The impact of upstream contraction flow on three-dimensional polymer extrudate swell from slit dies

Highlights

• Relevance of upstream contraction flow on slit die design.

• 3D simulation of edge/middle height and width die swell ratio.

• Combined effects of die geometry and PTT model parameters on extrudate swell.

• Interplay of stress and velocity redistribution on anisotropic swell behavior.

Abstract

The relevance of upstream contraction for extrudate swell behavior of polymer melts is numerically investigated for slit dies with an aspect ratio of 10 and a length-to-height ratio ranging from 2.5 to 40. Three-dimensional (3D) flow simulations are performed with ANSYS Polyflow software at different flow rates and a constant temperature of 200°C, selecting a differential multimode Phan-Thien-Tanner (PTT) constitutive model to describe the viscoelastic behavior of polypropylene. It follows that decreasing the die length results in an opposite trend of the swell ratio in the width and height directions. The width swell ratio decreases up to 28%, whereas the middle height swell ratio increases up to 55% and the edge height contraction increases with 37%, all highlighting the 3D anisotropy of the extrudate swell deformation. However, especially for low flow rates, the area swell ratio remains almost unchanged and cannot be used to capture the anisotropic swelling behavior. This is predominantly attributed to the similar relative redistribution degree of the axial velocity (v_x). An analysis of the transversal (v_y) and lateral velocity (v_z) combined with the stress field variation is performed as well to fully relate the anisotropic extrudate swell behavior to the various die lengths. The current study therefore contributes to completing the understanding of the relation of slit die design parameters and 3D extrudate flow under isothermal conditions, covering both developing and fully developed flow.

Introduction

Extrusion is one of the most important material forming operations widely considered in the polymer industry. Examples of processes in which polymer extrusion is employed include blow molding, and sheet, pipe and profile extrusion [1], [2], [3], [4], [5], [6], [7]. In extrusion, the phenomenon of die swell, i.e. the shape variation of the extrudate swell out of die exit, is of particular interest, as it is an important controlling factor to obtain a desired product profile. Different variables determine this die swell, including the processing conditions, the viscoelastic properties of the polymer melt, and the deformation history [8], [9], [10], [11].

It should be stressed that the deformation history can already be relevant upon the die entry with generally a converging flow transition region between the barrel and the die entrance. In this region, the flow cross-section decreases and a significant contraction deformation is applied to the flowing melt. Stemming from its much more complex flow behavior with extensional and shear flow taking place together, contraction flow is considered as a benchmark for evaluating the capability of constitutive models and numerical methods to capture the viscoelastic behavior of polymer melts or solutions [12,13].

As a consequence, there have been numerous publications related to contraction flow, covering both experimental and numerical results [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31]. For example, in a recent review, Musil et al. [22] pointed out that the converging flow transition region is the key trigger for polymer melt stagnation or secondary flow. Contraction leads to developing downstream flow, which exhibits considerable exit pressure therefore codetermining the extrudate swell behavior. Previous studies have often focused on flows through capillary or slit dies, which were considered as axisymmetric or planar flows, respectively [5,[23], [24], [25], [26]. Already in the 1970s, Han et al. [24] experimentally observed that increasing the contraction ratio, i.e. the ratio between the reservoir diameter and the die (inlet) diameter leads to an increase of the die swell of high density polyethylene (HDPE) melt through a capillary die. In the 1980s, Tanner and Luo [23,27,28] published seminal works on the simulation of extrudate swell of a highly viscoelastic low density polyethylene (LDPE) melt for both long and short capillary dies, using the integral Kaye-Bernstein-Kearsley-Zapas (KBKZ) model and the streamline finite element method (SFEM). It has been reported that by shortening the die length, the extrudate swell ratio increases. These improved models can capture general trends of more realistic flows at higher Weissenberg numbers or apparent shear rates. Hatzikiriakos, Mitsoulis and co-workers have put forward several contributions in which the effects of an upstream contraction flow on the extrudate swell behavior have been investigated for capillary and slit dies by using integral or differential viscoelastic models [5,9,12,29,32]. These authors discussed the applicability and limitations of various rheological models and numerical formulations to grasp polymer extrudate swell [5]. Recently, Robertson et al. [11,33] theoretically predicted the extrudate swell of axisymmetric constricted polystyrene (PS) melts with a variation in the broadness of the molar mass distribution, using the Rolie-Poly constitutive model. A more pronounced swelling for shorter dies at higher shear rates is noted, due to the larger contribution of unrelaxed chains thus chain stretching.

Notably most numerical simulations for extrudate die swell rely on a two-dimensional (2D) model for simplifying the calculations. However, in practice all die dimensions are finite, e.g. the width-to-height or aspect ratio of a common slit die is finite, and the shape of the upstream contraction or transition region is irregular [34,35], so that it is likely that polymer melt flow in these regions cannot be simplified by a 2D geometry model. Indeed in our previous work, first focusing on an aspect ratio of 10 and later on aspect ratios between 1 and 20, we highlighted already the relevance of 3D characteristics of the extrudate swell behavior of polypropylene (PP) melts at 200°C through slit dies, considering the case of fully developed flow by selecting a sufficiently long experimental die length [36,37]. For any aspect ratio, a significant change in the 3D extrudate deformation is reported, with absolute variations up to 30% in all Cartesian directions and relative variations up to 10% in individual such directions. However, a developing flow is expected before the die exit if the slit die length reduces to a certain value, further complicating the 3D swell behavior. Considering the anisotropic swell behavior in the extrudate width and height directions it is thus interesting to study the potential of 3D effects induced by the contraction flow for different slit die lengths. This type of research is further supported by taking into account that there are only limited reports available on this matter. Moreover, from an economic point of view, one wants to minimize the material amount and the complexity of a die set-up and thus control the die length for a given contraction configuration.

Therefore, in the present work, we investigate how the length of a slit die with a fixed aspect ratio affects extrudate swell behavior by its connection with a given upstream contraction region in which the cross-section is still variable. Focus is on the gradual transformation from developing flow to fully developed flow before the die exit, in which the length of the die part with a constant cross-section varies. In the finite element method based simulations, as conducted with POLYFLOW software, the latter die length is varied from 5 to 80 mm, considering an upstream contraction region of length 35 mm and the multimode Phan-Thien-Tanner (PTT) model for polypropylene melt at 200°C with the parameters previously tuned based on rheological data [36]. A comprehensive comparison of the swelling behavior in the extrudate width and height directions is carried out as a function of the variable die length accompanied by an analysis of the associated stress and velocity fields.