Population Balance Modeling of Polydispersed Bubbly Flow in Continuous-Casting Using Multiple-Size-Group Approach

Abstract

A population balance model based on the multiple-size-group (MUSIG) approach has been developed to investigate the polydispersed bubbly flow inside the slab continuous-casting mold and bubble behavior including volume fraction, breakup, coalescence, and size distribution. The Eulerian–Eulerian approach is used to describe the equations of motion of the two-phase flow. All the non-drag forces (lift force, virtual mass force, wall lubrication force, and turbulent dispersion force) and drag force are incorporated in this model. Sato and Sekiguchi model is used to account for the bubble-induced turbulence. Luo and Svendsen model and Prince and Blanch model are used to describe the bubbles breakup and coalescence behavior, respectively. A 1/4th water model of the slab continuous-casting mold was applied to investigate the distribution and size of bubbles by injecting air through a circumferential inlet chamber which was made of the specially-coated samples of mullite porous brick, which is used for the actual upper nozzle. Against experimental data, numerical results showed good agreement for the gas volume fraction and local bubble Sauter mean diameter. The bubble Sauter mean diameter in the upper recirculation zone decreases with increasing water flow rate and increases with increasing gas flow rate. The distribution of bubble Sauter mean diameter along the width direction of the upper mold increases first, and then gradually decreases from the SEN to the narrow wall. Close agreements between the predictions and measurements demonstrate the capability of the MUSIG model in modeling bubbly flow inside the continuous-casting mold.