Maximum entropy estimation of the bubble size distribution in fluidized beds

Abstract

This work presents a new methodology, based on the maximum entropy method, to obtain bubble characteristics in fluidized beds. The probability distributions (PDF) of bubble pierced length and velocity are obtained applying the maximum entropy principle to experimental measurements. In addition, the bubble diameter distribution has been inferred from experimental pierced length measurements. This method is applied to characterize bubbles in fluidized beds for the first time and the most general bubble geometry, a truncated spheroid, is considered. The distance between probes, s, which is the minimum pierced length that is possible to measure accurately using intrusive probes, has been introduced as a constraint in the derivation of the size distribution equation.

The maximum entropy method is applied to experimental measurements of bubble characteristics carried out using optical and pressure probes in a three-dimensional fluidized bed of Geldart B particles. Results on bubble size obtained from pressure and optical probes are very similar, although optical probes provide more local information and can be used at any position in the bed. The maximum entropy principle has been found to be a simple method that offers many advantages over other methods applied before for size distribution modeling in fluidized beds.