Non-isothermal free-surface viscous flow of polymer melts in pipe extrusion using an open-source interface tracking finite volume method

Polymer extrudate swelling is a rheological phenomenon that occurs after polymer melt flow emerges at the die exit of extrusion equipment due to molecular stress relaxations and flow redistributions. Specifically, with the growing demand for large scale and high productivity, polymer pipes have recently been produced by extrusion. This study reports the development of a new incompressible non-isothermal finite volume method, based on the Arbitrary Lagrangian–Eulerian (ALE) formulation, to compute the viscous flow of polymer melts obeying the Herschel–Bulkley constitutive equation. The Papanastasiou-regularized version of the constitutive equation is employed. The influence of the temperature on the rheological behavior of the material is controlled by the Williams–Landel–Ferry (WLF) function. The new method is validated by comparing the extrudate swell ratio obtained for Bingham and Herschel–Bulkley flows (shear-thinning and shear-thickening) with reference data found in the scientific literature. Additionally, the essential flow characteristics including yield-stress, inertia and non-isothermal effects were investigated.The authors would like to acknowledge the funding by FEDER funds through the COMPETE 2020 Programme and National Funds through FCT-Portuguese Foundation for Science and Technology under the projects UIDB/05256/2020 and UIDP/05256/202

An effective interface tracking method for simulating the extrudate swell phenomenon

The extrudate swell, i.e., the geometrical modifications that take place when the flowing material leaves the confined flow inside a channel and moves freely without the restrictions that are promoted by the walls, is a relevant phenomenon in several polymer processing techniques. For instance, in profile extrusion, the extrudate cross-section is subjected to a number of distortions that are motivated by the swell, which are very difficult to anticipate, especially for complex geometries. As happens in many industrial processes, numerical modelling might provide useful information to support design tasks, i.e., to allow for identifying the best strategy to compensate the changes promoted by the extrudate swell. This study reports the development of an improved interface tracking algorithm that employs the least-squares volume-to-point interpolation method for the grid movement. The formulation is enriched further with the consistent second-order time-accurate non-iterative Pressure-Implicit with Splitting of Operators (PISO) algorithm, which allows for efficiently simulating free-surface flows. The accuracy and robustness of the proposed solver is illustrated through the simulation of the steady planar and asymmetric extrudate swell flows of Newtonian fluids. The role of inertia on the extrudate swell is studied, and the results that are obtained with the newly improved solver show good agreement with reference data that are found in the scientific literatureSearch-ON2 (NORTE-07-0162-FEDER-000086) the HPC infrastructure of UMinho under NSRF through ERDF; and FCT I.P. through the Advanced Computing Project CPCA/A00/6057/2020 using the Minho Advanced Computing Center (MACC

Assessing the free surface tracking approach to simulate extrudate swell

The extrudate swell, the geometrical modifications that take place when the flowing material leaves the confined flow inside a channel and moves freely without the restrictions promoted by the walls, is a relevant phenomenon in several polymer processing techniques. For instance, in profile extrusion, the extrudate cross-section suffers a number of distortions motivated by swell, which are very difficult to anticipate, especially for complex geometries. As happens in many industrial processes, numerical modelling might provide useful information to support design tasks, enabling to identify the best strategy to compensate the changes promoted by the extrudate swell. There are different ways to model free-surface flows, which can be grouped in Interface Tracking (IT) and Interface Capturing (IC) approaches. When dealing with steady state processes, which is the case of profile extrusion, IT is usually the best alternative, since it does not present the problems related to interface diffusion inherent to the IC approaches. OpenFOAM comprises a solver to simulate free-surface flows following an IT approach, which was proposed by Tukovic & Jasak (2008) and Tukovic et al., (2012). This work aims to assess the capability of that solver to simulate the extrudate swell process in profile extrusion, by using the interfaceTrackingFvMesh and interTrackMeshMotion libraries available in OpenFOAM-v1912 to track the free surface movement with a dynamic mesh motion. For this purpose, the data provided by Mitsoulis et al., (2012) on simulation of the extrudate swell of a Newtonian fluid at different Reynolds number flows is considered as the reference for validation.The authors would like to acknowledge the funding by FEDER funds through the COMPETE 2020 Programme and National Funds through FCT - Portuguese Foundation for Science and Technology under the projects UIDB/05256/2020 and UIDP/05256/2020, TSSiPRO - Technologies for Sustainable and Smart Innovative Products (NORTE-01-0145-FEDER-000015) and FAMEST - Footwear, Advanced Materials, Equipment’s and Software Technologies (POCI-01-0247-FEDER-024529). The authors also acknowledge the support of the computational clusters Search-ON2 (NORTE-07-0162-FEDER-000086) and Minho Advanced Computing Center (MACC)

