polymer injection molding simulations in openfoam® · pdf filepolymer injection molding...
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![Page 1: Polymer injection molding simulations in OpenFOAM® · PDF filePolymer injection molding simulations in OpenFOAM® József Nagy, Herwig Juster, Klaus Straka, Georg Steinbichler Johannes](https://reader033.vdocuments.mx/reader033/viewer/2022051508/5a9e35d37f8b9aee4a8b558d/html5/thumbnails/1.jpg)
PFAU 9.0, Linz, Austria, 03.11.2014
Polymer injection molding simulations in OpenFOAM® József Nagy, Herwig Juster, Klaus Straka, Georg Steinbichler
Johannes Kepler University, Linz, Austria
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Introduction
Injection molding Communication
Medicine
Automotive
Packaging
etc…
Expensive development stage high pressure
high clamping forces
high viscosity
Simulation PolyFlow, Sigmasoft, Moldex3D, …
OpenFOAM®
Model implementation compressibility (pvT)
viscosity (non-Newtonian)
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Models in OpenFOAM®
Incompressible models: powerLaw: ν γ = ν0γ
𝑛−1 CrossPowerLaw:
ν γ =ν0−ν∞
1+ 𝑚γ 𝑛+ ν∞
BirdCarreau:
ν γ = ν∞ + ν0 − ν∞ 1 + 𝑚γ 𝑎𝑛−1
𝑎
Compressible models: perfectFluid:
ρ 𝑝 = ρ0 +𝑝
𝑅𝑇
adiabaticPerfectFluid:
ρ 𝑝 = ρ0𝑝+𝐵
𝑝0+𝐵
1
γ
𝝂 = 𝝂(𝜸 , 𝑻, 𝒑)
𝝆 = 𝝆(𝑻, 𝒑)
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Theory
VOF: ρ = αρ𝑙 + 1 − α ρ𝑔
𝜕α
𝜕𝑡+ 𝛻 ∙ α𝒖 + 𝛻 ∙ α 1 − α 𝒖𝑟 = 𝑆𝑝 + 𝑆𝑢
Continuity equation:
𝜕𝜌𝒖
𝜕𝑡+ 𝛻 ∙ 𝜌𝒖 = 0
Momentum equations:
𝜕𝜌𝒖
𝜕𝑡+ 𝛻 ∙ 𝜌𝒖𝒖 = −𝛻𝑝 + 𝛻 ∙ 𝜏 + 𝜌𝒈 + 𝑭σ
Energy equation:
𝜕𝜌𝑇
𝜕𝑡+ 𝛻 ∙ 𝜌𝒖𝑇 =
∆ 𝑘 𝑇 + 𝜏: 𝛻𝒖 ∙α
𝑐𝑣1+ 𝛻 ∙ 𝑝𝒖
α
𝑐𝑣1+
1−α
𝑐𝑣2
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New viscosity models in OpenFOAM®
tempPowerLaw (first order):
ν γ , 𝑇 = ν0γ 𝑛−1𝑒𝑐∙ 𝑇−𝑇0
CarreauYasudaWLF:
ν γ , 𝑇 = ν∞ ∙ 𝑎𝑇 𝑇 + ν0 − ν∞ 𝑎𝑇 𝑇 1 + 𝜆𝑎𝑇 𝑇 γ 𝑎𝑛−1
𝑎
log 𝑎𝑇 𝑇 =8.86∙ 𝑇0−𝑇𝑆
101.6+ 𝑇0−𝑇𝑆−
8.86∙ 𝑇−𝑇𝑆
101.6+ 𝑇−𝑇𝑆
𝝂 = 𝝂(𝜸 , 𝑻, 𝒑)
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New viscosity models in OpenFOAM®
CrossArrhenius:
ν γ , 𝑇 =ν0 𝑇
1+ν0 𝑇 γ
τ∗
1−𝑛
ν0 𝑇 = 𝐵 ∙ 𝑒𝑇𝑏 𝑇
CrossWLF:
ν γ , 𝑇, 𝑝 =ν0 𝑇,𝑝
1+ν0 𝑇,𝑝 γ
𝐷4
1−𝑛
ν0 𝑇 = 𝐷1 ∙ exp−𝐴1 ∙ 𝑇−𝐷2−𝐷3∙𝑝
𝐴2+𝑇−𝐷2−𝐷3∙𝑝
𝝂 = 𝝂(𝜸 , 𝑻, 𝒑)
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New viscosity models in OpenFOAM®
𝐏𝐒 − 𝟏𝟒𝟓𝐃
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New viscosity models in OpenFOAM®
𝐏𝐏 − 𝐇𝐆𝟑𝟏𝟑𝐌𝐎
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New compressibility models in OpenFOAM®
Schmidt:
𝑣 𝑝, 𝑇 =𝑃𝐹1
𝑃𝐹4+𝑝+
𝑃𝐹2∙𝑇
𝑃𝐹3+𝑝 𝑇 ≤ 𝑇𝑡𝑟𝑎𝑛𝑠
𝑣 𝑝, 𝑇 =𝑃𝑆1
𝑃𝑆4+𝑝+
𝑃𝑆2∙𝑇
𝑃𝑆3+𝑝 𝑇 ≥ 𝑇𝑡𝑟𝑎𝑛𝑠
𝑇𝑡𝑟𝑎𝑛𝑠 = 𝑃𝐾1 + 𝑃𝐾2 ∙ 𝑝
𝝆 = 𝝆(𝑻, 𝒑)
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New compressibility models in OpenFOAM®
Tait:
𝑣 𝑝, 𝑇 = 𝑣𝑠 𝑇 ∙ 1 − 𝐶 ∙ ln 1 +𝑝
𝐵𝑠 𝑇+𝑊𝑠 𝑇 𝑇 ≤ 𝑇𝑡𝑟𝑎𝑛𝑠
𝑣𝑠 𝑇 = 𝑏1𝑠 + 𝑏2𝑠 ∙ 𝑇 − 𝑏5
𝐵𝑠 𝑇 = 𝑏3𝑠 ∙ 𝑒−𝑏4𝑠∙ 𝑇−𝑏5
𝑊𝑠 𝑇 = 𝑏7 ∙ 𝑒𝑏8∙ 𝑇−𝑏5 −𝑏9∙𝑝
𝑣 𝑝, 𝑇 = 𝑣𝑚 𝑇 ∙ 1 − 𝐶 ∙ ln 1 +𝑝
𝐵𝑚 𝑇 𝑇 ≥ 𝑇𝑡𝑟𝑎𝑛𝑠
