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A diffuse-interface finite-element method has been applied to simulate the flow of two-component rheologically complex fluids. It treats the interfaces as having a finite thickness with a phase-field parameter varying continuously from one phase to the other. Adaptive meshing is applied to produce fine grid near the interface and coarse mesh in the bulk. It leads to accurate resolution of the interface at modest computational costs. An advantage of this method is that topological changes such as interfacial rupture and coalescence happen naturally under a short-range force resembling the van der Waals force. There is no need for manual intervention as in sharp-interface model to effect such event. Moreover, this energy-based formulation easily incorporates complex rheology as long as the free energy of the microstructures is known. The complex fluids considered in this thesis include viscoelastic fluids and nematic liquid crystals. Viscoelasticity is represented by the Oldroyd-B model, derived for a dilute polymer solution as linear elastic dumbbells suspended in a Newtonian solvent. The Leslie-Ericksen model is used for nematic liquid crystals，which features distortional elasticity and viscous anisotropy. The interfacial dynamics of such complex fluids are of both scientific and practical significance. The thesis describes seven computational studies of physically interesting problems. The numerical simulations of monodisperse drop formation in microfluidic devices have reproduced scenarios of jet breakup and drop formation observed in experiments. Parametric studies have shown dripping and jetting regimes for increasing flow rates, and elucidated the effects of flow and rheological parameters on the drop formation process and the final drop size. A simple liquid drop model is used to study the neutrophil, the most common type of white blood cell, transit in pulmonary capillaries. The cell size, viscosity and rheological properties are found to determine the transit time. A compound drop model is also employed to account for the cell nucleus. The other four cases concern drop and bubble dynamics in nematic liquid crystals, as determined by the coupling among interfacial anchoring, bulk elasticity and anisotropic viscosity. In particular, the simulations reproduce unusual bubble shapes seen in experiments, and predict self-assembly of microdroplets in nematic media.

A diffuse-interface finite-element method has been applied to simulate the flow of two-component rheologically complex fluids. It treats the interfaces as having a finite thickness with a phase-field parameter varying continuously from one phase to the other. Adaptive meshing is applied to produce fine grid near the interface and coarse mesh in the bulk. It leads to accurate resolution of the interface at modest computational costs. An advantage of this method is that topological changes such as interfacial rupture and coalescence happen naturally under a short-range force resembling the van der Waals force. There is no need for manual intervention as in sharp-interface model to effect such event. Moreover, this energy-based formulation easily incorporates complex rheology as long as the free energy of the microstructures is known. The complex fluids considered in this thesis include viscoelastic fluids and nematic liquid crystals. Viscoelasticity is represented by the Oldroyd-B model, derived for a dilute polymer solution as linear elastic dumbbells suspended in a Newtonian solvent. The Leslie-Ericksen model is used for nematic liquid crystals，which features distortional elasticity and viscous anisotropy. The interfacial dynamics of such complex fluids are of both scientific and practical significance. The thesis describes seven computational studies of physically interesting problems. The numerical simulations of monodisperse drop formation in microfluidic devices have reproduced scenarios of jet breakup and drop formation observed in experiments. Parametric studies have shown dripping and jetting regimes for increasing flow rates, and elucidated the effects of flow and rheological parameters on the drop formation process and the final drop size. A simple liquid drop model is used to study the neutrophil, the most common type of white blood cell, transit in pulmonary capillaries. The cell size, viscosity and rheological properties are found to determine the transit time. A compound drop model is also employed to account for the cell nucleus. The other four cases concern drop and bubble dynamics in nematic liquid crystals, as determined by the coupling among interfacial anchoring, bulk elasticity and anisotropic viscosity. In particular, the simulations reproduce unusual bubble shapes seen in experiments, and predict self-assembly of microdroplets in nematic media.

