Numerical solution of the upper-convected maxwell model for three-dimensional free surface flows

Communications in Computational Physics

Volumn 6, Issue 2, 2009, Pages 367-395

  Tomé, Murilo F ^a   Silva, Renato A P ^a   Oishi, Cassio M ^a   McKee, Sean ^b  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Finite difference; Free surface; Implicit techniques; Marker and Cell; Upper convected maxwell; Viscoelastic flow

Indexed keywords

EID: 67650989142     PISSN: 18152406     EISSN: None     Source Type: Journal    
DOI: 10.4208/cicp.2009.v6.p367     Document Type: Article

References (56)

1. J. Yoo and Y. Na, A numerical study of the planar contraction flow of a viscoelastic fluid using the simpler algorithm, Journal of Non-Newtonian Fluid Mechanics, Vol. 30, pp. 89-106 (1991).
2. E. Brasseur, M. Fyrillas, G. Georgiou and M. Crochet, The time-dependent extrudate-swell problem of an Oldroyd-B fluid with slip along the wall, Journal of Rheology, Vol. 42, pp. 549-566 (1998).
3. J. Étienne, E.J. Hinch, J. Li, A Lagrangian-Eulerian approach for the numerical simulation of free-surface flow of a viscoelastic material, Journal of Non-Newtonian Fluid Mechanics, Vol. 136, pp. 157-166 (2006).
4. J. Fang, R. G, Owens, L. Tacher, A. Parriaux, A numerical study of the SPH method for simulating transient viscoelastic free surface flows, Journal of Non-Newtonian Fluid Mechanics, Vol. 139, pp. 68-84 (2006).
5. S. Kihara, T. Gouda, K. Matsunaga, K. Funatsu, Numerical simulation of three-dimensional viscoelastic flow within dies, Polymer Engineering & Science, Vol. 39, pp. 152-163 (2004).
6. J. Ramirez, M. Laso, Micro-macro simulations of three-dimensional plane contraction flow, Modelling and Simulation in Materials Science and Engineering, Vol. 12, pp. 1293-1306 (2004).
7. T. Yamamoto, M. Ishiyama, M. Nakajima, K, Nakamura, N. Mori, Three-dimensional viscoelastic flows through a rectangular channel with a cavity, Journal of Non-Newtonian Fluid Mechanics, Vol. 114, pp. 13-31 (2003).
8. N. Fierier, M. O. Deville, Simulations of time-dependent flows of viscoleastic fluids with spectral element methods, Journal of Scientific Computing, Vol 17, pp. 649-657 (2002)
9. S. C. Xue, R. I. Tanner, N. Phan-Thien, Three-dimensional numerical simulation of viscoelastic flows - predictability and accuracy, Computer Methods in Applied Mechanics and Engineering, 180 305-331 (1999).
10. G. Mompean and M. Deville, Unsteady finite volume of Oldroyd-b fluid through a three-dimensional planar contraction, Journal of Non-Newtonian Fluid Mechanics, Vol. 72, pp. 253-279 (1997).
11. H. K. Rasmussen, O. Hassager, Three-dimensional simulations of viscoelastic instability in polymeric filaments, Journal of Non-Newtonian Fluid Mechanics, Vol. 82, pp. 189-202 (1999).
12. J. M. Kim, K. H. Ahn, S. J. Lee, S. J. Lee, Numerical simulation of moving free surface problems in polymer processing using volume-of-fluid method, Polymer Engineering and Science, Vol. 41, pp. 856-866 (2001).
13. A. Bonito, M. Picasso, M. Laso, Numerical simulation of 3d viscoelastic flows with free surface, Journal of Computational Physics, Vol. 215, pp. 691-716 (2006).
14. F. H. Harlow and J. E. Welch, Numerical calculation of time-dependent viscous imcompress-ible flow of fluid with free surface, Physics of Fluids, Vol. 8, pp. 2182-2189 (1965).
15. M. F. Tome and S. McKee, GENSMAC: a computational marker-and-cell method for free surface flows, Journal of Computational Physics, Vol. 110, pp. 171-186 (1994).
16. M. F. Tomé, B. R. Duffy and S. McKee, A numerical technique for solving unsteady Non-Newtonian free surface flows, Journal of Non-Newtonian Fluid Mechanics Vol. 62, pp. 9-34 (1996).
