Three-dimensional simulation of vortex growth within entry flow of a polymer melt
-
Huan-Chang Tseng
Abstract
The corner vortex phenomenon occurring in entry flow is relevant to both polymer rheology and polymer processing. The famous viscoelastic constitutive equations in numerical computations of fluid mechanics have always had limited relevance at low apparent shear rates. However, three-dimensional (3D) simulations of viscoelastic fluids have been rarely found in advanced rheology. Recently, the GNF-X (eXtended Generalized Newtonian Fluid) constitutive equation of the weighted shear/extensional viscosity developed in advanced rheology of complex fluids has been incorporated into state-of-the-art predictive engineering tools. Thereby, 3D numerical simulations of entry flow were performed for a LDPE (low-density polyethylene) melt. As a validation, the predicted vortex streamlines are in good agreement with related experimental observations. More importantly, the simulation results show the vortex growth with respect to apparent shear rates, contraction ratios, and inlet angles. In particular for extensional viscosity, the stronger extension hardening characteristic yields a large vortex size.
-
Author contributions: The author has accepted responsibility for the entire content of this submitted manuscript and approved submission.
-
Research funding: None declared.
-
Conflict of interest statement: The author declares no conflicts of interest regarding this article.
References
Ballenger, T.F. and White, J.L. (1971). The development of the velocity field in polymer melts in a reservoir approaching a capillary die. J. Appl. Polym. Sci. 15: 1949–1962, https://doi.org/10.1002/app.1971.070150813.Search in Google Scholar
Bird, R.B., Armstrong, R.C., and Hassager, O. (1987). Dynamics of polymeric liquids: fluid mechanics, 2nd ed. Wiley-Interscience: New York.Search in Google Scholar
Chang, R.Y. and Yang, W.H. (2001). Numerical simulation of mold filling in injection molding using a three-dimensional finite volume approach. Int. J. Numer. Methods Fluids 37: 125–148, https://doi.org/10.1002/fld.166.Search in Google Scholar
Giesekus, H. (1982). A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility. J. Non-Newtonian Fluid Mech. 11: 69–109, https://doi.org/10.1016/0377-0257(82)85016-7.Search in Google Scholar
Meissner, J., Stephenson, S.E., Demarmels, A., and Portman, P. (1982). Multiaxial elongational flows of polymer melts – classification and experimental realization. J. Non-Newtonian Fluid Mech. 11: 221–237, https://doi.org/10.1016/0377-0257(82)80031-1.Search in Google Scholar
Mitsoulis, E. (2001). Numerical simulation of entry flow of the IUPAC-LDPE melt. J. Non-Newton. Fluid Mech. 97: 13–30, https://doi.org/10.1016/s0377-0257(00)00183-x.Search in Google Scholar
Mitsoulis, E., Luger, H.J., Miethlinger, J., and Friesenbichler, W. (2018). Flow behavior of a polypropylene melt in capillary dies. Int. Polym. Proc. 33: 642–651, https://doi.org/10.3139/217.3581.Search in Google Scholar
Morrison, F.A. (2001). Understanding rheology. Oxford University, New York.Search in Google Scholar
Park, J.M. (2020). Comment on “a revisitation of generalized Newtonian fluids”. J. Rheol. 64: 493–503, https://doi.org/10.1122/1.5139198.Search in Google Scholar
Petrie, C.J.S. (2006). Extensional viscosity: a critical discussion. J. Non-Newtonian Fluid Mech. 137: 15–23, https://doi.org/10.1016/j.jnnfm.2006.01.011.Search in Google Scholar
Phan-Thien, N. and Tanner, R.I. (1977). A new constitutive equation derived from network theory. J. Non-Newtonian Fluid Mech. 2: 353–365, https://doi.org/10.1016/0377-0257(77)80021-9.Search in Google Scholar
Sarkar, D. and Gupta, M. (2001). Further investigation of the effect of elongational viscosity on entrance flow. J. Reinf. Plast. Compos. 20: 1473–1484, https://doi.org/10.1177/073168401772679101.Search in Google Scholar
Schunk, P.R. and Scriven, L.E. (1990). Constitutive equation for modeling mixed extension and shear in polymer solution processing. J. Rheol. 34: 1085–1119, https://doi.org/10.1122/1.550075.Search in Google Scholar
