Relationships between distributions of chord lengths and distributions of bubble sizes including their statistical parameters

Abstract

The performance of fluidized beds is strongly influenced by bubble behavior. Among various hydrodynamic properties, bubble size distributions are of prime concern, but in practice, bubble size is not readily measured. When a probe is used to determine bubble size, it intersects a bubble with a chord length other than the largest vertical dimension. The relationships between the size distribution of bubbles in the bed, the size distribution of bubbles touching the probe and the distribution of chord lengths must be resolved for correct interpretation of probe signals. A method for translating statistical parameters, namely mean and standard deviation of chord lengths to mean and standard deviation of bubble sizes, and an approach to infer the size distribution of bubbles touching the probe and the size distribution of bubbles in the bed system by using the distribution of chord lengths measured by a probe in closed form are proposed for the first time.