On the simulation of highly elastic complex flows

Abstract Consideration is given to a methodology for achieving highly elastic solutions of complex flows. Steady solutions are obtained through an unsteady finite element approach that employs a pressure-correction scheme. A simplified Phan-Thien-Tanner constitutive model is used with parameter values representative of polymer solutions to simulate viscoelastic flows for two planar problems, a 4:1 contraction flow and a mixing and separating flow. Highly elastic flows are studied for both problems. For mixing and separating flow, various bifurcations are investigated for Newtonian and viscoelastic fluids to reveal the effects of increasing inertia, elasticity and variation in geometric gap width. Good agreement with experimental observations is achieved.

[1]  J. M. Piau,et al.  Flow characteristics of viscoelastic fluids in an abrupt contraction by using numerical modeling , 1994 .

[2]  M. F. Webster,et al.  A Taylor–Galerkin‐based algorithm for viscous incompressible flow , 1990 .

[3]  R. Keiller.  Entry-flow calculations for the Oldroyd-B and FENE equations , 1993 .

[4]  P. Townsend,et al.  The iterative solution of Taylor—Galerkin augmented mass matrix equations , 1992 .

[5]  A. R. Davies,et al.  On corner flows of Oldroyd-B fluids , 1993 .

[6]  M. Fortin,et al.  A new approach for the FEM simulation of viscoelastic flows , 1989 .

[7]  P. Townsend,et al.  An Algorithm for the Three-Dimensional Transient Simulation of Non-Newtonian Fluid Flows , 1987 .

[8]  M. F. Webster,et al.  The use of dynamic data structures in finite element applications , 1992 .

[9]  M. Crochet,et al.  A new mixed finite element for calculating viscoelastic flow , 1987 .

[10]  I. Duff,et al.  Direct Methods for Sparse Matrices , 1987 .

[11]  J. Kan.  A second-order accurate pressure correction scheme for viscous incompressible flow , 1986 .

[12]  F. Baaijens.  Numerical analysis of unsteady viscoelastic flow , 1992 .

[13]  R. Armstrong,et al.  Finite element methdos for calculation of steady, viscoelastic flow using constitutive equations with a Newtonian viscosity , 1990 .

[14]  K. Walters,et al.  Further remarks on the lip-vortex mechanism of vortex enhancement in planar-contraction flows , 1989 .

[15]  M. F. Webster,et al.  On Newtonian and non-Newtonian flow in complex geometries , 1981, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[16]  F. Baaijens.  Numerical experiments with a discontinuous galerkin method including monotonicity enforcement on the stick-slip problem , 1994 .

[17]  F. Baaijens,et al.  Numerical analysis of start-up planar and axisymmetric contraction flows using multi-mode differential constitutive models , 1993 .

[18]  M. F. Webster,et al.  On dominating elastico-viscous response in some complex flows , 1982, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[19]  M. F. Webster,et al.  A taylor-petrov-galerkin algorithm for viscoelastic flow , 1993 .

[20]  J. Oldroyd.  On the formulation of rheological equations of state , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[21]  Abdelmalek Zine,et al.  An improved GMRES method for solving viscoelastic fluid flow problems , 1992 .

[22]  Calculation of steady viscoelastic flow using a multimode Maxwell model : application of the explicitly elliptic momentum equation (EEME) formulation , 1990 .

[23]  R. Tanner,et al.  A new constitutive equation derived from network theory , 1977 .