diameter dci would dissolve as it travels along the path of the particle, from beginning to end. This index is defined as
(18)
where
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.
5 Simulation Data Management
Since modeling has gained wider acceptance and is increasingly relied upon to support important decisions, capturing and cataloging simulation models, the data used for their input, and the calculated results are very important. Managing simulation data has become a challenge for many organizations engaged in process modeling. A good simulation data management (SDM) system allows models to be “recycled” and used again for a different set of operating conditions, and allows different users to access archived models and their data. Furthermore, a good system has cataloging and search features that allow users in need of modeling data to access it quickly, even if they are not familiar with the previous modeling study. That is, not only should a SDM system assist individual analysts to organize their results, but it should serve a larger enterprise, with many people in different and changing roles.
The interactions and associated transfer of information of different organizations within a glass processing enterprise are sketched in Figure 10. Whether simulations are performed to assist a technical‐support team or a technology‐development effort in R&D, the ultimate benefactor is the manufacturing operation. Although there are direct interactions between any two of these subgroups, an SDM system can be used to manage data collected and generated by the modeling and simulation activities.
Figure 8 Results of particle tracking post‐processing: (a) calculated distribution of particle residence times, (b) paths taken by fastest 0.1% particles, and (c) typical paths taken for median residence time. Same number of particles tracked in both cases.
Source: Courtesy of Glass Service, Inc.
An SDM system improves productivity by keeping data well organized and accessible to authorized individuals at various locations, who may be interested in a summary of results, build a new model based on a previous model, or mine data in search of correlations between certain operating conditions. By keeping official records, the SDM reduces problems of duplicated files or duplicated names of slightly different files. It also contributes to security by controlling access, minimizing the chance of inadvertently deleting files, and centralizing the backup of these data.
There are numerous ways to implement some kind of SDM system, ranging from a highly structured and well‐organized network‐attached storage system to highly sophisticated commercial offerings that either resemble product lifecycle management (PLM) systems or are even integrated into a PLM. In addition to administering simulation data, many of these systems also can be used to manage the simulation process, where workflow is defined within collaborative groups, computational resources are shared, and sequential, parametric simulations (e.g. a design optimization exploration) can be conducted with improved effectiveness. These SDM systems are designed to extract metadata from model files. Examples of commonly extracted metadata are methods to characterize viscous effects (i.e. laminar, turbulent k‐ε, turbulent RSM, etc.), mesh size, mesh type (i.e. hexahedra, tetrahedral, etc.), software version, etc. For glass processing, it is possible and recommended to provide a way to extract metadata associated with the glass process; examples of these include furnace footprint size, pull rate, glass type, batch characteristics, etc. Any organization which has collaborative efforts involved with modeling and simulation should thus implement some kind of data management system.
Figure 9 Pathways of sand particles dissolving in glass.
Source: courtesy of Glass Service, Inc.
Figure 10 Central role of simulation data management in sharing of information.
6 Perspectives
The use of mathematical modeling in other glass industry segments has also increased over the years. Examples of such work can be found in the container, specialty, and float‐glass industry for simulations of processes such as refining, homogenizing, tempering, shaping, gas generation [4, 16–18]. Striking results have, for instance, been obtained for containers for which simulations allow the shape and fabrication process to be optimized many times more rapidly (and less expensively) than in the traditional way. Not surprisingly, constructing a model to simulate a glass melting furnace is a larger, more time‐consuming task. Obtaining a converged solution while considering the uncertainties associated with material properties is also challenging. Small changes to a validated model can be applied, however, and new simulation results can be computed quickly.
The amount of information that can be extracted from simulation results is appreciated for its value in assessing conditions not possible without computational modeling. Sometimes, a particular post‐processing analysis is not desired until well after a simulation has been completed (i.e. weeks, months, or years later), but as long as the simulation data has been preserved, the analysis can be completed quickly.
Although advanced, modeling and simulation of glass processes can be improved. Some of the improvements are related to numerical implementation, but it is often the case that required transport properties cannot be measured without inordinate expense. Some improvements are related to achieving more accurate solutions, whereas other are related to improve post‐processing. For example, improved knowledge of heat transfer in a foam could significantly reduce the time required to tune and validate a simulation model (i.e. improved accuracy and efficiency), whereas more information about refractory dissolution or wear could improve post‐processing assessments of furnace life.
The
