Lagrangian finite element method for 3D time-dependent non-isothermal flow of K-BKZ fluids

Journal of Non-Newtonian Fluid Mechanics

Volumn 162, Issue 1-3, 2009, Pages 45-53

  Marín, Jose Manuel Román ^a   Rasmussen, Henrik Koblitz ^a  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

BKZ; Finite element; Lagrangian; Non isothermal; Pseudo time; Thermorheology; Viscoelastic

Indexed keywords

BKZ; FINITE ELEMENT; LAGRANGIAN; NON-ISOTHERMAL; PSEUDO TIME; THERMORHEOLOGY; VISCOELASTIC;

FLOW OF FLUIDS; FLOW SIMULATION; FLUIDS; INTERPOLATION; LAGRANGE MULTIPLIERS; THREE DIMENSIONAL;

FINITE ELEMENT METHOD;

EID: 69249229466     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2009.05.008     Document Type: Article

References (82)

1. Crochet M.J., and Naghdi P.M. A class of non-isothermal viscoelastic fluids. International Journal of Engineering Science 10 (1972) 755-800
2. Fang J., Kröger M., and Öttinger H.C. A thermodynamically admissible reptation model for fast flows of entangled polymers. II. Model predictions for shear and extensional flows. Journal of Rheology 44 (2000) 1293-1317
3. Öttinger H.C. A thermodynamically admissible reptation model for fast flows of entangled polymers. Journal of Rheology 43 (1999) 1461-1493
4. Hua C.C., and Schieber J.D. Segment connectivity, chainlength breathing, segmental stretch, and constraint release in reptation models. I. Theory and single-step strain predictions. Journal of Chemical Physics 109 (1998) 10018-10027
5. Hua C.C., Schieber J.D., and Venerus D.C. Segment connectivity, chainlength breathing, segmental stretch, and constraint release in reptation models. II. Double-step strain predictions. Journal of Chemical Physics 109 (1998) 10028-10032
6. Masubuchi Y., Ianniruberto G., Greco F., and Marrucci G. Entanglement molecular weight and frequency response of sliplink networks. Journal of Chemical Physics 109 (2003) 6925-6930
7. McLeish T.C.B., and Larson R.G. Molecular constitutive equations for a class of branched polymers: the pom-pom polymer. Journal of Rheology 42 (1998) 81-110
8. Wagner M.H., and Schaeffer J. Assessment of nonlinear strain measures for extensional and shearing flows of polymer melts. Rheologica Acta 33 (1994) 506-516
9. Wagner M.H., Kheirandish S., and Hassager O. Quantitative prediction of the transient and steady-state elongational viscosity of nearly monodisperse polystyrene melts. Journal of Rheology 49 (2005) 1317-1327
10. McLeish T.C.B., Allgaier J., Bick D.K., Bishko G., Biswas P., Blackwell R., Blottiere B., Clarke N., Gibbs B., Groves D.J., Heenan R.K., Hakiki A., Johnson J.M., Kant R., Read D.J., and Young R.N. Dynamics of entangled H-polymers: theory, rheology, and neutron-scattering. Macromolecules 32 (1999) 6734-6758
11. Archer L.A., and Juliani. Linear and nonlinear viscoelasticity of entangled multiarm (pom-pom) polymer liquids. Macromolecules 37 (2004) 1076-1088
12. Nielsen J.K., Rasmussen H.K., Denberg M., Almdal K., and Hassager O. Nonlinear branch-point dynamics of multiarm polystyrene. Macromolecules 39 (2006) 8844-8853
13. Rasmussen H.K., Skov A.L., Nielsen J.K., and Laillé P. Elongational dynamics of multiarm polystyrene. Journal of Rheology 53 (2009) 401-415
14. Rasmussen H.K., Laillé P., and Yu K. Large amplitude oscillatory elongation flow. Rheologica Acta 47 (2008) 97-103
15. Wagner M.H., Rolón-Garrido V.H., Nielsen J.K., Rasmussen H.K., and Hassager O. A constitutive analysis of transient and steady-state elongational viscosities of bidisperse polystyrene blends. Journal of Rheology 52 (2008) 67-86
16. Nielsen J.K., Rasmussen H.K., Hassager O., and McKinley G.H. Elongational viscosity of monodisperse and bidisperse polystyrene melts. Journal of Rheology 50 (2006) 453-476
