Multiple-bubble-size models distribution

The bubble size distribution resulting from purely random binary coalescence is well-represented by the geometric and exponential distributions. But these distributions completely miss the behavior of measured bubble size distributions that show relatively fewer of the smallest bubbles and more of the very largest ones. But a simple cluster coalescence model follows the Pareto distrihution, which matches these characteristic trends quite well. We conclude that multiple bubble interaction... 

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... 

In monolith reactors, the distribution of fluid into the channels is typically at least somewhat uneven [9] this is why it is very important to predict the flow distribution and include it in the quantitative modeling. Experimental techniques can also be used to study the flow distribution in monolith channels this method is introduced in Figure 9.9 [10]. CFD calculations make it possible to obtain the flow characteristics of the experimental system. In this case, the calculations were performed using the software CFX.4.4 [7]. The flow profiles in the gas and liquid phases were described by the turbulent k-e method (320,000 calculation elements), and to evaluate the distribution of gas bubbles, the multiple size group method was applied. The results from the CFD calculations gave the flow velocities for gas... 

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