Numerical simulation of three‐dimensional viscoelastic flow within dies

Abstract

In recent years, the development of CAE (Computer Aided Engineering) in polymer processing has been remarkable, and it is expected to be more realistic in viscoelastic numerical simulation, particularly in three-dimensional complex geometry. Because of the problems of computational memory capacity, CPU time, and the numerical convergence of viscoelastic flow simulation, three-dimensional viscoelastic simulation applicable to industrial flow behaviors has not yet been attempted. In this paper, we developed the numerical simulation of three-dimensional viscoelastic flow within dies using a decoupled method, streamwise integration, and penalty function methods to decrease memory, and the TME ("Transformation of Equation of Motion to the Elliptic Equation," S . Tanoue, T. Kajiwara, and K. F'unatsu, The Eleventh Annual Meeting, the Polymer Processing Society Seoul, Korea, Extended Abstracts p.439) method, which raises the stability of convergence. We confinned the reliability of this simulation technique to compare simulation results with experimental data of the stress field at a downstream wall shear rate of 5.41s' within a 60" angle tapered contraction die. We compared the predictions of a viscoelastic model (Phan-Thien and Tanner model) with a pure viscosity model (Carreau model) at a downstream wall shear rate of 120s' and discovered a remarkable effect of viscoelasticity in the shear stress and first normal stress difference in particular in the tapered region.

Finite‐Element Simulation of Polymer Flow and Extrudate Swell Through Hollow Profile Extrusion Die with the Multimode Differential Viscoelastic Model

“…The penalty finite element algorithm 15,16 is employed to solve the nonlinear system consisting of the continuity equation and the momentum equation. The penalty factor as a function obeying λ p = − p (∇ · u) is first introduced to avoid a direct calculation of the hydrostatic pressure, and the following momentum governing equation can be obtained:…”

Three‐dimensional simulation of planar contraction viscoelastic flow by penalty finite element method

“…The decoupled method is executed by decoupling the calculation of motion and continuity equations from constitutive equation. The penalty function formulation [15] is employed to improve the stability of pressure field calculation. A robust and efficient numerical scheme for viscoelastic flow is established by using DEVSS algorithm in cooperating with inconsistent SU approach.…”

“…The additional term of the weighted function (ku/(u·u))·∇ N i only affects the purely advective term u·∇s in the constitutive equation (15) and the following elemental constitutive equation is obtained:…”

Modeling and simulation of three‐dimensional extrusion swelling of viscoelastic fluids with PTT, Giesekus and FENE‐P constitutive models

“…The penalty factor as a function obeying λ p = − ( p ∕ ∇ ⋅ u ) is first introduced to avoid direct calculation of the hydrostatic pressure and the following relationship is thereby obtained : …”