17. M. F. Tomé, A. Castelo, J. A. Cuminato, N. Mangiavacchi and S. McKee, GENSMAC3D: A numerical method for solving three-dimensional free surface flows, International Journal for Numerical Methods in Fluids, Vol. 37, pp. 747-796 (2001).
18. A. Castelo, M. F. Tomé, J. A. Cuminato, C. N. L. César and S. McKee, Freeflow: an integrated simulation system for three-dimensional free surface flows, Computing and Visualization in Science, Vol. 2, pp. 199-210 (2000).
19. N. M. Ribe, A general theory of the dynamics of thin viscous sheets, Journal of Fluid Mechanics, Vol. 457, pp. 255-283 (2002).
20. N. M. Ribe, Periodic folding of viscous jets, Physical Review E, Vol. 68, Art. No. 036305 Part 2 (2003).
21. N. M. Ribe, Coiling of viscous jets, Proceedings of the Royal Society of London, Series A -Mathematical Physical and Engineering Sciences, Vol. 460, pp. 3223-3239 (2004).
22. M. F. Tomé, L. Grossi, A. Castelo, J. A. Cuminato, N. Mangiavacchi, V. G. Ferreira, F. S. Sousa and S. McKee, A numerical method for solving three-dimensional generalized Newtonian free surface flows, Journal of Non-Newtonian Fluid Mechanics, Vol. 123, pp. 85-103 (2004).
23. M. Nobrega, O. S. Carneiro, F. T. Pinho, G. S. Paulo, M. F. Tomé, A. Castelo, J. A. Cuminato, The phenomenon of jet buckling: experimental results and numerical predictions, Proceedings of the Polymer Processing Society, 23rd Annual Meeting (2007), Salvador, Brasil.
24. G. S. Paulo, M. F. Tomé and S. McKee, A marker-and-cell approach to viscoelastic free surface flows using the PTT model, Journal of Non-Newtonian Fluid Mechanics, Vol. 147, pp. 149-174 (2007).
25. M. F. Tomé, A. Castelo, V. G. Ferreira and S. McKee, A finite difference technique for solving the Oldroyd-B model for 3D-unsteady free surface flows, Journal of Non-Newtonian Fluid Mechanics, Vol. 154, pp. 179-206 (2008).
26. D. Rajagopalan, R. C. Armstrong and R. A. Brown, Finite element methods for calculation of steady, viscoelastic flow using constitutive equations with a Newtonian viscosity, Journal of Non-Newtonian Fluid Mechanics, Vol. 36, pp. 159-192 (1990).
27. M. Crochet, A. R. Davis and K. Walters, Numerical simulation of Non-Newtonian flow, Elsevier (1984).
28. G. K. Batchelor, An Introduction to Fluid Dynamics, Cambridge University Press (1967).
29. H. Miyata and S. Nishimura, Finite-diference simulation of nonlinear waves generated by ships of arbitrary three-dimensional configuration, Journal of Computational Physics, Vol. 60, pp. 391-436 (1985).
30. C. Lemos, Higher-order schemes for free surface flows with arbitrary configurations, International Journal for Numerical Methods in Fluids, Vol. 23, pp. 545-566 (1996).
31. B. D. Nichols, C. W. Hirt and R. S. Hotchkiss, SOLA-VOF: A solution algorithm for transient fluid flow with multiple free boundaries, Los Alamos Scientific Laboratory, Technical Report LA-8355 (1988).
32. V. Armenio, An improved MAC method (SIMAC) for unsteady high-Reynolds free surface flows, International Journal for Numerical Methods in Fluids, Vol. 24, pp. 185-214 (1997).
33. A. J. Chorin, Numerical solution of the Navier-Stokes equations, Journal of Computational Physics, Vol. 2, pp. 745-762 (1968).
34. J. B. Bell, P. Colella and H. M. Glaz, A second-order projection method for the incompressible Navier-Stokes equations, Journal of Computational Physics, Vol. 85, pp. 257-283 (1989).
35. D. L. Brown, R. Cortez, and M. L. Minion, Accurate projection methods for the incompressible Navier-Stokes equations, Journal of Computational Physics, Vol. 168, pp. 464-499 (2001).
36. H. Johnston and J. G. Liu, Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term, Journal of Computational Physics, Vol. 199, pp. 221-259 (2004).
37. W. Kress and P. Lotstedt, Time step restrictions using semi-explicit methods for incompressible Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering, Vol. 195, pp. 4433-4447 (2006).
