Abstract
The present study is concerned with finite element simulation of the planar entry flow of a viscoelastic plastic medium exhibiting yield stress. The numerical scheme is based on the Galerkin formulation. Flow experiments are carried out on a carbon black filled rubber compound. Steady-state pressure drops are measured on two sets of contraction or expansion dies having different lengths and a constant contraction or expansion ratio of 4:1 with entrance angles of 90, 45 and 15 degrees. The predicted and measured pressure drops are compared. The predicted results indicate that expansion flow has always a higher pressure drop than contraction flow. This prediction is in agreement with experimental data only at low flow rates, but not at high flow rates. The latter disagreement is possibly an indication that the assumption of fully-developed flow in the upstream and downstream regions is not realistic at high flow rates, even for the large length-to-thickness ratio channels employed. The evolution of the velocity, shear stress, and normal stress fields in the contraction or expansion flow and the location of pseudo-yield surfaces are also calculated.
Similar content being viewed by others
References
Bercovier M, Engleman M (1980) A finite element method for incompressible non-Newtonian flow. J Comp Phys 36:313–326
Beris AN, Tsamopoulos JA, Armstrong RC, Brown RA (1985) Creeping motion of a sphere through a Bingham plastic. J Fluid Mech 158:219–244
Beverly CR, Tanner RI (1989) Numerical analysis of extrudate swell in viscoelastic materials with yield stress. J Rheol 33:989–1009
Boger DV (1987) Viscoelastic flows through contractions. Annu Rev Fluid Mech 19:157–182
Crochet MJ (1989) Numerical simulation of viscoelastic flow: a review. Rubber Chem Tech 62:426–455
Crochet MJ, Bezy MJ (1979) Numerical solution for the flow of viscoelastic fluids. J Non-Newt Fluid Mech 5:201–218
Crochet MJ, Legat V (1992) The consistent streamline-upwind/Petrov-Galerkin method for viscoelastic flow revisited. J Non-Newt Fluid Mech 42:283–299
Crochet MJ, Pilate G (1976) Plane flow of a fluid of second grade through a contraction. J Non-Newt Fluid Mech 1:247–258
Davies AR, Lee SJ, Webster MIT (1984) Numerical simulations of viscoelastic flow: the effect of mesh size.J Non-Newt Fluid Mech 16:117–139
Ellood KRJ, Georgiou GC, Papanastasiou TC, Wilkes JO (1990) Laminar jet of Bingham-plastic liquids. J Rheol 34:787–812
Gartling DK, Phan-Thien N (1984) A numerical simulation of a plastic fluid in a parallel-plate plastometer. J Non-Newt Fluid Mech 14:347–360
Gerald CF, Wheatley PO (1989) Applied numerical analysis. Addison-Wesley Publisher, Reading
Han CD (1973) Wall normal stresses and die swell behavior of viscoelastic polymeric melts in flow through converging ducts. AICHE J 19:649–651
Huang YH, Isayev AI (1993) An experimental study of planar entry flow of rubber compound. Rheol Acta (next issue)
Isayev AI, Chung B (1985) Flow of polymeric melts in short tubes. Polym Eng Sci 25:264–270
Isayev AI, Fan X (1990) Viscoelastic plastic constitutive equation for flow of particle filled polymers. J Rheol 34:35–54
Isayev AI, Huang YH (1989) Unsteady flow of rubber compounds at injection molding conditions. Adv Polym Tech 9:167–180
Isayev AI, Upadhyay RK (1987) Flow of polymeric melts in juncture regions of injection molding, in injection and compression molding fundamentals, ed by Isayev AI. Marcel Decker, NY, Chap 2: pp 435–479
Isayev AI, Upadhyay RK (1985) Two-dimensional viscoelastic flows: experimentation and modelling. J Non-Newt Fluid Mech 19:125–160
Isayev AI, Huang YH (1992) Recent advances in non-Newtonian flows, ed by Siginer DA. ASME, New York 153:113–128
Kawahara M, Takeuchi N (1977) Mixed finite element method for analysis of viscoelastic liquids. Comp and Fluids 5:33–45
Keentok M, Milthorpe JF, O'Donovan EJ (1985) On the shearing zone around rotating vanes in plastic liquids: theory and experiment. J Non-Newt Fluid Mech 17:23–35
Keunings R (1986) On the high Weissenberg number problem. J Non-Newt Fluid Mech 20:209–226
Keunings R (1989) Simulation of viscoelastic flow, in fundamentals of computer modeling for polymer processing, ed by Tucker CL. Carl Hanser Verlag, Munich
Keunings R, Crochet MJ (1984) Numerical simulation of the flow of a viscoelastic fluid through an abrupt contraction. J Non-Newt Fluid-Mech 14:279–299
Lipscomb GG, Denn MM (1984) Flow of Bingham fluids in complet geometries. J Non-Newt Fluid Mech 14:337–346
Lipscomb GG, Keunings R, Denn MM (1987) Implications of boundary singularities in complex geometry. J Non-Newt Fluid Mech 24:85–96
Marchal JM, Crochet MJ (1986) Hermitian finite elements for calculating viscoelastic flow. J Non-Newt Fluid Mech 20:186–207
Mendelson MA, Yeh PW, Brown RA, Armstrong RJ (1982) Approximation error in finite element calculation of viscoelastic fluid mechanics. J Non-Newt Fluid Mech 10:31–54
Mitsoulis E, Vlachopoulos J, Mirza FA (1984) Numerical simulation of entry and exit flows in slit dies. Polym Eng Sci 24:707–715
O'Donovan EJ, Tanner RI (1984) Numerical study of the Bingham squeeze film problem. J Non-Newt Fluid Mech 13:75–83
Papanastasiou TC (1987) Flows of materials with yield. J Rheol 31:385–404
Scott PS, Mirza F, Vlachopoulos J (1988) Finite-element simulation of laminar viscoplastic flows with regions of recirculation. J Rheol 32:387–400
Upadhyay RK, Isayev AI (1986) Simulation of two-dimensional planar flow of viscoelastic fluid. Rheol Acta 25:80–94
Vinogradov GV, Malkin A Ya (1980) Rheology of polymers. Mir Publishers, Moscow
White SA, Gotsis AD, Baird DG (1987) Review of the entry flow problem: experimental and numerical. J Non-Newt Fluid Mech 24:121–160
Zienkiewicz OC (1977) The finite element method. McGraw-Hill, New York
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Isayev, A.I., Huang, Y.H. Two-dimensional planar flow of a viscoelastic plastic medium. Rheola Acta 32, 181–191 (1993). https://doi.org/10.1007/BF00366681
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00366681