Markus Frings

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.

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.

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...

A simplified simulation model for a HPDC die with conformal cooling channels

In general, the cooling phase of the high-pressure die casting process is based on complex physical phenomena: so-lidification of molten material; heat exchange between cast part, die and cooling fluid; turbulent flow inside the cooling channels that needs to be considered when computing the heat flux; interdependency of properties and temperature of the cooling liquid. Intuitively understanding and analyzing all of these effects when designing HPDC dies is not feasible. A remedy that has become available is numerical design, based for example on shape optimization methods. However, current computing power is not sufficient to perform optimization while at the same time fully resolving all physical phenomena. But since in HPDC suitable objective functions very often lead to integral values, e.g., average die temperature, this paper identifies possible simplifications in the modeling of the cooling phase. As a consequence, the computational effort is reduced to an acceptable level. A further aspect that arises in the context of shape optimization is the evaluation of shape gradients. The challenge here is to allow for large shape deformations without remeshing. In our approach, the cooling channels are described by their center lines. The flow profile of the cooling fluid is then estimated based on experimental data found in literature for turbulent pipe flows. In combination, the heat flux throughout cavity, die, and cooling channel can be described by one single advection-diffusion equation on a fixed mesh. The parameters in the equation are adjusted based on the position of cavity and cooling channel. Both results contribute towards a computationally efficient, yet accurate method, which can be employed within the frame of shape optimization of cooling channels in HPDC dies.In general, the cooling phase of the high-pressure die casting process is based on complex physical phenomena: so-lidification of molten material; heat exchange between cast part, die and cooling fluid; turbulent flow inside the cooling channels that needs to be considered when computing the heat flux; interdependency of properties and temperature of the cooling liquid. Intuitively understanding and analyzing all of these effects when designing HPDC dies is not feasible. A remedy that has become available is numerical design, based for example on shape optimization methods. However, current computing power is not sufficient to perform optimization while at the same time fully resolving all physical phenomena. But since in HPDC suitable objective functions very often lead to integral values, e.g., average die temperature, this paper identifies possible simplifications in the modeling of the cooling phase. As a consequence, the computational effort is reduced to an acceptable level. A further aspect that ar...

Mold-Based Production Systems

Mold-based production systems are vastly common in mass production processes, due to the high investment costs of production equipment. In order to address the challenge of a strong tendency towards individualized customer demands, companies in high-wage countries are forced to react towards these changes. This chapter describes recent advances in the field of individualized production for mold-based production systems regarding plastics profile extrusion and high-pressure die casting. A holistic methodology for an integrated product and mold design is presented based on the principles of simultaneous engineering. In addition, recent advances in the field of numerical optimization are shown. The advances in numerical optimization will be carried out based on the processes mentioned above. The monitoring and simulation of the viscoelastic swell will be shown for plastics profile extrusion. For the field of high-pressure die casting the strategy to optimize the entire process will be outlined and current experimental results shown. For both application cases the potential benefit of additive manufacturing technologies—such as Selective Laser Melting (SLM)—will be evaluated and validated inasmuch as possible.

Comparison of Shallow Water Models for Rapid Channel Flows

To model shallow free surface flows, the Saint-Venant Equations (SVE) are a convenient simplification of the incompressible Navier–Stokes Equations (NSE). In the present study, we compare the two models for one-dimensional channel flow over a hump (cf. Behr (XNS simulation program, 2016 [5]), Kusters (Comparison of a Navier–Stokes and a shallow water model using the example of flow over a semi-circular bump, 2013 [8]), Noelle et al. (J Comput Phys 226(1):29–58, 2007 [10]), Sikstel (Comparison of hydrostatic and non-hydrostatic shallow water models, 2016 [13])). Our numerical experiments show that the SVE fail for some rather standard transcritical flows, where the two models compute different water heights ahead of and different shock speeds behind the hump. Using numerical computations as well as a formal Cauchy–Kowalevski argument, we give a qualitative explanation of the shortcoming of the SVE. In addition, we examine a recently developed non-hydrostatic shallow water model Sainte-Marie et al. (Discrete and Cont Dyn Syst Ser B 20(4):361–388, 2014 [12]) which proposes to produce physically more realistic results.