### Abstract

In order to predict the die swell seen in the actual polymer processing, the planar, the capillary and the annular die swell simulations have been performed by the streamline-upwind finite element method with the sub-elements for stress components, which was shown effective to calculate up to high Weissenberg number (We) for the entry flow simulation in an earlier study. The calculation using the Giesekus model, which is the differential type viscoelastic model, was found feasible over hundreds of We in the planar and the capillary die swell simulations as long as the primary normal stress difference was not so large. The shape of free surface at high We under the condition of no gravitation once showed the maximum swell and became an equilibrium one after shrinking back a little. This tendency became remarkable for the model with larger We and larger primary normal stress difference. Through the examination of the velocity profile, it was found that the velocity near the free surface was accelerated during the swell after extrusion and was larger than the inside velocity in the neighborhood of the position which showed the maximum swell. Since the accelerated outer fluid dragged the inside fluid, the swelling ratio was supposed to take an equilibrium value after shrinking back a little. Also, as the primary normal stress difference became larger, the axial position of the maximum swell approached the die. This may be due to that the model with the large primary normal stress difference predicts faster swell, because the elastic recovery force after extrusion is large. The axial position of the maximum swell became distant from the die with increasing We. We interpreted that the axial position of the maximum swell shifted downstream as the representative relaxation time was longer, or the velocity became larger. On the other hand, the calculation became impossible for We>3 in the annular die swell simulation. In order to examine this reason, we performed the calculation for the planar die swell in two different analysis regions i. e. one being the whole flow region with two singular points and the other, the half flow region with one singular point in consideration of flow symmetry. The calculation in the whole flow region with two singular points was unsuccessful at high We. It seems that the presence of two singular points in the analysis region made it impossible to perform the annular die swell up to high Wesimulation.

Original language | English |
---|---|

Pages (from-to) | 130-137 |

Number of pages | 8 |

Journal | Nihon Reoroji Gakkaishi |

Volume | 21 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 1 1993 |

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### All Science Journal Classification (ASJC) codes

- Materials Science(all)
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering

### Cite this

**High Weissenberg Number Simulation of Die Swell for Differential Type Viscoelastic Model by the Streamline-Upwind Finite Element Method.** / Kuwano, Yoshifumi; Kajiwara, Toshihisa; Funatsu, Kazumori.

Research output: Contribution to journal › Article

*Nihon Reoroji Gakkaishi*, vol. 21, no. 3, pp. 130-137. https://doi.org/10.1678/rheology1973.21.3_130

}

TY - JOUR

T1 - High Weissenberg Number Simulation of Die Swell for Differential Type Viscoelastic Model by the Streamline-Upwind Finite Element Method

AU - Kuwano, Yoshifumi

AU - Kajiwara, Toshihisa

AU - Funatsu, Kazumori

PY - 1993/1/1

Y1 - 1993/1/1

N2 - In order to predict the die swell seen in the actual polymer processing, the planar, the capillary and the annular die swell simulations have been performed by the streamline-upwind finite element method with the sub-elements for stress components, which was shown effective to calculate up to high Weissenberg number (We) for the entry flow simulation in an earlier study. The calculation using the Giesekus model, which is the differential type viscoelastic model, was found feasible over hundreds of We in the planar and the capillary die swell simulations as long as the primary normal stress difference was not so large. The shape of free surface at high We under the condition of no gravitation once showed the maximum swell and became an equilibrium one after shrinking back a little. This tendency became remarkable for the model with larger We and larger primary normal stress difference. Through the examination of the velocity profile, it was found that the velocity near the free surface was accelerated during the swell after extrusion and was larger than the inside velocity in the neighborhood of the position which showed the maximum swell. Since the accelerated outer fluid dragged the inside fluid, the swelling ratio was supposed to take an equilibrium value after shrinking back a little. Also, as the primary normal stress difference became larger, the axial position of the maximum swell approached the die. This may be due to that the model with the large primary normal stress difference predicts faster swell, because the elastic recovery force after extrusion is large. The axial position of the maximum swell became distant from the die with increasing We. We interpreted that the axial position of the maximum swell shifted downstream as the representative relaxation time was longer, or the velocity became larger. On the other hand, the calculation became impossible for We>3 in the annular die swell simulation. In order to examine this reason, we performed the calculation for the planar die swell in two different analysis regions i. e. one being the whole flow region with two singular points and the other, the half flow region with one singular point in consideration of flow symmetry. The calculation in the whole flow region with two singular points was unsuccessful at high We. It seems that the presence of two singular points in the analysis region made it impossible to perform the annular die swell up to high Wesimulation.

AB - In order to predict the die swell seen in the actual polymer processing, the planar, the capillary and the annular die swell simulations have been performed by the streamline-upwind finite element method with the sub-elements for stress components, which was shown effective to calculate up to high Weissenberg number (We) for the entry flow simulation in an earlier study. The calculation using the Giesekus model, which is the differential type viscoelastic model, was found feasible over hundreds of We in the planar and the capillary die swell simulations as long as the primary normal stress difference was not so large. The shape of free surface at high We under the condition of no gravitation once showed the maximum swell and became an equilibrium one after shrinking back a little. This tendency became remarkable for the model with larger We and larger primary normal stress difference. Through the examination of the velocity profile, it was found that the velocity near the free surface was accelerated during the swell after extrusion and was larger than the inside velocity in the neighborhood of the position which showed the maximum swell. Since the accelerated outer fluid dragged the inside fluid, the swelling ratio was supposed to take an equilibrium value after shrinking back a little. Also, as the primary normal stress difference became larger, the axial position of the maximum swell approached the die. This may be due to that the model with the large primary normal stress difference predicts faster swell, because the elastic recovery force after extrusion is large. The axial position of the maximum swell became distant from the die with increasing We. We interpreted that the axial position of the maximum swell shifted downstream as the representative relaxation time was longer, or the velocity became larger. On the other hand, the calculation became impossible for We>3 in the annular die swell simulation. In order to examine this reason, we performed the calculation for the planar die swell in two different analysis regions i. e. one being the whole flow region with two singular points and the other, the half flow region with one singular point in consideration of flow symmetry. The calculation in the whole flow region with two singular points was unsuccessful at high We. It seems that the presence of two singular points in the analysis region made it impossible to perform the annular die swell up to high Wesimulation.

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U2 - 10.1678/rheology1973.21.3_130

DO - 10.1678/rheology1973.21.3_130

M3 - Article

AN - SCOPUS:84989144461

VL - 21

SP - 130

EP - 137

JO - Nihon Reoroji Gakkaishi

JF - Nihon Reoroji Gakkaishi

SN - 0387-1533

IS - 3

ER -