needs to be better understood. The effects of batch constituents (as well as the size and shape of individual particles), the manner in which the batch moves, transmits energy, reacts, and melts into glass need to be understood in a way that can be implemented in a numerical simulation. A similar comment can be made for foam. Despite these shortcomings, simulation results are very useful when applied and interpreted properly. When significant uncertainties exist or if validation fails to reconcile all metrics satisfactorily, then comparisons between simulations cases can be made in a semiquantitative manner, where the simulation results reveal general trends (e.g. increased recirculation, or lowering of exhaust gas temperatures). Results such as these provide guidance that would otherwise be unavailable.
4.2 Acknowledgements
The authors thank Glass Service Inc. for sharing nonproprietary model data from which some of the examples presented were taken. Also, they are grateful to their employer, Owens Corning, for supporting their effort to contribute to this volume.
References
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2 2 Incropera, F.P. and DeWitt, D.P. (1996). Fundamentals of Heat and Mass Transfer, 4the. New York: John Wiley & Sons.
3 3 Modest, M.F. (1993). Radiative Heat Transfer. New York: McGraw‐Hill.
4 4 Loch, H. and Krause, D. (eds.) (2002). Mathematical Simulation in Glass Technology. Berlin: Springer Verlag.
5 5 Barnes, H.A., Hutton, J.F., and Walter, K. (1993). An Introduction to Rheology. Amsterdam: Elsevier.
6 6 Crochet, M.J., Davies, A.R., and Walters, K. (1984). Numerical Simulation of Non‐Newtonian Flows. Amsterdam: Elsevier.
7 7 Patankar, S.V. (1980). Numerical Heat Transfer and Fluid Flow. Washington, DC: Hemisphere.
8 8 Reddy, J.N. (1993). An Introduction to The Finite Element Method, 2nde. New York: McGraw‐Hill.
9 9 Glicksman, L.R. (1968). The dynamics of a heated free jet of variable viscosity liquid at low Reynolds number. J. Basic Eng. Trans. ASME, Series D 90: 343–354.
10 10 Purnode, B.A. and Rubin, Y. (1998). Two dimensional finite element analysis of glass fiber forming. In: Proceedings of the. International Congress on Glass. San Francisco: ACerS.
11 11 Purnode, B.A. (2000). Transient axisymmetric study of glass fiber forming. In: Proceedingsof the ASME 2000 Fluids Engineering Division Summer Meeting. Boston: ASME.
12 12 Pierrot, L. (2004). Accuracy of the Rosseland approximation in toy models of glass tanks. In: Proceedings of the 20th International Congress on Glass. Kyoto: The Ceramic Society of Japan.
13 13 Choudhary, M.K., Purnode, B.A., Lankhorst, A.M., and Habraken, A.F. (2017). Radiative heat transfer in processing of glass‐forming melts. Int. J. Applied Glass Science: 1–17.
14 14 Shelby, J.E. (1997). in Introduction to Glass Science and Technology, 38–45. Cambridge: The Royal Society of Chemistry.
15 15 Pye, L.D., Montenero, A., and Joseph, I. (eds.) (2005). Properties of Glass‐Forming Melts. Boca Raton: CRC Press.
16 16 Johnson, W.W. Gas generation and transport within a reacting batch pile. In: Proceedings of the 12th International Seminar on Furnace Design – Operations & Process Simulation, 2013. Velke Karlovice, Czech Republic: Glass Service.
17 17 Jiao, J., Bamiro, O., Lewis, D., and Zhu, X. (2014). 3‐D transient non isothermal cfd modeling of gob formation. In: 75th Conference on Glass Problems (ed. S.K. Sundaram), 185–200. Columbus: Wiley.
18 18 Tiwary, R. (2015). An overview of float glass forming modeling. In: GMIC Symposium on Glass Forming. Columbus: GMIC.
Note
1 Reviewers: W. W. Johnson, Corning Incorporated, Corning, NY, USAE. Muijsenberg, Glass Service, Inc., Vsetin, Czech Republic
Section II. Structure
Figure 1 The atomic disorder of the glass structure (left) giving way to crystalline order (right): the boundary between a Zr‐bearing magnesium aluminosilicate glass and a ZrO2 crystal that precipitated in it. Bar scale: 5 nm. Abberation‐corrected, high‐resolution transmission‐electron micrograph courtesy Christian Patzig and Thomas Höche.
It is usually stated that the various properties of glasses and melts are determined by the structures of these phases. This statement is thermodynamically incorrect: a melt has a structure that is fixed instead by the minimum of its Gibbs free energy and, thus, by the temperature‐dependent balance between enthalpy and entropy factors that are themselves determined by the existing atomic interactions. This is the manner in which the structures of melts predicted in theoretical calculations are assumed to be those of glasses quenched from some pressure and high temperature.
Structural studies are nonetheless useful either at a small scale, for example, to figure out how the local environment of an ion determines its optical properties (Section VI), or at a larger scale to gain insights on property–composition relationships when the specific influence of chemical entities on the properties of interest can be evaluated in terms of well‐defined structural elements such as rings or coordination polyhedra. The method was pioneered in Antiquity by Plato (‐428–347): to each of the four elements then acknowledged, he assigned geometrical shapes accounting for their properties, namely the tetrahedron for fire, octahedron for air, icosahedron for water, and cube for earth. Of course, such assignments are no longer purely intellectual constructs; they have an experimental basis. Interestingly, however, one should realize that the first atomic models of glass were devised shortly before any experimental tool was available to determine their structural components (Chapter 10.11). In other words, glass structure represents a good example of a situation where theory not only preceded experiments but also defined their paradigmatic framework.
To set the frame of this second section of the Encyclopedia, a broad overview of the structure of amorphous materials and of associated theoretical models at different length scales is first given by A.C. Hannon for network oxide and chalcogenide glasses, with particular emphasis on the random‐network model (Chapter 2.1). Recently, progress in the analytical techniques used in structural studies has been enhanced by the availability of intense sources of electromagnetic radiation, namely lasers and synchrotron facilities. From X‐ray diffraction and absorption to vibrational and Mössbauer spectroscopies, these various methods and the information they yield are reviewed by G. Henderson (Chapter 2.2). Whether purposely produced in glass ceramics or formed spontaneously in industrial or natural processes, inhomogeneous glasses are also given increased attention (Figure 1). To determine their microstructure