𝑣𝑚 𝑇 = 𝑏1𝑚 + 𝑏2𝑚 ∙ 𝑇 − 𝑏5
𝐵𝑚 𝑇 = 𝑏3𝑚 ∙ 𝑒−𝑏4𝑚∙ 𝑇−𝑏5 𝑇𝑡𝑟𝑎𝑛𝑠 = 𝑏5 + 𝑏6 ∙ 𝑝 𝐶 = 0.0894
𝝆 = 𝝆(𝑻, 𝒑)
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New compressibility models in OpenFOAM®
𝐏𝐒 − 𝟏𝟒𝟓𝐃
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Discontinuous processing technique for polymer-additive systems
Injection molding machine:
– Plasticizing the polymer-additive system with single screw
– Shaping of the melt within the cavities in the mold
– One-stop production
Injection Molding Machine type e-mac; Source: ENGEL Austria GmbH
Juster, 17.06.2014; 6th International Congress on Pharmaceutical Engineering, Graz, Austria
Drug delivery system
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Trial simulation of injection process (coarse mesh) Influence of strain rate, density, temperature, pressure, viscosity etc.
Back coupling
Geometry – 1 tablet cavity
Fill time of 1 s
Wall temperature of 503 K
Inlet temperature of 553 K
Tait, CrossWLF for PS 145D
Problem setting – injection molding process
inlet
outlet
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Injection molding process
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Liquid phase fraction
t = 0.25 s t = 0.75 s
t = 0.5 s t = 1 s
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Velocity magnitude and vectors
t = 0.25 s t = 0.75 s
t = 0.5 s t = 1 s
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Pressure
t = 0.25 s t = 0.75 s
t = 0.5 s t = 1 s
t = 0.25 s t = 0.75 s
t = 0.5 s t = 1 s
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Temperature
t = 0.25 s t = 0.75 s
t = 0.5 s t = 1 s
t = 0.25 s t = 0.75 s
t = 0.5 s t = 1 s
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Density
t = 0.25 s t = 0.75 s
t = 0.5 s t = 1 s
t = 0.25 s t = 0.75 s
t = 0.5 s t = 1 s
t = 0.25 s t = 0.75 s
t = 0.5 s t = 1 s
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Dynamic viscosity
t = 0.25 s t = 0.75 s
t = 0.5 s t = 1 s
t = 0.25 s t = 0.75 s
t = 0.5 s t = 1 s
t = 0.25 s t = 0.75 s
t = 0.5 s t = 1 s
t = 0.25 s t = 0.75 s
t = 0.5 s t = 1 s
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Conclusions and outlook
Injection molding process in OpenFOAM®
Implemented viscosity models tempPowerLaw (first order)
CarreauYasudaWLF
CrossArrhenius
CrossWLF
Implemented compressibility models Schmidt
Tait
Adaptation of compressibleInterFoam
Next steps crystallization
fiber orientation
cure
etc…
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Thank you for your attention!
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23 Titel, Ersteller, Datum
Introduction to injection molding technique and its simulation
Figure 2: Injection molding cycle
Inje
ctio
n m
old
ing
sim
ula
tio
n In
jectio
n m
old
ing c
ycle
Step 2: End Plasticizing
Juster, 17.06.2014; 6th International Congress on Pharmaceutical Engineering, Graz, Austria
Research activities