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.