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 (in) Coupled (to Glass) | (no flow) | (no flow) | Fuel flow rates Oxidizer flow rates Outlet flow rate |
| Momentum (B) | No slip @ Walls velocity @ Batch Interface no shear @ Surface/Foam bubbler flows | Free surface @ Top no shear @ Glass interface | (no flow) | (no flow) | Inlet velocities No slip on walls, Turbulence wall functions |
| Energy (C) | Coupled | Batch inlet temperature Coupled | Coupled | Coupled convection and radiation on outside walls | Inlet temperatures Coupled turbulence wall functions |
| TKE(D) | (laminar) | (laminar) | (no flow) | (no flow) | Inlet conditions Turbulence wall functions |
| Turb. diss. (E) | (laminar) | (laminar) | (no flow) | (no flow) | Inlet conditions Turbulence wall functions |
| Electric (F) | Coupled | Coupled | (none) | Electrode voltages and phases | (none) |
| Species (G) | (none) | Coupled discharge to combustion zone | (none) | (none) | Mole/mass fractions of fuel and oxidizer species zero flux at walls coupled to batch discharge |
Figure 6 3‐D rendering of temperature contours within a glass furnace heated with two gas burners as calculated by a fully coupled simulation model.
Source: Courtesy of Glass Service, Inc.
4.2.4 Particle Tracking
Additional information is provided by particle tracking and associated analysis as applied to either combustion or glass (including batch) zones. To track the pathway, inert particles would take if they were introduced into the glass involves additional computation in a Lagrangian framework. Massless particles are commonly used as a kind of virtual flow visualization because the assumption is made that they do not affect the flow of glass. Depending only on glass velocities, their pathways can then be computed from converged solutions of glass flows. To simulate real phenomena, however, particles of specified density and size or gas bubbles can also be tracked, in which cases the velocity of each particle may differ locally from that of the glass because of the effects of gravity.
When massless particles are introduced into a melting tank through a random selection of a large number of starting locations on the batch inlets, their pathways over time can be tracked from the computed field of velocity vectors. When each particle passes through a target plane at the furnace exit, its residence time in the melter can also be recorded. A representative histogram of such times is shown in Figure 8a. The shortest are of primary interest since they are associated with portions of the glass that receive the least amount of thermal conditioning. A more detailed picture can thus be drawn from comparisons made between the pathways of particles with the shortest 0.1% and average residence times (Figure 8b–c), where the so‐called short‐circuit pathways of the former contrast with the large recirculation loops followed several times by the latter.
Figure 7 Combustion zone of a fiber glass melting furnace. (a) Photo of oxy‐fuel flames; (b) temperature contours calculated by a simulation model.
Other mathematical integrations are often performed along particle paths. One example is the dimensionless mixing index, which can be interpreted as the number of times a spherical
