Axial Profiles of Cross-Sectional Averaged Voidage

1 Axial Profiles of Cross-Sectional Averaged Voidage 

The S-shaped profiles of the voidage can be represented by an equation of the following form [Li and Kwauk, 1980]  

Equation (10.12) contains four parameters aa, a, Zo, and z-x. The value of Z0 represents the length of the transition region between the dilute and dense regions. Zo approaching 0 indicates a clear interface between the dense and dilute region, while Zo approaching infinity implies a uniform axial profile of the voidage. Zo can be empirically correlated by [Kwauk, 1992] 

Of primary significance is the location of the inflection point zi which is closely associated with the solids quantity in the downcomer and solids circulation rate in the CFB system. Consider the pressure balance across the circulating fluidized bed loop as given by 

The pressure drops in Eq. (10.16) can be obtained by assuming that the particles in the downcomer are in the incipient fluidization state. Neglecting the solids holdup in the connecting tube between the riser and the cyclone and in the cyclone, the mass balance of solid particles in the CFB loop can be expressed as 

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

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