Numerical Simulation of Viscoelastic Extrudate Swell Through Elliptical Ring Die

The numerical simulation of extrudate swell is significant in extrusion processing.Precise prediction of extrudate swell is propitious to the control of melt flow and the quality of final products.A mathematical model of three-dimensional（3D）viscoelastic flow through elliptical ring die for polymer extrusion was investigated.The penalty function formulation of viscoelastic incompressible fluid was introduced to the finite element model to analyze 3D extrusion problem.The discrete elastic viscous split stress（DEVSS）and streamline-upwind PetrovGalerkin（SUPG）technology were used to obtain stable simulation results.Free surface was updated by updating the streamlines which needs less memory space.According to numerical simulation results,the effect of zero-shear viscosity and elongation parameter on extrudate swell was slight,but with the increase of volumetric flow rate and relax time the extrudate swell ratio increased markedly.Finally,the numerical simulation of extrudate swell flow for low-density polyethylene（LDPE）melts was investigated and the results agreed well with others’work.These conclusions provided quantitative basis for the forecasting extrudate swell ratio and the controlling of extrusion productivity shape.

NUMERICAL INVESTIGATION ON EXTRUDATE SWELL FOR VISCOELASTIC FLUID: USING MAXWELL MODEL

The numerical investigation on extrudate swell through capillary die forviscoelastic fluid characteried by integral-type Maxwell constitutive equation was conducted byemploying the finite element method with the calculation of viscoelastic extra stress in theconventional finite element. The method of avoiding singularity was also adopted by integrating thestrain history of the Gauss points for each element near the wall and the free surface. Theconvergence solutions at high Weissenberg number can be obtained by using the appropriate methods toreduce errors and improve the speed of convergence of the calculation, which include adding arelaxation factor of velocity in iteration process, or enlarging the reference viscosity, orreducing the elapsed time. The highest Weissenberg number obtained here is up to 3. 8, while thesolution at the Weissenberg number of 3. 75 was given in the previous work with similar extrudateswell ratio and the exit pressure drop by using differential Maxwell model with Elastic-ViscousStress Split (EVSS) combined with Streamline Upwind Petrov-Galerkin (SUPG) scheme. The calculationsindicated that the method of dealing with integral consti- tutive equation introduced in this paperis suitable in simulating viscoelastic flow characterized by integral constitutive equation at highe-lastic level.

STUDY ON FINITE ELEMENT METHODS OF THE EXTRUDATE SWELL PROBLEM(Ⅰ)NEWTONIAN FLUID

The problem of a creeping flow of Newtonian fluid extruded from a plane slit or a circular pipe.in the absence of gravity,is simulated successfully by using the continuous-pressure-element method,the discontinuous-pressure-element method,the consistant penalty method,the reduced integration penalty method and the modified reduced integration penalty method proposed by Oden.Through comparisons between these methods,it is convinced that the discontinuous-pressure interpolation schemes result in more accurate mass conservation and,consequently,more rapid convergence of the free-surface iteration than the continuous one does.The reduced integration penalty method can further reduce the cost of computation while retaining sufficient accuracy of the solution.