Konrad Steiner

Lattice Boltzmann model for free-surface flow and its application to filling process in casting

A generalized lattice Boltzmann model to simulate free-surface is constructed in both two and three dimensions. The proposed model satisfies the interfacial boundary conditions accurately. A distinctive feature of the model is that the collision processes is carried out only on the points occupied partially or fully by the fluid. To maintain a sharp interfacial front, the method includes an anti-diffusion algorithm. The unknown distribution functions at the interfacial region are constructed according to the first-order Chapman-Enskog analysis. The interfacial boundary conditions are satisfied exactly by the coefficients in the Chapman-Enskog expansion. The distribution functions are naturally expressed in the local interfacial coordinates. The macroscopic quantities al the interface are extracted from the least-square solutions of a locally linearized system obtained from the known distribution functions. The proposed method does not require any geometric front construction and is robust for any interfacial topology. Simulation results of realistic filling process are presented: rectangular cavity in two dimensions and Hammer box, Campbell box, Sheffield box, and Motorblock in three dimensions. To enhance the stability at high Reynolds numbers, various upwind-type schemes are developed. Free-slip and no-slip boundary conditions are also discussed.

A free-surface lattice Boltzmann method for modelling the filling of expanding cavities by Bingham fluids.

The filling process of viscoplastic metal alloys and plastics in expanding cavities is modelled using the lattice Boltzmann method in two and three dimensions. These models combine the regularized Bingham model for viscoplastic fluids with a free-interface algorithm. The latter is based on a modified immiscible lattice Boltzmann model in which one species is the fluid and the other one is considered to be a vacuum. The boundary conditions at the curved liquid–vacuum interface are met without any geometrical front reconstruction from a first–order Chapman-Enskog expansion. The numerical results obtained with these models are found in good agreement with available theoretical and numerical analysis.

A lattice Boltzmann method for immiscible multiphase flow simulations using the level set method

We consider the lattice Boltzmann method for immiscible multiphase flow simulations. Classical lattice Boltzmann methods for this problem, e.g. the colour gradient method or the free energy approach, can only be applied when density and viscosity ratios are small. Moreover, they use additional fields defined on the whole domain to describe the different phases and model phase separation by special interactions at each node. In contrast, our approach simulates the flow using a single field and separates the fluid phases by a free moving interface. The scheme is based on the lattice Boltzmann method and uses the level set method to compute the evolution of the interface. To couple the fluid phases, we develop new boundary conditions which realise the macroscopic jump conditions at the interface and incorporate surface tension in the lattice Boltzmann framework. Various simulations are presented to validate the numerical scheme, e.g. two-phase channel flows, the Young-Laplace law for a bubble and viscous fingering in a Hele-Shaw cell. The results show that the method is feasible over a wide range of density and viscosity differences.

Numerical investigation of a combined lattice Boltzmann-level set method for three-dimensional multiphase flow

We simulate rising bubbles using a hybrid lattice Boltzmann scheme based on the lattice BGK model coupled with the level set method (Thömmes et al., 2009. A lattice Boltzmann method for immiscible multiphase flow simulations using the level set method. Journal of Computational Physics). This method uses special boundary conditions at the interface between the two phases which realise the macroscopic jump conditions on the kinetic level and incorporate surface tension into the model. Previous experience with the approach has already demonstrated that it is feasible over a wide range of density and viscosity differences. We utilise this method to simulate the classical immiscible multiphase problem of rising bubbles driven by buoyancy forces. In particular, simulations with large density ratios are performed. The numerical results are compared with available reference solutions.

Modeling and Simulation of Filtration Processes

Finding advanced filtration and separation solutions is often critical for the development of highly efficient and reliable products and tools, as well as for ensuring a high quality of life. In fact, it is difficult to find an industry where filters do not play an important role. A car, for example, contains filters for transmission fluid, fuel, engine air, cabin air, coolant, and brake fluid. Furthermore, the quality of our drinking water, the treatment of wastewater, and the air we breathe all depend critically on filtration solutions. The filtration and purification business is expanding greatly, with scores of large companies and thousands of SMEs competing fiercely to develop better filters. Industrial demand for innovative filtration solutions is growing rapidly, along with a more intensive usage of Computer Aided Engineering (CAE) in filter design processes. Comprehensive mathematical studies need to be carried out to provide engineers with proper CAE tools and approaches. The solid-liquid and solid-gas separation processes discussed in this chapter are intrinsically multiscale, multiphysics processes. Dust particle and pore size in filter media may vary from the sub-micron scale to hundreds of microns, while a filter element may range from several centimeters to several meters in size. Depending on the operating conditions and the material properties, the filter media may behave as a rigid body or be deformable. This chapter provides an overview of the industrial and mathematical challenges in modeling and simulating filtration processes, along with a summary of the basic achievements of the Fraunhofer ITWM in this area. Approaches for the microscale (pore scale) and macroscale (filter element scale) investigation of filtration processes are discussed in detail, along with a recently developed method for treating the coupled multiscale filtration problem. Software tools developed in the last decade are described. Finally, some success stories are presented to illustrate the potential of industrial mathematics for solving practical problems.

On Modeling and Simulation of Different Regimes for Liquid Polymer Moulding

Abstract In this paper we consider numerical algorithms for solving the system of nonlinear PDEs, arising in modeling of liquid polymer injection. We investigate the particular case where a porous preform is located within the mould, so that the liquid polymer is flowing through a porous medium during the filling stage. The nonlinearity of the governing system of PDEs is due to the non-Newtonian behavior of the polymer, as well as to the moving free boundary. The latter is related to the penetration front, and a Stefan type problem is formulated to take into account. A finite-volume method is used to approximate the given differential problem. Results from numerical experiments are presented. We also solve an inverse problem and present algorithms for determination of the absolute preform permeability coefficient for the case where the velocity of the penetration front is known from the measurements. In both considered cases (direct and inverse problems), we focus on the specificity related to the non-Newtonian behavior of the polymer. For completeness, we also discuss the Newtonian case. Results of some experimental measurements are presented and discussed.

