A Personal Perspective on the Use of Modelling Simulation for Polymer Melt Processing

Copyright 2015 Carl Hanser Verlag. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Carl Hanser Verlag. The authors are grateful to the publisher, Carl Hanser Verlag, for letting the manuscript being archived in this Open Access repository. The final publication is available at = http://dx.doi.org/10.3139/217.3020International audienceThis paper gives a personal view on the state of art in relation to the modelling of polymer melt processing. The paper briefly reviews both industrial, laboratory and modelling developments over the last forty years and highlights the key aspects now required for realistic modelling of polymer melt processing. The paper summarizes elements relating to the numerical simulation of specific and general polymer processes and also provides topical examples of the application of numerical modelling to certain commercial processes. The paper concludes with identifying areas of polymer processing that still remain a challenge in relation to accurate prediction

Numerical simulation of the plastics injection moulding process

The Hele-Shaw formulation is widely used for the simulation of the injection moulding process. The influence of the Hele-Shaw approximations is, however, unknown. A two-dimensional numerical model based on the Hele-Shaw formulation, and a model based on the Navier-Stokes equations without the Hele-Shaw approximations were developed. The solutions obtained with these two approaches were compared to investigate the influence of the Hele-Shaw approximations on the simulation of the injection moulding process. Weakly compressible, non-Newtonian flow of an amorphous polymer melt under non-isothermal conditions were simulated using constitutive equations generalized to non-Newtonian materials. The finite volume method, which is a very powerful method yet easy to use, was used to discretize the governing equations as compared to finite element methods used in most other reported models. The influence of the Hele-Shaw approximations on the solutions of specific flow cases was determined by comparing the solutions obtained with the model based on the Hele-Shaw formulation and the model based on the Navier-Stokes equations. Parametric studies were done to compare the solutions of the two numerical models for a wider range of flow cases. The following conclusions were made as a consequence of this study: Numerical models to simulate the injection moulding process can be simplified and the computer time required to solve these models can be reduced by using the Hele-Shaw formulation instead of solving the full Navier-Stokes equations. Numerical models based on the Hele-Shaw formulation are well suited to simulate the injection moulding process when the geometries and flow conditions fall within certain limits. These limits are determined by the combined effect of the geometry and the flow conditions represented by the Reynolds number. The simplicity of the finite volume method used in the generalized Hele-Shaw model makes it an attractive model to use for injection moulding simulations

A continuum model of multi-phase reactive transport in igneous systems

Multi-phase reactive transport processes are ubiquitous in igneous systems. A challenging aspect of modelling igneous phenomena is that they range from solid-dominated porous to liquid-dominated suspension flows and therefore entail a wide spectrum of rheological conditions, flow speeds, and length scales. Most previous models have been restricted to the two-phase limits of porous melt transport in deforming, partially molten rock and crystal settling in convecting magma bodies. The goal of this paper is to develop a framework that can capture igneous system from source to surface at all phase proportions including not only rock and melt but also an exsolved volatile phase. Here, we derive an n-phase reactive transport model building on the concepts of Mixture Theory, along with principles of Rational Thermodynamics and procedures of Non-equilibrium Thermodynamics. Our model operates at the macroscopic system scale and requires constitutive relations for fluxes within and transfers between phases, which are the processes that together give rise to reactive transport phenomena. We introduce a phase- and process-wise symmetrical formulation for fluxes and transfers of entropy, mass, momentum, and volume, and propose phenomenological coefficient closures that determine how fluxes and transfers respond to mechanical and thermodynamic forces. Finally, we demonstrate that the known limits of two-phase porous and suspension flow emerge as special cases of our general model and discuss some ramifications for modelling pertinent two- and three-phase flow problems in igneous systems.Comment: Revised preprint submitted for peer-reviewed publication: main text with 8 figures, 1 table; appendix with 3 figures and 2 table

Verification and validation of openInjMoldSim, an open-source solver to model the filling stage of thermoplastic injection molding

