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Étude numérique de la relaxation de capsules confinées par couplage des méthodes Volumes Finis - Éléments Finis via la méthode des frontières immergées IBM : influence de l'inertie et du degré de confinement. / Numerical study of the relaxation of confined capsules coupling the Finite Volume and Finite Element Methods via the Immersed Boundary Method IBM : influence of inertia and of the confinement ratioSarkis, Bruno 12 December 2018 (has links)
Les capsules, formées d’une goutte protégée par une membrane élastique, sont très présentes naturellement et dans diverses applications industrielles, mais peu d’études ont exploré les phénomènes transitoires de leur relaxation. L’objectif est d’étudier l’influence de l’inertie et du confinement sur la relaxation d’une capsule sphérique (1) pré-déformée en ellipsoïde et relâchée dans un canal carré où le fluide est au repos, (2) sous écoulement dans un canal carré à expansion soudaine (‘marche’). La capsule est modélisée comme un fluide Newtonien dans une membrane hyper-élastique sans épaisseur ni viscosité, et simulée en couplant les méthodes Volumes Finis - Eléments Finis - frontières immergées. Sa relaxation dans un fluide au repos comporte 3 phases : amorçage du mouvement du fluide, phases rapide puis lente de rétraction de la membrane. Trois régimes existent selon le rapport de confinement et le rapport des nombres de Reynolds et capillaire : amortissements pur, critique ou oscillant. Un modèle de Kelvin-Voigt inertiel est proposé pour prédire les temps de réponse et aussi appliqué à une capsule en écoulement dans le canal microfluidique avec marche. La comparaison aux simulations 3D montre sa pertinence aux temps courts de la relaxation. Ces travaux ouvrent la voie à l’étude d’écoulements transitoires de capsules confinées dans des systèmes microfluidiques complexes. / Capsules, made of a drop protected by an elastic membrane, are widly present in nature and in diverse industrial applications, but few studies have explored the transient phenomena governing their relaxation. The objective of the PhD is to study the influence of inertia and confinement on the relaxation of a spherical capsule (1) pre-deformed into an ellipsoid and released in a square channel where the fluid is quiescent, (2) flowing in a square channel with a sudden expansion (‘step’). The capsule is modeled as a Newtonian fluid in a hyperelastic membrane without thickness or viscosity and is simulated coupling the Finite Volume - Finite Element - Immersed Boundary Methods. Its relaxation in a quiescent fluid exhibits three phases: the initiation of the fluid motion, the rapid and then slow retraction phases of the membrane. Three regimes exist depending on the confinement ratio and the Reynolds to capillary number ratio: pure, critical or oscillating damping. A Kelvin-Voigt inertial model is proposed to predict the response time constants and also applied to a capsule flowing in the microfluidic channel with a step. The comparison to 3D simulations shows its relevance at short relaxation times. This work paves the way to the study of transient flows of capsules confined in microfluidic devices.
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Extension de la méthode LS-STAG de type frontière immergée/cut-cell aux géométries 3D extrudées : applications aux écoulements newtoniens et non newtoniens / Extension of the LS-STAG immersed boundary/cut-cell method to 3D extruded geometries : Application to Newtonian and non-Newtonian flowsNikfarjam, Farhad 23 March 2018 (has links)
La méthode LS-STAG est une méthode de type frontière immergée/cut-cell pour le calcul d’écoulements visqueux incompressibles qui est basée sur la méthode MAC pour grilles cartésiennes décalées, où la frontière irrégulière est nettement représentée par sa fonction level-set, résultant en un gain significatif en ressources informatiques par rapport aux codes MFN commerciaux utilisant des maillages qui épousent la géométrie. La version 2D est maintenant bien établie et ce manuscrit présente son extension aux géométries 3D avec une symétrie translationnelle dans la direction z (configurations extrudées 3D). Cette étape intermédiaire sera considérée comme la clé de voûte du solveur 3D complet, puisque les problèmes de discrétisation et d’implémentation sur les machines à mémoire distribuée sont abordés à ce stade de développement. La méthode LS-STAG est ensuite appliquée à divers écoulements newtoniens et non-newtoniens dans des géométries extrudées 3D (conduite axisymétrique, cylindre circulaire, conduite cylindrique avec élargissement brusque, etc.) pour lesquels des résultats de références et des données expérimentales sont disponibles. Le but de ces investigations est d’évaluer la précision de la méthode LS-STAG, d’évaluer la polyvalence de la méthode pour les applications d’écoulement dans différents régimes (fluides newtoniens et rhéofluidifiants, écoulement laminaires stationnaires