Stefanie Nicole Elgeti

Fully-implicit log-conformation formulation of constitutive laws

Abstract Subject of this paper is the derivation of a new constitutive law in terms of the logarithm of the conformation tensor that can be used as a full substitute for the 2D governing equations of the Oldroyd-B, Giesekus and other models. One of the key features of these new equations is that – in contrast to the original log-conf equations given by Fattal and Kupferman (2004) – these constitutive equations combined with the Navier–Stokes equations constitute a self-contained, non-iterative system of partial differential equations. In addition to its potential as a fruitful source for understanding the mathematical subtleties of the models from a new perspective, this analytical description also allows us to fully utilize the Newton–Raphson algorithm in numerical simulations, which by design should lead to reduced computational effort. By means of the confined cylinder benchmark we will show that a finite element discretization of these new equations delivers results of comparable accuracy to known methods.

An ultraweak DPG method for viscoelastic fluids

Abstract We explore a vexing benchmark problem for viscoelastic fluid flows with the discontinuous Petrov-Galerkin (DPG) finite element method of Demkowicz and Gopalakrishnan [1] , [2] . In our analysis, we develop an intrinsic a posteriori error indicator which we use for adaptive mesh generation. The DPG method is useful for the problem we consider because the method is inherently stable—requiring no stabilization of the linearized discretization in order to handle the advective terms in the model. Because stabilization is a pressing issue in these models, this happens to become a very useful property of the method which simplifies our analysis. This built-in stability at all length scales and the a posteriori error indicator additionally allows for the generation of parameter-specific meshes starting from a common coarse initial mesh. A DPG discretization always produces a symmetric positive definite stiffness matrix. This feature allows us to use the most efficient direct solvers for all of our computations. We use the Camellia finite element software package [3] , [4] for all of our analysis.

Simplex space‐time meshes in two‐phase flow simulations

Summary In this paper, we present the numerical solution of two-phase flow problems of engineering significance with a space-time finite element method that allows for local temporal refinement. Our basis is the method presented in [?behr2008simplex], which allows for arbitrary temporal refinement in preselected regions of the mesh. It has been extended to adaptive temporal refinement that is governed by a quantity that is part of the solution process, namely, the interface position in two-phase flow. Due to local effects such as surface tension, jumps in material properties, etc., the interface can in general be considered a region that requires high flexibility and high resolution, both in space and in time. The new method, which leads to tetrahedral (for 2D problems) and pentatope (for 3D problems) meshes, offers an efficient yet accurate approach to the underlying two-phase flow problems. This article is protected by copyright. All rights reserved.

Design Criteria in Numerical Design of Profile Extrusion Dies

Abstract. The rather unintuitive and non-linear behavior of plastics melts is a well-known obstacle in the design and manufacturing cycle of profile extrusion dies. This is reflected, for example, in the so-called running-in experiments, in which the already manufactured die is modified up to 15 times until the final product, shaped by the die, matches the quality requirements. Besides a homogeneous outflow velocity and thus homogeneous material distribution, an appropriate die swell is a second design objective which complicates the reworking of the manufactured die. We are conducting work to shorten the manual running-in process by the means of numerical shape optimization, making this process significantly less costly and more automatic. From a numerical point of view, the extrusion process is not as challenging as high-speed flows, since it can be described by steady Stokes equations without major loss of accuracy. The drawback, however, is the need for ac- curate modeling of the plastics behavior, which generally calls for shear-thinning or even viscoelastic models, as well as for 3D computations, leading to large computational grids. The intention of this paper is to investigate the application of specific geometry features in extrusion dies and their influence on objective functions in an optimization framework. However, representative objective functions concerning die swell and the incorporation of known geometry features, as used by experienced die designers, into the optimization framework still remain a challenge. Hence, the topics discussed are the influence of the mentioned geometry features on existing objective functions as well as an outlook on an algorithmic implementation into the optimization process with regard to representative objective functions.

Study on objective functions for the slow shot phase in high-pressure die casting

High-pressure die casting is an important process in the field of aluminum processing. Especially during the slow shot phase, the process parameters immensely influence the cast part quality. At the current state of the art, the appropriate process parameters are identified based on running-in trials and significant experience. To translate this experience into a mathematical framework is the aim of this work. The idea is to shift the running-in trials to the computer—now in the form of a numerical optimization. In view of the optimization, this paper presents a selection of objective functions. These are assessed with the respect to (1) their suitability as an overall quality measure of the casting process and (2) the extent to which they reflect the goals of the casting process.

Design methodology for modular tools

Serving individual customer needs at reasonable prices can be a profitable target market in high-wage countries. The dilemma between scale and scope-oriented production is one major research topic within the Cluster of Excellence “Integrative Production Technology for High-Wage Countries” at the RWTH Aachen University. One main objective of this project is to bridge the existing gap between individual manufacturing and mass production. Modularization is a widely accepted approach in tool-based manufacturing processes. In this paper, we propose a flexible design methodology for modular tools and dies. The methodology will assist the design engineer in setting up a series of modularized tools in a conceptually closed manner. The described methodology covers modularization in a broad sense, i.e. it includes hardware modularization as well as modularization of the construction process. The methodology consists of three phases: initiation, analysis and design phase.

