Une methode de pseudo-concentration pour Ia simulation 3D volumique du remplissage de monies d 'injection
Keywords:
full 3D mould filling, injection moulding, finite element method, control volume method, pseudo-concentration functionAbstract
A full 3D filling algorithm for injection moulding of molten polymers is presented. The non-Newtonian fluid flows governing equations are solved using a mixed velocitypressure finite element formulation with a mini-element. To track the polymer front, a transport equation of a pseudo-concentration function is solved using a control volume technique. The ability of the proposed algorithm to simulate the filling of three-dimensional moulds is demonstated through complicated flows and geometries examples.
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[ABB 98) ABBES B., AYAD R., PRUDHOMME J.-C. and 0NTENIENTE J.-P., <
simulation of thermoplastic wheat starch injection molding process », Polym. Eng. Sci.,
Vol. 38, W 12, 1998, p. 2029-2038.
(AGA 96) AGASSANT J.-F., AVENAS P., SERGENT J.-Ph., VERGNES B. et VINCENT M., La mise
en forme des matieres plastiques, Lavoisier - Technique et Documentation, 1996.
[BIR 87] BIRD R.B., ARMSTRONG R.C. and HASSAGER 0., Dynamics of polymeric liquids,
Wiley, New York, 1987
[BRE 91] BREZZI F. and FoRTIN M., Mixed and hybrid finite element methods, SpringerVerlag,
[DHA 90] DHATT G., GAO D.M. and BEN CHEIKH A., << A finite element simulation of metal
flow in moulds», Int. J. Numer. Meth. Eng., vol. 30, 1990, p. 821-831.
[FOR 84] FORTIN A., Methodes d'elements finis pour les equations de Navier-Stokes, These
de doctorat, Universite Laval, Quebec, 1984.
[FOR 95) FORTIN A., BELIVEAU A. and DEMAY Y., <
equations with applications to non-Newtonian fluids », in M.M. MARQUES and J.F.
RODRIGUES (Eds.), Trends in Applications of Mathematics to Mechanics, Longman,
Harlow, 1995, p. 311-322.
[FRE 81] FREDERIKSEN C.S. and WATTS A.M.,<< Finite element method for time dependent
incompressible free surface flow», J. Comput. Phys., Vol. 39, 1981, p. 282-304.
[GAO 91] GAo D.M., Modelisation numerique du remplissage des moules de fonderie par Ia
methode des elements finis, These de doctorat, Universite de Technologie de Compiegne,
[GER 86] GERMAIN P., Mecanique, Ellipses, Paris, 1986, p. 389-397.
[HAA 971 HAAGH G.A.A.H., ZUIDEMA H., VAN DE VOSSE F.N., PETERS G.W.M. and MEUER
H.E.H., «Towards a 3-D finite element model for the gaz-assisted injection moulding
process>>, Intern. Polym. Process. XII, Vol. 3, 1997.
[HAA 981 HAAGH G.A.A.H. and VAN DE VOSSE F.N., «Simulation of three-dimensional
polymer using a pseudo-concentration method», Int. J. Numer. Meth. Fluids, Vol. 28,
, p. 1355-1369.
[HET 981 HETU J.-F., GAO D.M., GARCIA-REJON A. and SALLOUM G., << 3D finite element
method for the simulation of the filling stage in injection molding », Polym. Eng. Sci.,
Vol. 38, W 2, 1998, p. 223-236.
[HIR 81 I HIRT C.W. and NICHOLS B.D., <
free boundaries>>, J. Comput. Phys., Vol. 39, 1981, p. 201-225.
[KOT 91 I KOTHE D.B., MJOLSNESS R.C. and TORREY M.D., <
for incompressible flows with free surfaces>>, Technical Report LA-12007-MS, Los
Alamos National Laboratory- Los Alamos (New Mexico), 1991.
[LEE 771 VAN LEER B., <
approach to numerical convection>>, J. Comput. Phys., Vol. 23, 1977, p. 276-299.
[LEL 981 VAN DER LELU A.J., <
British Plastics and Rubber, April 1998, p. 24-27.
[MAS 951 MASHAYEK F. and ASHGRIZ N., «Advection of axisymmetric interfaces by the
volume-of-fluid method>>, Int. J. Numer. Meth. Fluids, Vol. 20, 1995, p. 1337-1361.
[NIC 71 I NICHOLS B.D. and HIRT C.W., <
numerical incompressible flow calculations>>, J. Comput. Phys., Vol. 8, 1971, p. 434-448.
[PIC 981 PICHELIN E. and COUPEZ T., «Finite element solution of the 3D mold filling
problem for viscous incompressible fluid>>, Comput. Meth. Appl. Mech. Engrg., Vol. 163,
, p. 359-371.
[POL 901 PoLYFLOW, Reference Manual, 1990.
[SCH 981 SCHMIDT L.R., <
in injection molding >>, Plastics Engineering, October 1998, p. 27-31.
(SWA 941 SWAMINATHAN C.R. and VOLLER V.R., <>, Appl.
Math. Modelling, Vol. 18, 1994, p. 101-108.
[THO 861 THOMPSON E., << Use of pseudo-concentration to follow creeping viscous flow
during transient analysis>>, Int. J. Numer. Meth. Fluids, Vol. 6, 1986, p. 749-761.
[TOR 851 TORREY M.D., CLOUTMAN L.D., MJOLSNESS R.C. and HIRT C.W., << NASAVOF2D:
A computer program for incompressible flows with free surfaces », Technical
Report LA-10612-MS, Los Alamos National Laboratory - Los Alamos (New Mexico),
(USM 921 USMANI A.S., CROSS J.T. and LEWIS R.W., «A finite element model for the
simulations of the mould filling in metal casting and the associated heat transfer >>, Int. J.
Numer. Meth. Eng., Vol. 35, 1992, p. 787-806.
[VOL 951 VOLLER V.R. and PENG S., <
molds», Polym. Eng. Sci., Vol. 35, N° 22, 1995, p. 1758-1765.
[WAN 94a] WANG K.K., «Twenty years of CIMP research towards CAE for injection
molding», Adv. CAE Polym. Process., Vol. 49, 1994, p. 1-5.
[WAN 94b] WANG S.P. and WANG K.K., «A net inflow method for incompressible viscous
flow with moving free surface», Int. J. Numer. Meth. Fluids, Vol. 18, 1994, p. 669-694.
[ZAN 93] VANDERZANDEN A.J.J., The thermodynamics of a moving fluid-liquid contact line,
Ph.D. Thesis, Eindhoven University of Technology, 1993.