La microfiltration est largement utilisée pour la clarification, la stabilisation et la concentration de nombreuses suspensions à base de fruits (jus de fruits, agro-déchets, vin, etc.). Malgré ses divers avantages, la microfiltration présente néanmoins un inconvénient majeur qui est le phénomène de colmatage qui s’installe pendant l’opération de filtration et entraîne une diminution de la perméabilité membranaire. Si de nombreux mécanismes de colmatage (adsorption, blocage de pores, etc.) sont observés pendant la filtration de suspensions polydisperses comme les jus de fruits ou certains coproduits liquides, le dépôt de particules sur la membrane est souvent supposé être le mécanisme limitant. La formation de ce dépôt est fortement dépendante de l’équilibre entre forces convectives (imposées par le flux de perméat), qui attirent les particules de la suspension à proximité de la membrane, et forces de rétrotransport, qui éloignent les particules de la surface membranaire. La stratégie la plus employée pour maitriser le colmatage membranaire par dépôt est la filtration tangentielle qui permet d’imposer de forts cisaillements à la surface membranaire qui favorisent les mécanismes de rétrotransport des particules. Si cette stratégie de maîtrise du colmatage est amplement utilisée à l’échelle industrielle pour la microfiltration des suspensions à base de fruits, elle nécessite des coûts d’investissement et de fonctionnement non négligeables qui limitent son implantation aux industries présentant de fortes capacités de production et d’investissement. Au regard de cela, l’utilisation d’une configuration de filtration à membranes immergées pour la microfiltration de suspensions à base de fruits pourrait être une alternative intéressante. Cette configuration repose sur l’immersion de la membrane (modules plans ou fibres creuses) dans la suspension à filtrer, et est associée à un mode de filtration externe-interne, frontal ou quasi-frontale. Si l’absence de conditions hydrodynamiques intenses au voisinage de la membrane est associée à des flux relativement bas, les nombreux avantages de ce mode opératoire (coûts de fonctionnement réduits, simplicité opérationnelle, forte compacité, etc.) pourraient favoriser son emploi par les petits producteurs de jus de fruits et/ou les industries de valorisation des coproduits présentant des capacités limitées d’investissement et enclins à minimiser leurs couts opérationnels. Ce travail a ainsi étudié pour la première fois la possibilité d’utiliser un tel système pour la microfiltration de suspensions à base de fruits variées (jus de fruits et coproduits vinicoles). Ce travail de thèse a ciblé ainsi plusieurs objectifs : (i) caractériser le potentiel et le comportement colmatant de suspensions à base de fruits, en lien avec les caractéristiques physicochimiques propres à chaque suspension et au regard de leur filtration par membranes immergées, (ii) étudier des performances d’un système de microfiltration de suspensions à base de fruits par membranes immergées, performances en termes de productivité et de sélectivité et enfin (iii) dégager des pistes de réflexion qui conduiraient à une choix pertinent de conditions de filtration (mode immergé ou tangentiel) pour un type de suspension ciblé. Ce travail fournit ainsi des résultats d’identification de paramètres physico-chimiques clefs qui pourraient constituer un premier guide pour le choix de la configuration membranaire la plus adaptée au produit, permettant d’assurer une productivité acceptable lors de la microfiltration de suspensions à base de fruits. / Microfiltration is widely used to ensure clarification, stabilization, and concentration of various fruit-based suspensions (e.g. fruit juices, food by-products, wine). However, the performances of membrane filtration remain highly challenged by membrane fouling. During microfiltration of polydisperse suspensions, such as fruit-based suspensions, membrane fouling is generally associated to the deposition of particles on the membrane layer. This type of fouling is mainly governed by the equilibrium between convective forces (permeate flow), leading particles to flow towards the membrane, and back-transport forces, removing particles away from the membrane surface. The filtration performances depend strongly on this equilibrium, which is mostly governed by the hydrodynamic conditions of the filtration process and the particles size distribution of the suspension. In food industries, cross-flow microfiltration is generally used to limit membrane fouling. In this configuration, high cross-flow velocities are applied in order to enhance the back-transport forces limiting the deposition of foulant materials on the membrane surface. However, this working mode is well known to be highly energy consuming and might not always be relevant depending on the suspension characteristics. In the light of this, using immersed membranes configuration for the microfiltration of fruit-based suspensions might be an interesting alternative, especially for small producers with limiting investment capacity. In this configuration, widely used in other fields, the membranes are immersed in the suspension and filtration is performed in operating conditions close to that of dead-end filtration with limited back-transport forces and low operating costs. However, the performances of this filtration configuration remain little studied for the microfiltration of fruit-based suspensions. In this respect, this work investigated for the first time the possibility of using immersed membranes configuration for the microfiltration of various fruit-based suspensions (fruit juices and winery byproducts). Firstly, a characterization of the fouling potential of various suspensions during their microfiltration using immersed membranes filtration was performed in relation with their physicochemical properties (particle size distribution). Then, this work allowed highlighting the promising performances of immersed membranes configuration when used for the microfiltration of fruit-based suspensions, in terms of productivity and in terms of selectivity (clarification, concentration of bioactive compounds). Finally, it allowed drawing preliminary results about the relation between the physicochemical characteristics of a suspension and its fouling behavior while using (i) immersed membranes filtration or (ii) conventional cross-flow filtration. These results might be of great interest for the identification of relevant physicochemical parameters to predict the usefulness of using high cross-flow velocity to prevent membrane fouling during the microfiltration of fruit-based suspensions.

