Introduction

A self-wiping co-rotating parallel twin-screw extruder (TSE) is a versatile polymer-processing machine for pelletizing, blending, alloying, compounding, devolatilization, chemical reaction, and die forming of molten polymers1. To control product quality, engineers need to consider the thermal history and un-favored degradation of the resin.2 The thermal history is related to the residence time distribution and temperature distribution of the TSE. The resin distribution on the screws is required to determine the residence time distribution. The resin distribution is an important process parameter for twin-screw extrusion and is dependent on the screw design, screw speed, feed rate, and rheological properties of the resin. There remains a strong demand from the industry for a means of numerical simulation of the detailed resin distribution in the entire TSE.
There are two approaches to realizing the theoretical calculations of resin distribution. One is a flow analysis network (FAN) method that focuses on the axial direction of the screw. The other is a three-dimensional calculation that employs a smoothed particle hydrodynamics (SPH) method.
The first approach, originating from the FAN method for injection molding flow, was proposed by Tadmor et al.3,4 The FAN method is applied to the confined flows of variable thickness and is based on the Hele–Shaw approximation of the hydrodynamic lubrication theory. The theory neglects the transverse velocity component as being minimal in comparison to the components in the flow plane.3 White et al. proposed an approximation calculation method for flow behavior in an unfolded screw of a twin screw based on the hydrodynamic lubrication theory5-10. The AKRO-CO-TWIN-SCREW proprietary software was released in 1990. In 1994, this software was updated to include heat transfer and non-Newtonian fluids. Plastification and melting behavior support was added to the software in 1998. Vergnes et al. developed a one-dimensional (1D) model and linked it to the Ludovic software11. Tomiyama et al. proposed a devolatilization model based on the FAN method, bubble nucleation, and growth in the polymer melt12. The FAN method is the most straightforward and robust method for calculating pressure, temperature, and resin distribution for entire screws with short calculation times; however, it is limited as it can analyze the resin profile only in the screw axial direction.
The other approach to theoretical analysis is the three-dimensional (3D) numerical simulation of fully filled screw elements based on the finite element method13-20. Recently, SPH was applied to complex flow in partially filled twin-screw element21-23. The SPH method can obtain a detailed resin distribution in the radial, circumferential, and axial directions on the screws while it requires a long calculation time and the application limits to the small set of screw segments.
The FAN method reduced the number of dimensions to one, and the resin distribution of the circumference direction is no longer considered. The SPH method remains inapplicable to the analysis of whole screws because of the available computational capacity. The current state of the numerical simulation method is such that it can provide either a one-dimensional distribution of the whole screw or a three-dimensional distribution of a small number of screw elements. To design and operate TSEs more efficiently, a numerical simulation method that provides the resin distribution over the entire screws is required. The calculation of the resin distribution for all the screws would provide a detailed insight into the TSE process and reduce the number of time-consuming experiments. Therefore, in this study, we reconstructed the FAN method to calculate the resin profile on the axial and circumferential directions of the screw using the Hele–Shaw flow model and finite element method. The reconstructed method considers the flow velocities in the axial and circumferential directions. This concept is based on the 2.5 D FEM, which has conventionally been used in the injection molding CAE field 24,25.
The remainder of this manuscript is organized as follows: In the following sections, the mathematical formulation of the Hele–Shaw model is described, and then, the experimental apparatus and method are explained. In the Results and discussion section, the numerical simulation results of resin pressure, temperature, and resin distribution are compared with the experimental data.