Die Dynamik von elastischen Membranen, Kapseln und Schalen hat sich zu einem aktiven Forschungsgebiet in der simulationsgestützten Physik und Biologie entwickelt. Die dünne Oberfläche dieser elastischen Materialien ermöglicht es, sie effizient als Hyperfläche zu approximieren. Solche Oberflächen reagieren auf Dehnungen in Oberflächenrichtung und Verformungen in Normalenrichtung mit einer elastischen Kraft. Zusätzlich können Oberflächenspannungskräfte auftreten. In dieser Arbeit präsentieren wir eine neuartige Arbitrary Lagrangian-Eulerian (ALE) Methode um solche in (Navier-Stokes) Fluiden eingebetteten elastischen Schalen zu simulieren. Dadurch, dass das Gitter an die elastische Oberfläche angepasst ist, kombiniert die vorgeschlagene Methode hohe Genauigkeit mit Effizienz in der Berechnung der Lösungen. Folglich kann man die Simulationen mit einer verhältnismäßig geringen Gitterauflösung durchführen. Der Fokus dieser Arbeit liegt bei achsensymmetrischen Formen und Strömungen, wie sie bei vielen biophysikalischen Anwendungen zu finden sind. Neben einer allgemeinen dreidimensionalen Beschreibung formulieren wir achsensymmetrische Kräfte auf der Oberfläche, für welche wir eine Diskretisierung mit der Finite Differenzen Methode vorschlagen, welche an eine Finite-Elemente Methode für die umgebenden Fluide gekoppelt ist. Weiterhin entwickeln wir eine Strategie zur impliziten Kopplung der Kräfte, um Zeitschrittrestriktionen zu reduzieren. In verschiedenen numerischen Tests werden wir zeigen, dass akkurate Ergebnisse schon in einer Größenordnung von Minuten auf einer Single-Core CPU erreicht werden können. Die Methode wurde in drei aktuellen Anwendungen verwendet, wobei mindestens zwei davon nach unserer Kenntnis im Moment mit keiner anderen numerischen Methode simuliert werden können: Zunächst präsentieren wir Simulationen von biologischen Zellen, die im Zuge eines RT-DC (Real-Time Deformability Cytometry) Experiments durch einen schmalen mikrofluidischen Kanal advektiert und dabei verformt werden. Danach zeigen wir die Ergebnisse erster Simulationen der uniaxialen Kompression biologischer Zellen zwischen zwei parallelen Platten im Zuge eines AFM Experiments. Schließlich präsentieren wir Resultate erster Simulationen von neuartigen mikroschwimmenden Schalen, welche lediglich durch äußere Einflüsse (wie z.B. Ultraschall), zum Schwimmen angeregt werden können. / The dynamics of membranes, shells, and capsules in fluid flow has become an active research area in computational physics and computational biology. The small thickness of these elastic materials enables their efficient approximation as a hypersurface, which exhibits an elastic response to in-plane stretching and out-of-plane bending, possibly accompanied by a surface tension force. In this work, we present a novel arbitrary Lagrangian-Eulerian (ALE) method to simulate such elastic surfaces immersed in Navier-Stokes fluids. The method combines high accuracy with computational efficiency, since the grid is matched to the elastic surface and can therefore be resolved with relatively few grid points. The focus of this work is on axisymmetric shapes and flow conditions, which are present in a wide range of biophysical problems. Next to a general three-dimensional description, we formulate axisymmetric elastic surface forces and propose a discretization with surface finite-differences coupled to evolving finite elements. We further develop an implicit coupling strategy to reduce time step restrictions. Several numerical test cases show that accurate results can be achieved at computational times on the order of minutes on a single core CPU. Three state-of-the-art applications are demonstrated, where to our knowledge at least two of them cannot be simulated with any other numerical method so far. First, simulations of biological cells being advected through a microfluidic channel and therefore being deformed during an RT-DC (Real-Time Deformability Cytometry) experiment are presented. Then, the uniaxial compression of the cortex of a biological cell during an AFM experiment is investigated. Finally, we present the results of first simulations of the observed shape oscillations of novel microswimming shells which can be locomoted by exterior influences (e.g. ultrasound waves) only.

