5 Linear stability analysis of fountain flow. Conclusions. Transient finite element techniques can be a powerful tool to examine the stability behavior of complex ...
An Investigation of Flow Mark Surface Defects in Injection Molding of Polymer Melts A.M.Grillet1 , A.C.B.Bogaerds1 , M. Bulters2 , G.W.M.Peters1 & F.P.T.Baaijens1 1 Dutch Polymer Institute, Eindhoven University of Technology,
P.O. Box 513, 5600 MB Eindhoven, the Netherlands 2 DSM Research, P.O.Box 18, 6160 MD Geleen, The Netherlands
Steady flow of strain softening fluid
Introduction Flow instabilities during injection molding can result in surface defects on polymer parts. In filled polypropylene systems, the regular dull surface of finished parts is broken by periodic shiny bands perpendicular to the flow direction referred to as flow marks, tiger stripes or ice lines [1, 2, 3, 4]. We apply recent developements in numerical stabilty analysis using finite element simulations to a model injection molding flow. Our objectives are:
1 2 3 4 5 6 7 8 9 10 11
9
8 5
4 3
2.583E-04 1.353E-01 2.702E-01 4.052E-01 5.402E-01 6.752E-01 8.102E-01 9.452E-01 1.080E+00 1.215E+00 1.350E+00
Fig. 3 Steady results for Wi = 5.0, ε = 0.90: left – streamlines, right – scaled birefringence.
Linear stability
✄ Determine the mechanism of the instability. ✄ Understand the dependence on polymer rheology.
Unstable Flow During Injection Molding Unstable flow shown by two color short shot experiments performed on filled polypropylene at DSM Research.
Fig. 4 Strain softening fluid (ε = 0.90) Wi = 5: a) Steady velocity vectors (scale 0.256); b) Perturbation velocity vectors (scale ∼ 105 ); c) swirling flow near the free surface.
Finite Element Simulations We performed steady and transient finite element simulations of injection molding flow using fully implicit DEVSS/GSUPG method. We write our governing equations incorporating the exponential form of the Phan-Thien Tanner constitutive equation with ξ = 0. ∇·u =0; ∇ · pI − τ = 0 ∂τ c + u · ∇τ − τ · ∇u − (∇u) · τ Wi ∂t +eεWi tr(τ ) τ − D = 0 ε 10
u
Uwall λ Wi = L
4
10
6
ε=0.05 ε=0.3 ε=0.9
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10
Viscosity ηE [Pa ⋅s]
Viscosity η [Pa ⋅s]
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ε=0.05 ε=0.3 ε=0.9 1
10 −2 10
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Eigenvalue Analysis 0 −0.2
−5
−0.4 −0.6 −0.8 −1
−10 0
5
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15 time
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ε=0.05 ε=0.30 ε=0.90 0.2
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Fig. 5 Linear stability analysis of fountain flow.
Conclusions Transient finite element techniques can be a powerful tool to examine the stability behavior of complex flows, as demonstrated here for injection molding. The linear stability analysis shows that the most unstable eigenmode is a swirling flow near the free surface which is in qualitative agreement with the experimentally observed flow instability. We plan to continue our analysis of this flow to clarify the dependence on rheology and to isolate the mechanism of the fountain flow instability. References:
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[1] M.Bulters and A.Schepens. Proceedings of the 16th Annual Meeting of the Polymer Processing Society. (2000) Shanghai, China.
3
0
10 Shear rate γ˙ [s−1]
Wi=1 Wi=2 Wi=3 Wi=4 Wi=5
Real (Eigenvalue)
Fig. 1 Experiments by M. Bulters and A. Schepens [1].
ln( norm of the perturbation )
Linear Stability of Fountain Flow: PTT ε=0.90, ∆ t=0.02 5
10 −2 10
0
10 Strain rate ε˙ [s−1]
2
10
Fig. 2 Viscosity of model Phan-Thien Tanner fluids : left – steady shear, right – uniaxial extension.
No slip boundary conditions are applied on the walls and the free surface is treated as an impenetrable slip surface.
[2] S.Y.Hobbs. Poly. Eng. Sci. (1996) 32 p1489. [3] H.Hamada and H.Tsunasawa. J. Appl. Poly. Sci. (1996) 60 p.353. [4] B.Monasse, L.Mathieu, M.Vincent, JM.Haudin, J.P.Gazonnet, V.Durand, J.M.Barthez, D.Roux and J.Y.Charmeau. Proceedings of the 15th Annual Meeting of the Polymer Processing Society. (1999) s’Hertogenbosch, The Netherlands.
