Three-dimensional two-fluid modeling of a cylindrical fluidized bed and validation of the Maximum Entropy method to determine bubble properties

Abstract

Diameter and velocity of bubbles from a three-dimensional two-fluid model simulation of a cylindrical fluidized bed are presented. Two methods for obtaining the bubble size and velocity are compared: (i) estimation from the chord lengths and velocities of the detected bubbles using information from two virtual voidage probes (pierced bubble method) and (ii) calculation from the bubble volume and velocity directly obtained from the instantaneous 3D voidage field (tomography method). The Maximum Entropy method (MaxEnt) is employed to convert probability density functions of chord lengths into the corresponding diameter distributions. The algorithm for the direct evaluation of the bubble volume and velocity, based on the tomography reconstruction of the 3D field, is explicitly explained and used to evaluate the results obtained from the virtual void probe signals. Results show a good agreement between the bubble sizes obtained using the MaxEnt treatment of the chord lengths and the directly obtained bubble sizes, which confirms the robustness of the MaxEnt method to infer bubble behavior in 3D bubbling beds. In particular, the mean bubble diameter obtained with the MaxEnt method applied to chord lengths was less than 4.5% different to the result from the tomography reconstruction. It was found that the bubble velocities obtained from virtual voidage probes are higher than the bubble velocities calculated with the tomography method, but the differences were not greater than 17% in the worst case. The probability density functions of bubble size and velocity obtained with the two methods were similar in terms of the location of the most probable values and the variation of the distribution with the distance to the distributor.