Interactions between three immiscible phases, including incompressible viscoelastic structures and fluids, form standard constellations for countless scenarios in natural science. The complexity of many such scenarios has motivated various research efforts in scientific computing. This work presents novel numerical approaches for two specific of these ternary fluid-structure interaction constellations. The potential of these approaches is demonstrated by diverse applications. First, a phase field model is developed describing the interaction between a fluid and a viscoelastic solid. For this purpose, a Navier-Stokes-Cahn-Hilliard system is considered together with a hyperelastic neo-Hookean model. Based on this, an arbitrary Lagrangian-Eulerian (ALE) method is implemented to simulate the indentation of the solid material in the context of atomic force microscopy, capable of predicting physical parameters. Next, the second approach is developed to describe the interaction between a two-phase fluid and a viscoelastic solid, where fluid and solid are defined on separate domains but aligned at the interface between them. The previously introduced phase field model is used to represent the fluid and an ALE method is used for the motion of the grid, where the fluid-solid interface moves with flow velocity. A unified system is solved in all subdomains, which includes both the balance of mass and momentum and the balance of forces at the fluid-solid interface. Simulations of static and dynamic soft wetting are subsequently presented, in particular a contact line moving over a substrate with oscillating stick-slip behavior. This work combines the advantages of phase field and ALE methods for meaningful simulations and emphasizes validity and numerical stability in all approaches.

L'application de la Directive Cadre sur l'Eau et l'obligation de surveillance de la qualité d'eau pour la consommation humaine et les activités récréatives ou industrielles, telles que la production d'eau potable, entraînent une forte demande pour des systèmes d'évaluation et de suivi de la qualité de l'eau. Le projet de recherche MIGR'HYCAR (http://www.migrhycar.com) a donc été mis en place pour répondre à un besoin opérationnel et à un défaut d'outils d'aide à la décision adaptés face aux déversements d'hydrocarbures en eaux continentales (rivières, lacs et estuaires) qui représente plus de 50% des déversements accidentels en France. Au cours du projet de recherche MIGR'HYCAR, un modèle mathématique de dérive de nappe d'hydrocarbures, composé d'un modèle lagrangien couplé à un modèle eulérien, a été développé dans la plate-forme hydro-informatique TELEMAC (http://www.opentelemac.org). Le modèle lagrangien décrit le mouvement de la nappe en surface en considérant celle-ci comme un ensemble de particules. Ainsi le modèle développé est capable de modéliser les principaux phénomènes agissant sur une nappe d'hydrocarbures une fois celle-ci déversée : convection, diffusion, échouage, re-largage, étalement, évaporation, dissolution et volatilisation. Bien que le phénomène de dissolution ne concerne qu'un très faible volume d'hydrocarbures, ce processus peut avoir des conséquences importantes du point de vue de la toxicité. Afin de suivre l'évolution du pétrole dissous, un modèle eulérien de suivi de traceurs a été adopté. La quantité de traceur dépend directement de la masse dissoute des particules lagrangiennes. Cette approche permet le suivi des hydrocarbures dissous dans la colonne d'eau. Des cinétiques effectuées en laboratoire ont pour but la calibration du modèle numérique. En complément de cas tests issus de la littérature et de cas réels, des résultats expérimentaux issus d'expérimentations effectuées en canal d'essai doivent permettre de vérifier et valider la qualité des simulations numériques sur des situations où les conditions ne sont que partiellement contrôlées / The application of the European Water Framework Directive on water quality for human consumption and industrial activities creates a need for water quality assessment and monitoring systems. The MIGR'HYCAR research project (http://www.migrhycar.com) was initiated to provide decisional tools for risks connected to oil spills in continental waters (rivers, lakes and estuaries), which represent more than 50% of accidental spills in France. Within the framework of this project, a new numerical oil spill model has been developed, as part of the Telemac hydro-informatics system (see: (http://www.opentelemac.org), by combining Lagrangian and Eulerian methods. The Lagrangian model describes the transport of an oil spill near the free surface. The oil spill model enables to simulate the main processes driving oil plumes: advection, diffusion, oil beaching, oil re-floating, evaporation, dissolution, spreading and volatilization. Though generally considered as a minor process, dissolution is important from the point of view of toxicity. To model dissolved oil in water, an Eulerian advection-diffusion model is used. The fraction of dissolved oil is represented by a passive tracer. This approach is able to follow dissolved hydrocarbons in the water column. Laboratory experiments were conducted to characterise the numerous kinetics of the processes listed above. In addition, meso-scale dynamic experiments in artificial channels and test cases derived from the literature are used to validate the numerical model