In the present study, the simulation of the three-dimensional (3D) non-isothermal, non-Newtonian fluid flow of polymer melts is investigated. In particular, the filling stage of thermoplastic injection molding is numerically studied with a solver implemented in the open-source computational library O p e n F O A M ® . The numerical method is based on a compressible two-phase flow model, developed following a cell-centered unstructured finite volume discretization scheme, combined with a volume-of-fluid (VOF) technique for the interface capturing. Additionally, the Cross-WLF (Williams–Landel–Ferry) model is used to characterize the rheological behavior of the polymer melts, and the modified Tait equation is used as the equation of state. To verify the numerical implementation, the code predictions are first compared with analytical solutions, for a Newtonian fluid flowing through a cylindrical channel. Subsequently, the melt filling process of a non-Newtonian fluid (Cross-WLF) in a rectangular cavity with a cylindrical insert and in a tensile test specimen are studied. The predicted melt flow front interface and fields (pressure, velocity, and temperature) contours are found to be in good agreement with the reference solutions, obtained with the proprietary software M o l d e x 3 D ® . Additionally, the computational effort, measured by the elapsed wall-time of the simulations, is analyzed for both the open-source and proprietary software, and both are found to be similar for the same level of accuracy, when the parallelization capabilities of O p e n F O A M ® are employed.This work is funded by FEDER funds through the COMPETE 2020 Programme and National Funds through FCT (Portuguese Foundation for Science and Technology) under the projects UID-B/05256/2020, UID-P/05256/2020, MOLDPRO-Aproximações multi-escala para moldação por injeção de materiais plásticos (POCI-01-0145-FEDER-016665), and FAMEST-Footwear, Advanced Materials, Equipment’s and Software Technologies (POCI-01-0247-FEDER-024529)

Preferential Paths of Air-water Two-phase Flow in Porous Structures with Special Consideration of Channel Thickness Effects.

Accurate understanding and predicting the flow paths of immiscible two-phase flow in rocky porous structures are of critical importance for the evaluation of oil or gas recovery and prediction of rock slides caused by gas-liquid flow. A 2D phase field model was established for compressible air-water two-phase flow in heterogenous porous structures. The dynamic characteristics of air-water two-phase interface and preferential paths in porous structures were simulated. The factors affecting the path selection of two-phase flow in porous structures were analyzed. Transparent physical models of complex porous structures were prepared using 3D printing technology. Tracer dye was used to visually observe the flow characteristics and path selection in air-water two-phase displacement experiments. The experimental observations agree with the numerical results used to validate the accuracy of phase field model. The effects of channel thickness on the air-water two-phase flow behavior and paths in porous structures were also analyzed. The results indicate that thick channels can induce secondary air flow paths due to the increase in flow resistance; consequently, the flow distribution is different from that in narrow channels. This study provides a new reference for quantitatively analyzing multi-phase flow and predicting the preferential paths of immiscible fluids in porous structures

Development of a multiphase flow simulator for drilling applications

Drilling, or gas kick, simulators are becoming prevalent in industry due to their ability to replicate wellbore conditions that are not feasible in a laboratory setting. This is becoming more desirable as deeper wells are being explored. One of the biggest dangers that could happen during drilling operations is the onset of a gas kick. This occurs when a zone in the formation whose pressure is higher than that of the wellbore is breached. This allows for the undesired influx of formation fluids into the wellbore. If left uncontrolled, it could develop into a blowout. Gas kick simulators allow for testing of procedures that could be used to contain kicks at such depths. Furthermore, the use of drilling simulators could provide more insight into other phenomena. These include wellbore breathing and fracture ballooning, that cause similar kick symptoms at the surface and lead to expensive misdiagnosis, and the dissolution of gas into oil based mud, which could delay the identification of a kick. This thesis investigates the development of the initial integration of a drilling simulator into UTWELL, the wellbore simulator program developed at The University of Texas at Austin, by implementing a gas kick module. The transport equations of mass and momentum conservation were discretized using a Semi-Implicit Homogeneous Method over a one dimensional staggered grid. The multiphase phenomena were modelled using a Drift Flux approach as opposed to a mechanistic, Two Fluid approach. This was due to increased stability of the solution and faster computation time, despite the risk of loosing accuracy. The simulator was successful at simulating single phase flows for fluids with distinct rheology models, and with wellbores with discontinuities in the geometry. When attempting to simulate the well control of a gas kick in water based mud, the results were mixed. Attempt at simulating a `Floating Mud Cap' method failed due to the simulator's inability to perform drainage functions that allow for the raising and lowering of the mud level in the wellbore. However, the simulator was successful at capturing the behaviour of the gas kick as it entered and migrated through the wellbore, matching literature results. The simulator was compared to experimental data gathered from a test well. Three different scenarios were tested: No Drillstring, Semi-Submerged Drillstring and Drillstring at the Bottom. In all three cases, there was a good match between the experimental and simulation results for the bottomhole and choke pressures. The pit gain was severely overestimated in the 'No Drillstring' and 'Semi-Submerged Drillstring Case', however this was due to a higher influx of simulated gas having entered the wellbore during simulations. The 'Drillstring at the Bottom' simulation matched well with all data and with other simulators. Recommendations included full integration and testing of a compositional model to simulate oil based mud cases, implementation of automatic choke control and special flux splitting techniques in the discretization in order to better handle pressure waves caused by discontinuities.Petroleum and Geosystems Engineerin