Modellierung und Simulation von Filtrationsprozessen

Innovative Filtrations- und Separationstechniken sind in vielen Fallen von wesentlicher Bedeutung bei der Entwicklung von hochwertigen Produkten bzw. effizienten Geraten oder wenn es gilt, eine moglichst hohe Lebensqualitat zu gewahrleisten. Es ist schwierig einen Industriebereich zu benennen, in dem Filter keine wichtige Rolle spielen. In einem ublichen PKW gibt es eine Vielzahl von Filtern. Andere Bereiche, die in hochstem Mase von der eingesetzten Filtertechnik abhangen, sind die Aufbereitung von Trink- und Brauchwasser sowie der Einsatz von Entstaubungsanlagen im Energie- und Produktionssektor. Der Filtrationsmarkt wachst schnell und dementsprechend hoch ist der Innovationsdruck bei der Produktentwicklung. Daher kommt in zunehmendem Umfang Computer Aided Engineering (CAE) bei der Produktauslegung zum Einsatz. Damit den Entwicklungsingenieuren auch hierfur geeignete CAE-Werkzeuge zur Verfugung stehen, ist viel an mathematischer Forschung erforderlich. Die Fest-Flussig- und Fest-Gasformig-Filtrationsprobleme, die hier betrachtet werden sollen, sind von Natur aus Multiskalen- und Multiphysikphanomene. Die Grosen der Schmutzpartikel und der Fasern im Filtermaterial reichen vom Nanometerbereich bis hin zu mehreren hundert Mikrometern. Die Abmessungen von Filtergehausen dagegen konnen von wenigen Millimetern bis hin zu mehreren Metern betragen. Zudem kann sich das Filtermaterial (Filtermedium) je nach Anwendungsfall wie ein starrer Korper verhalten oder verformen. Dieses Kapitel gibt einen Uberblick uber die industriellen Anforderungen bei der Filterauslegung und die mathematischen Herausforderungen bei der Modellierung und Simulation von Filtrationsvorgangen. Dabei werden die Herangehensweisen zur rechnergestutzten Untersuchung der Filtrationsprozesse auf der mikroskopischen Ebene (Partikel- und Porenskala), auf der makroskopischen Ebene (Filterelement, Gehause) und deren Kopplung behandelt. Die Beitrage des Fraunhofer ITWM zu diesem Forschungsgebiet in Form von neuen Simulationsmethoden und Software werden kurz vorgestellt und ihre Bedeutung fur die Praxis an Hand von Beispielen erfolgreicher Industrieanwendungen illustriert.

PHREASIM – Ein Expertensystem zur Simulation von Fließverhältnissen in Grundwassermessstellen und deren unmittelbarem Nahfeld

ZusammenfassungDie vorliegende Arbeit stellt eine Studie zur rechnergestützten Modellierung stationärer Fließverhältnisse an und in horizontal durchströmten Bohrbrunnen vor. Basierend auf einem neuartigen 3D-Navier-Stokes-Brinkman-Gleichungslöser wird ein Lösungsansatz für das interaktive System Porengrundwasserleiter/Filterkies/Filterrohr/Brunnenraum vorgestellt. Er ermöglicht es, stationäre Strömungsszenarien gekoppelt aus freiem und porösem Fließen am Computer zu simulieren. Für die Anwendung des Gleichungslösers wurde das Expertensystem PHREASIM entwickelt, mit dem Modellgeometrien erstellt und im Anschluss an die Simulation stationäre Fließszenarien visualisiert werden können. Zur Validierung wurden in Laborexperimenten beispielhaft verschiedene Brunnenmodellkonstruktionen untersucht und anschließend mit PHREASIM simuliert. Der Abgleich zwischen Ergebnissen aus Laborexperimenten und Simulationen zeigt, dass mit PHREASIM quasistationäre Fließszenarien bei identischen Randbedingungen und gleichen Geometrien realitätsnah abgebildet werden können. Bei genauer Kenntnis der Brunnengeometrien und der strömungsmechanischen Randbedingungen kann mit PHREASIM die Fließsituation an beliebigen Stellen innerhalb sowie außerhalb eines horizontal durchströmten Brunnenabschnitts am Computer simuliert werden. Ein Einsatzbereich von PHREASIM ist die Unterstützung der Interpretation von Fließmessdaten, die beispielsweise mit dem PHREALOG-Fließmesssystem gewonnen werden.AbstractIn this study, a new numerical solver based on a coupling of the Navier-Stokes and Brinkman equations is presented. The solver can model 3D horizontal steady-state flow conditions with interactions between the aquifer, gravel-pack, well screen, and open borehole at the interface between the borehole and the surrounding porous filter and aquifer, thus solving the critical transition from porous to free flow. The solver is embedded in the workflow of the PHREASIM expert system. It allows for designing a broad variety of well designs and flow scenarios while considering the permeabilities and geometries of the involved microstructures. Stationary flow scenarios can be visualized in any cross-section and at any discrete point within the model. In order to verify the validity of the numerical approach, a variety of flow scenarios were investigated in sand tank model experiments and simulated with PHREASIM. By comparing the results of both simulations and experimental measurements performed using identical boundary conditions, PHREASIM proved to be viable for accurately replicating virtually steady-state flow conditions. PHREASIM aims to support the interpretation and significance of flow data gained by borehole flow measuring systems like PHREALOG.