Numerical simulation of bubble number density in glass melt

Kenji Oda, AGC Flat Glass Japan

There have been innumerable contributions to clarify bubble behaviour in glass melt, where various approaches have been carried out. Computer simulation of thermal convection in glass furnace has presented velocity and temperature. Quality index is estimated by these field variables, which is statistically related to glass quality. It is available for specified range of glass composition, operation, or furnace dimension.
Experimental result shows bubble quality is represented by number density, diameter, and standard deviation of diameter, which depend on time and temperature. According to in-situ observation of bubble, diameter of bubble is function of temperature, and the standard deviation is independent of temperature or time. When soda lime glass melt contains SO₃, bubble size grows rapidly by decomposition of sodium sulphate. Sulphate is supposed to control bubble size over the decomposition temperature, and bubble grows with diffusion of decomposed SO₂ and shrinks with the resorption in glass melt.
In this study, mathematical model of bubble number density is newly developed to quantify not only fining but also refining. “Fining” is induced by the decomposition, and is prior reaction to “refining” by which bubble number density is lowered from 10¹ or 10⁰ to 10^-3 or 10^-4[pieces/cm³]. Calculated results show the number decreases from 10⁴ to 10¹ or 10⁰ in smaller furnace, which reproduces fining effect. It is assumed behaviour of SO₂ is reversible, and that bubble size only depends on temperature. It effects on velocity component in depth direction of bubble transport. The number density without sulphate is calculated to be about double of that with sulphate.

Larger furnace has two loops of thermal convection of glass melt, which prevents downstream circulation from upstream one to avoid dispersion of bubble. In flat bottom furnace, distribution of bubble number density in depth direction is different from that in stepped bottom furnace, but the density at upstream of hot spot is about  10², whichever be furnace geometry, and is about 10^-3 at the downstream or in product. Simulation demonstrates that calculated order of the density is nearly the same as actual one. This study makes it clear that the mathematical model is valid and accurate to predict bubble quality in glass melt.

 

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