In this dissertation, we study the behavior of microscopic organisms utilizing lateral and spiral bending waves to swim in a fluid. More specifically, spermatozoa encounter different fluid environments filled with mucus, cells, hormones, and other large proteins. These networks of proteins and cells are assumed to be stationary and of low volume fraction. They act as friction, possibly preventing or enhancing forward progression of the swimmers. The flow in the medium is described as a viscous fluid with a resistance term known as a Brinkman fluid. It depends on the Darcy permeability parameter affecting the swimming patterns of the flagella. To further understand these effects we study the asymptotic swimming speeds of an infinite-length swimmer propagating planar or spiral bending waves in a Brinkman fluid. We find that, up to the second order expansion, the swimming speeds are enhanced as the resistance increases. The work to maintain the planar bending and the torque exerted on the fluid are also examined. The Stokes limits of the swimming speeds, the work and the torque are recovered as resistance goes to zero. The analytical solutions are compared with numerical results of finite-length swimmers obtained from the method of Regularized Brinkmanlets (MRB). The study gives insight on the effects of the permeability, the length and the radius of the cylinder on the performance of the swimmers. In addition, we develop a grid-free numerical method to study the bend and twist of an elastic rod immersed in a Brinkman fluid. The rod is discretized using a Kirchhoff Rod (KR) model. The linear and angular velocity of the rod are derived using the MRB. The method is validated through a couple of benchmark examples including the dynamics of an elastic rod, and the planar bending of a flagellum in a Brinkman fluid. The studies show how the permeability and stiffness coefficients affect the waveforms, the energy, and the swimming speeds of the swimmers. Also, the beating pattern of the spermatozoa flagellum depends on the intracellular concentrations of calcium ([Ca2+]). An increase of [Ca2+] is linked to hyperactivated motility. This is characterized by highly asymmetrical beating, which allows spermatozoa to reach the oocyte (egg) or navigate along the female reproductive tract. Here, we couple the [Ca2+] to the bending model of a swimmer in a Brinkman fluid. This computational framework is used to understand how internal flagellar [Ca2+] and fluid resistance in a Brinkman fluid alter swimming trajectories and flagellar bending.

archives@tulane.edu / Discrete fracture networks (DFNs) can be modeled with polygonal representations that are useful for geophysical modeling of nuclear waste containment and hydrofrac- turing. Flow and transport calculations are possible, but computationally expensive, limiting the feasibility for model uncertainty quantification. Graphs are used to re- duce model complexity and computation time. We present the formulation of using a graph as a reduced model for DFNs and pose the inversion problem central to this research. We present a novel alternative to Darcy’s law on graphs using the well known Brinkman formulation on the continuum. We apply the Levenberg-Marquardt algorithm to optimize graphs, calibrating them to observed data through the inversion problem. We present the deficiencies in physically motivated graphs, and show how optimized graphs produce better results overall. Our solution finds lumped parameters representing the fracture properties, and is used to reduce the computational time required for particle transport calculations. Breakthrough curves are produced on our obtained solutions, which closely match the high fidelity model. We present examples of creating these reduced models for DFNs with 500 fractures to illustrate the methodology and optimization scheme used to obtain an improved result over a previous formulation. / 1 / Jaime Lopez-Merizalde

Fluid-structure interactions play a central role in an overwhelming number of physical phenomena. All fluid dynamic students are familiar with the common assumption of a "smooth boundary". While this assumption often is enough to provide a high level understanding of the dynamics and physics at hand in practice this is not true.  Much of the detail and the unique phenomena can be traced back to surface properties that deviate from this elementary assumption.  In this work we investigate three problems all motivated by the existence of non-smooth surfaces.   The first paper considers how inhomogeneous surfaces can generate a lift force for lubricated contacts. This work showcases how subtle changes to surface texture or chemistry modeled by a slip length can invoke non-trivial forces. These forces result in striking particle trajectories not possible in the presence of a smooth no-slip wall.    The next work focuses on porous surfaces. Often the geometry of surfaces in nature and industry are complex covering a wide range of length scales. Resolving all the scales of motion arising from fluid interaction with such surfaces are computationally expensive. Effective equations are often applied to reduce the cost of such simulations. The Brinkman equation is one common model choice for free-fluid and porous surface interface. Despite the common application of the Brinkman equation, fundamental questions about what the effective viscosity should be remain open. We compare pore-scale Stokes flow solutions to the Brinkman model for several porous surfaces. This study provides a scaling for the effective viscosity as well as error quantification of the Brinkman model.    Lastly, we investigate how porous surfaces modify a turbulent boundary layer. Streamwise preferential porous surfaces have recently been suggested as a surface modification that has the potential to reduce drag. We compare particle image velocimetry measurements with direct numerical simulations focusing on the near wall features that are modified from the canonical smooth wall case. We present some preliminary turbulent statistics and flow visualizations in the current report.