Contribution to the Non-Lagrangian Formulation of Geotechnical and Geomechanical Processes

Numerical simulations of geomechanical and geotechnical processes, such as vibro-injection pile installation, require suitable algorithms and sufficiently realistic models. These models have to account for large deformations, the evolution of material interfaces including free surfaces and contact interfaces, for granular material behavior in different flow regimes as well as for the interaction of the different materials and phases. Although the traditional Lagrangian formulation is well-suited to handling complex material behavior and maintaining material interfaces, it generally cannot represent large deformation, shear and vorticity. This is because in Lagrangian numerical methods the storage points (nodes resp. material points) move with the local material velocity, which may cause mesh tangling resp. clustering of points. The present contribution addresses the development of models for geotechnical and geomechanical processes by utilizing Eulerian and Arbitrary Lagrangian-Eulerian (ALE) formulations. Such non-Lagrangian viewpoints introduce additional difficulties which are discussed in detail. In particular, we investigate how to track interfaces and to model interaction of different materials with respect to an arbitrarily moving control volume, and how to validate non-Lagrangian numerical models by small-scale experimental tests

Experimental investigation and process simulation of the compression molding process of Sheet Molding Compound (SMC) with local reinforcements

Die ganzheitliche virtuelle Auslegung von Faserverbundbauteilen aus Sheet Molding Compund (SMC) ermöglicht es durch die Berücksichtigung von Fertigungseffekten in der Struktursimulation, bedarfsgerechtere und somit leichtere und günstigere Bauteile zu fertigen. Hierfür muss jedoch die Prozesssimulation in der Lage sein, die SMC-spezifischen Blockströmung auf Grund der niedrig-viskosen Randschicht richtig zu beschreiben. Nur so kann das richtige Füllverhalten und somit auch die richtige Faserorientierungsverteilung vorhergesagt werden. Dies wird gerade im Kontext des zunehmenden Einsatzes von semi-strukturellen SMC-Formulierungen besonders wichtig. Darüber hinaus gibt es neue Konzepte der Hybridisierung von SMC mit lokalen unidirektionalen Verstärkungen, welche ebenfalls in der Prozesssimulation berücksichtigt werden müssen, um die Positionierung der Verstärkungen abzusichern. Aus diesem Grund wurde in dieser Arbeit ein neuer dreidimensionaler Ansatz für die Prozesssimulation von SMC entwickelt, der sowohl die durch Dehnviskosität dominierte Kernschicht, als auch die niedrig-viskose Randschicht berücksichtigt. Durch die Verwendung des gekoppelten Euler-Lagrange-Ansatzes, kann auch die Interaktion zwischen SMC und lokalen Verstärkungen abgebildet und vorhergesagt werden. Um die Informationen aus der Prozesssimulation in die Struktursimulation zu übertragen, wurde eine CAE-Kette weiterentwickelt, die das Übertragen der Information vom Prozess- zum Strukturnetz ermöglicht. Hierbei wird sowohl eine Cluster-Bildung, als auch eine Homogenisierung auf Basis der Faserorientierungsverteilung durchgeführt. Zur experimentellen Analyse des Fließverhaltens, sowie zur Bereitstellung der benötigten validen Materialparameter für die Prozesssimulation, wurde ein neues rheologisches Fließpresswerkzeug entwickelt. Mit diesem Werkzeug wurden erstmal das kompressible Verhalten von semi-strukturellen SMC Formulierungen nachgewiesen und über einen phänomenologischen Ansatz beschrieben. Auf Basis dieser Kompressibilitätsformulierung konnte ein neues rheologisches Model entwickelt, das eine genauere Charakterisierung ermöglicht. Durch die Charakterisierung von fünf unterschiedlichen SMC-Materialformulierungen, konnten einige Gesetzmäßigkeiten der Materialparameter abgeleitet werden