Cg Christina Giannopapa

Development of a computer simulation model for blowing glass containers

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 reinitialization 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.

A computer simulation model for the blow-blow forming process of glass containers

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 extend and further develop our finite element model [1] to be used for industrial purposes. To achieve this both steps of the forming of glass containers, namely blow-blow needs to be simulated and tested against real industrial problems. The model should be able to correctly represent the flow of glass, the energy exchange during the process and provide the final thickness of the final product. For tracking the geometry of the deforming inner and outer interface of glass, the level set technique is applied on a 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. A non uniform temperature distribution is considered for the blowing of the preform. 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 fast marching re-initialization algorithm is applied after each time step in order to let the level sets re-attain 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.Copyright

A Computer Simulation Model for the Stretch Blow Moulding Process of Polymer Containers

Stretch blow moulding is a widely used technique e.g. for the production of PET bottles. In a stretch blow moulding process a hot preform of polymer is simultaneously stretched and blown into a mould shape. The process takes place at a fast rate and is characterised by large deformations and temperature gradients. In this paper the computer simulation model presented in is applied to the stretch blow process for the production of PET bottles. The model was previously developed by the authors for the simulation of 2D axial-symmetrical blow processes for the production of glass containers. The model is based on finite element methods and uses a level set method to track the interfaces between air and the material. The simulation model is modified in order to correctly describe the material behaviour of PET, take into account the stretch process and substitute the process parameters for stretch blow moulding. Furthermore, it is verified that the PET behaviour can be modelled as a non-newtonian, isothermal fluid flow, based on a viscoplastic material model. An application presented is the stretch blow moulding of a realistic PET water bottle.Copyright

Development of a Computer Simulation Model for Blowing Glass Containers

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 re-attain 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.Copyright

On the derivation of SPH schemes for shocks through inhomogeneous media

Smoothed Particle Hydrodynamics (SPH) is typically used for the simulation of shock propagation through solid media, commonly observed during hypervelocity impacts. Although schemes for impacts into monolithic structures have been studied using SPH, problems occur when multimaterial structures are considered. This study begins from a variational framework and builds schemes for multiphase compressible problems, coming from different density estimates. Algorithmic details are discussed and results are compared upon three one-dimensional Riemann problems of known behavior.

Wave Propagation in Thin-Walled Aortic Analogues

Research on wave propagation in liquid filled vessels is often motivated by the need to understand arterial blood flows. Theoretical and experimental investigation of the propagation of waves in flexible tubes has been studied by many researchers. The analytical one-dimensional frequency domain wave theory has a great advantage of providing accurate results without the additional computational cost related to the modern time domain simulation models. For assessing the validity of analytical and numerical models, well defined in vitro experiments are of great importance. The objective of this paper is to present a frequency domain analytical model based on the one-dimensional wave propagation theory and validate it against experimental data obtained for aortic analogs. The elastic and viscoelastic properties of the wall are included in the analytical model. The pressure, volumetric flow rate, and wall distention obtained from the analytical model are compared with experimental data in two straight tubes with aortic relevance. The analytical results and the experimental measurements were found to be in good agreement when the viscoelastic properties of the wall are taken into account.

Level-set method used to track the glass-air interface in the blow step of glass containers

An application of the level‐set method in a finite element library for the simulation of the glass forming process is described. The forming process of containers (i.e bottles, jars) results in a thermomechanical problem with an evolving glass air interface posing a great challenge in modeling. The finite element method is used in our computations to accurately simulate the glass flow, the process’ energy exchange with the heavily temperature dependent viscosity of the glass. Our model uses the level set method to track the glass‐air interface. In this way remeshing can be avoided and computational costs can be significantly reduced. The glass‐air interface can be seen as two interfaces: inner glass air interface and an outer glass‐air interface. Thus, we solve two level set equations which allow us to apply the correct material parameters to the aforementioned equations without explicitly having to trace the glass surfaces. Numerical examples are provided tracking the glass‐air interface of the blowing o...

Modelling Preform and Mould Shapes in Blow Moulding

Blow moulding is an essential stage of manufacturing glass and polymer containers, i.e. bottles or jars. A preform is brought into a mould and subsequently blown into the mould shape to produce the container. Two different problems regarding blow moulding are considered: the forward problem, which consists of determining the mould shape from the preform shape, and the inverse problem, which consists of determining the optimal preform shape corresponding to the designed container shape. This paper is concerned with the constraints on the mould surface and sensitivity to perturbations in the shape for both problems.

Towards a unified solution method for fluid-structure interaction problems : progress and challenges

The paper presents the progress in the development of a novel unified method for solving coupled fluid-structure interaction problems as well as the associated major challenges. The new approach is based on the fact that there are four fundamental equations in continuum mechanics: the continuity equation and the three momentum equations that describe Newton’s second law in three directions. These equations are valid for fluids and solids, the difference being in the constitutive relations that provide the internal stresses in the momentum equations: in solids the stress tensor is a function of the strain tensor while in fluids the viscous stress tensor depends on the rate of strain tensor. The equations are written in such a way that both media have the same unknown variables, namely the three velocity components and pressure. The same discretisation method (finite volume) is used to discretise the four partial differential equations and the same methodology to handle the pressurevelocity coupling. A common set of variables as well as a unified discretisation and solution method leads to a strong coupling between the two media and is very beneficial for the robustness of the algorithm. Significant challenges include the derivation of consistent boundary conditions for the pressure equation in boundaries with prescribed traction as well as the handling of discontinuity of pressure at the fluid-structure interface.

Smoothed Particle Hydrodynamics for Hypervelocity Impacts Into Inhomogeneous Materials

Smoothed Particle Hydrodynamics numerical method is extensively used in the study of hypervelocity impacts and subsequent shock propagation into solids. During impacts into inhomogeneous materials, effects produced on the interface of adjacent materials by shock waves need to be resolved. The present study discusses an SPH mutliphase scheme for compressible processes, that is based on the number density estimate and exhibits the scheme’s performance at shock propagation through inhomogeneous materials. In specific, a one-dimensional Riemann problem with known solution validates the scheme and results of two-dimensional hypervelocity impact scenarios into materials with (large-scale and small-scale) inhomogeneities are studied.Copyright