A marker-and-cell approach to viscoelastic free surface flows using the PTT model

G. S. de Paulo, M. F. Tomé, S. McKee

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

This work is concerned with the development of a numerical method capable of simulating two-dimensional viscoelastic free surface flows governed by the non-linear constitutive equation PTT (Phan-Thien-Tanner). In particular, we are interested in flows possessing moving free surfaces. The fluid is modelled by a marker-and-cell type method and employs an accurate representation of the fluid surface. Boundary conditions are described in detail and the full free surface stress conditions are considered. The PTT equation is solved by a high order method which requires the calculation of the extra-stress tensor on the mesh contour. The equations describing the numerical technique are solved by the finite difference method on a staggered grid. In order to validate the numerical method fully developed flow in a two-dimensional channel was simulated and the numerical solutions were compared with known analytic solutions. Convergence results were obtained throughout by using mesh refinement. To demonstrate that complex free surface flows using the PTT model can be computed, extrudate swell and a jet flowing onto a rigid plate were simulated.

LanguageEnglish
Pages149-174
Number of pages26
JournalJournal of Non-Newtonian Fluid Mechanics
Volume147
Issue number3
Early online date22 Aug 2007
DOIs
Publication statusPublished - 17 Dec 2007

Fingerprint

Viscoelastic Flow
Free Surface Flow
Free Surface
markers
Numerical Methods
Fluid
Staggered Grid
High-order Methods
Mesh Refinement
Cell
Stress Tensor
Constitutive Equation
Numerical Techniques
cells
Analytic Solution
Convergence Results
Difference Method
Finite Difference
Nonlinear Equations
Numerical Solution

Keywords

  • 2D-viscoelastic flows
  • analytic solution
  • finite difference technique
  • free surface
  • PTT model

Cite this

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abstract = "This work is concerned with the development of a numerical method capable of simulating two-dimensional viscoelastic free surface flows governed by the non-linear constitutive equation PTT (Phan-Thien-Tanner). In particular, we are interested in flows possessing moving free surfaces. The fluid is modelled by a marker-and-cell type method and employs an accurate representation of the fluid surface. Boundary conditions are described in detail and the full free surface stress conditions are considered. The PTT equation is solved by a high order method which requires the calculation of the extra-stress tensor on the mesh contour. The equations describing the numerical technique are solved by the finite difference method on a staggered grid. In order to validate the numerical method fully developed flow in a two-dimensional channel was simulated and the numerical solutions were compared with known analytic solutions. Convergence results were obtained throughout by using mesh refinement. To demonstrate that complex free surface flows using the PTT model can be computed, extrudate swell and a jet flowing onto a rigid plate were simulated.",
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A marker-and-cell approach to viscoelastic free surface flows using the PTT model. / de Paulo, G. S.; Tomé, M. F.; McKee, S.

In: Journal of Non-Newtonian Fluid Mechanics, Vol. 147, No. 3, 17.12.2007, p. 149-174.

Research output: Contribution to journalArticle

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AU - Tomé, M. F.

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AB - This work is concerned with the development of a numerical method capable of simulating two-dimensional viscoelastic free surface flows governed by the non-linear constitutive equation PTT (Phan-Thien-Tanner). In particular, we are interested in flows possessing moving free surfaces. The fluid is modelled by a marker-and-cell type method and employs an accurate representation of the fluid surface. Boundary conditions are described in detail and the full free surface stress conditions are considered. The PTT equation is solved by a high order method which requires the calculation of the extra-stress tensor on the mesh contour. The equations describing the numerical technique are solved by the finite difference method on a staggered grid. In order to validate the numerical method fully developed flow in a two-dimensional channel was simulated and the numerical solutions were compared with known analytic solutions. Convergence results were obtained throughout by using mesh refinement. To demonstrate that complex free surface flows using the PTT model can be computed, extrudate swell and a jet flowing onto a rigid plate were simulated.

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