Bubble transport in three-dimensional laminar gravity-driven flow – numerical results

This paper is the second part of a study on bubble transport, growth and shrinkage in three-dimensional gravity driven flow. Sample calculations with applications to glass melting furnaces are presented. First, a consistent set of thermophysical properties of the most common composition [74 SiO2-16 Na2O-10 CaO (mol.%)] of soda-lime silicate glass or similar compositions over the temperature range of 1000 to 2000 K is reported. The population balance equation is solved for the bubble density function using the backward method of characteristics. The zeroth to third order moments, i.e, number of bubbles, average radius, molar gas fraction, interfacial area, and void fraction are computed by numerical integration. Results for both transient and steady state operations are presented and analysed. Two cases are considered (1) bubbles containing only CO2 and (2) bubbles containing a diffusing gas (O2) and a non-diffusing gas (CO2). The feasibility of such complex calculation is demonstrated and is in qualitative agreement with reported results.