17. Nielsen J.K., and Rasmussen H.K. Reversed extension flow. Journal of Non-Newtonian Fluid Mechanics 155 (2008) 15-19
18. A. Kaye, College of Aeronautics, Cranheld, Note no 134, 1962.
19. Bernstein B., Kearsley E.A., and Zapas L.J. Study of stress relaxation with finite strain. Transactions of the Society of Rheology 7 (1963) 391-410
20. Doi M., and Edwards S.F. Dynamics of concentrated polymer systems. III. The constitutive equation. Journal of the Chemical Society-Faraday Transactions II 74 (1978) 1818-1832
21. Doi M., and Edwards S.F. Dynamics of concentrated polymer systems. IV. Rheological properties. Journal of the Chemical Society-Faraday Transactions II 75 (1979) 38-54
22. Feigl K., and Öttinger H.C. The equivalence of the class of Rivlin-Sawyers equations and a class of stochastic models for polymer stress. Journal of Mathematical Physics 42 (2001) 796-817
23. Schieber J.D., Nair D.M., and Kitkrailard T. Comprehensive comparisons with nonlinear flow data of a consistently unconstrained Brownian slip-link model. Journal of Rheology 51 (2007) 1111-1141
24. Luo X.-L., and Tanner R.I. A streamline element scheme for solving viscoelastic flowproblems. Part II. Integral constitutive models. Journal of Non-Newtonian Fluid Mechanics 22 (1986) 61-89
25. Dupont S., and Crochet M.J. The vortex growth of a K.B.K.Z. fluid in an abrupt contraction. Journal of Non-Newtonian Fluid Mechanics 29 (1988) 81-91
26. Luo X.-L., and Mitsoulis E. A numerical study of the effect of elongational viscosity on vortex growth in contraction flows of polyethylene melts. Journal of Rheology 34 (1990) 309-342
27. Bernstein B., Feigl K.A., and Olsen E.T. Steady flows of viscoelastic fluids in axisymmetric abrupt contraction geometry: a comparison of numerical results. Journal of Rheology 38 (1994) 53-71
28. Feigl K.A., and Öttinger H.C. The flow of a LDPE melt through an axisymmetric contraction: a numerical study and comparison to experimental results. Journal of Rheology 38 (1994) 847-874
29. Barakos G., and Mitsoulis E. Numerical simulation of extrusion through orifice dies and prediction of Bagley correction for an IUPAC-LDPE melt. Journal of Rheology 39 (1995) 193-209
30. Feigl K.A., and Öttinger H.C. A numerical study of the flow of a low-density-polyethylene melt in a planar contraction and comparison to experiments. Journal of Rheology 40 (1996) 21-35
31. Sun J., Phan-Thien N., and Tanner R.I. Extrudate swell through an orifice die. Rheologica Acta 35 (1996) 1-12
32. Olley P., and Wagner M.H. A modification of the convective constraint release mechanism in the molecular stress function model giving enhanced vortex growth. Journal of Non-Newtonian Fluid Mechanics 135 (2006) 68-81
33. Luo X.L., and Tanner R.I. Finite element simulation of long and short circular die extrusion experiments using integral models. International Journal for Numerical Methods in Engineering 25 (1988) 9-22
34. Barakos G., and Mitsoulis E. A convergence study for the numerical simulation of the IUPAC-LDPE extrusion experiments. Journal of Non-Newtonian Fluid Mechanics 58 (1995) 315-329
35. Wagner M.H., Ehrecke P., Hachmann P., and Meissner J. A constitutive analysis of uniaxial, equibiaxial and planar extension of a commercial linear high-density polyethylene melt. Journal of Rheology 42 (1998) 621-638
36. Bach A., Rasmussen H.K., Longin P.-Y., and Hassager O. Growth of non-axisymmetric disturbances of the free surface in the filament stretching rheometer: experiments and simulation. Journal of Non-Newtonian Fluid Mechanics 108 (2002) 163-186
37. Eriksson T., and Rasmussen H.K. The effects of polymer melt rheology on the replication of surface microstructures in isothermal moulding. Journal of Non-Newtonian Fluid Mechanics 127 (2005) 191-200
38. Rasmussen H.K., and Bach A. On the bursting of linear polymer melts in inflation processes. Rheologica Acta 44 (2005) 435-445