Orientador: José Antônio Perrella Balestieri / Abstract: Direct injection spark ignition (DISI) engines aim at reducing specific fuel consumption and achieving the strict emission standards in state of the art internal combustion engines. Therefore, in this work the goal is to develop code for simulations of the internal flow in DISI engines, as well as the phenomenon of fuel spray injection into the combustion chamber using a Lagrangian-Eulerian approach for representing the multiphase flow, and Large-eddy Simulations (LES) for modeling the turbulence of the continuum medium by means of the open-source CFD library OpenFOAM. In order to validate the obtained results and the developed models, experimental data from the Darmstadt optical engine, and the non-reactive “Spray G” gasoline injection case, along with the reactive “Spray A” case from the Engine Combustion Network (ECN) will be employed. Finally, a novel open-source solver will be proposed to simulate the Darmstadt optical engine in motored and fired operation under stratified mixture condition, using data compiled by the Darmstadt Engine Workshop (DEW) for validation. Moreover, a deep learning framework is presented to train an artificial neural network (ANN) with the engine LES data generated in this work, in order to make predictions of the small scale turbulence behavior. / Resumo: Motores de ignição a centelha com injeção direta (direct injection spark ignition engines, DISI engines) visam reduzir o consumo específico de combustível e respeitar os restritos níveis de emissão em motores de combustão interna de última geração. Assim, pretende-se com este trabalho desenvolver código para simulação do escoamento interno em motores DISI, assim como os fenômenos de injeção de combustível no interior da câmara de combustão utilizando uma abordagem Lagrangeana-Euleriana para representação do escoamento multifásico e Simulação de Grandes Escalas (Large-eddy simulation, LES) para a modelagem da turbulência no meio contínuo, por intermédio da biblioteca CFD de código aberto OpenFOAM. De modo a validar os resultados e os modelos desenvolvidos, dados experimentais serão utilizados, obtidos do motor óptico de Darmstadt, e do caso de teste de injeção de gasolina não-reativo “Spray G”, juntamente com o caso reativo “Spray A” da Rede de Combustão em Motores (Engine Combustion Network, ECN). Enfim, um novo código aberto será proposto para simular o motor óptico de Darmstadt em condições de escoamento a frio (sem combustão) e com combustão em condição de mistura estratificada, usando dados compilados pelo Workshop do Motor de Darmstadt (Darmstadt Engine Workshop, DEW) para validação. Além disso, uma abordagem de aprendizado profundo (deep learning) será apresentada para treinar uma rede neural artificial (artificial neural network, ANN) com dados de simulação LES de moto... (Resumo completo, clicar acesso eletrônico abaixo) / Doutor

A three-dimensional, parallel, finite volume solver which uses Roe&#039 / s upwind flux differencing scheme for spatial and Runge-Kutta explicit multistage time stepping scheme for temporal discretization on unstructured meshes is developed for the unsteady solution of external viscous flow around rotating bodies. The main aim of this study is to evaluate the aerodynamic dynamic stability derivative coefficients for rotating missile configurations. Arbitrary Lagrangian Eulerian (ALE) formulation is adapted to the solver for the simulation of the rotation of the body. Eigenvalues of the Euler equations in ALE form has been derived. Body rotation is simply performed by rotating the entire computational domain including the body of the projectile by means of rotation matrices. Spalart-Allmaras one-euqation turbulence model is implemented to the solver. The solver developed is first verified in 3-D for inviscid flow over two missile configurations. Then inviscid flow over a rotating missile is tested. Viscous flux computation algorithms and Spalarat-Allmaras turbulence model implementation are validated in 2-D by performing calculations for viscous flow over flat plate, NACA0012 airfoil and NLR 7301 airfoil with trailing edge flap. The ALE formulation is validated in 2-D on a rapidly pitching NACA0012 airfoil. Afterwards three-dimensional validation studies for viscous, laminar and turbulent flow calculations are performed on 3-D flat plate problem. At last, as a validation test case, unsteady laminar and turbulent viscous flow calculations over a spinning M910 projectile configuration are performed. Results are qualitatively in agreement with the analytical solutions, experimental measurements and previous studies for steady and unsteady flow calculations.

The aim of this study is to simulate the unsteady flow around rotating or oscillating airfoils. This will help to understand the rotor aerodynamics, which is essential in turbines and propellers. In this study, a pre-existing Euler solver with finite volume method that is developed in the Mechanical Engineering Department of Middle East Technical University (METU) is improved. This structured pre-existing code was developed for 2-D internal flows with Lax-Wendroff scheme. The improvement consist of firstly, the generalization of the code to external flow / secondly, implementation of first order Roe&rsquo / s flux splitting scheme and lastly, the implementation of rotation with the help of Arbitrary Lagrangian Eulerian (ALE) method. For the verification of steady and unsteady results of the code, the experimental and computational results from literature are utilized. For steady conditions, subsonic and transonic cases are investigated with different angle of attacks. For the verification of unsteady results of the code, oscillating airfoil case is used. The flow is assumed as inviscid, unsteady, adiabatic and two dimensional. The gravity is neglected and the air is taken as ideal gas. The developed code is run on computers housed in METU Mechanical Engineering Department Computational Fluid Dynamics High Performance Computing (CFD-HPC) Laboratory.