Les procédés d’élaboration de pièces composites par infusion de résine, malgré leurs nombreux avantages, peinent à s’imposer dans les phases de production industrielle en raison de difficultés pour les maitriser. Ainsi, en partenariat avec ESI Group, un modèle complet pour la simulation de ces procédés est développé à l’ENSM-SE depuis les travaux précurseurs de P. Celle.Nos travaux portent sur la généralisation de ce modèle afin de traiter des cas, ainsi que sur son extension à la simulation des écoulements « post-infusion ». L'approche repose sur un découpage du domaine en trois zones (drainant, préformes imprégnées, préformes sèches) consistant ainsi à coupler un écoulement de Stokes dans le drainant à un écoulement de Darcy dans les préformes. De plus, l'influence mutuelle de la résine sur le comportement des préformes et de la déformation des préformes sur la perméabilité est considérée, à travers la loi de Terzaghi et des lois exprimant la perméabilité en fonction de la fraction de fibres, paramètre accessible uniquement dans une approche 3D mécanique couplée. Enfin, le procédé est découpé en trois phases : compression initiale des préformes sèches, remplissage et « post-infusion ». Les méthodes numériques, développées dans ces travaux, s'appliquent à des cas réels d'infusion souvent mis de côté dans les publications récentes car inaccessibles, impliquant des perméabilités très faibles (~10-15 m²), un drainant fin (~1 mm) et des géométries complexes.Cette approche innovante a été implémentée dans un code de calcul industriel (ProFlotTM), validée analytiquement sur des cas tests et expérimentalement sur des cas industriel dans le cadre du projet européen INFUCOMP. / Composite manufacturing processes by resin infusion, despite their many benefits, struggle to establish themselves in the industrial production phases due to difficulties to control them. So, in partnership with ESI Group, a comprehensive model for the simulation of these processes is developed at the ENSM-SE since the pioneering work of P. Celle.Our work focuses on the generalization of this model to handle complex industrial cases in three dimensions, as well as its extension to “post-infusion” flow simulation. The approach is based on three domains decomposition of the field (Distribution medium, impregnated preforms, dry preforms) consisting in coupling a Stokes flow in the distribution medium with a Darcy flow in the preforms. In addition, the mutual influence of the resin on the preforms and of the preforms deformation on the permeability is considered, through Terzaghi’s law and models expressing the permeability as a function of the fibre fraction, data only accessible with a 3D coupled mechanical approach. Finally, the process is divided into three phases: initial compression of dry preforms, filling and “post-infusion”. The numerical methods developed in this work, apply to real infusion cases often discarded in recent publications, involving very low permeability (~10-15 m²), thin distribution medium (~ 1 mm) and complex geometries (3D curved).This innovative approach has been implemented in an industrial simulation code (ProFlotTM), validated analytically over test cases and experimentally over industrial cases in the European project INFUCOMP.

[pt] O presente trabalho foca em uma investigação numérica do escoamento através de meios porosos com macroporos, como os carbonatos. A presença de vugs e fraturas tem um forte efeito na característica do escoamento. O fluxo através da matriz porosa é geralmente descrito pela equação de Darcy e o fluxo através dos macroporos pela equação de Stokes. O acoplamento entre essas duas abordagens distintas traz grande complexidade para a modelagem de tais fluxos. Neste trabalho, utilizamos a formulação de Brinkman que é capaz de descrever ambos os fluxos através da matriz porosa e macroporos com uma única equação diferencial. Resolvemos o sistema de equações diferenciais usando o modelo de elementos finitos e implementamos o código com auxílio da plataforma FEniCS. Primeiro, resolvemos o fluxo 1-D através de placas paralelas com uma das paredes sendo um material poroso. O objetivo foi comparar as previsões obtidas pela formulação de Brinkman com aquela obtida usando a condição de contorno de Beavers-Joseph. Então, resolvemos um fluxo 2-D através de um meio poroso com macroporos. A geometria da estrutura porosa foi obtida a partir de cortes 2D de imagens tomográficas de carbonatos. O objetivo desta análise foi avaliar uma permeabilidade equivalente em função da área e estrutura dos macroporos. / [en] The present work focuses on a numerical investigation of the flow through porous media with macropores, such as carbonates. The presence of vugs and fractures have a strong effect on the flow characteristics. The flow through the porous matrix is usually described by the Darcy equation and the flow through the macropores by Stokes equation. The coupling between these two distinct approaches brings great complexity to the modeling of such flows. In this work, we use Brinkman formulation that is able to describe the flow, both in the porous matrix and macropores with a single differential equation. We solved the set of differential equations using the finite element model and implemented the code in the FEniCS platform. We first solved the 1-D flow through parallel plates with one of the walls being a porous material. The goal was to compare the predictions obtained with the Brinkman formulation to that obtained by using the Beavers-Joseph boundary condition. Then, we solved a 2-D flow through a porous medium with macropores. The geometry of the pore structure was obtained from 2D slices of tomographic images of carbonates. The goal of this analysis was to evaluate an equivalent permeability as a function of macropores area and structures.

