Numerical Simulations Of Flows And Extrudate Swell For Viscoelastic Polymer Melt

The die is a major factor determining the product quality. Analyzing the flow of polymer melt through dies is an important means to improve the quality of die. The contraction flow and extrudate swell of viscoelastic polymer melt are the typical flow for polymer extrusion processing. Numerical simulations of the two flows are the basis of optimum design for dies and important research areas of non-Newtonian fluid. The research is a continuation of "Key mechanical problems and calculation method of rubber and plastic products molding and mold design", which is one of National natural science fund key project. In this paper, the numerical method for simulating the slit flows and extrudate swell of viscoelastic fluid with complicated constitutive equation is researched.The slit channel is one of the most common channels in extrusion dies.The size of flow direction in slit flow channel is much longer than the thickness in the Z direction. For this feature, a new finite element of fluid is presented. A finite piece method is proposed to simulate three-dimensional slit flows viscoelastic fluid. The adaptive discrete elastic viscous split stress and the streamline upwind (DEVSS/SU) algorithm based on optimizations of the motion equation and the constitutive equation are established. The finite piece method is about to construct an approximation function of the velocity and the extra-stress by using the finite element interpolating polynomial in flow directions and by continuous smooth Fourier series fitting the boundary conditions in thickness directions, so the number of equations is greatly reduced.Numerical simulations are carried out for the flows of viscoelastic PTT, K-BKZ and Carreau-Yasuda melt through slit channel, contraction channel, the fishtail and the coat-hanger sheet dies by using the finite piece method. For the flow channel with varying thickness, the volumetric flow is used as unknown variable of equations. Because the volumetric flow is continuous at node, the global stiffness matrix equation for all the elements can be assembled after the elemental calculation. The distribution functions of the velocity, volumetric flow and pressure are acquired. The sensitivity of the simulation results with respect to the mesh size is investigated. The most reasonable mesh size for the coat-hanger sheet dies is presented. The results of the finite piece method are compared with the three-dimensional (3D) finite element method (FEM) simulation and experiments. For the whole die the volumetric flow distributions obtained by the finite piece method show satisfactory agreement with that of the three-dimensional finite element method. The pressure predicted by the finite piece method is slight smaller. The discrepancies caused by varying thickness of channel are restricted to a small region. The overall agreement of the uniformity index between the finite piece method and the experiment is good. Because the number of the elements is much less than3D FEM, a substantial amount of computing time and memory requirement can be saved. It shows that the finite piece method is not only convenient but also accurate. So it can be used to solve large-scale3D problems. The finite piece method showed widely potential application.A new numerical method for three-dimensional extrudate swells of non-Newtonian melts with K-BKZ integral constitutive model based on the finite element method is proposed. The iterative algorithm is established to calculate free surface of extrudate swell. The three-dimensional mesh is redivided after per iteration. The stress of K-BKZ constitutive model is calculated using step-by-step Gauss integral along the particle tracking. Extrudate swells of the axisymmetric and rectangular flow channel with different dimension are analyzed. The results are compared with the two-dimensional axisymmetric simulations and experiments. It indicates that the method is accurate for the three-dimensional extrudate swell of viscoelastic fluid. Finally, Influence of length, convergence angle, ratio of width to thickness and shear rate on swell ratios is analyzed. Internal factors affecting the swell ratio are investigated. This will provide the theoretical theory basis for optimizing design of the dies.