Modelling of non-isothermal viscoelastic flows

The modelling of non-isothermal flow of viscoelastic materials using differential constitutive equations is investigated. The approach is based on the concept of a slip tensor describing the nonaffine motion of the stress-carrying structure of the fluid. By specifying a slip tensor and the elastic behaviour of the structure, the constitutive model is determined. This slip tensor also appears in the energy equation and thus, for a given constitutive model, the form of the energy equation is known. Besides the partitioning between dissipated and elastically stored energy, also the difference between entropy and energy elasticity is discussed. Numerical simulations are based on a stabilized Discontinuous Galerkin method to solve the mass, momentum and constitutive equations and a Streamline Upwind Petrov-Galerkin formulation to solve the energy equation. Coupling is achieved by a fixed point iteration. The flow around a confined cylinder is investigated, showing differences between viscous and viscoelastic modelling, and between limiting cases of viscoelastic modelling.

[1]  A class of simple solids with fading memory , 1969 .

[2]  H. Braun.  A model for the thermorheological behavior of viscoelastic fluids , 1991 .

[3]  R. Bird,et al.  Constitutive equations for polymeric liquids , 1995 .

[4]  N. Phan-Thien,et al.  Nonisothermal flow of polymer melts , 1988 .

[5]  R. Larson.  Constitutive equations for polymer melts and solutions , 1988 .

[6]  R. Larson.  A Constitutive Equation for Polymer Melts Based on Partially Extending Strand Convection , 1984 .

[7]  F. Baaijens,et al.  An experimental and numerical investigation of a viscoelastic flow around a cylinder , 1994 .

[8]  R. Bird.  Dynamics of Polymeric Liquids , 1977 .

[9]  Robert A. Brown,et al.  Report on the VIIIth international workshop on numerical methods in viscoelastic flows , 1994 .

[10]  A. B. Metzner,et al.  Modeling of Nonisothermal Polymer Processes , 1982 .

[11]  F. Baaijens,et al.  Viscoelastic flow past a confined cylinder of a polyisobutylene solution , 1995 .

[12]  J. F. Dijksman,et al.  IUTAM Symposium on Numerical Simulation of Non-Isothermal Flow of Viscoelastic Liquids : proceedings of an IUTAM symposium held in Kerkrade, the Netherlands, 1-3 November 1993 , 1995 .

[13]  A. S. Lodge,et al.  Viscous heating correction for thermally developing flows in slit die viscometry , 1991 .

[14]  M. Fortin,et al.  A new mixed finite element method for computing viscoelastic flows , 1995 .

[15]  C. Friedrich,et al.  Transient processes in Couette flow of a Leonov fluid influenced by dissipation , 1989 .

[16]  R. Tanner,et al.  A pseudo-time integral method for non-isothermal viscoelastic flows and its application to extrusion simulation , 1987 .

[17]  C. Friedrich,et al.  Dissipative behaviour of viscoelastic fluids derived from rheological constitutive equations , 1990 .

[18]  Leslie Morland,et al.  Stress Analysis for Linear Viscoelastic Materials with Temperature Variation , 1960 .

[19]  R. C. Larson.  Convected derivatives for differential constitutive equations , 1987 .

[20]  Jpw Hans Baaijens.  Evaluation of constitutive equations for polymer melts and solutions in complex flows , 1994 .

[21]  David Abir,et al.  Topics in applied mechanics , 1965 .

[22]  G. Homsy,et al.  Numerical simulation of non-newtonian free shear flows at high reynolds numbers , 1994 .

[23]  J. Wiest.  Time-temperature superposition in nonisothermal flow , 1988 .

[24]  R. Larson.  Convection and diffusion of polymer network strands , 1983 .

[25]  G. C. Sarti,et al.  The dissipative mechanism in flowing polymers: theory and experiments , 1976 .