Reduced Gradient Bubble Model

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... 

A simple isothermal model of the flow with gaseous bubbles in the anode channel of a DMFC has been developed by Kulikovsky [171, 172] (Fig. 8.13). The model is based on continuity equations for time-average concentrations in the anode channel. The model shows that formation of bubbles (i) accelerates the flow and (ii) increases the gradient of time-average concentration of methanol along the channel. The latter effect is found to dramatically reduce the limiting current... 

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