Boundary-conforming free-surface flow computations: Interface tracking for linear, higher-order and isogeometric finite elements

Abstract The simulation of certain flow problems requires a means for modeling a free fluid surface; examples being viscoelastic die swell or fluid sloshing in tanks. In a finite-element context, this type of problem can, among many other options, be dealt with using an interface-tracking approach with the Deforming-Spatial-Domain/Stabilized-Space-Time (DSD/SST) formulation. A difficult issue that is connected with this type of approach is the determination of a suitable coupling mechanism between the fluid velocity at the boundary and the displacement of the boundary mesh nodes. In order to avoid large mesh distortions, one goal is to keep the nodal movements as small as possible; but of course still compliant with the no-penetration boundary condition. Standard displacement techniques are full velocity, velocity in a specific coordinate direction, and velocity in normal direction. In this work, we investigate how the interface-tracking approach can be combined with isogeometric analysis for the spatial discretization. If NURBS basis functions of sufficient order are used for both the geometry and the solution, both a continuous normal vector as well as the velocity are available on the entire boundary. This circumstance allows the weak imposition of the no-penetration boundary condition. We compare this option with an alternative that relies on strong imposition at discrete points. Furthermore, we examine several coupling methods between the fluid equations, boundary conditions, and equations for the adjustment of interior control point positions.

Improving the automated optimization of profile extrusion dies by applying appropriate optimization areas and strategies

The rheological design of profile extrusion dies is one of the most challenging tasks in die design. As no analytical solution is available, the quality and the development time for a new design highly depend on the empirical knowledge of the die manufacturer. Usually, prior to start production several time-consuming, iterative running-in trials need to be performed to check the profile accuracy and the die geometry is reworked. An alternative are numerical flow simulations. These simulations enable to calculate the melt flow through a die so that the quality of the flow distribution can be analyzed. The objective of a current research project is to improve the automated optimization of profile extrusion dies. Special emphasis is put on choosing a convenient starting geometry and parameterization, which enable for possible deformations. In this work, three commonly used design features are examined with regard to their influence on the optimization results. Based on the results, a strategy is derived to s...

CFD-based optimization in plastics extrusion

This paper presents novel ideas in numerical design of mixing elements in single-screw extruders. The actual design process is reformulated as a shape optimization problem, given some functional, but possibly inefficient initial design. Thereby automatic optimization can be incorporated and the design process is advanced, beyond the simulation-supported, but still experience-based approach. This paper proposes concepts to extend a method which has been developed and validated for die design to the design of mixing-elements. For simplicity, it focuses on single-phase flows only. The developed method conducts forward-simulations to predict the quasi-steady melt behavior in the relevant part of the extruder. The result of each simulation is used in a black-box optimization procedure based on an efficient low-order parameterization of the geometry. To minimize user interaction, an objective function is formulated that quantifies the products’ quality based on the forward simulation. This paper covers two aspects: (1) It reviews the set-up of the optimization framework as discussed in [1], and (2) it details the necessary extensions for the optimization of mixing elements in single-screw extruders. It concludes with a presentation of first advances in the unsteady flow simulation of a metering and mixing section with the SSMUM [2] using the Carreau material model.This paper presents novel ideas in numerical design of mixing elements in single-screw extruders. The actual design process is reformulated as a shape optimization problem, given some functional, but possibly inefficient initial design. Thereby automatic optimization can be incorporated and the design process is advanced, beyond the simulation-supported, but still experience-based approach. This paper proposes concepts to extend a method which has been developed and validated for die design to the design of mixing-elements. For simplicity, it focuses on single-phase flows only. The developed method conducts forward-simulations to predict the quasi-steady melt behavior in the relevant part of the extruder. The result of each simulation is used in a black-box optimization procedure based on an efficient low-order parameterization of the geometry. To minimize user interaction, an objective function is formulated that quantifies the products’ quality based on the forward simulation. This paper covers two aspe...

Comparison of optimization algorithms for the slow shot phase in HPDC

High-pressure die casting (HPDC) is a popular manufacturing process for aluminum processing. The slow shot phase in HPDC is the first phase of this process. During this phase, the molten metal is pushed towards the cavity under moderate plunger movement. The so-called shot curve describes this plunger movement.A good design of the shot curve is important to produce high-quality cast parts. Three partially competing process goals characterize the slow shot phase: (1) reducing air entrapment, (2) avoiding temperature loss, and (3) minimizing oxide caused by the air-aluminum contact. Due to the rough process conditions with high pressure and temperature, it is hard to design the shot curve experimentally. There exist a few design rules that are based on theoretical considerations. Nevertheless, the quality of the shot curve design still depends on the experience of the machine operator.To improve the shot curve it seems to be natural to use numerical optimization. This work compares different optimization st...