Fluid motion has always been of great importance for humanity since much of our progress has been related to our understanding of fluid dynamics and to our control over the fluids surrounding us. In particular, the experimental techniques and the methods for numerical simulation developed during the last century allowed for great progresses both in creating new technologies and in improving old ones. Despite the great importance of experimental techniques, measuring all properties of a fluid throughout the whole domain, without intefering with the flow to be studied, is impossible. Also, building models even in scale is usually expansive. Both of these reasons have driven the development of numerical methods to the point they became an invaluable tool for fluid dynamic studies and the main tool for developing engineering solutions. If numerical methods are to be of any use, though, they have to correctly describe the problem geometry as well as capture the rich dynamics in a variety of flow situations, such as turbulence, boundary-layers and shock-waves. This thesis addresses two of these problems. In particular, I show modified versions of two immersed-interface methods to describe the geometry, simplifying their implementations with no impact to their applicability. I also introduce two methods for handling shock-waves: first aiming to minimize computational costs, then improving shock-wave resolution without increasing the number of grid points. / O movimento dos fluidos sempre foi de grande importância para a humanidade, dado que muito de nosso progresso esteve intimamente relacionado a um entendimento mais profundo de fluidodinâmica e de como controlar os flúidos ao nosso redor. Em particular, os métodos experimentais e de simulação computacional, desenvolvidos no último século, nos permitiram grandes avanços na criação de novas tecnologias e na otimização das já existentes. Apesar de sua grande importância, as dificuldades de se mensurar todas as propriedades de um flúido em todo o espaço, sem interferir com o comportamento do fluxo, além dos custos de se elaborar experimentos em tamanho real ou em escala, fez com que cada vez mais os métodos numéricos se tornassem uma importante ferramenta no estudo da fluido dinâmica e a principal ferramenta para o desenvolvimento de soluções de engenharia. Porém, para efetivamente substituir experimentos, os métodos numéricos tem que ser capazes de corretamente descrever a geometria do problema, além de capturarem todo tipo de comportamento apresentado pelos flúidos, como turbulência, camada limite e ondas de choque. Esta tese busca contribuir com dois destes desafios. Em particular, mostro versões modificadas de métodos de interface imersa para a descrição da geometria, simplificando as implementações originais sem prejudicar sua aplicabilidade. Também abordo métodos para tratar ondas de choque: primeiro buscando minimizar o esforço computacional e depois buscando aumentar a resolução do choque sem precisar refinar a malha computacional.

