Encyclopedia of Glass Science, Technology, History, and Culture. Группа авторов
in Glass Processes
Patrick J. Prescott and Bruno Purnode
Owens Corning Science & Technology Center, Granville, OH, USA
1 Introduction
Numerical simulations of glass processes are performed in lieu of physical trials, which often involve conditions too harsh to allow measurements, are difficult to control, or are prohibitively expensive. Used as a screening tool, a simulation model can thus allow technologists to avoid several iterations of actual physical trials on an industrial apparatus. Alternatively, simulations can be used to examine phenomena which are too difficult to observe in practice because of the extreme environment of glassmaking. Moreover, numerical simulation allows for fundamental phenomena to be studied, thanks to its capability of identifying and controlling factors that influence the process. Such factors cannot usually be independently modified in the real process, in view of its complexity, and the insights gained from such virtual experiments can be used to guide technology development efforts.
Following the advent of electronic computers in the mid‐twentieth century, these methods were pioneered in the 1960s to deal with glassmaking problems elementary enough to be handled with the simplifying assumptions required by the then limited computing power. Much more complex and realistic 3‐D problems can of course be tackled now as massive increase in this computing power has dramatically changed engineering analysis in general. Concomitant with hardware advances have been significant developments in software, including both computational algorithms and user interfaces. Several commercial offerings of the relevant software are available for glassmaking. Process engineers are encouraged to utilize such tools. Some of these software packages are general purpose, adaptable to a wide range of situations, whereas others serve the glass‐processing industry specifically.
Both general‐purpose and niche‐software products will be used in the example simulations presented in this chapter where the focus will be put on the mathematical techniques used to simulate the two major phenomena involved in glassmaking, namely fluid flow and heat transfer. Mathematical models, formulated from the classical laws of physics, are used to calculate relevant field variables, such as temperature, velocity, stress, etc., within a glass manufacturing process. Modeling results are then interpreted with post‐processing procedures, which are less abstract than ever before, thanks to modern techniques capable of displaying results in a geometrical context. When applied to fluid flow and heat transfer, these techniques are collectively referred to as computational fluid dynamics (CFD).
To review these new methods, we will first summarize the main six steps they successively involve from the definition of the problem of interest to its solution. The various physical phenomena relevant and their mathematical description and computational treatment will then be expounded. Subsequently, a few representative examples of model simulation will be presented to demonstrate the capabilities and the value of modeling to a glass manufacturing enterprise. Finally, a brief section on the importance of managing simulation data will be provided.
2 A Brief Overview
Numerical simulation is a process made up of the six steps summarized in Table 1. These are: (1) identify the objectives of the modeling study, (2) construct a geometrical domain and discretization of the system of interest (i.e. meshing or grid generation), (3) build the simulation model by selecting physical phenomena and applying various physical data (e.g. material properties, boundary conditions), (4) choose numerical parameters to execute the calculations and effect a solution, (5) post‐process the simulation results, and (6) document them and archive the modeling data. Each of these is important, and some are mutually dependent on one another.
Table 1 Summary of simulation process steps.
| Step | Process | Description |
|---|---|---|
| 1 | Objective | Identify needed results – quantitative summaries – qualitative insights – comparisons. |
| 2 | Geometry and mesh | Construct CAD model and discretize into elements or cells. |
| 3 | Physical conditions | Assign materials and properties to regions, boundary conditions, sources, and other abstractions to account for physical behavior. (Can affect Step 2) |
| 4 | Solve | Select solver options, such as under‐relaxation coefficients, gradient estimation methods, convergence criteria, etc., and solve. (Can affect Step 2 or 3) |
| 5 | Post‐process | Review computed results, prepare contour plots, vector plots, flow pathlines, and other computed values from results. |
| 6 | Document and archive | Prepare presentation or report and store all information in appropriate database. |
The first step of identifying the objective cannot be overemphasized. It will drive the rest of the process and will lead to key assumptions to be applied along the way. The complexity of the model or its level of detail can very much depend on its purpose. Thus, the second step of geometrically defining the computational domain and discretizing it very much relies on the modeling objectives and requires good judgment in order to resolve the details of interest without adding human and computational effort that are not key to the objectives sought. Therefore, it is crucial to determine a good balance between model accuracy and the effort needed to reach a solution.
Generating a mesh is often the main bottleneck in the modeling process, as it is often rendered difficult by geometrical details which have a negligible effect on the results of interest. Meshing software with de‐featuring options may be helpful, but good guidance at the outset of the modeling project is very valuable. This point is well illustrated in Figure 1a where are sketched two ways to represent a burner block used in a forehearth (i.e. the heated canal lined with refractory material separating the melting furnace from the forming machinery). The geometry shown in Figure 1a more accurately represents the actual shape of the burner block, but it yields highly skewed and undesirable mesh cells. The low‐quality mesh is the result of three surfaces, one of which is curved, intersecting at a point, which will either cause divergence of the computational algorithm or lead to spurious results. Extreme grid refinement thus is required to achieve acceptable mesh quality. An alternative that alleviates the meshing problem, without having a significant effect on computed results, is shown in Figure 1b.
Sound engineering judgment is also needed to build the simulation model, the third step of the simulation process. Many decisions are required. For example, can symmetry be assumed? Another example is linked to the steadiness of the process and whether an assumption of steady state is justified or if transient conditions must be considered. Treating fundamental properties like viscosity (Chapter 4.1) and thermal conductivity (Chapter 4.5) as constant or temperature‐dependent represents another decision that must be made by the numerical analyst. Sometimes, it is advantageous to use constant properties to establish an initial solution, followed by another solution attempt with variable properties. This strategy has been used effectively where