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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 cord of glass of specified initial diameter d_ci would dissolve as it travels along the path of the particle, from beginning to end. This index is defined as

(18)

where is the species diffusion coefficient in glass. In a manner similar to that of residence times, a distribution of mixing indices can thus be determined from the massless particle traces, and other similar indices also be computed.

Another analysis involves tracking and particles to account for the dissolution of each particle along its pathway as shown in Figure 9 for particles emanating from the batch layer and disappearing in the glass. The top and side views shown in Figure 9 are of the same melting tank illustrated in Figure 8. A distribution of survival times, average temperatures, and final temperatures can be assembled and compared with distributions gathered from other simulations representing different conditions. Such comparisons can be useful in assessing the likelihood of introducing unmelted batch stones into the front‐end. Similar tracking techniques can of course be applied to gas bubbles.