This paper summarizes our studies on the numerical flow analysis of polymeric liquids and its application to the industrial problems in the polymer processing. The contents include three parts. The first part is a review about development of numerical technique of viscoelastic flow analysis to obtain the solution at high deformation rate. We used the streamline-upwind (SU) finite element method with the sub-elements for stress components to simulate the extrudate swell at high Weissenberg number (We) . The calculation using the Giesekus model with a single relaxation time was feasible over hundreds of We in the planar and capillary extrude swell, but the calculation was impossible for We > 3 in the annular extrudate swell. We proposed the new technique of under-relaxation method, which introduced the virtual Newtonian stress in order to increase the numerical stability. The calculation by the new technique combined with the SU method was successful in obtaining the solution over hundreds of We in the annular extrudate swell problem. The second part is a review of numerical studies on polymeric liquid flow in the basic flow fields. We performed the viscoelastic flow analysis using the several kinds of constitutive models in the contraction flow and extrudate swell. The simulation results using the viscoelastic model with a single relaxation time were compared with the experimental data of stress field measured by the flow birefringence technique and the agreement better than 20-30% in accuracy was obtained in the lower shear rate region. The simulation results also gave the several explanations about the mechanism of corner vortex and entrance pressure drop in the contraction flow, swelling phenomena in the extudate swell, etc. On the other hand, the simulation using the constitutive models with multiple relaxation times gave the useful information, especially on the effect of material polymer. The last part is application to the industrial problems in polymer processing. The technique of viscoelastic flow analysis was applied to the film casting and the effect of elongational viscosity on the film shape was found. The technique was also applied to the development of prediction of prison formation in blow molding. The viscous non-Newtonian flow analysis was applied to the three-dimensional flow analysis and the evoluation of mixing performance in the twin screw extruder.
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