Three-dimensional Finite Element Solution of the Flow in Single and Twin-Screw Extruders
-
F. Ilinca
Abstract
This work is aimed at the numerical modeling of the flow inside single and twin-screw extruders. Numerical solutions are obtained using a recently developed immersed boundary finite element method capable of solving the flow in the presence of complex non-stationary solid boundaries. The method is first validated against the solution obtained on a body-conforming grid for a single screw extruder and then applied to a twin-screw mixer. The time dependent single screw problem can also be solved in a rotating reference frame for which a steady state solution can be obtained. This allows the evaluation of time integration errors of the moving immersed interface algorithm. For instance the flow is considered isothermal and the material behaves as a Generalized Newtonian fluid. Because the viscosity depends on the shear rate, solutions will be shown for various rotation velocities of the screw and compared with solutions obtained on body-conforming grids. The method is shown to give very accurate results and can be used for a more in-depth investigation of the material behavior in extruders.
References
Bertrand, F., et al., “Adaptive Finite Element Simulations of Fluid Flow in Twin-Screw Extruders”, Comp. Chem. Eng., 27, 491–500(2003), DOI: 10.1016/S0098-1354(02)00236-3Suche in Google Scholar
Bravo, V. L., et al., “Numerical Simulation of Pressure and Velocity Profiles in Kneading Elements of a Co-rotating Twin Screw Extruder”, Polym. Eng. Sci., 40, 525–541(2000), DOI: 10.1002/pen.11184Suche in Google Scholar
Cheng, H., Manas-Zloczower, I., “Study of Mixing Efficiency in Kneading Discs of Co-rotating Twin-Screw Extruders”, Polym. Eng. Sci., 37, 1082–1090(1997), DOI: 10.1002/pen.11753Suche in Google Scholar
Cheng, H., Manas-Zloczower, I., “Distributive Mixing in Conveying Elements of a ZSK-53 Co-rotating Twin Screw Extruders”, Polym. Eng. Sci., 38, 926–935(1998), DOI: 10.1002/pen.10260Suche in Google Scholar
Franca, L. P., Frey, S. L., “Stabilized Finite Element Methods: II. The Incompressible Navier-Stokes Equations”, Comp. Methods Appl. Mech. Eng., 99, 209–233(1992), DOI: 10.1016/0045-7825(92)90041-HSuche in Google Scholar
Glowinski, R., et al., “A Fictitious Domain Method for External Incompressible Viscous Flows Modeled by Navier-Stokes Equations”, Comput. Meth. Appl. Mech. Eng., 112, 133–148(1994), DOI: 10.1016/0045-7825(94)90022-1Suche in Google Scholar
Hughes, T. J. R., et al., “A new Finite Element Formulation for Computational Fluid Dynamics: V. Circumventing the Babuška-Brezzi Condition: A Stable Petrov-Galerkin Formulation of the Stokes Problem Accommodating Equal-order Interpolations”, Comput. Meth. Appl. Mech. Eng., 59, 85–99(1986), DOI: 10.1016/0045-7825(86)90025-3Suche in Google Scholar
Ilinca, F., Hétu, J.-F., “A Finite Element Immersed Boundary Method for Fluid Flow around Rigid Objects”, Int. J. Numer. Methods Fluids, (2010a), DOI: 10.1002/fld.2222Suche in Google Scholar
Ilinca, F., Hétu, J.-F., “A Finite Element Immersed Boundary Method for Fluid Flow around Moving Objects”, Comput. Fluids, 39, 1656–1671(2010b), DOI: 10.1016/j.compfluid.2010.06.002Suche in Google Scholar
Ilinca, F., Hétu, J.-F., “Three-dimensional Filling and Post-filling Simulation of Polymer Injection Moulding”, Int. Polym. Proc., 16, 291–301(2001)Suche in Google Scholar
Ilinca, F., Hétu, J.-F., “Three-dimensional Finite Element Solution of Gas-assisted Injection Moulding”, Int. J. Numer. Methods Eng., 53, 2002–2017(2003)Suche in Google Scholar
Ishikawa, T., et al., “3-D Numerical Simulations of Nonisothermal Flow in Co-rotating Twin Screw Extruders”, Polym. Eng. Sci., 40, 357–364(2000), DOI: 10.1002/pen.11169Suche in Google Scholar
Kajiwara, T., et al., “Numerical Study of Twin-screw Extruders by Three-dimensional Flow Analysis – Development of Analysis Technique and Evaluation of Mixing Performance for Full Flight Screws”, Polym. Eng. Sci., 36, 2142–2152(1996), DOI: 10.1002/pen.10611Suche in Google Scholar
