A new similarity rule for fluidized bed scale‐up

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Abstract
A rule of hydrodynamic similarity for a scale change of fluidized beds has been developed based on the governing equations of bubble and interstitial gas dynamics. When geometrically similar scale‐up is to be carried out maintaining hydrodynamic similarity, the proposed similarity rule requires that two conditions be satisfied. The first condition assures a similarity in bubble coalescence. The second assures the similarities in bubble splitting and in the interstitial flow pattern. The present work proves theoretically that these two conditions are the necessary, and almost sufficient, conditions for hydrodynamic similarity. They consider not only bubble coalescence but also bubble splitting. The theory proposed was first tested by previous correlations for bubble diameter and grid zone structure, and second by experiment. It has been proved that as long as the present rule is satisfied, the longitudinal distribution of the average bubble diameter, stochastic variation around it, and the radial distribution of superficial bubble velocity can be maintained similar for a scale change.Application of the present rule to predict the bubbling and solid circulation characteristics in a large‐scale unit by a small‐scale experiment has thus proved promising, at least for Geldart group B particles. In order to further study the possibility of a similarity in mass transfer and chemical reactions, computation was carried out using the three‐phase bubble assemblage model. If the effect of molecular diffusion is negligible, as in the case of fluidized bed combustion, even a chemical similarity is found to be possible.

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