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.
| Language | English |
|---|---|
| Pages | 149-174 |
| Number of pages | 26 |
| Journal | Journal of Non-Newtonian Fluid Mechanics |
| Volume | 147 |
| Issue number | 3 |
| Early online date | 22 Aug 2007 |
| DOIs | |
| Publication status | Published - 17 Dec 2007 |
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Keywords
- 2D-viscoelastic flows
- analytic solution
- finite difference technique
- free surface
- PTT model
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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 journal › Article
TY - JOUR
T1 - A marker-and-cell approach to viscoelastic free surface flows using the PTT model
AU - de Paulo, G. S.
AU - Tomé, M. F.
AU - McKee, S.
PY - 2007/12/17
Y1 - 2007/12/17
N2 - 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.
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.
KW - 2D-viscoelastic flows
KW - analytic solution
KW - finite difference technique
KW - free surface
KW - PTT model
UR - http://www.scopus.com/inward/record.url?scp=36549027315&partnerID=8YFLogxK
UR - https://www.sciencedirect.com/journal/journal-of-non-newtonian-fluid-mechanics
U2 - 10.1016/j.jnnfm.2007.08.003
DO - 10.1016/j.jnnfm.2007.08.003
M3 - Article
VL - 147
SP - 149
EP - 174
JO - Journal of Non-Newtonian Fluid Mechanics
T2 - Journal of Non-Newtonian Fluid Mechanics
JF - Journal of Non-Newtonian Fluid Mechanics
SN - 0377-0257
IS - 3
ER -