Rising bubbles, velocity

If the bed is slugging, bubble motion is retarded by the bed wall, and the bed or tube diameter, Z9, rather than the actual bubble diameter, determines the bubble rise velocity, ie... 

The velocity of a bubble ia a bubbling bed has been observed to be higher than equation 14 predicts, and it has been suggested that the actual bubble rise velocity in a bubbling bed (15) is... 

This empirical equation attempts to account for complex bubble coalescence, spHtting, irregular shapes, etc. Apparent bubble rise velocity in vigorously bubbling beds of Group A particles is lower than equation 16 predicts. 

Studies of individual bubbles rising in a two-dimensional gas—Hquid—soHd reactor provide detailed representations of bubble-wake interactions and projections of their impact on performance (Fig. 9). The details of flow, in this case bubble shapes, associated wake stmctures, and resultant bubble rise velocities and wake dynamics are important in characteri2ing reactor performance (26). 

For a better understanding of the interactions between parameters, it is often helpful to calculate the effective bubble rise velocity from measurea valves of for example, the data of Mersmann (loc. cit.) indicated = 0.6 for = 0.05 iti/s, giving U, = 0.083 m/s, which agrees with the data reported in Fig. 14-43 for the rise velocity of bubble clouds. The rise velocity of single bubbles, for d - 2 mm, is about 0.3 m/s, for liquids with viscosities not too different from water. Using this value in Eq. (14-220) and comparing with Fig. 14-104, one finds that at low values of the rise velocity of the bubbles... 

In design of separating chambers, static vessels or continuous-flow tanks may be used. Care must be taken to protect the flow from turbulence, which coiild cause back mixing of partially separated fluids or which could cany unseparated hquids rapidly to the separated-hquid outlet. Vertical baffles to protect rising biibbles from flow currents are sometimes employed. Unseparated fluids should be distributed to the separating region as uniformly and with as little velocity as possible. When the bubble rise velocity is quite low, shallow tanks or flow channels should be used to minimize the residence time required. 

When the bubble diameter approaches the diameter of the containing vessel, slug flow is said to exist. In such cases, the bubble rise velocity is given by... 

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 bubble size at formation varied with particle characteristics. It was further observed that the bubble size decreased with increasing fluidization intensity (i.e., with increasing liquid velocity). The rate of coalescence likewise decreased with increasing fluidization intensity the net rate of coalescence had a positive value at distances from 1 to 2 ft above the orifice, whereas at larger distances from the orifice the rate approached zero. The bubble rise-velocity increased steadily with bubble size in a manner similar to that observed for viscous fluids, but different to that observed for water. An attempt was made to explain the dependence of the rate of coalescence on fluidization intensity in terms of a relatively high viscosity of the liquid fluidized bed. 

Anderson (A2) has derived a formula relating the bubble-radius probability density function (B3) to the contact-time density function on the assumption that the bubble-rise velocity is independent of position. Bankoff (B3) has developed bubble-radius distribution functions that relate the contacttime density function to the radial and axial positions of bubbles as obtained from resistivity-probe measurements. Soo (S10) has recently considered a particle-size distribution function for solid particles in a free stream ... 

Gas holdup and liquid circulation velocity are the most important parameters to determinate the conversion and selectivity of airlift reactors. Most of the reported works are focused on the global hydrodynamic behavior, while studies on the measurements of local parameters are much more limited [20]. In recent years, studies on the hydrodynamic behavior in ALRs have focused on local behaviors [20-23], such as the gas holdup, bubble size and bubble rise velocity. These studies give us a much better understanding on ALRs. 

Bubble size in the circulating beds increases with Ug, but decreases with Ul or solid circulation rate (Gs) bubble rising velocity increases with Ug or Ul but decreases with Gs the ffequeney of bubbles increases with Ug, Ul or Gs. The axial or radial dispersion coefficient of liquid phase (Dz or Dr) has been determined by using steady or unsteady state dispersion model. The values of Dz and D, increase with increasing Ug or Gs, but decrease (slightly) with increasing Ul- The values of Dz and Dr can be predicted by Eqs.(9) and (10) with a correlation coefficient of 0.93 and 0.95, respectively[10]. 