A diffuse-interface finite-element method has been applied to simulate the flow of two-component rheologically complex fluids. It treats the interfaces as having a finite thickness with a phase-field parameter varying continuously from one phase to the other. Adaptive meshing is applied to produce fine grid near the interface and coarse mesh in the bulk. It leads to accurate resolution of the interface at modest computational costs. An advantage of this method is that topological changes such as interfacial rupture and coalescence happen naturally under a short-range force resembling the van der Waals force. There is no need for manual intervention as in sharp-interface model to effect such event. Moreover, this energy-based formulation easily incorporates complex rheology as long as the free energy of the microstructures is known. The complex fluids considered in this thesis include viscoelastic fluids and nematic liquid crystals. Viscoelasticity is represented by the Oldroyd-B model, derived for a dilute polymer solution as linear elastic dumbbells suspended in a Newtonian solvent. The Leslie-Ericksen model is used for nematic liquid crystals，which features distortional elasticity and viscous anisotropy. The interfacial dynamics of such complex fluids are of both scientific and practical significance. The thesis describes seven computational studies of physically interesting problems. The numerical simulations of monodisperse drop formation in microfluidic devices have reproduced scenarios of jet breakup and drop formation observed in experiments. Parametric studies have shown dripping and jetting regimes for increasing flow rates, and elucidated the effects of flow and rheological parameters on the drop formation process and the final drop size. A simple liquid drop model is used to study the neutrophil, the most common type of white blood cell, transit in pulmonary capillaries. The cell size, viscosity and rheological properties are found to determine the transit time. A compound drop model is also employed to account for the cell nucleus. The other four cases concern drop and bubble dynamics in nematic liquid crystals, as determined by the coupling among interfacial anchoring, bulk elasticity and anisotropic viscosity. In particular, the simulations reproduce unusual bubble shapes seen in experiments, and predict self-assembly of microdroplets in nematic media. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

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Two immersed boundary methods (IBM) for the simulation of conjugate heat transfer problems with complex geometries are introduced: a finite element (IFEM) and a finite volume (IFVM) immersed boundary methods are discussed. In the IFEM a projection approach is presented for the coupled system of time-dependent incompressible Navier-Stokes equations (NSEs) and energy equation in conjunction with the immersed boundary method for solving fluid flow and heat transfer problems in the presence of rigid objects not represented by the underlying mesh. The IBM allows solving the flow for geometries with complex objects without the need of generating a body-fitted mesh. Dirichlet boundary constraints are satisfied applying a boundary force at the immersed body surface. Using projection and interpolation operators from the fluid volume mesh to the solid surface mesh (i.e., the “immersed” boundary) and vice versa, it is possible to impose the extra constraint to the NSEs as a Lagrange multiplier in a fashion very similar to the effect pressure has on the momentum equations to satisfy the divergence-free constraint. The IFEM approach presented shows third order accuracy in space and second order accuracy in time when the simulation results for the Taylor-Green decaying vortex are compared to the analytical solution. For the IFVM a ghost-cell approach with sharp interface scheme is used to enforce the boundary condition at the fluid/solid interface. The interpolation procedure at the immersed boundary preserves the overall second order accuracy of the base solver. The developed ghost-cell method is applied on a staggered configuration with the Semi-Implicit Method for Pressure-Linked Equations Revised algorithm. Second order accuracy in space and first order accuracy in time are obtained when the Taylor-Green decaying vortex test case is compared to the IFVM analytical solution. Computations were performed using the IFEM and IFVM approaches for the two-dimensional flow over a backward-facing step, two-dimensional flow past a stationary circular cylinder, three-dimensional flow past a sphere and two and three-dimensional natural convection in an enclosure with/without immersed body. The numerical results obtained with the discussed IFEM and IFVM were compared against other IBMs available in literature and simulations performed with the commercial computational fluid dynamics code STAR-CCM+/V7.04.006. The benchmark test cases showed that the numerical results obtained with the implemented immersed boundary methods are in good agreement with the predictions from STAR-CCM+ and the numerical data from the other IBMs. The immersed boundary method based of finite element approach is numerically more accurate than the IBM based on finite volume discretization. In contrast, the latter is computationally more efficient than the former.

