Non-isothermal viscoelastic flow computations in an axisymmetric contraction at high Weissenberg numbers by a finite volume method

Abstract

This paper presents a numerical study of non-isothermal viscoelastic flows in a 4:1 axisymmetric abrupt contraction. The model retained for the simulations is an upper convected Maxwell (UCM) constitutive equation whose temperature dependence is described by a WLF equation. General thermodynamical framework leads to introduce the complex energy conversion mechanism from elastic to thermal energy occurring in viscoelastic fluid flow. The mass, momentum, constitutive and energy equations are discretized using a finite volume method on a staggered grid with upwind scheme for the convective-type terms. A decoupled algorithm stabilized by a pseudo-transient stress term and an elastic viscous stress splitting (EVSS) formulation are employed. Convergence is reached by a fixed-point iteration. The Stokes problem is solved by a fast augmented Lagrangian method and convective-type equations by a bi-conjugate gradient stabilized iterative procedure. Elastic effects are investigated in both isothermal and non-isothermal flow situations. Thermodynamical behaviour related to pure energy elasticity and pure entropy elasticity is considered. Various temperature boundary conditions corresponding to an external cooling of the flow are prescribed at the wall in order to investigate the temperature dependence in flows with large temperature gradients. Without encountering any upper limit for convergence, the present method provides solutions up to Weissenberg number We=10.00 and is able to take into account great temperature changes. General difficulties involved in thermal control processing are underlined.