Lagrangian finite element method for 3D time-dependent non-isothermal flow of K-BKZ fluids

Marín, José Manuel Román; Rasmussen, Henrik Koblitz

doi:10.1016/j.jnnfm.2009.05.008

Cited by 8 publications

(5 citation statements)

References 78 publications

(66 reference statements)

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“…The work was extended to include extrudate swell in the same geometry [130], and comparison with experimentally measured velocity fields in a planar step contraction flow [131] at Weissenberg numbers up to 1.39. Reference [132] deals with transient 3D simulation of the flow of a KBKZ fluid using a Lagrangian kinematics formulation with a temperature-dependent pseudotime based on the assumption of a thermo-rheologically simple material. Convergence of the calculations was demonstrated by comparison with analytic results for a non-isothermal planar contraction flow at a Deborah number of 1.…”

Section: Viscoelastic Flow Simulationsmentioning

confidence: 99%

Computer-aided design and optimization of profile extrusion dies for thermoplastics and rubber: a review

Pittman

2011

Proceedings of the Institution of Mechanical Engineers, Part E:

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A review is provided of issues and techniques in design and optimization of profile extrusion dies for thermoplastics and rubber, with particular emphasis on unplasticized polyvinyl chloride and rubber compounds. Traditional profile die design methods are contrasted with computer-based ones, with respect to efficiency and economic benefits. The main types of die construction are outlined. Physical phenomena relevant to the design and performance of dies are summarized, including: rheology and kinematics of the flow, wall slip, extrusion instabilities, residence time and degradation, extrudate swell, draw-down, and thermal effects. Approaches and strategies for die design are explained, including: flow balancing – with guidance from analytic flow results, the Avoid-Cross-Flow strategy, use of flow separators, and designing for extrudate swell. Published computer simulations of die flow used to assist with design are reviewed. Introducing automatic die design, the structure and elements of a computerized design optimization environment are set out. Key components and options within this are described, including: objective functions, constraints, design variables, optimization algorithms, design parameterization and flow domain meshing, and optimization strategies. Published implementations of computerized profile die design optimization are described. Automatic design optimization is compared with the work of a designer assisted by flow simulations in the industrial environment, showing how substantial reductions in demands on the designer's time are possible. The nature and potential of robust design is outlined, with techniques for its implementation. Conclusions are drawn as to the present state of the art in computer-assisted profile die design and optimization, and potential advances.

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Section: Viscoelastic Flow Simulationsmentioning

confidence: 99%

Computer-aided design and optimization of profile extrusion dies for thermoplastics and rubber: a review

Pittman

2011

Proceedings of the Institution of Mechanical Engineers, Part E:

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“…The approach to non-isothermal flow commonly follows the assumption of polymer melts as a thermorheological simple material (Morland and Lee [32]), applying a pseudo time (Crochet and Naghdi [33]). The currently only existing numerical method for non-isothermal time-dependent flow of polymers as a structured liquid based on the pseudo time approach is the 3D Lagrangian finite element method by Marín et al [34]. This numerical method is a non-isothermal extension of the numerical method used here.…”

Section: Flow Modeling Of Polymer Melts In Nilmentioning

confidence: 99%

3D Simulation of Nano-Imprint Lithography

2009

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A proof of concept study of the feasibility of fully three-dimensional (3D) time-dependent simulation of nano-imprint lithography of polymer melt, where the polymer is treated as a structured liquid, has been presented. Considering the flow physics of the polymer as a structured liquid, we have followed the line initiated by de Gennes, using a Molecular Stress Function model of the Doi and Edwards type. We have used a 3D Lagrangian Galerkin finite element methods implemented on a parallel computer architecture. In a Lagrangian techniques, the node point follows the particle movement, allowing for the movement of free surfaces or interfaces. We have extended the method to handle the dynamic movement of the contact line between the polymer melt and stamp during mold filling.

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“…The numerical implementation was validated with the calculation of various transient and steady drag correction factors for the motion of a sphere in a cylinder containing an upper convected Maxwell fluid. Later, Marín and Rasmussen [ 29 ] extended the Galerkin finite element method for simulating three-dimensional transient and non-isothermal flows of K–BKZ type fluids. Tomé et al [ 27 ] proposed a novel numerical approach to tackle the simulation of 3D viscoelastic unsteady free surface flows governed by the Oldroyd-B differential constitutive equation.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Three-Dimensional Free Surface Flows Using the K–BKZ–PSM Integral Constitutive Equation

Bertoco,

Castelo,

Ferrás

et al. 2023

Polymers

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This work introduces a novel numerical method designed to address three-dimensional unsteady free surface flows incorporating integral viscoelastic constitutive equations, specifically the K–BKZ–PSM (Kaye–Bernstein, Kearsley, Zapas–Papanastasiou, Scriven, Macosko) model. The new proposed methodology employs a second-order finite difference approach along with the deformation fields method to solve the integral constitutive equation and the marker particle method (known as marker-and-cell) to accurately capture the evolution of the fluid’s free surface. The newly developed numerical method has proven its effectiveness in handling complex fluid flow scenarios, including confined flows and extrudate swell simulations of Boger fluids. Furthermore, a new semi-analytical solution for velocity and stress fields is derived, considering fully developed flows of a K–BKZ–PSM fluid in a pipe.

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Lagrangian finite element method for 3D time-dependent non-isothermal flow of K-BKZ fluids

Cited by 8 publications

References 78 publications

Computer-aided design and optimization of profile extrusion dies for thermoplastics and rubber: a review

Computer-aided design and optimization of profile extrusion dies for thermoplastics and rubber: a review

3D Simulation of Nano-Imprint Lithography

Numerical Simulation of Three-Dimensional Free Surface Flows Using the K–BKZ–PSM Integral Constitutive Equation

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