Finite element(FE) method has been used to model cutting process since 1970s. However, it requires special techniques to cope with the difficulties in simulating extremely large strain when compare to static or small deformation problems. With the advancement of FE techniques, researchers can now have a deeper insight of the mechanism of material flow and chip formation of metal cutting process. Even the stagnation effect of the workpiece material in front of the cutting edge radius can be captured by using FE techniques such as Remeshing and Arbitrary Lagrangian Eulerian(ALE) formulation. However most of this models are limited to plane strain assumption which means they are 2-dimensional. Although 3D models are existing in the literatures, most of them employ Remeshing technique which is very computationally intensive and has many critics regarding its accuracy due to its frequent remeshing and mapping process. The rest of the 3D models employ Lagrangian formulation. The 3D models by Lagrangian formulation have the same limitations and drawbacks as in 2D models, as it requires failure criteria and in most of the cases predefined partition surfaces are also required. ALE technique on the other hand resolves all the drawbacks of the other formulations, it not only inherits the advantages of the other techniques but also has its own unique advantages such as it can simulate a longer time span up to couple seconds more economically by fixing the number of elements used. Although it's commonly accepted that ALE formulation is superior to other formulations of techniques in modeling metal cutting process, its usage is only limited to 2D models. Limited 3D ALE metal cutting models is available in the literature. Thus the main objective of this research is to explore the possibility of building a 3D metal cutting model with ALE formulation. The reliability and limitations will also be studied. Furthermore, Couple Eulerian-Lagrangian(CEL) formulation is a recent developed formulation that has a lot of potential in modeling metal cutting process in 3D. It will be compared with ALE models to study its potential and limitations in modeling metal cutting process. A new frictional model will also be proposed, which suggests that the frictional phenomenon in metal cutting is a consolidated effect of both friction between material interface and shear yield of the workpiece material. This idea provide a brand new perspective of viewing the friction phenomenon of metal cutting compared to those existed models. / Thesis / Master of Science (MSc)

O fenômeno de molhamento, estudo de como um líquido se deposita em um sólido, apresenta problemas ainda em aberto, dos pontos de vista da modelagem física e da simulação numérica. O maior interesse acadêmico neste tipo de escoamento é a linha tríplice (ou linha de contato) formada da interação sólido-líquido-gás. A condição de contorno clássica de não escorregamento na interface líquido-sólido leva a uma singularidade no tensor de tensões nesta linha. Além disso, ainda não está estabelecido qual o melhor modelo para descrever o ângulo de contato formado entre a superfície livre e o substrato (o sólido). Neste trabalho, são discutidos métodos numéricos para a simulação de linhas de contato dinâmicas. Os efeitos da tensão superficial são estudados com a abordagem do princípio do trabalho virtual, o qual leva o problema à equações na formulação variacional, linguagem natural para o tratamento numérico com o método dos elementos finitos (FEM). O domínio é discretizado por uma malha não-estruturada de forma que as interfaces separadoras são explicitamente representadas pela malha. As derivadas temporais são tratadas em uma abordagem Lagrangeana-Euleriana arbitrária (ALE). Finalmente, são apresentados os resultados numéricos obtidos com o método ALE-FEM, discutindo alguns aspectos da sua convergência temporal e espacial. / Wetting phenomena, study of how of a liquid spreads out on a solid substrate, presents challenges both in physical modeling and in numerical simulation. The triple line (or contact line) formed by the solid-liquid-gas interaction has increasingly attracted the attention of the fluid dynamic community. The classical no-slip boundary condition on the liquid-solid interface leads to a singularity in the stress tensor at contact lines. Furthermore, there is no consensus on what the best model to describe the dynamics of the contact angle formed by the solid substrate and free surface. In this work, numerical methods for simulating dynamic contact lines are considered. The capillarity effects are studied in the approach of the virtual-work principle, which describes the problem in the variational formulation, natural language for numerical treatment with the finite element method (FEM). The domain is discretized by a dynamic unstructured mesh, where the separating interfaces are explicit represented by the mesh. Time derivatives present in the governing equations are treated with the arbitrary Lagrangian-Eulerian (ALE) framework. Finally, we discuss some temporal and spatial convergence issues ofthe ALE-FEM method.