Silicones exhibit an apparently low solubility in different oils. In fact, there is actually a slow rate of dissolution that depends on the viscosity of the oil and the concentration of the dispersed drops. The mechanisms of the critical bubble size and the reason a significantly faster coalescence occurs at a lower concentration of silicone can be explained in terms of the higher interfacial mobility, as can be measured by the bubble rise velocities. 

For various flow regimes, they used the terminal bubble rise velocity as the local bubble slip velocity. 

It can be seen that, for small terminal bubble rise velocities, the distribution parameter Co can be obtained by... 

Figure 11. Relationship between local mean bubble size and local mean bubble rise velocity in beds of different diameters (u0 = 9 cm/sec). (From Werther, 1974.)...

Glicksman and McAndrews (1985) determined the effect of bed width on the hydrodynamics of large particle bubbling beds. Sand particles with a mean diameter of 1 mm were fluidized by air at ambient conditions. The bed width ranged from 7.6 cm to 122 cm while the other cross sectional dimension remained constant at 122 cm. Most experiments were carried out with an open bed. The bubble rise velocity increased with the bed width, in the representation of bubble velocity as... 

Figure 13. Variation of bubble rise velocity with wall spacing I standard deviation, Fdenotes with tubes. O tf> = U./(gD /2 x - Ub- QbJ(gDb)1/2 V =Ub-(U -U(From Glicksman and Me Andrews, 1985.)...

The larger particles were thrown high in the splash zone higher than predicted by a ballistic trajectory using the bubble rise velocity as the initial velocity and neglecting any air drag. Later observations of this model showed that, when bubbles erupt at the surface, the accompanying... 

Table 1. Average Bubble Rise Velocities (m/s) Calculated from the Force Probe Measurements and Comparison with Results from the Movies 40.6-cm Diameter Jet Assembly...

Fig. 3a indicates that the bubble-rise velocity measured based on the displacement of the top surface of the bubble ( C/bt) quickly increases and approaches the terminal bubble rise velocity in 0.02 s. The small fluctuation of Ubt is caused by numerical instability. The bubble-rise velocity measured based on the displacement of the bottom surface of the bubble (Ubb) fluctuates significantly with time initially and converges to Ubt after 0.25 s. The overshooting of Ubb can reach 45-50 cm/s in Fig. 3a. The fluctuation of Ubb reflects the unsteady oscillation of the bubble due to the wake flow and shedding at the base of the bubble. Although the relative deviation between the simulation results of the 40 X 40 x 80 mesh and 100 x 100 x 200 mesh is notable, the deviation is insignificant between the results of the 80 x 80 x 160 mesh and those of the 100 X 100 x 200 mesh. The agreement with experiments at all resolutions is generally reasonable, although the simulated terminal bubble rise velocities ( 20 cm/s) are slightly lower than the experimental results (21 25 cm/s). A lower bubble-rise velocity obtained from the simulation is expected due to the no-slip condition imposed at the gas-liquid interface, and the finite thickness for the gas-liquid interface employed in the computational scheme.

Fig. 3. (a) Comparison of the simulation results and experimental results of the bubble rise velocity, (b) Comparison of the simulation and experimental results of the bubble aspect ratio. 

For the discrete bubble model described in Section V.C, future work will be focused on implementation of closure equations in the force balance, like empirical relations for bubble-rise velocities and the interaction between bubbles. Clearly, a more refined model for the bubble-bubble interaction, including coalescence and breakup, is required along with a more realistic description of the rheology of fluidized suspensions. Finally, the adapted model should be augmented with a thermal energy balance, and associated closures for the thermophysical properties, to study heat transport in large-scale fluidized beds, such as FCC-regenerators and PE and PP gas-phase polymerization reactors. 

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