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 the initial constant property solution serves as the initial estimate for the more accurate, variable property simulation. It is recommended to begin a simulation project erring on the side of simplicity, and then to add complexity in subsequent simulations.
It is also the case that the physical modeling decisions will affect the geometrical and meshing procedures. For example, a perforated plate through which a fluid flows could require extremely detailed meshing (Figure 2); or the effects of the hole pattern could be accounted for with a much less refined mesh using a more abstract method, in which the screen is characterized by a permeability which relates velocity and pressure drop. The decision on how to proceed will depend on the objectives of the study.
Post‐processing (Step 5) is also very important, as it requires the analyst to execute good judgment on the results obtained. Before extracting information and insights from the results, the analyst must scrutinize the calculated field variables, as well as checking for balanced conservation laws; that is, checking for sufficient numerical convergence must be performed. Finally, management of simulation data (i.e. electronic model files) should not be overlooked since it determines the efficiency with which the simulation process is executed.
Figure 1 Examples of burner block geometry. (a) Accurate representation with poor mesh quality; (b) slight modification with improved mesh quality.
Figure 2 Example of a screen with small‐scale features requiring a high mesh density to be resolved.
3 Fundamental Phenomena, Governing Equations, and Simulation Tools
3.1 Glass as a Continuum
The basic principles of engineering science are applied in CFD simulations. These involve fluid mechanics and usually various other phenomena that are typically considered to fall within the category of thermal sciences. A brief overview is provided, but for complete development, interested readers not yet familiar with the details are referred to various textbooks (e.g. [1–3]). Physical phenomena specific to glass processes must be accounted for within the framework of three fundamental principles and will be reviewed later with respect to a few chosen examples. Readers are also directed to a volume edited by Krause and Loch [4] for a collection of excellent examples of numerical simulations applied to glass processes.
Forming the foundation on which CFD models are constructed, the fundamental principles of classical physics account for conservation of mass, momentum, and energy. Conservation of momentum follows from Newton's three laws of motion, whereas energy conservation is of course the first law of thermodynamics. Contrary to what is done for the very small systems simulated in theoretical studies (Chapters 2.8 and 2.9), it is impractical to account for the motion or energy level of each individual atom or structural entity at the scale relevant to industrial processes. Instead, it is recognized that, for length scales of engineering practicality, substances can be characterized with intensive properties (i.e. per unit volume or mass). Because it describes the mass per unit volume of a particular substance, density is a simple example of such a property that is independent of the size of the system. This abstraction allows substances to be treated as a continuum and allows for powerful mathematical models to be constructed.
3.2 Transport by Advection and Diffusion
Referring again to well‐recognized texts [1, 2], we will remind that the principle of conservation of mass, applied to an infinitesimally small control volume (CV), is mathematically expressed as
(1)
where ρ is the density and
(2)
whose left‐hand side represents the time rate of change of momentum (i.e. mass times acceleration), and the right the forces acting upon the fluid by adjacent fluid particles (i.e. the divergence of the stress tensor,
An important requirement for mathematical modeling of fluid flows is to relate internal fluid stresses to characteristics of the fluid's motion. Such a relationship, which depends on the substance, is termed a constitutive relationship. There are many types of material behavior, requiring different constitutive models, but the most commonly used model relates shear stresses to strain rate (i.e. velocity gradient) in a linear manner. Fluids to which this linear relationship applies are known as Newtonian fluids. For example, a shear stress component τxy for a Newtonian fluid is characterized with
