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Title: Level-Set Method Used To Track The Glass-Air Interface In The Blow Step Of Glass Containers

Abstract

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 of a preform with non-uniform temperature.

Authors:
;  [1]
  1. Dept. of Mathematics and Computer Science, Technische Universiteit Eindhoven, PO Box 513, 5600 MB Eindhoven (Netherlands)
Publication Date:
OSTI Identifier:
21057379
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 908; Journal Issue: 1; Conference: NUMIFORM '07: 9. international conference on numerical methods in industrial forming processes, Porto (Portugal), 17-21 Jun 2007; Other Information: DOI: 10.1063/1.2741028; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AIR; COMPUTERIZED SIMULATION; CONTAINERS; ENERGY TRANSFER; FINITE ELEMENT METHOD; GLASS; INTERFACES; MATERIALS WORKING; SURFACES; TEMPERATURE DEPENDENCE; VISCOSITY

Citation Formats

Giannopapa, C. G., and Groot, J. A. W. M.. Level-Set Method Used To Track The Glass-Air Interface In The Blow Step Of Glass Containers. United States: N. p., 2007. Web. doi:10.1063/1.2741028.
Giannopapa, C. G., & Groot, J. A. W. M.. Level-Set Method Used To Track The Glass-Air Interface In The Blow Step Of Glass Containers. United States. doi:10.1063/1.2741028.
Giannopapa, C. G., and Groot, J. A. W. M.. Thu . "Level-Set Method Used To Track The Glass-Air Interface In The Blow Step Of Glass Containers". United States. doi:10.1063/1.2741028.
@article{osti_21057379,
title = {Level-Set Method Used To Track The Glass-Air Interface In The Blow Step Of Glass Containers},
author = {Giannopapa, C. G. and Groot, J. A. W. M.},
abstractNote = {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 of a preform with non-uniform temperature.},
doi = {10.1063/1.2741028},
journal = {AIP Conference Proceedings},
number = 1,
volume = 908,
place = {United States},
year = {Thu May 17 00:00:00 EDT 2007},
month = {Thu May 17 00:00:00 EDT 2007}
}
  • A hybrid of the Front-Tracking (FT) and the Level-Set (LS) methods is introduced, combining advantages and removing drawbacks of both methods. The kinematics of the interface is treated in a Lagrangian (FT) manner, by tracking markers placed at the interface. The markers are not connected – instead, the interface topology is resolved in an Eulerian (LS) framework, by wrapping a signed distance function around Lagrangian markers each time the markers move. For accuracy and efficiency, we have developed a high-order “anchoring” algorithm and an implicit PDE-based re-distancing. We have demonstrated that the method is 3rd-order accurate in space, near themore » markers, and therefore 1st-order convergent in curvature; in contrast to traditional PDE-based re-initialization algorithms, which tend to slightly relocate the zero Level Set and can be shown to be non-convergent in curvature. The implicit pseudo-time discretization of the re-distancing equation is implemented within the Jacobian-Free Newton Krylov (JFNK) framework combined with ILU(k) preconditioning. We have demonstrated that the steady-state solutions in pseudo-time can be achieved very efficiently, with iterations (CFL ), in contrast to the explicit re-distancing which requires 100s of iterations with CFL . The most cost-effective algorithm is found to be a hybrid of explicit and implicit discretizations, in which we apply first 10-15 iterations with explicit discretization (to bring the initial guess to the ball of convergence for the Newton’s method) and then finishing with 2-3 implicit steps, bringing the re-distancing equation to a complete steady-state. The eigenscopy of the JFNK-ILU(k) demonstrates the efficiency of the ILU(k) preconditioner, which effectively cluster eigenvalues of the otherwise extremely ill-conditioned Jacobian matrices, thereby enabling the Krylov (GMRES) method to converge with iterations, with only a few levels of ILU fill-ins. Importantly, due to the Level Set localization, the bandwidth of the Jacobian matrix is nearly constant, and the ILU preconditioning scales as , which implies efficiency and good scalability of the overall algorithm. The numerical examples include the well-established tests for interface kinematics under translational, rotational and tearing/stretching motion. We have shown that the mass conservation is not an issue anymore, as demonstrated using the Rider&Kothe’s time-reversed tests with extreme deformation. We are able to stretch interface structures to the under-resolved/subgrid (on the chosen Eulerian mesh) scales, and recover them back without any change in shape/loss of mass.« less
  • A level set simulation methodology developed for modeling coupled reactive transport and structure evolution has been applied to dissolution in fracture apertures and porous media. The coupled processes such as fluid flow, reactant transport and dissolution at the solid-liquid interfaces are handled simultaneously. The reaction-induced evolution of solid-liquid interfaces is captured using the level set method, with the advantage of representing the interface with sub-grid scale resolution. The coupled processes are simulated for several geometric models of fractures and porous media under various flow conditions and reaction rates. Quantitative relationships between permeability and porosity are obtained from some of themore » simulation results and compared with analytical constitutive relations (i.e., the conventional cubic law and the Carman-Kozeny law) based on simplified pore space geometries and reaction induced geometric evolutions. The drastic deviation of the simulation results from these analytical theories is explained by the development of large local concentration gradients of reactants within fracture apertures and individual pores observed in the simulation results and consequently the complex geometric evolution patterns of fracture apertures and pores due to mineral dissolution. The simulation results support the argument that traditional constitutive relations based on simplified geometries and conditions have limited applicability in predicting field scale reactive transport and that incorporation of micro-scale physics is necessary.« less
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