Numerical modelling of the blowing phase in the production of glass containers

Abstract

The industrial manufacturing of glass containers consists of several phases, one of which is the blowing phase. This paper describes the development of a numerical simulation tool for this phase. The hot liquid glass is modelled as a viscous fluid and its flow is governed by the Stokes equations. We use the boundary element method to solve the Stokes equations and obtain the velocity profile at the glass surface. The movement of the surface obeys an ordinary differential equation. We describe three methods to perform a time integration step and update the shape of the glass surface. All calculations are performed in three dimensions. This allows us to simulate the blowing of glass containers that are not rotationally symmetric. The contact between glass and mould is modelled using a partial-slip condition. A number of simulations on model glass containers illustrates the results.

Mathematical Modelling of Glass Forming Processes

“…Exceptions are [75], in which a Finite Volume Method is used, and [16], in which Boundary Element Methods are used. FEM in models for forming processes usually go together with re-meshing techniques, sometimes combined with an Eulerian formulation or a Lagrangian method.…”

“…In this case it can be recommended to use Boundary Element Methods to solve the flow problem [15,16].…”

“…There are several ways to accomplish this. One approach is to solve the partial differential equation [50,58,68] ∂φ ∂τ 16) withφ(x, 0) =φ 0 := φ(x, t), to steady state. If properly implemented the functionφ converges rapidly to the signed distance function around the interface [50,68].…”