Semi-solid thixoforming processes rely on a material microstructure made of globular solid grains more or less connected to each other, thus developing a solid skeleton deforming into a liquid phase. During processing, the material structure changes with the processing history due to the agglomeration of the particles and the breaking of the grains bonds. This particular evolutive microstructure makes semi-solid materials behave as solids at rest and as liquids during shearing, which causes a decrease of the viscosity and of the resistance to deformation while shearing. Thixoforming of aluminum and magnesium alloys is state of the art and a growing number of serial production lines are in operation all over the world. But there are only few applications of semi-solid processing of higher melting point alloys such as steel. This can partly be attributed to the high forming temperature combined with the intense high temperature corrosion that requires new technical solutions. However the semi-solid forming of steels reveals high potential to reduce material as well as energy consumption compared to conventional process technologies, such as casting and forging. Simulation techniques exhibit a great potential to acquire a good understanding of the semi-solid material process. Therefore, this work deals with the development of an appropriate constitutive model for semi-solid thixoforming of steel. The constitutive law should be able to simulate the complex rheology of semi-solid materials, under both steady-state and transient conditions. For example, the peak of viscosity at start of a fast loading should be reproduced. The use of a finite yield stress is appropriate because a vertical billet does not collapse under its own weight unless the liquid fraction is too high. Furthermore, this choice along with a non-rigid solid formalism allows predicting the residual stresses after cooling down to room temperature. Several one-phase material modeling have been proposed and are compared. Thermo-mechanical modeling using a thermo-elasto-viscoplastic constitutive law has been developed. The basic idea is to extend the classical isotropic hardening and viscosity laws to the non solid state by considering two non-dimensional internal parameters. The first internal parameter is the liquid fraction and depends on the temperature only. The second one is a structural parameter that characterizes the degree of structural build up in the microstructure. Those internal parameters can depend on each other. The internal parameters act on the the viscosity law and on the yield surface evolution law. Different formulations of viscosity and hardening laws have been proposed and are compared to each other. In all cases, the semi-solid state is treated as a particular case, and the constitutive modeling remains valid over the whole range of temperature, starting from room temperature to above the liquidus. These models are tested and illustrated by mean of several representative numerical applications.

La predicción precisa de los efectos producidos por el acoplamiento fluido estructura para cuerpos parcial o totalmente sumergidos, incluyendo superficies libres, es un problema de gran relevancia en la ingeniería naval así como en muchos otros campos del diseño de estructuras sometidas a la acción de fluidos.Las dificultades que se encuentran en la resolución de los problemas de interacción fluido estructura se deben principalmente a las siguientes causas:1. La dificultad de resolver numéricamente las ecuaciones de la dinámica de un fluido incompresible que, en general, si descartamos el caso más simple del modelo del flujo potencial, tienen un importante carácter no lineal. 2. Los obstáculos que se presentan al resolver la ecuación de la superficie libre, que constriñen el movimiento de las partículas a una superficie fluida de posición a priori desconocida.3. Las dificultades asociadas a la resolución del problema del movimiento de un cuerpo sumergido debido a las fuerzas de interacción, minimizando la deformación de los elementos de la malla y reduciendo, de esta manera, la necesidad del remallado.En la presente tesis se presenta un método estabilizado basado en el método de los elementos finitos que pretende solventar cada uno de los problemas anteriores. La metodología se basa en la modificación de las ecuaciones diferenciales de la dinámica de fluidos que gobiernan el flujo viscoso incompresible y el movimiento de la superficie libre, mediante la aplicación del método de cálculo finitesimal (FIC) propuesto en este trabajo.En el presente caso las ecuaciones modificadas son resueltas usando un esquema de pasos fraccionados semi-implícito y el método de los elementos finitos (FEM). El movimiento del cuerpo sumergido en el fluido debido a las fuerzas de interacción se calcula resolviendo un problema estructural dinámico, para el cual las fuerzas del fluido son las condiciones iniciales. Se incluye, además, un algoritmo para el movimiento de la malla debido a la deformación del dominio de cálculo. Este método minimiza la distorsión de la malla debida al movimiento del sólido rígido y al cambio de posición de la superficie libre. Este algoritmo se basa en la solución iterativa por el método de elementos finitos de un problema lineal, donde la malla de cálculo se considera un sólido elástico sometido a la deformación prescrita por el cambio en el dominio de cálculo. Las características de elasticidad del sólido, y en concreto su rigidez, se aplican de manera que los elementos que más se deforman tienen una rigidez mayor. Por último se presentan varios ejemplos de interés industrial, aplicación de la metodología propuesta en diferentes campos de la ingeniería naval.