Numerical prediction of three-dimensional time-dependent viscoelastic extrudate swell using differential and algebraic models

Author(s)

Mompean, G. ^{[1, 2]} ; Thais, L. ^{[1, 2]} ; Tome, M. F. ^[3] ; Castelo, A. ^[3]

Affiliation

^[1] Univ Lille Nord France, F-59000 Lille - France

^[2] Univ Lille 1, Ctr Hyperfrequences & Semicond, CNRS, UMR 8107, LML, F-59655 Villeneuve Dascq - France

^[3] Univ Sao Paulo, Dept Appl Math & Stat, Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: COMPUTERS & FLUIDS; v. 44, n. 1, p. 68-78, MAY 2011.
• Web of Science Citations: 8

Abstract

This study investigates the numerical simulation of three-dimensional time-dependent viscoelastic free surface flows using the Upper-Convected Maxwell (UCM) constitutive equation and an algebraic explicit model. This investigation was carried out to develop a simplified approach that can be applied to the extrudate swell problem. The relevant physics of this flow phenomenon is discussed in the paper and an algebraic model to predict the extrudate swell problem is presented. It is based on an explicit algebraic representation of the non-Newtonian extra-stress through a kinematic tensor formed with the scaled dyadic product of the velocity field. The elasticity of the fluid is governed by a single transport equation for a scalar quantity which has dimension of strain rate. Mass and momentum conservations, and the constitutive equation (UCM and algebraic model) were solved by a three-dimensional time-dependent finite difference method. The free surface of the fluid was modeled using a marker-and-cell approach. The algebraic model was validated by comparing the numerical predictions with analytic solutions for pipe flow. In comparison with the classical UCM model, one advantage of this approach is that computational workload is substantially reduced: the UCM model employs six differential equations while the algebraic model uses only one. The results showed stable flows with very large extrudate growths beyond those usually obtained with standard differential viscoelastic models. (C) 2010 Elsevier Ltd. All rights reserved. (AU)

• FAPESP's process: 07/07038-2 - Numerical solution nematic liquid crystal
• Grantee: Pedro Alexandre da Cruz
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 04/16064-9 - Mechanics of non-stationary fluids: applications in aeronautics and rheology
• Grantee: José Alberto Cuminato
• Support Opportunities: Research Projects - Thematic Grants