluxes that differ from each other by an odd tensorial rank exist. (An example is the coupling effect between diffusion of surfactants and the hydrodynamics of bubble velocity as treated in Section III.) As yet no analytical solution of the complete set of equations has been found because of the mathematical difficulties involved. To simplify matters, the pertinent transfer equation is usually solved independently, with some simplifying assumptions. 

The model in its present form cannot be used for the design of gas-liquid contacting systems, for several reasons. The model requires a knowledge of the average bubble velocity relative to the fluid, U, a variable that is not available in most cases. This model only permits the calculation of the average rate per unit of area, and unless data are available from other sources on the total surface area available in the vessel, the model by itself does not permit the calculation of the overall absorption rate. 

FORSTER and ZUBER(85,86J who employed a similar basic approach, although the radial rate of growth dr/dt was used for the bubble velocity in the Reynolds group, showed that ... 

Such a behavior agrees with results reported by Agostini et a. (2008). It was found that the elongated bubble velocity increased with increasing bubble length until a plateau was reached. An analytical model has been proposed that is able to predict this trend. 

Agostini B, Revellin R, Thome J (2008) Elongated bubbles in micro-channels. Part I Experimental study and modeling of elongated bubble velocity. Int. J. Multiphase Flow 34 590-601 Bankoff SG, Haute T (1957) Ebullition from solid surfaces in the absence of pre-existing gaseous phase. Trans ASME 79 735-740... 

Cracking catalysts are members of a broad class characterized by diameters of 30-150 im, density of 1.5 g/mL or so, appreciable expansion of the bed before fluidization sets In, minimum bubbling velocity greater than minimum fluidizing velocity, and rapid disengagement of bubbles. 

Rough correlations have been made of minimum fluidization velocity, minimum bubbling velocity, bed expansion, bed level fluctuation, and disengaging height. Experts recommend, however, that any real design be based on pilot plant work. 

Fig. 6 shows the FFT spectrum for calculated bed pressure drop fluctuations at various centrifugal accelerations. The excess gas velocity, defined by (Uo-U ,, was set at 0.5 m/s. Here, 1 G means numerical result of particle fluidization behavior in a conventional fluidized bed. In Fig. 6, the power spectrum density function has typical peak in each centrifugal acceleration. However, as centrifugal acceleration increased, typical peak shifted to high frequency region. Therefore, it is considered that periods of bubble generation and eruption are shorter, and bubble velocity is faster at hi er centrifugal acceleration. 

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