Transient 3D flow of polymer solutions: A Lagrangian computational method

Journal of Non-Newtonian Fluid Mechanics

Volumn 165, Issue 19-20, 2010, Pages 1241-1257

  Morrison, N F ^a   Rallison, J M ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

3D; Delaunay; Dilute polymer solution; FENE; Finite element; Lagrangian mesh; Particle migration; Sphere in cylinder

Indexed keywords

3D; DELAUNAY; DILUTE POLYMER SOLUTIONS; FENE; FINITE ELEMENT; LAGRANGIAN MESH; PARTICLE MIGRATION; SPHERE IN CYLINDER;

COMPUTATIONAL METHODS; CYLINDERS (SHAPES); LAGRANGE MULTIPLIERS; NON NEWTONIAN FLOW; NON NEWTONIAN LIQUIDS; PIPE; THREE DIMENSIONAL;

SPHERES;

EID: 84755161675     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2010.06.008     Document Type: Article

References (50)

1. Harlen O.G., Rallison J.M., Szabó P. A split Lagrangian-Eulerian method for simulating transient viscoelastic flows. J. Non-Newtonian Fluid Mech. 1995, 60(1):81-104.
2. Fortin M., Esselaoui D. A finite-element procedure for viscoelastic flows. Int. J. Numer. Methods Fluids 1987, 7(10):1035-1052.
3. Rasmussen H.K. Time-dependent finite-element method for the simulation of three-dimensional viscoelastic flow with integral models. J. Non-Newtonian Fluid Mech. 1999, 84(2-3):217-232.
4. Rasmussen H.K. Lagrangian viscoelastic flow computations using the Rivlin-Sawyers constitutive model. J. Non-Newtonian Fluid Mech. 2000, 92(2-3):227-243.
5. Rasmussen H.K. Lagrangian viscoelastic flow computations using a generalized molecular stress function model. J. Non-Newtonian Fluid Mech. 2002, 106(2-3):107-120.
6. Petera J. A new finite element scheme using the Lagrangian framework for simulation of viscoelastic fluid flows. J. Non-Newtonian Fluid Mech. 2002, 103(1):1-43.
7. Bhat P.P., Basaran O.A., Pasquali M. Dynamics of viscoelastic liquid filaments: low capillary number flows. J. Non-Newtonian Fluid Mech. 2008, 150(2-3):211-225.
8. Hirt C.W., Amsden A.A., Cook J.L. An arbitrary Lagrangian-Eulerian computing method for all flow speeds. J. Comput. Phys. 1974, 14(3):227-253.
9. Wapperom P., Keunings R., Legat V. The backward-tracking Lagrangian particle method for transient viscoelastic flows. J. Non-Newtonian Fluid Mech. 2000, 91(2-3):273-295.
10. Wapperom P., Keunings R. Simulation of linear polymer melts in transient complex flow. J. Non-Newtonian Fluid Mech. 2000, 95(1):67-83.
11. Rasmussen H.K., Hassager O. Simulation of transient viscoelastic flow. J. Non-Newtonian Fluid Mech. 1993, 46(2-3):289-305.
12. Edelsbrunner H. Triangulations and meshes in computational geometry. Acta Numer. 2000, 9:133-213.
13. Szabó P., Rallison J.M., Hinch E.J. Start-up of flow of a FENE-fluid through a 4:1:4 constriction in a tube. J. Non-Newtonian Fluid Mech. 1997, 72(1):73-86.
14. Everitt S.L., Harlen O.G., Wilson H.J. Bubble growth in a two-dimensional viscoelastic foam. J. Non-Newtonian Fluid Mech. 2006, 137(1):46-59.
15. Malidi A., Harlen O. A Lagrangian simulation method for suspensions in viscoelastic fluids. Proceedings of the European Conference on Computational Fluid Dynamics 2006.
16. Morrison N.F., Harlen O.G. Viscoelasticity in inkjet printing. Rheol. Acta 2010, 49(6):619-632.
17. Chilcott M.D., Rallison J.M. Creeping flow of dilute polymer solutions past cylinders and spheres. J. Non-Newtonian Fluid Mech. 1988, 29:381-432.
18. Liron N., Shahar R. Stokes flow due to a Stokeslet in a pipe. J. Fluid Mech. 1978, 186(4):727-744.
19. Rallison J.M., Hinch E.J. The flow of an Oldroyd fluid past a reentrant corner: the downstream boundary layer. J. Non-Newtonian Fluid Mech. 2004, 116(2-3):141-162.
20. Ladyzhenskaya O.A. The Mathematical Theory of Viscous Incompressible Flow 1969, Gordon and Breach, New York. 2nd edition.
21. Babuška I. Error-bounds for finite element method. Numer. Math. 1971, 16:322-333.
22. Brezzi F. On the existence, uniqueness and approximation of saddle point problems arising from Lagrangian multipliers. RAIRO Anal. Numér. 1974, 8(R-2):129-151.
23. Brezzi F., Pitkäranta J. On the stabilization of finite element approximations of the Stokes problem. Efficient Solutions of Elliptic Systems, Notes on Numerical Fluid Mechanics, vol. 10 1984, 11-19. Vieweg, Braunschweig. W. Hackbusch (Ed.).
