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

C.M. Oishi, F.P. Martins, Murilo F. Tome, Jose Cuminato, Sean Mckee

Research output: Contribution to journalArticle

36 Citations (Scopus)

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.
LanguageEnglish
Pages165-179
Number of pages15
JournalJournal of Non-Newtonian Fluid Mechanics
Volume166
Issue number3-4
Early online date12 Nov 2010
DOIs
Publication statusPublished - Feb 2011

Fingerprint

Viscoelastic Flow
Free Surface Flow
Numerical Solution
Free Surface
Swelling
Channel Flow
Mesh Refinement
Low Reynolds number
Convergence of numerical methods
Unsteady Flow
Channel flow
Projection Method
Finite difference method
Difference Method
Governing equation
Numerical methods
Finite Difference
Momentum
low Reynolds number
Reynolds number

Keywords

  • free surface flows
  • implicit techniques
  • viscoelastic fluids
  • Pom-Pom model
  • finite difference method
  • extrudate swell

Cite this

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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.",
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Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows. / Oishi, C.M.; Martins, F.P.; Tome, Murilo F.; Cuminato, Jose; Mckee, Sean.

In: Journal of Non-Newtonian Fluid Mechanics, Vol. 166, No. 3-4, 02.2011, p. 165-179.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

AU - Oishi, C.M.

AU - Martins, F.P.

AU - Tome, Murilo F.

AU - Cuminato, Jose

AU - Mckee, Sean

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N2 - 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.

AB - 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.

KW - free surface flows

KW - implicit techniques

KW - viscoelastic fluids

KW - Pom-Pom model

KW - finite difference method

KW - extrudate swell

UR - http://www.mathstat.strath.ac.uk/downloads/publications/23paper_xpp_05out__2_.pdf

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