et instationnaires, écoulements granulaires) et de comparer ses performances avec de méthodes numériques bien établies (méthodes non structurées et de frontières immergées) / The LS-STAG method is an immersed boundary/cut-cell method for viscous incompressible flows based on the staggered MAC arrangement for Cartesian grids where the irregular boundary is sharply represented by its level-set function. This approach results in a significant gain in computer resources compared to commercial body-fitted CFD codes. The 2D version of LS-STAG method is now well-established and this manuscript presents its extension to 3D geometries with translational symmetry in the z direction (3D extruded configurations). This intermediate step will be regarded as the milestone for the full 3D solver, since both discretization and implementation issues on distributed memory machines are tackled at this stage of development. The LS-STAG method is then applied to Newtonian and non-Newtonian flows in 3D extruded geometries (axisymmetric pipe, circular cylinder, duct with an abrupt expansion, etc.) for which benchmark results and experimental data are available. The purpose of these investigations is to evaluate the accuracy of LS-STAG method, to assess the versatility of method for flow applications at various regimes (Newtonian and shear-thinning fluids, steady and unsteady laminar to turbulent flows, granular flows) and to compare its performance with well-established numerical methods (body-fitted and immersed boundary methods)
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Simulação de escoamentos não-periódicos utilizando as metodologias pseudo-espectral e da fronteira imersa acopladas / Simulation of non-periodics flows using the fourier pseudo-spectral and immersed boundary methodsMariano, Felipe Pamplona 06 March 2007 (has links)
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Modern engineering increasingly requires the comprehension of phenomena related to
combustion, aeroacustics, turbulence transition, among others. For these purposes the
Computational Fluids Dynamics (CFD) requires the used high order methods. One of these
methods is the Fourier pseudo-spectral method, that provides an excellent numerical
accuracy, and with the use of the Fast Fourier Transform algorithm (FFT), it presents a low
computational cost in comparison to anothers high-order methods. Another important issue is
the projection method of the pression term, which does not require the pressure computation
from the Navier-Stokes equations. The procedure to calculate the pression field is usually the
most onerous in classical methodologies. Nevertheless, the pseudo-spectral method can be
only applied to periodic boundary flows, thus limiting its use. Aiming to solve this restriction, a
new methodology is proposed at the present work, which has the objective of simulating nonperiodic
flows using the Fourier pseudo-spectral method. For this purpose the immersed
boundary method, that represents the boundary conditions through a force field imposed at
Navier-Stokes equations is used. As a test to this new methodology, a classic problem of
Computational Fluid Dynamics, The Lid Driven Cavity was simulated. The obtained results
are promising and demonstrate the possibility to simulating non-periodic flows making use of
the Fourier pseudo-spectral method. / Para compreender fenômenos relacionados à combustão, aeroacústica, transição a
turbulência entre outros, a Dinâmica de Fluídos Computacional (CFD) utiliza os métodos de
alta ordem. Um dos mais conhecidos é o método pseudo-espectral de Fourier, o qual alia:
alta ordem de precisão na resolução das equações, com um baixo custo computacional.
Este está ligado à utilização da FFT e do método da projeção do termo da pressão, o qual
desvincula os cálculos da pressão da resolução das equações de Navier-Stokes. O
procedimento de calcular o campo de pressão, normalmente é o mais oneroso nas
metodologias convencionais. Apesar destas vantagens, o método pseudo-espectral de
Fourier só pode ser utilizado para resolver problemas com condições de contorno
periódicas, limitando o seu uso no campo da dinâmica de fluídos. Visando resolver essa
restrição uma nova metodologia é proposta no presente trabalho, que tem como objetivo
simular escoamentos não-periódicos utilizando o método pseudo-espectral de Fourier. Para
isso, é utilizada a metodologia da Fronteira Imersa, a qual representa as condições de
contorno de um escoamento através de um campo de força imposto nas equações de
Navier-Stokes. Como teste, para essa nova metodologia, foi simulada uma cavidade com
tampa deslizante (Lid Driven Cavity), problema clássico da mecânica de fluídos, que objetiva
validar novas metodologias e códigos computacionais. Os resultados obtidos são
promissores e demostram que é possível simular um escoamento não-periódico com o
método pseudo-espectral de Fourier. / Mestre em Engenharia Mecânica
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