38. C. M. Oishi, M. F. Tome, J. A. Cuminato, S. McKee, An implicit technique for solving 3D low Reynolds number moving free surface flows, Journal of Computational Physics, Vol. 227, pp. 7446-7468 (2008).
39. F. S. de Sousa, N. Mangiavacchi, L. G. Nonato, A. Castelo, M. F. Tome, V. G. Ferreira, J. A. Cuminato and S. McKee, A front-tracking/front-capturing method for the simulation of 3D multi-fluid flows with free surfaces, Journal of Computational Physics, Vol. 198, pp. 469-499 (2004).
40. C. M. Oishi, J. A. Cuminato, V. G. Ferreira, M. F. Tomé, A. Castelo, N. Mangiavacchi and S. McKee, A stable semi-implicit method for free surface flows, Transactions of ASME Journal of Applied Mechanics, Vol. 73, pp. 940-947 (2006).
41. M. Alves, P. Oliveira, and F. T. Pinho, A convergent and universally bounded interpolation scheme for the treatment of advection, International Journal for Numerical Methods in Fluids, Vol. 41, pp. 47-75 (2003).
42. V. G. Ferreira, A. C. Brandi, F. A. Kurokawa, P. Seleghim, A. Castelo and J. A. Cuminato, Incompressible turbulent flow simulation using k-e model and upwind schemes, Mathematical Problems in Engineering, Vol. 2007, pp 1-26 (2007).
43. M. F. Tomé, N. Mangiavacchi, J. A. Cuminato, A. Castelo and S. McKee, A numerical technique for solving unsteady viscoelastic free surface flows, Journal of Non-Newtonian Fluid Mechanics Vol. 106, pp. 61-106 (2002).
44. R. A. P. Silva, Solução Numérica do Modelo de Maxwell para Escoamentos Tridimensionals com Superfícies Livres, MSc Thesis, ICMC-USP, (2007).
45. V. G. Ferreira, M. F. Tomé N. Mangiavacchi, A. Castelo, J. A. Cuminato, A. O. Fortuna and S. McKee, High-order upwinding and the hydraulic jump, International Journal for Numerical Methods in Fluids, Vol. 39, pp. 549-583 (2002).
46. J. O. Cruickshank and B. R. Munson, Viscous fluid buckling of plane and axisymmetric jets, Journal of Fluid Mechanics Vol. 113, pp. 221-239 (1981).
47. R. I. Tanner, A theory of die-swell, J. Polymer Science Vol. 8, pp. 2067-2078 (1970).
48. M. R Tomé, L. Grossi, A. Castelo, J. A. Cuminato, S. McKee and K. Walters, Die-swell, splashing drop and a numerical technique for solving the Oldroyd-B model for axisymmetric free surface flows, Journal of Non-Newtonian Fluid Mechanics, Vol. 141, pp. 148-166 (2007).
49. A. L. N. Silva, M. C. G. Rocha, R M. B. Coutinho, Study of rheological behavior of elastomer/polypropylene blends, Polymer Testing, Vol. 21, pp. 289-293 (2002).
50. J-Z. Liang, Estimation of melt shear modulus from extrudate swell ratio and exit-pressure drop data, Journal of Thermoplastic Composite Materials, Vol. 17, pp. 545-556 (2004).
51. Y. Liang, A. Ozetkin, and S. Neti, Dynamics of viscoelastic jets of polymeric liquid extrudate, Journal of Non-Newtonian Fluid Mechanics, Vol. 81, pp. 105-132 (1999).
52. N. Sombatsompop, N.-T. Intawong, A comparative study on extrudate swell ratio of polystyrene in a capillary rheometer and a single screw extruder, Polymer Testing, Vol 24, pp. 948-952 (2005).
53. S. X. Huang, C. J. Lu, Stress relaxation characteristics and extrudate swell of the IUPAC-LDPE melt, Journal of Non-Newtonian Fluid Mechanics, Vol. 136, pp. 147-156 (2006).
54. R. P. G. Rutgers, M. R. Mackley, The effect of channel geometry and wall boundary conditions on the formation of extrusion surface instabilities for LLDPE, Journal of Non-Newtonian Fluid Mechanics, Vol. 98, pp. 185-199 (2001).
55. E. Mitsoulis, Three-dimensional non-Newtonian computations of extrudate swell with the finite element method, Computer Methods in Applied Mechanics and Engineering, Vol. 180, pp. 333-344 (1999).
56. R. I. Tanner, A theory of die-swell revisited, Journal of Non-Newtonian Fluid Mechanics, Vol. 129, pp. 85-87 (2005).