Development of a Computer Simulation Model for Blowing Glass Containers

Abstract

In glass container manufacturing (e.g. production of glass bottles and jars) an important process step is the blowing of the final product. This process is fast and is characterized by large deformations and the interaction of a hot glass fluid that gets into contact with a colder metal, the mould. The objective of this paper is to create a robust finite element model to be used for industrial purposes that accurately captures the blowing step of glass containers. The model should be able to correctly represent the flow of glass and the energy exchange during the process. For tracking the geometry of the deforming inner and outer interface of glass, level set technique is applied on structured and unstructured fixed mesh. At each time step the coupled problem of flow and energy exchange is solved by the model. Here the flow problem is only solved for the domain enclosed by the mould, whereas in the energy calculations, the mould domain is also taken into account in the computations. For all the calculations the material parameters (like viscosity) are based on the glass position, i.e. the position of the level sets. The velocity distribution, as found from this solution procedure, is then used to update the two level sets by means of solving a convection equation. A re-initialization algorithm is applied after each time step in order to let the level sets reattain the property of being a signed distance function. The model is validated by several examples focusing on both the overall behavior (such as conservation of mass and energy) and the local behavior of the flow (such as glass-mould contact) and temperature distributions for different mesh size, time step, level set settings and material parameters.

Mathematical Modelling of Glass Forming Processes

“…Thus the motion of glass melt and pressurised air is described by the Navier-Stokes equations for incompressible fluids. These involve the momentum equations, ρ ∂u ∂t 22) and the continuity equation, which follows directly from (2.19), Flow problem (2.22)-(2.23) is coupled to the energy problem (2.10) in two ways: firstly the viscosity is temperature dependent and secondly the heat transfer is partly described by convection and diffusion.…”

“…They can be classified in two main categories [22]: interface-tracking techniques (ITT) and interfacecapturing techniques (ICT).…”

“…For examples of Level Set Methods in mathematical modelling of glass blow processes the reader is referred to [2,22].…”

“…In [49] remeshing was completely avoided by using an arbitrary Euler-Lagrangian approach to compute the mesh for the changing computational domain due to the motion of the plunger and by using a PseudoConcentration Method to track the glass-air interfaces. In [22] a Level Set Method was used to track the glass-air interfaces in a FEM based model for glass blowing.…”

Simulation of the solidification in a channel of a water-cooled glass flow

“…Boundary conditions for the momentum equation were no-slip at all solid surfaces and slip at the upper boundary of the tube, while for the energy equation constant and uniform temperature were considered on the outside wall of the tube, zero heat flux at the bottom, and ambient air temperature at the upper boundary of the tube. Giannopapa (2006) developed a computational model to simulate the blowblow forming process of glass containers, which characterized the glass flow and the heat transfer. He was able to track the geometry of the deforming interface of glass by applying structured and unstructured fixed meshes.…”