A type-A-choking-oriented unified model for fast fluidization dynamics

Starting from analysis to Yangʹs formula for type A choking, a unified and self-consistent model for fast fluidization dynamics, named the separate-phase-coexistence model, was proposed in this paper. The basic assumptions used in the model are that all the gas from outside enters the solid-saturated upward dilute phase, to which the Yangʹs formula is still applied, yet revised with an effective velocity factor F(β); while the clusters fall down freely at a velocity consistent with their voidage. The impact of falling clusters on the upward dilute phase was considered with the equivalent wall friction, from which the method to predict the apparent solids holdup of upper dilute region was obtained. The force balance for falling clusters was also analyzed, from which the cluster voidage was determined. When the cluster viodage reaches its minimum value, a small part of outside gas will invade the cluster, resulting in the so-called “secondary fluidization of clusters”. It well predicted that the solids holdups of upper dilute region and bottom dense region did not change obviously with further increase of the solid circulation rate, the most impressive feature of high-density fast beds. Furthermore, by analogy to bubbling beds, the phenomena of clusters in risers of fast beds were analyzed in a meso-scale mechanism, from which the effective velocity factors of dilute phase F(β) were theoretically determined. And the solid-wall friction factors in Yangʹs formula and the Harrisʹs correlation for cluster size were also reconstructed based on the experimental data available in the literatures. Without any model parameters adjusted, the unified model predicted successfully the type C choking, the solids holdups for both upper dilute region and bottom dense region, and the transitions to high-density fast bed and dense suspension up-flow. The predictions were compared with several hundreds of experimental data available in the literatures, which verified well the modelʹs unification and acceptable accuracy.