Mathematical model of bubble number density in glass tank furnace

Abstract

There have been innumerable contributions to clarify bubble behaviour in glass melt, where various approaches have been carried out. Experimental results show bubble quality is represented by bubble number density, bubble diameter, and standard deviation of the diameter, which depend on time and temperature. The latest experiment implies growth of bubble is strongly dependent on temperature, and the standard deviation is independent of time and temperature. Not only appeared location but also number density of small bubble (seeds) is of major concern for manufacturers to produce high quality glass. A new mathematical model is developed to predict bubble number density, which quantifies effect of both fining and refining on the density by introducing an exhausting effect of bubbles from upstream of the highest temperature area, i.e. hot spot, and the downstream in melter, i.e. stagnant. Inlet bubble number density with melting down is extrapolated from the published data. Monitored diameter obtained in experiment is applied to calculation. Calculated bubble number density is compared with measured one in an actual flat glass furnace, which makes it clear that the mathematical model is valid to predict order of the density in the glass melt. Numerical simulation gives reasonable suggestion about fining effect.

Dynamics of rising bubble population undergoing mass transfer and coalescence in highly viscous liquid

“…Pilon and Viskanta [21] applied the previous model on the modeling of a glass furnace limiting to two gas species using a modified characteristic method to solve the population balance equation [22] without coalescence. Finally, Oda and Kaminoyama [23] studied the fining process coupling with the bubble density conservation in two dimensional geometry. Despite these contributions, the development of the population balance equation taking into account mass transfer and coalescence in glass melting process is not yet provided.…”

Role of Glass Melt Flow in Container Furnace Examined by Mathematical Modelling

“…Much effort has been devoted to the examination of melting kinetics either by a theoretical approach and laboratory experiments [1][2][3][4][5][6][7][8][9][10][11] or by mathematical modeling under conditions of the flowing melt [12][13][14][15]; we will mention only a few of them. Cooper [16] discussed the role of longitudinal and transversal melt circulations in the horizontal melting space on the course of the homogenization phenomena and underlined the urgent need of criteria enabling to find optimal flow behavior.…”

Numerical study of glass fining in a pot melting space with different melt-flow patterns

“…In the past, the rate of the fining process has been extensively examined through laboratory experiments, with the important role of the fining agents, as well as the temperature, pressure and glass composition being defined [1][2][3][4][5][6][7]. The mathematical models of bubble behaviour in a quiescent glass melt were constituted [8][9][10][11] and subsequently applied in continual glass melting furnaces [12][13][14][15]. However, the quantitative expression of the impact of the melt flow character on the rate of the bubble removal (fining) process was realised neither in continuous nor discontinuous (pot melting) spaces.…”