[pt] Rochas carbonáticas possuem atributos únicos que as distinguem das siliciclasticas e necessitam de diferentes métodos de estudo para caracterizar sua textura. Rochas carbonáticas são resultado de interações entre processos deposicionais químicos e biológicos. Os processos diagenéticos que formam e alteram estas rochas contribuem para o acúmulo de heterogeneidades. Devido ao alto teor de heterogeneidade, as propriedades medidas (e.g. porosidade e permeabilidade) variam com a escala de investigação e estudos com o compromisso a significância dos detalhes e representação espacial. Ampliar uma escala menor para maior, exige procedimentos que preservem a essência dos processos físicos de um nível mais detalhada para um mais grosseiro. Métodos simplificados para dimensionar propriedades não aditivas em outras escalas, tal como permeabilidade, geralmente não honram a heterogeneidade presente em sistemas complexos. Com isso a dinâmica dos fluidos em rochas complexas exige abordagens e métodos mais sofisticados. Este estudo é focado em desenvolver uma metodologia de avaliação da permeabilidade como parâmetro de escala para meios porosos heterogêneos. A permeabilidade é retro calculada ao emular o experimento de Darcy e resolver o fluxo no meio poroso utilizando uma formulação de elementos finitos para equação de Brinkman. O estudo iniciou com foco em sistemas paramétricos de células periódicas e posteriormente a duas microtomogra fia de rochas carbonáticas, do qual uma foi selecionada para um estudo de representatividade espacial. As células periódicas foram utilizadas para avaliar os efeitos da formação de canais e espaços vazios, em analogia a fraturas e vugos, assim como os efeitos da permeabilidade da matriz porosa. As amostras carbonáticas consistem de casos nos quais é possível observar a presença de uma combinação dos fenômenos estudadas. Por fim um estudo de representatividade foi conduzido segmentando uma amostra de micro-tomografia em suficientes sub-amostras que capazes de reproduzir a heterogeneidade espacial da amostra original. / [en] Carbonate rocks have unique attributes that distinguish them from siliciclastics and that require diferent methods of study to characterize their texture. Carbonates rocks are formed as a result of close interactions between biological and chemical depositional processes. The underlying diagenetic processes that form and alter these rocks contribute to a build-up of heterogeneities. Because of the high heterogeneity content measured properties (e.g. porosity and permeability) change with the scale of investigation and studies have struggle with a trade-off between significance of details and space representativeness. Extending a smaller scale to a larger requires scaling up procedures that preserves the essence of physical processes at one level to be summarized at the coarser level. Simplistic methods for scaling-up non-additive properties such as permeability generally do not honour the original heterogeneity present in complex systems. Therefore the dynamics of fluid flow in complex rocks demand more sophisticate methods and approaches. This study was focused in developing a methodology to evaluate the permeability as a scaling-up parameter for heterogeneous porous media. The permeability is back-calculated by emulating Darcy s experiment and solving the pore-scale ow using a Finite element formulation of Brinkman flow equation. The study was initially focused on parametric systems of periodic cells and later extended to two micro-tomography carbonate samples in which one has been selected for a spatial representativeness study. The parametric cells were used to evaluate the shape effects of channels and void spaces in an analogy to geological fractures and vugs as well as the permeability of the porous matrix. The micro-tomography carbonate samples consisted of a real case scenario in which, to a certain degree, could be observed a combination of the previously studied periodic cells. Finally a representativeness study was conducted segmenting the micro-tomography sample into suficiently sub-samples that would be capable of reproducing the spatial heterogeneity of the sample.

