J. M. Nóbrega

Computer aided rheological design of extrusion dies for profiles

Abstract A global methodology for the rheological design of profile extrusion dies is proposed. This methodology accounts for: (i) flow defects due to maximum admissible stresses, pressure drop and melt temperature increase; (ii) post-extrusion phenomena (shrinkage upon cooling, draw-down promoted by pulling and swelling after die exit) and (iii) flow balancing. The part of the methodology, that is concerned with flow balancing, was implemented and is here illustrated in two case studies, each one leading to the adoption of a different constructive solution. The software is based on a finite-volume method, which performs the required three-dimensional simulations, and is also briefly described.

Flow balancing in extrusion dies for thermoplastic profiles. Part III: Experimental Assessment

Abstract A computer code, previously developed by the authors for the automatic die design, is used to optimise the flow distribution in a profile extrusion die using two alternative strategies: one based on length optimisation and the other on thickness optimisation. The numerical predictions are then compared with experimental data gathered during extrusion experiments. The numerical predictions and the experimental results agree within the experimental uncertainty thus showing the effectiveness of the computer code, the optimisation algorithm and the design strategies implemented. Generally speaking, measured and predicted values of pressure drop and flow rate are in good agreement (within 8 % and 6 %, respectively). It also is confirmed that optimisation based on thickness control leads to final profiles that are more prone to distortion.

Flow Balancing in Extrusion Dies for Thermoplastic Profiles: Part I: Automatic Design

Abstract To achieve a specified geometry for an extruded profile, together with a minimal degree of internal stresses, flow balancing of the die is required. To attain this objective, the flow along a profile die channel must be accurately described, and this demands a computational code able to predict complex 3D non-isothermal flow patterns. In this work new methodologies for flow balancing are implemented and illustrated. The design code developed to carry out the automatic search of a final geometry consists of an optimisation routine coupled with geometry and mesh generators and a 3D computational code based on the finite volume method. The issues discussed and described here encompass recent developments, namely the implementation of two alternative optimisation algorithms for the automatic search of a final solution, the enhancement of the strategies previously developed to balance the flow, some improvements in the routine used to generate the mesh and the adoption of a progressive mesh refinement technique. The examples show that the proposed methodology performs well and the solution is attained in just a few minutes of calculation without any user intervention during the calculation process.

Analytical and numerical study of the electro-osmotic annular flow of viscoelastic fluids

In this work we present semi-analytical solutions for the electro-osmotic annular flow of viscoelastic fluids modeled by the Linear and Exponential PTT models. The viscoelastic fluid flows in the axial direction between two concentric cylinders under the combined influences of electrokinetic and pressure forcings. The analysis invokes the Debye-Hückel approximation and includes the limit case of pure electro-osmotic flow. The solution is valid for both no slip and slip velocity at the walls and the chosen slip boundary condition is the linear Navier slip velocity model. The combined effects of fluid rheology, electro-osmotic and pressure gradient forcings on the fluid velocity distribution are also discussed.

Flow Balancing in Extrusion Dies for Thermoplastic Profiles: Part II: Influence of the Design Strategy

Abstract To achieve a specified geometry for an extruded profile with minimal level of stress gradient induced by pulling, flow balancing of the die is required. To fulfil this requisite, a set of operating conditions and polymer rheological properties is considered during the design step. However, fluctuations of the operating conditions and/or slight variations of the polymer rheological properties are expected to occur during long-term production. Their effect on the performance of an extrusion die will depend, among other things, on the sensitivity of the flow distribution within the die. In this work, an extrusion die is optimised (balanced) using four different design methodologies and the final shapes of the die are compared in terms of their absolute quality (when used in the optimal conditions) and stability to the factors considered. For this purpose, a finite-volume based computational code is used to perform the required simulations of the non-isothermal three-dimensional flows, under conditions defined by a statistic Taguchi technique. The influence of some operating conditions on the flow distribution is assessed and the effect of the polymer melt rheology is also investigated. It was concluded that the use of different design methodologies lead to different results in terms of flow balancing and sensitivity to the factors considered and that the most balanced and stable extrusion die was that generated by the strategy based on the parallel zone thickness control.

Electro-osmotic and pressure-driven flow of viscoelastic fluids in microchannels: Analytical and semi-analytical solutions

In this work, we present a series of solutions for combined electro-osmotic and pressure-driven flows of viscoelastic fluids in microchannels. The solutions are semi-analytical, a feature made possible by the use of the Debye–Huckel approximation for the electrokinetic fields, thus restricted to cases with small electric double-layers, in which the distance between the microfluidic device walls is at least one order of magnitude larger than the electric double-layer thickness. To describe the complex fluid rheology, several viscoelastic differential constitutive models were used, namely, the simplified Phan-Thien–Tanner model with linear, quadratic or exponential kernel for the stress coefficient function, the Johnson-Segalman model, and the Giesekus model. The results obtained illustrate the effects of the Weissenberg number, the Johnson-Segalman slip parameter, the Giesekus mobility parameter, and the relative strengths of the electro-osmotic and pressure gradient-driven forcings on the dynamics of thes...

Modeling of Plasticating Injection Molding – Experimental Assessment

Abstract A computational model for the description of polymer flow during the plasticating phase of the injection molding process is proposed. The polymer behavior is determined during the dynamic and static phases of the process. The model takes into account the backwards movement of the screw, the presence of a non-return valve and the conduction of heat during the idle times. Results for the dynamic and static phases of the plasticization are presented. The model is also used to study the influence of some important operative process parameters, such as, screw speed, backpressure, barrel temperatures and injection chamber length. The assessment of the computational results is made experimentally by comparing the average temperature calculated with measurements made in front of the screw nozzle using both, an IR camera and an IR thermometer. The differences between the computational and the IR camera measurements are below 5%.

Development Length in Planar Channel Flows of Newtonian Fluids Under the Influence of Wall Slip

ðÞ , varying in the range 0 < kl � 1. The simulations were carried out for low Reynolds number flows in the range 0 < Re � 100, making use of a rigorous mesh refinement with an accuracy error below 1%. The development length is found to be a nonmonotonic function of the slip velocity coefficient, increasing up to kl � 0:1 � 0:4 (depending on Re) and decreasing for higher kl. We present a new nonlinear relationship between L, Re, and kl that can accurately predict the development length for Newtonian fluid flows with slip velocity at the wall for Re of up to 100 and kl up to 1. [DOI: 10.1115/1.4007383]

Design Guidelines to Balance the Flow Distribution in Complex Profile Extrusion Dies

Abstract In this work a novel methodology to balance the flow distribution in complex extrusion dies is proposed. For this purpose, the profile cross section geometry is divided into simpler geometries (L and T shaped profiles), which are balanced with a surrogate model obtained by a detailed numerical study. The numerical simulations are performed considering the non-isothermal flow of Bird-Carreau inelastic fluids, and the numerical computations are performed with a solver implemented in OpenFOAM computational library. The proposed methodology is assessed with some case studies.

Monitoring the Production of Polymer Nanocomposites by Melt Compounding with On-line Rheometry

Abstract Polymer nanocomposites are often prepared by melt compounding due to the suitability of the latter to industrial scale production. Even though monitoring the production process for quality control and/or optimization purposes is generally done off-line, the possibility of using on-line oscillatory rheometry has many inherent advantages. This work illustrates the use of a prototype rheometer to monitor the production of polymer nanocomposites by making measurements at specific locations along the extruder axis. The device is presented and its operation is explained. Examples of its use to characterize polypropylene and polyamide matrix nanocomposites with organoclays and carbon nanotubes are discussed, thus demonstrating the usefulness of the device.