A 3D flow analysis performed using COMSOL Multiphysics chemical module has analyzed the flow properties and verified operating points of a test domain. The test was conducted on an extruder die within the Arcada laboratory where the maximum output of the extruder screw was predetermined. The analysis used material properties known for a special melt of LDPE material.
Getting started
Design of dies, unlike other parts of machine components, has been considered more an art than a science. The usual methods of design depend on numerous trial-and-error loops, mainly relying on the designer’s experience. However, advances in fields of mechanical, chemical and material engineering have made it easier to visualize the flow and set the parameters required in such a complex design.
Recently developed software packages for mathematical modeling of polymer flows make the trial-and-error procedure a lot shorter. The main objective of this study is to achieve efficient design modeling methods that predict operational variables of the melt flow through the cavities of the die.
Analysis of melt flow is not a simple, straight-forward calculation. Some important assumptions to simplify the derivations are needed. The issues are complex, and many factors are involved. That is why software like the Comsol Multiphysics software is so helpful in analyzing these complex phenomena.
In this study a 3-dimensional flow analysis for an existing die was successfully investigated using COMSOL Multiphysics software. The operational point of a die was obtained and the results were compared to both theoretical and experimental values of the operating point values of the die. This enhances the current operation point calculation by including the most realistic temperature-dependent varying viscosity values instead of just using a constant viscosity. The non-Newtonian module of the software was used to study the flow of an exemplary material LDPE at 220 C. The model used was an exact replica of the 2-hole capillary die in Arcada University of Applied Science.
The material data for LDPE was obtained from the manufacturer to plot the logarithmic viscosity shear rate graph. After retrieving the necessary rheological information of the polymer melt, it was fitted to the Carreau-Yasuda viscosity model. Using the extruder maximum output value as an input value for the initial subboundary condition, the pressure was solved using the parametric solver. The results were compared to the continuity equation and the pressure which fulfills the condition was identified.
Numerical model
After having the necessary information about the rheology of the polymer at hand, the next step was to study the 3D model analysis of the flow geometry for an example die in the Arcada workshop. The purpose of this model was to visualize the viscosity and pressure distribution of the flow domain – and most importantly, to compare the result of the simulation to the real value of the operating point.
3D FEA analysis for the flow of LDPE was done using the COMSOL Multiphysics, non-Newtonian (Chemical Engineering Module). After re-modeling the existing die in the Solid edge 3D software, the Boolean feature was used to obtain the flow domain of the melt. Then the resulting model was imported to COMSOL software work station.
Parametric analysis is the most important part of the modeling where the parameters for solving any complicated function are defined. In this case, the aim of this model is to solve for the pressure drop in the die. Since the pressure at the outlet is zero, finding the operating pressure, p_in, at the inlet of the die is sufficient.
To help the convergence of the solution and reduce solution time and error of the iteration, a range of arbitrary but reasonable p_in parametric values were inserted. An approximated range for p_in values of 400 kPa to 2.8 MPa with a sweep of 400 kPa was chosen as a range since that is extruder common operating range.
Results and Discussion
The parametric solver solves the different input values of pressure in an ascending order. And hence, the value of p_in solved last (the highest value) will be displayed as a contour plot by default as the software converges.
Figure 1, pressure distribution in the die.
Figure 2, operating pressure distribution.
Figure 3, Operating point value.
Pressure distribution in the die shows a condition when p_in value is equal to 28 MPa, Fig. 1. This figure does not necessarily imply that this value of 28 MPa is the operating pressure. For this to be an operating-point pressure it should deliver a uniform quantity of melt complying with the assumption of fully developed and incompressible flow.
The operating pressure distribution, Fig 2, shows the dynamic viscosity and shear rate values throughout the flow range respectively. These values were obtained using the power law model assuming the viscosity to be constant.
Operating point value, Fig 3, shows an operating pressure of 11 MPa. The total pressure distribution in the flow domain can be seen in this figure.
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