Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

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• 作者：C.M. Oishi^a ; ^{cassiooishi@gmail.com} ; F.P. Martins^a ; ^{fpmartins@fct.unesp.br} ; M.F. Tomé ; ^b ; ^{murilo@icmc.usp.br} ; J.A. Cuminato^b ; ^{jacumina@icmc.usp.br} ; S. McKee^c ; ^{s.mckee@strath.ac.uk} ; ^{smck@maths.strath.ac.u}
• 关键词：Free surface flows ; Implicit techniques ; Viscoelastic fluids ; Pom-Pom model ; Finite difference method ; Extrudate swell
• 刊名：Journal of Non-Newtonian Fluid Mechanics
• 出版年：2011
• 出版时间：February 2011
• 年：2011
• 卷：166
• 期：3-4
• 页码：165-179
• 全文大小：1429 K

文摘

Abstract

In this paper we present a finite difference method for solving two-dimensional viscoelastic unsteady free surface flows governed by the single equation version of the eXtended Pom-Pom (XPP) model. The momentum equations are solved by a projection method which uncouples the velocity and pressure fields. We are interested in low Reynolds number flows and, to enhance the stability of the numerical method, an implicit technique for computing the pressure condition on the free surface is employed. This strategy is invoked to solve the governing equations within a Marker-and-Cell type approach while simultaneously calculating the correct normal stress condition on the free surface. The numerical code is validated by performing mesh refinement on a two-dimensional channel flow. Numerical results include an investigation of the influence of the parameters of the XPP equation on the extrudate swelling ratio and the simulation of the Barus effect for XPP fluids.