We present an immersed interface method for the incompressible Navier Stokes equations capable of handling rigid immersed boundaries. The immersed boundary is represented by a set of Lagrangian control points. In order to guarantee that the no-slip condition on the boundary is satisfied, singular forces are applied on the fluid at the immersed boundary. The forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity, and are interpolated using cubic splines. The strength of singular forces is determined by solving a small system of equations at each time step. The Navier-Stokes equations are discretized on a staggered Cartesian grid by a second order accurate projection method for pressure and velocity. / Singapore-MIT Alliance (SMA)

Aerothermodynamics is an integral component in the design and implementation of hypersonic transport systems. Accurate estimates of the aerodynamic forces and heat transfer rates are critical in trajectory analysis and for payload weight considerations. The present work seeks to investigate the ability of an unstructured Cartesian grid framework in modeling hypersonic viscous flows. The effectiveness of modeling viscous phenomena in hypersonic flows using the immersed boundary ghost cell methodology of this solver is analyzed. The capacity of this framework to predict the surface physics in a hypersonic non-reacting environment is investigated. High velocity argon gas flows past a 2-D cylinder are simulated for a set of freestream conditions (Reynolds numbers), and impact of the grid cell sizes on the quality of the solution is evaluated. Additionally, the formulation is verified over a series of hypersonic Mach numbers for the flow past a hemisphere, and compared to experimental results and empirical estimates. Next, a test case that involves flow separation and the interaction between a hypersonic shock wave and a boundary layer, and a separation bubble is investigated using various adaptive mesh refinement strategies. The immersed boundary ghost cell approach is tested with two temperature clipping strategies, and their impact on the overall solution accuracy and smoothness of the surface property predictions are compared. Finally, species diffusion terms in the conservation equations, and collision cross-section based transport coefficients are installed, and hypersonic flows in thermochemical nonequilibrium environments are studied, and comparisons of the off-surface flow properties and the surface physics predictions are evaluated. First, a 2-D cylinder in a hypersonic reacting air flow is tested with an adiabatic wall boundary condition. Next, the same geometry is tested to evaluate the viscous chemistry prediction capability of the solver with an isothermal wall boundary condition, and to identify the strengths and weaknesses of the immersed boundary ghost cell methodology in computing convective heating rates in such an environment.

Plunger pumps are needed for heavy duty sludge pumping at wastewater treatment facilities. America's leading pump manufacturer Wastecorp Inc. brought their plunger pump problem to us in late 2009. It was found that when the ow rate reaches a critical value, the plunger pump starts to generate a clicking noise. A one-dimensional model was built for studying the ow of a typical plunger pump operation. The velocities and pressures are calculated at certain interesting locations. Pressure jumps have been found while opening or closing the valves. The valve motion is then modeled with considerations to its geometry. The results show that as the plunger speed reaches a critical value, the valve moves more rapidly and more likely to hit the wall and generates a noise. We also provide a methodology to study the ow across the valve in higher resolution. A nite-di erence approach to the Navier-Stokes equations are presented with the immersed boundary method. / UOIT

Virtual knot theory, introduced by Kauffman, is a generalization of classical knot theory of interest because its finite-type invariant theory is potentially a topological interpretation of Etingof and Kazhdan's theory of quantization of Lie bi-algebras. Classical knots inject into virtual knots}, and flat virtual knots is the quotient of virtual knots which equates the real positive and negative crossings, and in this sense is complementary to classical knot theory within virtual knot theory. We classify flat virtual tangles with no closed components and give bases for its ``infinitesimal'' algebras. The classification of the former can be used as an invariant on virtual tangles with no closed components and virtual braids. In a subsequent paper, we will show that the infinitesimal algebras are the target spaces of any universal finite-type invariants on the respective variants of the flat virtual tangles.

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.

