Voidage average

The voidage distribution model permits the derivation of analytical expressions for the integrated average voidage taken through the whole height, defined as... 

Optical fiber measurement of local solids concentrations of FCC catalyst fluidized in a 9-cm-i.d. column gave the results shown typically in Fig. 26. Analysis of these data showed that the radial voidage profile could be described solely by the cross-section-average voidage e, calculated as shown in Sec. 5.1, and the reduced radial coordinate r/R ... 

Figure 8 Axial profiles of cross-sectionally averaged voidage under different grid resolutions for IPE and ETH risers.

Axial Profiles of Cross-Sectional Averaged Voidage... 

Figure 10.11. Effects of gas and solids flow rates on the axial profile of the cross-sectional averaged voidage in a riser with an abrupt exit (from Brereton and Grace, 1993b) (a) Abrupt exit geometry (b) Voidage profiles.

Equation (9.3) also permits analytical evaluation of the integrated average voidage e taken through the whole bed height, above the point of inflection z for the dilute region at the top, and below zx for the dense region at the bottom ... 

Figure 60 charts the variation of the average voidages for the dense- and dilute-phase regions, sA and B, with gas velocity u0 for fixed rates of solids... 

Fig. 2. Average voidage as a function of solids circulation rate and gas velocity (after Li and Wang, 1985).

The influence of gas velocity and solids circulation rate on flow regime transition was measured in a fast fluidization, 90-mm i.d. and 8-m high (Li and Kwauk, 1980a). Figure 4 shows the change of the average voidage, e,... 

The preceding equation shows that as long as the cross-sectional average voidage E is known, then the three-dimensional voidage profile could be calculated. 

Fig. 30. Effect of average voidage on radial gas velocity profile (after Zhang, 1990).

The average voidage of the system e is formulated additively from the dense and dilute phases as... 

As gas velocity Ut increases, the average voidage e in Fig. 12a increases while the cluster fraction / in Fig. 12c decreases, until at some gas velocity a sudden change takes place with / dropping to zero for the idealized case, denoting the disappearance of the cluster phase. At this point single-phase solids transport begins to take over the two-phase structure which has hitherto... 

The characteristic axial and radial distributions of heat transfer coefficients computed from the preceding formula are shown in Fig. 12. In the calculation, the sectional average voidage e can be established from any of the known... 

If the gas velocity is increased and a constant average voidage is kept,... 

For an inclined cylindrical moving bed with average voidage s,... 

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