Bridging the scales in capillary rise dynamics with complexity-reduced models

Dynamic wetting processes inherently manifest as multiscale phenomena. While the capillary length is typically millimeters, solid-liquid interactions occur at the nanometer scale. These short-range interactions significantly affect macroscopic behaviors like droplet spreading and menisci dynamics. The Navier slip length, determined by liquid viscosity and solid-liquid friction, plays a crucial role in three-phase contact line dynamics. It varies from nanometers (hydrophilic) to microns (hydrophobic). However, resolving it in computational fluid dynamics (CFD) simulations can be computationally expensive. In this study, we propose simplified ordinary differential equation (ODE) models, leveraging local dissipation rates from Stokes flow solutions near the moving contact line, to bridge the nanoscale physics and macroscopic dynamics. Our ODE model accurately predicts the impact of the slip parameter in fully resolved CFD simulations, focusing on capillary rise dynamics.Comment: 10 pages, 2 figure

On Computational Investigation of the Supercooled Stefan Problem

In the present paper a computational model for the macroscopic freezing mechanism under supercooled conditions relying on the physical and mathematical description of the two-phase Stefan problem is formulated. The relevant numerical algorithm based on the finite volume method is implemented into the open source software OpenFOAM©. For the numerical capturing of the moving interface between the supercooled and the solidified liquid an appropriate level set formulation is utilized. The heat transfer equations are solved in both the liquid phase and solid phase independently from each other. At the interface a Dirichlet boundary condition for the temperature field is imposed and a ghost-face method is applied to ensure accurate calculation of the normal derivative needed for the jump condition, i.e. for the interface-velocity in the normal direction. For the sake of updating the level set function a narrow-band around the interface is introduced. Within this band, whose width is temporally adjusted to the maximum curvature of the interface, the normal-to-interface velocity is appropriately expanded. The physical model and numerical algorithm are validated along with the analytical solution. Understanding instabilities is the first step in controlling them, so to quantify all sorts of instabilities at the solidification front the Mullins-Sekerka theory of morphological stability is investigated

On Computational Investigation of the Supercooled Stefan Problem

In the present paper a computational model for the macroscopic freezing mechanism under supercooled conditions relying on the physical and mathematical description of the two-phase Stefan problem is formulated. The relevant numerical algorithm based on the finite volume method is implemented into the open source software OpenFOAM©. For the numerical capturing of the moving interface between the supercooled and the solidified liquid an appropriate level set formulation is utilized. The heat transfer equations are solved in both the liquid phase and solid phase independently from each other. At the interface a Dirichlet boundary condition for the temperature field is imposed and a ghost-face method is applied to ensure accurate calculation of the normal derivative needed for the jump condition, i.e. for the interface-velocity in the normal direction. For the sake of updating the level set function a narrow-band around the interface is introduced. Within this band, whose width is temporally adjusted to the maximum curvature of the interface, the normal-to-interface velocity is appropriately expanded. The physical model and numerical algorithm are validated along with the analytical solution. Understanding instabilities is the first step in controlling them, so to quantify all sorts of instabilities at the solidification front the Mullins-Sekerka theory of morphological stability is investigated

On the effect of the Navier slip length in capillary rise dynamics

Dynamic wetting processes inherently manifest as multiscale phenomena. While the capillary length is typically millimeters, solid-liquid interactions occur at the nanometer scale. These short-range interactions significantly affect macroscopic behaviors like droplet spreading and menisci dynamics. The Navier slip length, determined by liquid viscosity and solid-liquid friction, plays a crucial role in three-phase contact line dynamics. It varies from nanometers (hydrophilic) to microns (hydrophobic). However, resolving it in computational fluid dynamics (CFD) simulations can be computationally expensive. In this study, we propose simplified ordinary differential equation (ODE) models, leveraging local dissipation rates from Stokes flow solutions near the moving contact line, to bridge the nanoscale physics and macroscopic dynamics. Our ODE model accurately predicts the impact of the slip parameter in fully resolved CFD simulations, focusing on capillary rise dynamics