Kalyon, D. M., Malik, M., “An Integrated Approach For Numerical Analysis of Coupled Flow and Heat Transfer in Co-rotating Twin Screw Extruders”, Int. Polym. Proc., 22, 293–302(2007)Suche in Google Scholar
Kim, S.-W., Turng, L.-S., “Developments of Three-dimensional Computer-aided Engineering Simulation for Injection Moulding”, Modell. Simul. Mater. Sci. Eng., 12, 151–173(2004), DOI: 10.1088/0965-0393/12/3/S07Suche in Google Scholar
Malik, M., Kalyon, D. M., “3D Finite Element Simulation of Processing of Generalized Newtonian Fluids in Counter-rotating and Tangential TSE and Die Combination”, Int. Polym. Proc., 20, 398–409(2005)Suche in Google Scholar
Margnat, F., Morinière, V., “Behaviour of an Immersed Boundary Method in Unsteady Flows over Sharp-edged Bodies”, Comput. Fluids, 38, 1065–1079(2009), DOI: 10.1016/j.compfluid.2008.09.013Suche in Google Scholar
Mittal, R., Iaccarino, G., “Immersed Boundary Methods”, Annu. Rev. Fluid Mech., 37, 239–261(2005), DOI: 10.1146/annurev.fluid.37.061903.175743Suche in Google Scholar
Ottino, J. M., et al., “A Framework for Description of Mechanical Mixing of Fluids”, AIChE J., 27, 565–577(1981), DOI: 10.1002/aic.690270406Suche in Google Scholar
Peskin, C. S., “Flow Patterns around Heart Valves: A Numerical Method”, J. Comput. Phys., 10, 252–271(1972), DOI: 10.1016/0021-9991(72)90065-4Suche in Google Scholar
Peskin, C. S., “Numerical Analysis of Blood flow in the Heart”, J. Comput. Phys., 25, 220–252(1977), DOI: 10.1016/0021-9991(77)90100-0Suche in Google Scholar
Speur, J. A., et al., “Flow Patterns in Calender Gap of a Counterrotating Twin Screw Extruder”, Adv. Polym. Tech., 7, 39–48(1987), DOI: 10.1002/adv.1987.060070105Suche in Google Scholar
Tezduyar, T. E., et al., “Incompressible Flow Using Stabilized Bilinear and Linear Equal-Order-Interpolation Velocity-Pressure Elements”, Research Report, Univ. of Minnesota/Supercomputer Inst. (1990)Suche in Google Scholar
Yao, C.-H., Manas-Zloczower, I., “Influence of Design on Dispersive Mixing Performance in an Axial Discharge Continuous Mixer – LCMAX 40”, Polym. Eng. Sci., 38, 936–946(1998), DOI: 10.1002/pen.10261Suche in Google Scholar
Zhang, X.-M., et al., “Numerical Simulation and Experimental Validation of Mixing Performance of Kneading Discs in a Twin Screw Extruder”, Polym. Eng. Sci., 49, 1772–1783(2009), DOI: 10.1002/pen.21404Suche in Google Scholar
© 2010, Carl Hanser Verlag, Munich
Artikel in diesem Heft
- Contents
- Contents
- Regular Contributed Articles
- The Filling Behavior of Reinforcing Glass Fiber in Micro Injection Molding
- Modeling and Characterization of the Relationship between Cell Size and Mechanical Behavior of Microcellular PP/Mica Composites
- Three-dimensional Finite Element Solution of the Flow in Single and Twin-Screw Extruders
- Entry Flow of Polyethylene Melts in Tapered Dies
- Rheological and Molecular Investigations of Polyethylene Degradation in a Batch Mixer
- RheoDSC Analysis of Hardening of Semi-Crystalline Polymers during Quiescent Isothermal Crystallization
- Rapid Communications
- Effect of Process Parameters on Mechanical Properties of Rice Husk Polypropylene Composites
- PPS-News
- PPS News
- Seikei Kakou Abstracts
- Seikei-Kakou Abstracts
Artikel in diesem Heft
- Contents
- Contents
- Regular Contributed Articles
- The Filling Behavior of Reinforcing Glass Fiber in Micro Injection Molding
- Modeling and Characterization of the Relationship between Cell Size and Mechanical Behavior of Microcellular PP/Mica Composites
- Three-dimensional Finite Element Solution of the Flow in Single and Twin-Screw Extruders
- Entry Flow of Polyethylene Melts in Tapered Dies
- Rheological and Molecular Investigations of Polyethylene Degradation in a Batch Mixer
- RheoDSC Analysis of Hardening of Semi-Crystalline Polymers during Quiescent Isothermal Crystallization
- Rapid Communications
- Effect of Process Parameters on Mechanical Properties of Rice Husk Polypropylene Composites
- PPS-News
- PPS News
- Seikei Kakou Abstracts
- Seikei-Kakou Abstracts