39. Rasmussen H.K., and Yu K. On the burst of branched polymer melts during inflation. Rheologica Acta 47 (2008) 149-157
40. Rasmussen H.K., and Eriksson T. Gas displacement of polymer melts in a cylinder: experiments and viscoelastic simulations. Journal of Non-Newtonian Fluid Mechanics 143 (2007) 1-9
41. Wagner M.H., Bastian H., Hachmann P., Münstedt H., Meissner J., Kurzbeck S., and Langouche F. The strain hardening behaviour of linear and long-chain-branched polyolefin melts in extensional flows. Rheologica Acta 39 (2000) 97-109
42. Morland L.W., and Lee E.H. Stress analysis for linear viscoelastic materials with temperature variation. Transactions of the Society of Rheology 4 (1960) 233-263
43. McGuirt C.W., and Lianis G. Experimental investigation of non-linear, non-isothermal viscoelasticity. International Journal of Engineering Science 7 (1969) 579-599
44. Matsui M., and Bogue D.C. Studies in non isothermal rheology. Transactions of the Society of Rheology 21 (1977) 133-148
45. Matsumoto T., and Bogue D.C. Non-isothermal rheological response during elongational flow. Transactions of the Society of Rheology 21 (1977) 453-468
46. Barakos G., and Mitsoulis E. Non-isothermal viscoelastic simulations of extrusion through dies and prediction of the bending phenomenon. Journal of Non-Newtonian Fluid Mechanics 62 (1996) 55-79
47. Luo X.-L., and Tanner R.I. A pseudo-time integral method for non-isothermal viscoelastic flows and its application to extrusion simulation. Rheologica Acta 26 (1987) 499-507
48. Goublomme A., and Crochet M.J. Numerical prediction of extrudate swell of a high-density polyethylene: further results. Journal of Non-Newtonian Fluid Mechanics 41 (1993) 281-287
49. Hassager O., and Bisgaard C. A finite-element code for initial-value problems with a Maxwell model. Rheologica Acta 21 (1982) 534-536
50. Hassager O., and Bisgaard C. A Lagrangian finite-element method for the simulation of flow of non-Newtonian liquids. Journal of Non-Newtonian Fluid Mechanics 12 (1983) 153-164
51. Peters E.A.J.F., Hulsen M.A., and van den Brule B.H.A.A. Instationary Eulerian viscoelastic flow simulations using time separable Rivlin-Sawyers constitutive equations. Journal of Non-Newtonian Fluid Mechanics 89 (2000) 209-228
52. Hulsen M.A., Peters E.A.J.F., and van den Brule B.H.A.A. A new approach to the deformation fields method for solving complex flows using integral constitutive equations. Journal of Non-Newtonian Fluid Mechanics 98 (2001) 201-211
53. Wapperom P., and Keunings R. Simulation of linear polymer melts in transient complex flow. Journal of Non-Newtonian Fluid Mechanics 95 (2001) 67-83
54. Wapperom P., and Keunings R. Numerical simulation of branched polymer melts in transient complex flow using pom-pom models. Journal of Non-Newtonian Fluid Mechanics 97 (2001) 267-281
55. Egholm R.D., Christensen S.F., and Szabo P. Stress-strain behaviour in uniaxial compression of polymer gel beads. Journal of Applied Polymer Science 102 (2006) 3037-3047
56. Tome M.F., de Araujo M.S.B., Alves M.A., and Pinho F.T. Numerical simulation of viscoelastic flows using integral constitutive equations: a finite difference approach. Journal of Computational Physics 227 (2008) 4207-4243
57. Rasmussen H.K. Time-dependent finite-element method for the simulation of three-dimensional viscoelastic flow with integral models. Journal of Non-Newtonian Fluid Mechanics 84 (1999) 217-232
58. Rasmussen H.K. Lagrangian viscoelastic flow computations using Rivlin-Sawyers constitutive model. Journal of Non-Newtonian Fluid Mechanics 92 (2000) 227-243
59. Rasmussen H.K. Lagrangian viscoelastic flow computations using a generalized molecular stress function model. Journal of Non-Newtonian Fluid Mechanics 106 (2002) 107-120