Les aquifères karstiques sont caractérisés par un écoulement rapide dans les conduits karstiques et un écoulement lent dans la roche encaissante (matrice). En raison de cet écoulement rapide, ces aquifères sont fortement vulnérables à la pollution. L'objectif principal de cette thèse est d'évaluer l'importance des échanges d'eau à l'interface entre les conduits et la matrice et par conséquent l'impact de ces échanges sur le transport de soluté dans le système karstique. Pour investiguer l'apport de l'équation de Brinkman à l'évaluation des écoulements d'eau, un modèle dont la géométrie du conduit est décrite par la fonction sinus a été établi. Deux scénarii sont appliqués. Le scénario A emploie la loi de Darcy dans le conduit et la matrice. Le scénario B emploie l'équation de Brinkman et la loi de Darcy dans le conduit et la matrice, respectivement. Le terme supplémentaire de l'équation de Brinkman décrivant les forces de cisaillement joue un rôle prédominant sur l'échange d'eau entre le conduit et la matrice lorsque les conduits sont sinueux. Le modèle hydrodynamique - transport a été appliqué au système karstique du Val d'Orléans. La calibration a démontré que le meilleur diamètre moyen du conduit est de 5 m, la perméabilité dans la roche encaissante est de 5,7×10-10 m2 et celle du conduit de 1,65×10-5 m2 à 5,5×10-5 m2. Les prédictions du modèle hydrodynamique - transport ont été comparées aux crues de la Loire observées dans les années 1992 et 1993 durant lesquelles les concentrations en chlorure (traceur naturel conservatif) ont été dosées dans la Loire et à la source du Bouillon. Avec un coefficient d'emmagasinement dans la matrice de 0,9 m-1, la distance pénétrée par l'eau de la crue dans la matrice est d'environ 530 m en deux mois pour une crue de 2 m (exemple de 1993).

Les procédés d'élaboration de pièces composites par infusion de résine, malgré leurs nombreux avantages, peinent à s'imposer dans les phases de production industrielle en raison de difficultés pour les maitriser. Ainsi, en partenariat avec ESI Group, un modèle complet pour la simulation de ces procédés est développé à l'ENSM-SE depuis les travaux précurseurs de P. Celle.Nos travaux portent sur la généralisation de ce modèle afin de traiter des cas, ainsi que sur son extension à la simulation des écoulements " post-infusion ". L'approche repose sur un découpage du domaine en trois zones (drainant, préformes imprégnées, préformes sèches) consistant ainsi à coupler un écoulement de Stokes dans le drainant à un écoulement de Darcy dans les préformes. De plus, l'influence mutuelle de la résine sur le comportement des préformes et de la déformation des préformes sur la perméabilité est considérée, à travers la loi de Terzaghi et des lois exprimant la perméabilité en fonction de la fraction de fibres, paramètre accessible uniquement dans une approche 3D mécanique couplée. Enfin, le procédé est découpé en trois phases : compression initiale des préformes sèches, remplissage et " post-infusion ". Les méthodes numériques, développées dans ces travaux, s'appliquent à des cas réels d'infusion souvent mis de côté dans les publications récentes car inaccessibles, impliquant des perméabilités très faibles (~10-15 m²), un drainant fin (~1 mm) et des géométries complexes.Cette approche innovante a été implémentée dans un code de calcul industriel (ProFlotTM), validée analytiquement sur des cas tests et expérimentalement sur des cas industriel dans le cadre du projet européen INFUCOMP.

京都大学 / 0048 / 新制・課程博士 / 博士(農学) / 甲第21151号 / 農博第2277号 / 新制||農||1059(附属図書館) / 学位論文||H30||N5125(農学部図書室) / 京都大学大学院農学研究科地域環境科学専攻 / (主査)教授 村上 章, 教授 川島 茂人, 教授 藤原 正幸 / 学位規則第4条第1項該当 / Doctor of Agricultural Science / Kyoto University / DFAM