Tseng, H.C. (2020). A revisitation of generalized Newtonian fluids. J. Rheol. 64: 493–504, https://doi.org/10.1122/1.5139198.Search in Google Scholar
White, J.L. and Kondo, A. (1977). Flow patterns in polyethylene and polystyrene melts during extrusion through a die entry region: measurement and interpretation. J. Non-Newtonian Fluid Mech. 3: 41–64, https://doi.org/10.1016/0377-0257(77)80011-6.Search in Google Scholar
White, J.L. and Metzner, A.B. (1963). Development of constitutive equations for polymeric melts and solutions. J. Appl. Polym. Sci. 7: 867–1889, https://doi.org/10.1002/app.1963.070070524.Search in Google Scholar
White, S.A. and Baird, D.G. (1988a). Flow visualization and birefringence studies on planar entry flow behavior of polymer melts. J. Non-Newtonian Fluid Mech. 29: 245–267, https://doi.org/10.1016/0377-0257(88)85056-0.Search in Google Scholar
White, S.A. and Baird, D.G. (1988b). Numerical simulation studies of the planar entry flow of polymer melts. J. Non-Newtonian Fluid Mech. 30: 47–71, https://doi.org/10.1016/0377-0257(88)80017-x.Search in Google Scholar
© 2022 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Research Articles
- In-situ leakage behavior of polymer-metal hybrids under mechanical load
- Multi-objective optimization of injection molding process parameters based on BO-RFR and NSGAⅡ methods
- Effect of processing conditions on the rheological and mechanical properties of composites based on a PBS matrix and enzymatically treated date palm fibers
- Effect of additives on degradation of poly vinyl alcohol (PVA) using ultrasound and microwave irradiation
- Visualization analysis of temperature distribution in the cavity of conventional PPS and high-thermal-conductivity PPS during the filling stage of injection molding
- Conveyor belt modelling in extrusion flow simulation
- Analysis and optimization of FFF process parameters to enhance the mechanical properties of 3D printed PLA products
- Investigation of the interface behavior of a viscous fluid under free surface shear flow using an eccentric transparent Couette cell
- Effect of stacking sequence on mechanical, water absorption, and biodegradable properties of novel hybrid composites for structural applications
- Comparison of fibre reorientation of short-and long-fibre reinforced polypropylene by injection molding with a rotating mold core
- The impact of accelerated aging on the mechanical and thermal properties and VOC emission of polypropylene composites reinforced with glass fibers
- Three-dimensional simulation of vortex growth within entry flow of a polymer melt
Articles in the same Issue
- Frontmatter
- Research Articles
- In-situ leakage behavior of polymer-metal hybrids under mechanical load
- Multi-objective optimization of injection molding process parameters based on BO-RFR and NSGAⅡ methods
- Effect of processing conditions on the rheological and mechanical properties of composites based on a PBS matrix and enzymatically treated date palm fibers
- Effect of additives on degradation of poly vinyl alcohol (PVA) using ultrasound and microwave irradiation
- Visualization analysis of temperature distribution in the cavity of conventional PPS and high-thermal-conductivity PPS during the filling stage of injection molding
- Conveyor belt modelling in extrusion flow simulation
- Analysis and optimization of FFF process parameters to enhance the mechanical properties of 3D printed PLA products
- Investigation of the interface behavior of a viscous fluid under free surface shear flow using an eccentric transparent Couette cell
- Effect of stacking sequence on mechanical, water absorption, and biodegradable properties of novel hybrid composites for structural applications
- Comparison of fibre reorientation of short-and long-fibre reinforced polypropylene by injection molding with a rotating mold core
- The impact of accelerated aging on the mechanical and thermal properties and VOC emission of polypropylene composites reinforced with glass fibers
- Three-dimensional simulation of vortex growth within entry flow of a polymer melt