24. Paige C.C., Saunders M.A. Solution of sparse indefinite systems of linear equations. SIAM J. Numer. Anal. 1975, 12:617-629.
25. Wathen A.J., Silvester D.J. Fast iterative solution of stabilized Stokes systems. Part I: using simple diagonal preconditioners. SIAM J. Numer. Anal. 1993, 30:630-649.
26. Courant R., Friedrichs K., Lewy H. Über die partiellen Differenzengleichungen der mathematischen Physik. Math. Ann. 1928, 100:32-74.
27. Rajan V.T. Optimality of the delaunay triangulation in Rd. Proceedings of the 7th Annual Symposium on Computational Geometry 1991, 357-363.
28. Labelle F., Shewchuk J.R. Isosurface stuffing: fast tetrahedral meshes with good dihedral angles. ACM Trans. Graph. (Proc. SIGGRAPH 2007) 2007, 26(3):57.
29. Křížek M. On the maximum angle condition for linear tetrahedral elements. SIAM J. Numer. Anal. 1992, 29(2):513-520.
30. Acosta G., Durán R.G. The maximum angle condition for mixed and nonconforming elements: application to the Stokes equations. SIAM J. Numer. Anal. 1999, 37(1):18-36.
31. Joe B. Construction of three-dimensional improved-quality triangulations using local transformations. SIAM J. Sci. Comput. 1995, 16:1292-1307.
32. Tözeren H. Drag on eccentrically positioned spheres translating and rotating in tubes. J. Fluid Mech. 1983, 129:77-90.
33. Harlen O.G. High-Deborah-number flow of a dilute polymer solution past a sphere falling along the axis of a cylindrical tube. J. Non-Newtonian Fluid Mech. 1990, 37(2-3):157-173.
34. Higdon J.J.L., Muldowney G.P. Resistance functions for spherical particles, droplets and bubbles in cylindrical tubes. J. Fluid Mech. 1995, 298:193-210.
35. Happel J., Brenner H. Low Reynolds Number Hydrodynamics 1965, Prentice-Hall, New Jersey.
36. Satrape J.V., Crochet M.J. Numerical simulation of the motion of a sphere in a Boger fluid. J. Non-Newtonian Fluid Mech. 1994, 55(1):91-111.
37. Segré G., Silberberg A. Radial particle displacements in Poiseuille flow of suspensions. Nature 1961, 189:209-210.
38. Segré G., Silberberg A. Behaviour of macroscopic rigid spheres in Poiseuille flow. Part 2. Experimental results and interpretation. J. Fluid Mech. 1962, 14:136-157.
39. Yang B.H., Wang J., Joseph D.D., Hu H.H., Pan T.-W., Głowiński R. Migration of a sphere in tube flow. J. Fluid Mech. 2005, 540:109-131.
40. Becker L.E., McKinley G.H., Rasmussen H.K., Hassager O. The unsteady motion of a sphere in a viscoelastic fluid. J. Rheol. 1994, 38(2):377-403.
41. Tanner R.I. Observations on the use of Oldroyd-type equations of state for viscoelastic liquids. Chem. Eng. Sci. 1964, 19:349-365.
42. Dhahir S.A., Walters K. On non-Newtonian flow past a cylinder in a confined flow. J. Rheol. 1989, 33:781-804.
43. Carew E.O.A., Townsend P. Slow visco-elastic flow past a cylinder in a rectangular channel. Rheol. Acta 1991, 30:58-64.
44. Dagan Z., Weinbaum S., Pfeffer R. An infinite-series solution for the creeping motion through an orifice of finite length. J. Fluid Mech. 1982, 115:505-523.
45. Rothstein J.P., McKinley G.H. Extensional flow of a polystyrene Boger fluid through a 4:1:4 axisymmetric contraction/expansion. J. Non-Newtonian Fluid Mech. 1999, 86(1-2):61-88.
46. Rothstein J.P., McKinley G.H. The axisymmetric contraction-expansion: the role of extensional rheology on vortex growth dynamics and the enhanced pressure drop. J. Non-Newtonian Fluid Mech. 2001, 98(1):33-63.
47. Binding D.M., Phillips P.M., Phillips T.N. Contraction/expansion flows: the pressure drop and related issues. J. Non-Newtonian Fluid Mech. 2006, 137:31-38.
48. Kolte M.I., Rasmussen H.K., Hassager O. Transient filament stretching rheometer II: numerical simulation. Rheol. Acta 1997, 36(3):285-302.
49. Étienne J., Hinch E.J., Li J. A Lagrangian-Eulerian approach for the numerical simulation of free-surface flow of a viscoelastic material. J. Non-Newtonian Fluid Mech. 2006, 136(2-3):157-166.
50. Klingner B.M., Shewchuk J.R. Aggressive tetrahedral mesh improvement. Proceedings of the 16th International Meshing Roundtable 2007, 3-23.