In this dissertation, we explore direct-forcing immersed boundary methods (IBM) under the framework of the lattice Boltzmann method (LBM), which is called the direct-forcing immersed boundary-lattice Boltzmann method (IB-LBM). First, we derive the direct-forcing formula based on the split-forcing lattice Boltzmann equation, which recovers the Navier-Stokes equation with second-order accuracy and enables us to develop a simple and accurate formula due to its kinetic nature. Then, we assess the various interface schemes under the derived direct-forcing formula. We consider not only diffuse interface schemes but also a sharp interface scheme. All tested schemes show a second-order overall accuracy. In the simulation of stationary complex boundary flows, we can observe that the sharper the interface scheme is, the more accurate the results are. The interface schemes are also applied to moving boundary problems. The sharp interface scheme shows better accuracy than the diffuse interface schemes but generates spurious oscillation in the boundary forcing terms due to the discontinuous change of nodes for the interpolation. In contrast, the diffuse interface schemes show smooth change in the boundary forcing terms but less accurate results because of discrete delta functions. Hence, the diffuse interface scheme with a corrected radius can be adopted to obtain both accurate and smooth results. Finally, a direct-forcing immersed boundary method (IBM) for the thermal lattice Boltzmann method (TLBM) is proposed to simulate non-isothermal flows. The direct-forcing IBM formulas for thermal equations are derived based on two TLBM models: a double-population model with a simplified thermal lattice Boltzmann equation (Model 1) and a hybrid model with an advection-diffusion equation of temperature (Model 2). The proposed methods are validated through natural convection problems with stationary and moving boundaries. In terms of accuracy, the results obtained from the IBMs based on both models are comparable and show a good agreement with those from other numerical methods. In contrast, the IBM based on Model 2 is more numerically efficient than the IBM based on Model 1. Overall, this study serves to establish the feasibility of the direct-forcing IB-LBM as a viable tool for computing various complex and/or moving boundary flow problems.

Study of turbulent flow over a rough bed is highly important due to its numerous applications in the areas of sediment transport and pollutant discharge in streams, rivers and channels. Over the past few decades, many experimental studies have been conducted in this respect to understand the underlying phenomenon. However, there is a scarcity in the number of computational studies conducted on this topic. Therefore, a Large Eddy Simulation (LES) of turbulent flow over a rough channel bed was conducted to contribute further understanding of the influence of bed roughness on turbulent flow properties. For this purpose, an efficient, second order accurate 'immersed boundary method' was implemented into the LES code Hydro3d-GT, and validated for flow past bluff bodies. LES results from the present study showed excellent agreement with previous experimental studies on flow over rough beds. An in-depth analysis of time varying turbulent quantities (like the velocity fluctuations) revealed the presence of coherent structures in the flow. Also, a three dimensional visualization of the turbulent structures provided a good picture of the flow, especially in the near bed region, which is quite difficult to accomplish using experimental studies.

Lime softening, chlorination, clarification and filtration have been long recognized treatment processes for beverage water specifically the carbonated soft drink (CSD) because it provides consistent water quality required for bottling plants, however these processes are becoming uneconomical and causes more problems than the benefits they offer. These processes require very large foot print, occupy large plant volume, and generate large volume of sludge which causes disposal problems. Chlorination produces trihalomethanes (THMs) and other by-products which are detrimental to health and imparts tastes to the final products. Using the newly developed submerged spiral wound ultrafiltration membranes in conjunction with lime softening may replace the conventional lime softening, clarification and filtration processes. This research was conducted to demonstrate the feasibility of integrating immersed ultrafiltration (UF) membrane with lime softening. The objectives of this research was to achieve the water quality required by the CSD bottlers; determine the relationships of operating parameters such as pH and membrane flux with trans-membrane pressure (TMP), and membrane permeability; determine the optimum dosage of lime; evaluate the operating parameters as basis for the design and construction of the full scale plant; and predict the membrane cleaning intervals. A pilot unit consisting of lime reactor and UF system was designed and built for this research. The pilot unit was operated at various pH ranging from 7.3 to 11.2 and at membrane flux rates of 15, 30 and 45 gfd. The pilot unit was also operated at the CSD bottler’s operating conditions which is pH 9.8 at flux of 30 gfd. The pilot unit operated for a total of 1800 hours. The raw water source was from city water supply. The filtrate from the pilot unit achieved alkalinity reduction to 20 to 30 mg/L preferred by CSD bottlers, with lime dosage close to the calculated value. The filtrate turbidity during the test was consistently within 0.4 to 0.5 NTU. The TMP values obtained during the test ranges from 0.1 to 2.5 psi, while the permeability values ranges from 18.19 to 29.6 gfd/psi. The increase in flux results to corresponding increase in TMP, and increase in operating pH, increases the rate of TMP. Permeability decreases with increasing operating pH. The TOC reduction ranges from 2.6 % to 15.8% with increasing operating pH. No scaling of the UF membranes was observed during the test. Thirty days UF membrane cleaning interval was predicted. The results from this research can use as the basis of designing and operating a full scale Lime Softening UF Treatment Plant.