Mathematical Modeling of Flow and Heat Transfer Phenomena in Glass Melting, Delivery, and Forming Processes

Abstract

This article reviews the scientific and engineering principles and practices involved in the mathematical modeling of flow and heat transfer phenomena in industrial-scale glass melting, delivery, and forming processes. The approach taken is to highlight the characteristic features of flow and heat transfer in each of the three processes, summarize the relevant transport and constitutive equations and boundary conditions, and illustrate practical applications of mathematical models. The article also describes modeling approaches used for auxiliary processes and phenomena associated with melting, delivery, and forming operations. Thus, modeling of batch melting, electric heating of glass melt, convection due to bubbling, combustion, turbulence, and viscoelasticity are discussed. Unlike melting and delivery processes, which share many similarities across the various glass industry segments, forming tends to be segment specific. So, the article focuses on one forming process (container) and, through it, emphasizes the key technical attributes of forming models. A selection of results is provided to bring out modeling capabilities and limitations. The article also provides a historical perspective on the development of advanced mathematical models and their industrial applications. Finally, key areas needing research and development are identified to further enhance the practical utility of mathematical models for the glassmaking processes.

Glass production rate in electric furnaces for radioactive waste vitrification

“…Even though certain aspects of glass processing have been studied in minute detail, the complexity of chemical and physical phenomena occurring in the batch blanket and at the batch‐melt and batch‐gas interfaces present formidable obstacles to executing realistic models. As a result, existing mathematical models of glass melting furnaces have paid little attention to the cold cap and its close proximity, where the heat transfer determines the rate of melting . Successful modeling would have to deal with the complexities associated with the transition zone between the cold cap and the melt, which contains dissolving solids, gas bubbles ascending from the melt, and is being stirred by horizontally moving large bubbles (cavities) from collapsing primary foam .…”

Numerical modeling and analysis of glass fiber drawing process from large sized silica preform

“…The transmission and absorption of radiative energy in optically transparent silica preform is estimated by adopting apparent thermal conductivity with Rosseland diffusion approximation and its effect is added into effective thermal conductivity of silica glass (Paek, 1999;Choudhary et al, 2010). Molecular thermal conductivity of silica glass is merely 2.68 W/m·K, but this radiative transmission and absorption into preform enables radially uniform preform heating much more effectively.…”

Modelling of the Glass Melting Process for Real-Time Implementation

“…The Partial Differential Equations (PDE) used for forehearth heat transfer modelling describe the distribution of temperatures in molten glass in the defined domain and are parabolic type with Neumann type boundary conditions [13]. Since the material parameters strongly depend on the temperature, both sub-models are strongly coupled.…”