Data interpretation techniques for inferring bubble size distribution from probe signals in fluidized systems

Bubble behavior in fluidized beds may have a profound effect on other aspects of bed hydrodynamics. Submersible probes are often used to study the local bubble properties in these systems. Generally, the axes of the pierced bubbles need not be aligned with the vertical axis of the bed. This matter is further complicated by the fact that there is a distribution of bubble sizes. Therefore, data interpretation of probe signals should be performed carefully to yield bubble size distribution information. In this paper an analytic data interpretation technique in closed form has been presented based on the assumption that the bubble rise velocity depends on bubble size (usually the velocity increases as the square root of the linear size). A method employing a non-parametric approach to infer the bubble size distribution from the probe time signals (pierced time durations) without need for information about the nature of the pierced time duration distribution has also been described. A statistical data transformation approach for obtaining the average bubble size and the standard deviation of the local bubble size distribution has been established. Monte-Carlo simulations have been conducted to demonstrate the correctness of these techniques.