Entrainment rate

Flue particles ia a fluidized bed are analogous to volatile molecules ia a Foiling solution. Therefore, the concentration of particles ia the gas above a fluidized bed is a function of the saturation capacity of the gas. To calculate the entrainment rate, it is first necessary to determine what particle sizes ia the bed can be entrained. These particles are the ones which have a terminal velocity less than the superficial gas velocity, assuming that iaterparticle forces ia a dilute zone of the freeboard are negligible. An average particle size of the entrainable particles is then calculated. If all particles ia the bed are entrainable, the entrained material has the same size distribution as the bed material. 

Figure 18 is an entrainment or gas-carryiag capacity chart (25). The operating conditions and particle properties determine the vertical axis the entrainment is read off the dimensionless horizontal axis. For entrainment purposes, the particle density effect is considered through the ratio of the particle density to the density of water. When the entrainable particle-size distribution is smaller than the particle-size distribution of the bed, the entrainment is reduced by the fraction entrainable, ie, the calculated entrainment rate from Figure 18 is multipfled by the weight fraction entrainable. 

Fig. 21. CFB pressure balance, where AP p = AP + high gas velocity ia a fast bed results ia a high soHds entrainment rate. Head...

Continuous Cylindrical Surface The continuous surface shown in Fig. 6-48b is apphcable, for example, for a wire drawn through a stagnant fluid (Sakiadis, AIChE ]., 7, 26-28, 221-225, 467-472 [1961]). The critical-length Reynolds number for transition is Re = 200,000. The laminar boundary laver thickness, total drag, and entrainment flow rate may be obtained from Fig. 6-49 the drag and entrainment rate are obtained from the momentum area 0 and displacement area A evaluated at x = L. 

E = superficial liquid entrainment rate, Ib/hr/ff Fj, Fj = correlation factors defined by equations... 

Having completed the survey, the next stage is to draw the system showing the sources of dust and the duct runs. An assessment must then be made on the air volumes and velocities required giving control. This is largely a matter of experience, as air-entrainment rates are derived empirically. It is possible to calculate the rates but is unusual in general engineering. There are published lists for air rates and many companies have their own standards. 

In order to develop the above burn-out mechanism further, it will be necessary to know more about the entrainment and deposition processes occurring. Experimentally, it is likely that these processes will be very difficult to measure separately and under conditions comparable to those prevailing in a boiling channel. From analysis of their film flow-rate data, Staniforth et al. (S8) have deduced that under burn-out conditions, the deposition of liquid droplets from the vapor core plays an important part in reinforcing the liquid film, particularly at high mass velocities. At low mass velocities, they conclude that deposition and entrainment rates must be nearly equal, and, therefore, since a thin liquid film can be expected to be tenacious and give rise to very little entrainment, they argue that both deposition and entrainment tend to zero near the burn-out location with low mass velocities. 

Ssi = solid surface per unit length in each subchannel of type i GEi = entrainment rate from solid surface in a subchannel of type i GDi = deposition rate from gas core onto solid surface in a subchannel of type i... 

Entrainment from fluidized beds is also affected by temperature and pressure. Increasing system pressure increases the amount of solids carried over with the exit gas because the drag force on the particles increases at higher gas densities. May and Russell (1953) and Chan and Knowlton (1984) both found that pressure increased the entrainment rate from bubbling fluidized beds significantly. The data of Chan and Knowlton are shown in Fig. 13. 

Effect of Downcomer Aeration. When only the central gas flows (No. 7 and No. 8 flows) were employed without downcomer aeration, the solids circulation rate depended primarily on the entrainment rate of the jets. The linear relationship for both bed materials (hollow epoxy and polyethylene) in Fig. 8 shows that the volumetric concentration of the solids inside the draft tube after acceleration (or the gas voidage) is approximately constant, independent of particle density. This can be readily realized by expressing the volumetric solid loading in the draft tube as follows ... 

Solid Entrainment Rate into Gas and Gas-Solid Two-Phase Jets. 

The overall entrainment rate into the jet or the rate of solid circulation induced by the jet is then... 

The solids entrainment rate into a jet in a fluidized bed can be calculated from Eqs. (61) and (23) if the empirical constants C1 and C2 and the jet half-angle 6 are known. The jet half-angle 6 can be taken to be 10° as suggested by Anagbo (1980), a value very close to 7.5° obtained from solid particle trajectories reported here. The real jet half-angle will be larger than 7.5° because of the truncation of the jet by the front plate of the semicircular bed. 

The model as formulated in this section cannot be used to predict a priori the solids entrainment rate into the jet because of the two empirical constants in Eq. (61). Lefroy and Davidson (1969) have developed a theoretical model based on a particle collision mechanism for entrainment of solid particles into a jet. The resulting equation for particle entrainment velocity is... 

Yang, W. C., and Keaims, D. L., Solid Entrainment Rate into Gas and Gas-Solid, Two-Phase Jets in a Fluidized Bed, Powder Technol., 33 89 (1982)... 

Equation (10.10) gives the mass flow rate in the plume. This is exactly equal to the entrainment rate if we neglect the mass flow rate of the fuel. The latter is small, especially as z increases. For an idealized point source, the entrainment rate consistent with the far-field results of Table 10.1 is... 

Figure 10.16 Flame entrainment rate by data from Zukoski [8] and the correlation of Quintiere and Grove [12]...

The flame height is intimately related to the entrainment rate. Indeed, one is dependent on the other. For a turbulent flame that can entrain n times the air needed for combustion (Equation (10.34)), and r, the mass stoichiometric oxygen to fuel ratio, the mass rate of fuel reacted over the flame length, Zf, is... 

The dimensionless fuel supply and air inflow rate can be described, accordingly, as and m A respectively. The entrainment rate depends on the height over which entrainment... 

Ct is an empirical constant that appears to increase as the entrainment rate decreases, as shown from the evidence in Table 11.3. Also from Equation (11.32), the temperature will decrease as the dimensionless fuel supply rate increases. Equation (11.39) holds for the overventilation regime, and therefore it should not be used at a point where /ttp/tttair = 1 /.v or <[> 1 without at least modifying Q 0. 

Entrainment limit, heat pipe, 13 230 Entrainment rate, calculating, 11 814-816 Entrance span areas, in thermal design, 13 258... 

The underlying questions with these clusters are What is the mechanism for their existence Where are the clusters formed and How do clusters affect entrainment rates Based on evidence from pilot and commercial scale plants along with highspeed video of a cold-flow fluidized bed, the mechanism of particle clustering in and above fluidized beds and its effect on entrainment were examined. 

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