60. Rasmussen H.K., and Hassager O. Simulation of transient viscoelastic flow. Journal of Non-Newtonian Fluid Mechanics 46 (1993) 289-305
61. Rasmussen H.K., and Hassager O. Simulation of transient viscoelastic flow with 2nd-order time integration. Journal of Non-Newtonian Fluid Mechanics 56 (1995) 65-84
62. Rasmussen H.K., and Hassager O. On the sedimentation velocity of spheres in polymeric liquid. Chemical Engineering and Science 51 (1996) 1431-1440
63. Mu Y., and Zhao G.Q. Numerical study of nonisothermal polymer extrusion flow with a differential viscoelastic model. Polymer Engineering and Science 140 (2008) 316-328
64. Khalifeh A., and Clermont J.R. Numerical simulations of non-isothermal three-dimensional flows in an extruder by a finite-volume method. Journal of Non-Newtonian Fluid Mechanics 126 (2005) 7-22
65. Peters G.W.M., and Baaijens F.P.T. Modelling of non-isothermal viscoelastic flows. Journal of Non-Newtonian Fluid Mechanics 68 (1997) 205-224
66. Wapperon P., Hulsen M.A., and van der Zanden J.P. A numerical method for steady and non isothermal viscoelastic fluid flow for high Deborah and Péclet numbers. Rheologica Acta 37 (1998) 73-88
67. Sugeng F., Phan-Thien N., and Tanner R.I. A study of non-isothermal extrudate swell by a mixed boundary element and finite element method. Journal of Rheology 31 (1987) 37-58
68. Kunisch K., and Marduel X. Optimal control of non-isotherm viscoelastic fluid flows. Journal of Non-Newtonian Fluid Mechanics 88 (2000) 261-301
69. Nobrega J.M., Pinho F.T., Oliveira P.J., and Carneiro O.S. Accounting for temperature-dependent properties in viscoelastic duct flows. International Journal of Heat and Mass Transfer 47 (2004) 1141-1158
70. Wachs A., and Clermont J.-R. Non-isothermal viscoelastic flow computations in an axisymmetric contraction at high Weissenberg numbers by a finite volume method. Journal of Non-Newtonian Fluid Mechanics 95 (2000) 147-184
71. Marín J.M.R., and Rasmussen H.K. Lagrangian finite-element method for the simulation of K-BKZ fluids with third order accuracy. Journal of Non-Newtonian Fluid Mechanics 156 (2009) 177-188
72. Keunings R. Finite element methods for integral viscoelastic fluids. In: Binding D.M., and Walters K. (Eds). Rheology Reviews 2003 (2003), British Society of Rheology 167-195
73. Lamb H. Hydrodynamics. 6th edition (1932), Cambridge University Press, Cambridge
74. Bird R.B., Armstrong R.C., and Hassager O. Dynamics of Polymeric Liquids, vol. I. 2nd edition (1987), Wiley, New York
75. Wapperom P., and Hassager O. Numerical simulation of wire-coating: the influence of temperature boundary conditions. Polymer Engineering and Science 39 (1999) 2007-2018
76. Zienkiewicz O., and Morgan K. Finite Elements and Approximation (1983), Wiley/Interscience, New York
77. Keast P. Moderate degree tetrahedral quadrature formulas. Computer Methods in Applied Mechanics and Engineering 55 (1986) 339-348
78. Schenk O., and Gärtner K. Solving unsymmetric sparse systems of linear equations with PARDISO. Journal of Future Generation Computer Systems 20 (2004) 475-487
79. Schenk O., and Gärtner K. On fast factorization pivoting methods for symmetric indefinite systems. Electronic Transaction on Numerical Analysis 23 (2006) 158-179
80. Hassager O. Variational principle for the K-BKZ rheological equation of state with potential function. Journal of Non-Newtonian Fluid Mechanics 9 (1981) 321-328
81. Baumgaertel M., Schausberger C., and Winter H.H. The relaxation of polymers with linear flexible chains of uniform length. Rheologica Acta 29 (1990) 400-408
82. Currie P.K. Constitutive equations for polymer melts predicted by the Doi-Edwards and Curtiss-Bird kinetic theory models. Journal of Non-Newtonian Fluid Mechanics 11 (1982) 53-68