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.

1.
Tooley
,
F. V.
, 1984,
The Handbook of Glass Manufacture
,
Aslee
,
New York
, Vol
II
.
2.
Loch
,
H.
, and
Krause
,
D.
, 2002,
Mathematical Simulation in Glass Technology
,
Springer-Verlag
,
Berlin
.
3.
Moreau
,
P.
,
Marechal
,
C.
, and
Lochegnies
,
D.
, 1999, “
Optimum Parson Shape for Glass Blowing
,”
Int. J. Form. Processes
1292-7775,
2
(
1-2
), pp.
81
94
.
4.
Lochegnies
,
D.
,
Moreau
,
P.
, and
Oudin
,
J.
, 1996, “
Finite Element Strategy for Glass Sheet Manufacture by Creep Forming
,”
Commun. Numer. Methods Eng.
1069-8299,
12
, pp.
331
341
.
5.
Marechal
,
C.
,
Moreau
,
P.
, and
Lochegnies
,
D.
, 2004, “
Numerical Optimization of a New Robotized Glass Blowing Process
,”
Eng. Comput.
0177-0667,
19
, pp.
233
240
.
6.
Lochegnies
,
D.
,
Moreau
,
P.
, and
Guilbait
,
R.
, 2005, “
Finite Element Interface-Tracking and Interface-Capturing Techniques for Flows With Moving Boundaries and Interfaces
,”
Glass Technol.
0017-1050,
46
(
2
), pp.
116
120
.
7.
Tezduyar
,
T. E.
, 2001, “
Finite Element Interface-Tracking and Interface-Capturing Techniques for Flows With Moving Boundaries and Interfaces
,”
Proceedings of the ASME Symposium on Fluid-Physics and Heat Transfer for Macro- and Micro-Scale Gas-Liquid and Phase-Change Flows (CD-ROM)
,
ASME
,
New York
, ASME Paper No. IMECE2001/HTD-24206.
8.
Hirth
,
C. W.
, and
Nichols
,
B. D.
, 1981, “
Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries
,”
J. Comput. Phys.
0021-9991,
39
, pp.
201
225
.
9.
Sethian
,
J. A.
, 1999,
Level Set Methods and Fast Marching Methods
,
Cambridge University Press
,
Cambridge
.
10.
Sussman
,
M.
,
Smereka
,
P.
, and
Osher
,
S. J.
, 1994, “
A Level Set Method for Computing Solutions to Incompressible Two-Phase Flow
,”
J. Comput. Phys.
0021-9991,
114
, pp.
146
159
.
11.
Cesar de Sa
,
J. M. A.
, 1986, “
Numerical Modeling of Glass Forming Processes
,”
Eng. Comput.
0263-4759,
3
, pp.
226
275
.
12.
Hyre
,
M.
, 2002, “
Numerical Simulation of Glass Forming and Conditioning
,”
J. Am. Ceram. Soc.
0002-7820,
85
(
5
), pp.
1047
1056
.
13.
Rawson
,
H.
, 1974, “
Physics of Glass Manufacturing Process
,”
Phys. Technol.
0305-4624,
5
(
2
), pp.
91
114
.
14.
Manthuruthil
,
J.
,
Sikri
,
T. R.
, and
Simmsons
,
G. A.
, 1974, “
Simplified Mathematica Model Simulating Heat Transfer in Glass-Forming Moulds
,”
J. Am. Ceram. Soc.
0002-7820,
57
(
8
), pp.
345
350
.
15.
Humpherys
,
C. E.
, 1991, “
Mathematical Modeling of Glass Flow During a Pressing Operation
,” Ph.D. thesis, University of Sheffield, Sheffield, UK.
16.
Bathe
,
K. J.
, 1997,
Finite Element Procedures
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
17.
van der Vorst
,
H. A.
, 1992, “
BI-CGSTAB: A Fast and Smoothly Converging Variant of BI-CG for the Solution of Non-Symmetric Linear Systems
,”
SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput.
0196-5204,
13
(
2
), pp.
631
644
.
18.
Johnson
,
C.
,
Nävert
,
U.
, and
Pitkäranta
,
J.
, 1984, “
Finite Element Methods for Linear Hyperbolic Problems
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
45
, pp.
285
312
.
19.
Brooks
,
A. N.
, and
Hughes
,
T. J. R.
, 1982, “
Stream-Line Upwind/Petrov-Galerkin Formulation for Convection Dominated Flows With Particular Emphasis on the Incompressible Navier-Stokes Equations
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
32
, pp.
199
259
.
20.
Shakib
,
F.
, 1989, “
Finite Element Analysis of the Compressible Euler and Navier–Stokes Equation
,” Ph.D. thesis, Stanford University, Stanford, CA.
21.
Sethian
,
J. A.
, 1996, “
A Marching Level Set Method for Monotonically Advancing Fronts
,”
Proc. Natl. Acad. Sci. U.S.A.
0027-8424,
93
, pp.
1591
1595
.
22.
Sethian
,
J. A.
, 1999, “
Fast Marching Methods
,”
SIAM Rev.
0036-1445,
41
(
2
), pp.
199
235
.
23.
Chopp
,
D. L.
, 2001, “
Some Improvements of the Fast Marching Method
,”
SIAM J. Sci. Comput. (USA)
1064-8275,
23
(
I
), pp.
230
244
.
24.
Cuvelier
,
C.
,
Segal
,
A.
, and
van Steenhoven
,
A.
, 1986,
Finite Element Methods and Navier Stokes Equations, Mathematics and its Applications
,
Reidel
,
The Netherlands
.
25.
Gunzberger
,
M.
, 1989, “
Finite Element Methods for Viscous Incompressible Flows
,”
Computer Science and Scientific Computing
,
Academic
,
New York
.
26.
Hageman
,
L. A.
, and
Young
,
D.
, 1981,
Applied Iterative Methods
1st ed.
,
Academic
,
New York
.
You do not currently have access to this content.