[pt] Nesta dissertação é apresentado um estudo comparativo entre dois métodos de descrição do escoamento de fluidos em meios porosos heterogêneos e compostos de elementos arquiteturais de permoporosidade elevada, chamados fraturas e carstes. Fraturas são descontinuidades nas formações desencadeadas por tensão mecânica e carstes são espaços vazios na rocha formados por dissolução. Ambos são característicos das rochas carbonáticas do Pré-Sal, principais reservatórios produtores de petróleo do Brasil. A presença destes elementos traz grande dificuldade de caracterização e, por consequência, introduz grande incerteza nas curvas de produção previstas para cada campo. Os simuladores numéricos em diferenças finitas de Engenharia de Reservatórios, responsáveis pela geração destas curvas, representam de forma aproximada o escoamento nos espaços vazios da rocha devido à formulação aplicada. Além disso, devido à escala de quilômetros de extensão em que normalmente são utilizados, usam células que incluem os três meios (matriz porosa, carste e fratura), cujas escalas são menores que a de cada célula. Nesta dissertação, busca-se entender a equivalência entre simuladores numéricos black oil e o modelo de Brinkman, ainda não utilizado amplamente, que é um modelo físico constituído por equações que representam mais fielmente o escoamento, tanto na matriz porosa, quanto nas regiões de altíssima porosidade e nas fronteiras entre elas. Para esse objetivo, foi desenvolvido um simulador de Brinkman de fluxo monofásico em duas dimensões e capaz de representar o regime não permanente, utilizando o método dos elementos finitos para resolução das equações diferenciais. Os comportamentos não permanente e permanente do simulador criado foram validados por meio de exemplos da literatura. Os valores obtidos para a propagação da pressão e velocidade de fluxo foram comparados com os de um simulador numérico black oil na reprodução do escoamento em camadas selecionadas do modelo do carbonato do Lajedo Arapuá. Foram realizados estudos com modelos de duplo contínuo (que representam, através de parâmetros específicos, o fluxo na matriz porosa e nas fraturas, com um termo de transferência entre eles) buscando, através da variação da permeabilidade efetiva da fratura e do fator de forma, convergência aos resultados do modelo de contínuo único de referência, selecionado após análise dos resultados comparativos com Brinkman. Os resultados mostraram pouca variação entre os resultados dos métodos em cenários nos quais o sistema cárstico é composto por vugs dispersos e desconectados, enquanto que carstes em forma de condutos e com configurações complexas causam alterações na propagação da onda de pressão e nas velocidades de fluxo entre os modelos, principalmente em cenários com valores de permeabilidade mais próximos entre carste e matriz porosa na simulação black oil. A análise em duplo contínuo mostrou ser possível obter, através de modelos homogêneos e com escala até 10 vezes maiores, resultados semelhantes aos obtidos com uma modelagem black oil heterogênea com caracterização do sistema cárstico. Também foi possível concluir que a permeabilidade efetiva de fratura é suficiente como parâmetro de ajuste para encontrar um modelo equivalente, dentro de um critério de valor de variação, ao modelo de contínuo único. / [en] This dissertation presents a comparative study between two porous media fluid flow description methods applied to heterogeneous reservoirs composed of architectural elements of high permo-porosity, called fractures andkarsts. Fractures are formation discontinuities triggered by mechanical stressand karsts are empty cavities inside the formation generated by dissolution.Both are characteristic of Pre-Salt carbonate rocks, which are the main oil producing reservoirs in Brazil. The existence of these elements brings complexityin characterization and, hence, increases the uncertainty in field productionprediction curves. The Reservoir Engineering numerical simulators, based onfinite differences, that generate these curves model the flow behavior insidethe cavities in an approximate manner due to the mathematical formulationapplied. Besides, due to the kilometric scale in which they are usually applied,these models use cells that comprehend the three media (matrix, karst andfractures), whose scales are smaller than the cell’s. This dissertation evaluatesthe equivalence between black oil simulation and the Brinkman model, still notwidely used, which is a physical model made of equations that represent porousmedia flow inside high porosity regions as well as at the porous matrix andits boundaries. With this objective, a two-dimensional single-phase Brinkmansimulator, capable of representing transient flow, was designed using the finiteelements method to solve differential equations. The simulator s transient andpermanent behaviors were validated through literature analytical solutions.The pressure propagation and flow velocity values obtained while simulatingfluid flow inside selected layers from Lajedo Arapuá s carbonate formation werecompared to the ones from a black oil simulator. Studies were performed usingdual-continuum models (which calculate the fluid flow inside porous matrixand fractures separately and use a transfer term to account for the flow between them) seeking, through variation of the fracture effective permeabilityand the shape factor, convergence to the mono-continuum reference model thatwas selected after Brinkman s results comparative analysis. The results showsmall variation between the two methods when the karst system is composedof sparse and disconnected vugs, while conduit shaped karsts with complexconfiguration increase the variation in pressure wave propagation and flowvelocity values between models, especially in scenarios where matrix permeability values were closer to karst permeability values in the black oil model.The dual-continuum analysis showed that it is possible to obtain, through homogeneous and even ten times coarser models, similar results to those obtainedby a heterogeneous black oil model with karst system characterization. It wasalso possible to conclude that fracture effective permeability was sufficient asa fitting parameter in order to achieve equivalent results to those from themono-continuum model, using a threshold criteria.