adjustments based on foam conditions, without requiring detailed information regarding its phenomenological behavior. For example, foam can be treated as a layer of material that acts to impede heat transfer between combustion and glass zones, but ignores advection transport within it. A relatively small number of parameters can be used to characterize the thermal behavior of the foam, which can be adjusted, within reason, to render a well‐tuned model.
A similar set of questions arises when considering the batch. Whereas the foam is a two‐phase mixture of liquid membranes enclosing gas cells, the batch is a multiphase mixture of solid particles, with interstitial gas and liquid, whose proportions depend on temperature. Unlike in the foam, advective energy transport within the batch zone cannot be ignored without large compromises such that, therefore, the velocity field within the batch layer must be computed. A common way to accomplish it is to treat the batch as a pseudo‐fluid with a characteristic viscosity that depends on temperature. The batch is assumed to float on top of the glass and to provide an inflow of melt whenever the temperature at its interface with the glass achieves or exceeds a specified temperature where melting occurs. In this way, the batch zone is treated as another fluid zone governed by equations similar to those of the glass. In addition to providing an inlet flow of melt to the glass zone, the batch zone also produces a small amount of gases into the combustion zone because of the chemical reactions that occur upon melting.
The model described in the preceding paragraphs is an example of a powerful tool constructed from well‐defined assumptions and mathematical abstractions. It is summarized in Table 3, which indicates for each zone of the furnace the governing equations and interactions with other zones. The required boundary conditions and other physical parameters needed to specify the operating conditions are summarized in Table 4 where a “coupled” condition indicates an internal boundary condition between two zones where the field variable and associated flux are forced to be the same. In addition, many numerical parameters must be specified in such a way as to bring about a converged solution that satisfies the various conservation principles. Modeling procedures and material properties for glass are discussed in greater detail elsewhere [15].
Table 3 Interacting zones of a complete glass melting‐furnace model.
| Zone couplings | |||||||
|---|---|---|---|---|---|---|---|
| Zone | Equations (Table 2) | Radiation treatment | Glass | Batch | Foam | Walls | Combustion |
| Glass | A,B,C,F | Rosseland | |||||
| Batch | A,B,C,F | Surface emissivity | Mass, momentum, energy, electric current | ||||
| Foam | C | Surface emissivity and transparency | Energy | Energy | |||
| Walls | C,F | Surface emissivity | Energy, electric current | Energy, electric current | Energy | ||
| Combustion | A,B,C,D,E,G | DOM | Energy | Mass, energy | Energy | Energy | |
| Glass | Batch | Foam | Walls | Combustion |
4.2.3 Post‐processing Assessments
One gains additional insights by displaying the computed field variables in a graphical form. A common illustration is a temperature‐contour plot, sometimes with flow streaks superimposed. A 3‐D rendering of a glass melting furnace (Figure 6.), for instance, clearly shows the batch layer that melts at the glass surface and the flame developing from the rear wall, the extent of these zones being important operational characteristics. An alternative to horizontal flames is presented in Figure 7, where the pair of flames from oxy‐fuel burners yield the temperature contours and flow streaks shown for a cross‐section of the combustion zone. The fuel and oxidizer react as they flow downward from their nozzles mounted in the furnace crown, and the resulting flame directly impinges on the batch and promotes improved melting efficiency. Similar plots can be drawn on different sections or in different orientations within combustion or glass zones. Furthermore, contour plots of electric potential, Joule dissipation, oxygen concentration, or other field variables can be made directly from the computed solution to provide important insights, especially when comparisons are made between plots drawn for differing possible operating conditions.
Other important information can be gleaned from a converged simulation. For example, quantified values of the energy transfers between the zones illustrated in Figure 5 can be extracted from the simulation results. Examining and comparing these values is very insightful, as it can draw the attention to various things such as how the batch is melted and the sources of inefficiency.
Other quantifiable data that can be directly extracted from a model solution include operating currents and potentials of electrodes, average glass temperature, total volume of batch layer, and temperatures at prescribed locations (e.g. where control or monitoring thermocouples are installed in the actual furnace). These data are essential for validating a model.
Table 4 Required boundary conditions for a complete glass melting‐furnace model.
| Zone | |||||
|---|---|---|---|---|---|
| Governing equation | Glass | Batch | Foam | Walls | Combustion |
| Continuity (A) | Pull rate (out) Coupled (from Batch) |
Pull rate
|