Ce travail de thèse porte sur la modélisation de la cinétique de stratification des phases liquides oxyde et métallique dans un bain de corium (système U-O-Zr-acier) du point de vue de la diffusion multi-composants et multiphasique. Cette démarche de recherche s’inscrit dans le cadre du développement d’une modélisation « fine » du comportement d’un bain de corium basée sur une approche CFD (« Computational Fluid Dynamics ») de la thermo-hydraulique. Elle vise à améliorer la compréhension des phénomènes mis en jeu et construire des lois de fermetures adéquates pour des modèles macroscopiques intégraux.Pour ce faire, la méthode du champ de phase couplée avec une fonctionnelle d’énergie utilisant la méthode CALPHAD se révèle être un outil pertinent.Dans une première partie, nous nous sommes intéressés au système binaire U-O. Nous avons développé un modèle à interface diffuse (basé sur une équation de Cahn-Hilliard) pour décrire la diffusion dans ce système. Nous avons procédé à la mise en place du couplage entre ce modèle et une base de données thermodynamiques CALPHAD, ainsi qu’au paramétrage d’un tel modèle avec en particulier une procédure d’élargissement de l’interface.Ensuite, dans le cadre d’une modélisation sur le système ternaire U-O-Zr nous avons proposé une généralisation du modèle à interface diffuse par le biais d’une hypothèse d’équilibre local des mécanismes d’oxydo-réduction. Nous avons porté une attention particulière à l’analyse de ce modèle par le biais de simulations numériques 1D en nous intéressant notamment à l’état stationnaire et aux profils de composition obtenus.Finalement, nous avons montré l’application de ce modèle au système U-O-Zr-Fe. Pour cela, nous avons considéré une configuration similaire aux essais expérimentaux à « petite échelle » relatifs à l’étude de la stratification d’un bain oxyde-métal. / This Ph.D. topic is focused on the modelling of stratification kinetics for an oxide-metal corium pool (U-O-Zr-steel system) in terms of multicomponent and multiphase diffusion. This work is part of a larger research effort for the development of a detailed corium pool modelling based on a CFD approach (“Computational Fluid Dynamics”) for thermal-hydraulics. The overall goal is to improve the understanding of the involved phenomena and obtain closure laws for integral macroscopic models.The phase-field method coupled with an energy functional using the CALPHAD method appears to be relevant for this purpose.In a first part, this works has been focused on the U-O binary system. We have developed a diffuse interface model (based on a Cahn-Hilliard equation) in order to describe the diffusion process in this system. This model has been coupled with a CALPHAD thermodynamic database and its parameterization has been developed with, in particular, an upscaling procedure related to the interface thickness.Then, within the framework of a modelling for the U-O-Zr ternary system, we have proposed a generalization of the diffuse interface model through an assumption of local equilibrium for redox mechanisms. A particular attention was paid to the model analysis by 1D numerical simulations with a special focus on the steady state composition profiles.Finally we have applied this model to the U-O-Zr-Fe system. For that purpose, we have considered a configuration close to small-scale experimental tests dedicated to the study of oxide-metal corium pool stratification.

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No description available.

We present a discretization method of the Navier–Stokes Cahn–Hilliard equations which offers an impressing simplicity, making it easy to implement a scalable parallel code from scratch. The method is based on a special pressure projection scheme with incomplete pressure iterations. The resulting scheme admits solution by an explicit Euler method. Hence, all unknowns decouple, which enables a very simple implementation. This goes along with the opportunity of a straightforward parallelization, for example, by few lines of Open Multi-Processing (OpenMP) or Message Passing Interface (MPI) routines. Using a standard benchmark case of a rising bubble, we show that the method provides accurate results and good parallel scalability. / Wir stellen eine Diskretisierungsmethode der Navier-Stokes-Cahn-Hilliard-Gleichungen vor, welche es erlaubt, mit wenig Aufwand einen einfachen, skalierbar parallelen Code zu implementieren. Die Methode basiert auf einem Druckprojektionsschema mit unvollständigen Druckiterationen was eine Lösung durch eine explizite Euler-Methode erlaubt. Somit sind alle Unbekannten entkoppelt, was eine sehr einfache Implementierung mit einer unkomplizierten Parallelisierung ermöglicht, zum Beispiel durch Open Multi-Processing (OpenMP) oder Message Passing Interface (MPI) Routinen. Anhand eines Standard-Benchmark-Falls einer aufsteigenden Blase zeigen wir, dass die Methode genaue Ergebnisse und eine gute parallele Skalierbarkeit liefert.