Emulsion phase voidage

The first term, (1 - ty) /(I - z), corrects for the voidage difference between that in thejet and that in the emulsion phase. The second term, ( - z) /(I - z), takes into account the fact that only a fraction of the particles having the entrainment velocity Ve will be entrained, the remainder rebounding back to thejet wall due to collisions with the particles already in thejet. Substituting Eq. (63) into Eq. (62), we have... 

Thus, the bubbling region, which is an important feature of beds operating at gas velocities in excess of the minimum fluidising velocity, is usually characterised by two phases — a continuous emulsion phase with a voidage approximately equal to that of a bed at its minimum fluidising velocity, and a discontinous or bubble phase that accounts for most of the excess flow of gas. This is sometimes referred to as the two-phase theory of fluidisation. 

The dense emulsion phase is perfectly mixed and is at incipient fluidization conditions with constant voidage. 

Consider a bubble rising in a fluidized bed. It is assumed that the bubble is solids-free, is spherical, and has a constant internal pressure. Moreover, the emulsion phase is assumed to be a pseudocontinuum, incompressible, and inviscid single fluid with an apparent density of pp(l — amf) + pamf. It should be noted that the assumption of incompressibility of the mixture is not strictly valid as voidage in the vicinity of the bubble is higher than that in the emulsion phase [Jackson, 1963 Yates et al., 1994]. With these assumptions, the velocity and pressure distributions of the fluid in a uniform potential flow field around a bubble, as portrayed by Fig. 9.10, can be given as [Davidson and Harrison, 1963]... 

Nakajima, M., Harada, M., Asai, M., Yamazaki, R., and Jimbo, G. Bubble fraction and voidage in an emulsion phase in the transition to a turbulent fluidized bed, in Circulating Fluidized Bed Technology III (P. Basu, M. Horio and M. Hasatani, eds.), pp. 79-84. Pergamon Press, 1991. 

Let us consider a shallow fluidized bed combustor with multiple coal feeders which are used to reduce the lateral concentration gradient of coal (11). For simplicity, let us assume that the bed can be divided into N similar cylinders of radius R, each with a single feed point in the center. The assumption allows us to use the symmetrical properties of a cylindrical coordinate system and thus greatly reduce the difficulty of computation. The model proposed is based on the two phase theory of fluidization. Both diffusion and reaction resistances in combustion are considered, and the particle size distribution of coal is taken into account also. The assumptions of the model are (a) The bed consists of two phases, namely, the bubble and emulsion phases. The voidage of emulsion phase remains constant and is equal to that at incipient fluidization, and the flow of gas through the bed in excess of minimum fluidization passes through the bed in the form of bubbles (12). (b) The emulsion phase is well mixed in the axial... 

The voidage of the emulsion phase is taken to be that at minimum fluidization 8 ,f. The mean bed voidage is then given by... 

The two-phase theory of fluidization was first proposed by Toomey and Johnstone (1952). The model assumed that the aggregative fluidization eonsists of two phases, i.e., the particulate (or emulsion) phase and the bubble phase. The flow rate through the emulsion phase is equal to the flow rate for minimum fluidization, and the voidage is essentially constant at Sn,f. Any flow in excess of that required for minimum fluidization appears as bubbles in the separate bubble phase. Mathematically, the two-phase theory can be expressed as... 

From the computer enhanced video images of rising bubbles in fluidized beds, Yates et al. (1994) observed that the bubbles are surrounded by a region of emulsion phase in which the solids concentration is lower than that in the emulsion phase far from the bubbles. This region of increasing voidage was called the shell by Yates et al. The volumetric gas in the bubble and in the shell can be correlated as... 

The bubble phase is assumed to consist of spherical bubbles surrounded by spherical clouds. The voidage within the cloud is assumed to be the same as that in the emulsion phase, and the diameter of the bubbles and that of clouds is given by Davidson (1961) as... 

Almost all of the models proposed to date are based on the two phase theory of fluidization originally proposed by Toomey and Johnstone (97) and later modified by Davidson and Harrison (98). According to the theory, the fliiidized bed is assumed to consist of two phases, viz., l) a continuous, dense particulate phase (emulsion phase) and 2) a discontinuous, lean gas phase (bubble phase) with exchange of gas between the bubble phase and emiilsion phase. The gas flow rate through the emulsion phase is assumed to be at minimum fluidization and that in excess of the minimum fluidization velocity passes throu the bubble phase. This formulation of the two phase theory is based on the ass mq)tion that the voidage of the emulsion phase remains constant. However, as pointed out by Rowe (22) and Horio and Wen (lOO) this assumption may be an over-simplification. In particular, experiments with fine powders (dp < 60 ym) conducted by Rowe show that the dense phase voidage changes with gas velocity, and as much as 30 percent of the gas flow occurs interstitially. This effect can be... 

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