This work details the development of a computational tool that can accurately model strongly-coupled fluid-structure-interaction (FSI) problems, with a particular focus on thin-walled structures undergoing large, geometrically non-linear deformations, which has a major interest in, amongst others, the aerospace and biomedical industries. The first part of this work investigates improving the efficiency with which a stable and robust in-house code, Elemental, models thin structures undergoing dynamic fluid-induced bending deformations. Variations of the existing finite volume formulation as well as linear and higher-order finite element formulations are implemented. The governing equations for the solid domain are formulated in a total Lagrangian or undeformed conguration and large geometrically non-linear deformations are accounted for. The set of equations is solved via a single-step Jacobi iterative scheme which is implemented such as to ensure a matrix-free and robust solution. Second-order accurate temporal discretisation is achieved via dual-timestepping, with both consistent and lumped mass matrices and with a Jacobi pseudo-time iteration method employed for solution purposes. The matrix-free approach makes the scheme particularly well-suited for distributed memory parallel hardware architectures. Three key outcomes, not well documented in literature, are highlighted: the issue of shear locking or sensitivity to element aspect ratio, which is a common problem with the linear Q4 finite element formulation when subjected to bending, is evaluated on the finite volume formulations; a rigorous comparison of finite element vs. finite volume methods on geometrically non-linear structures is done; a higher-order finite volume solid mechanics procedure is developed and evaluated. The second part of this work is concerned with fluid-structure interaction (FSI) modelling. It considers the implementation and coupling of a higher order finite element structural solver with the existing finite volume fluid-flow solver in Elemental. To the author’s knowledge, this is the first instance in which a strongly-coupled hybrid finite element–finite volume FSI formulation is developed. The coupling between the fluid and structural components with non-matching nodes is rigorously assessed. A new partitioned fluid-solid interface coupling methodology is also developed, which ensures stable partitioned solution for strongly-coupled problems without any additional computational overhead. The solver is parallelised for distributed memory parallel hardware architectures. The developed technology is successfully validated through rigorous temporal and mesh independent studies of representative two-dimensional strongly-coupled large-displacement FSI test problems for which analytical or benchmark solutions exist. / Dissertation (MEng)--University of Pretoria, 2012. / Mechanical and Aeronautical Engineering / unrestricted

A new implicit and compact optimization-based method is presented for high order derivative calculation for finite-volume numerical method on unstructured meshes. Highorder approaches to gradient calculation are often based on variants of the Least-Squares (L-S) method, an explicit method that requires a stencil large enough to accommodate the necessary variable information to calculate the derivatives. The new scheme proposed here is applicable for an arbitrary order of accuracy (demonstrated here up to 3rd order), and uses just the first level of face neighbors to compute all derivatives, thus reducing stencil size and avoiding stiffness in the calculation matrix. Preliminary results for a static variable field example and solution of a simple scalar transport (advection) equation show that the proposed method is able to deliver numerical accuracy equivalent to (or better than) the nominal order of accuracy for both 2nd and 3rd order schemes in the presence of a smoothly distributed variable field (i.e., in the absence of discontinuities). This new Optimization-based Gradient REconstruction (herein denoted OGRE) scheme produces, for the simple scalar transport test case, lower error and demands less computational time (for a given level of required precision) for a 3rd order scheme when compared to an equivalent L-S approach on a two-dimensional framework. For three-dimensional simulations, where the L-S scheme fails to obtain convergence without the help of limiters, the new scheme obtains stable convergence and also produces lower error solution when compared to a third order MUSCL scheme. Furthermore, spectral analysis of results from the advection equation shows that the new scheme is better able to accurately resolve high wave number modes, which demonstrates its potential to better solve problems presenting a wide spectrum of wavelengths, for example unsteady turbulent flow simulations.

Computational thermo-fluid models of a free surface flow under the dominant radiative transfer have been developed for the design and control of a modern optic fiber drawing process. Although modeling of the fiber drawing process has been of interest for the past three decades, most of the previous studies were limited to low draw speeds and small preforms. Large preforms drawn at high speeds have been used in modern fiber drawing systems to improve production efficiency and reduce cost. Several assumptions commonly made in previous studies have to be relaxed to address the new challenges. In this study, instead of using the Rosseland approximation, the radiative transfer equation (RTE) was solved directly for the radiation fluxes using the finite volume method (FVM). The complete two-dimensional free surface flow was simulated along with the coupling of the radiative transfer. Unlike most of the previous studies that only considered the furnace domain and that assumed the glass velocity at the exit, we included the post-chamber in the computation domain and predicted the fiber solidification location. Furthermore, the mixed convection of the air in the post-chamber was also considered, and was shown to have significant effects on the fiber solidification. On the basis of the computational model, a reduced order model (ROM) was developed for a mixed HŁ /LQG controller designed to regulate the fiber diameter under the effects of disturbances. The ROM was derived on the basis of the computational model. Optimal numerical eigenfunctions were obtained through the Karhunen-Loeve expansion using the computational model. The GalerkinŁ s method was then applied to obtain the state space ROM. The numerical model was shown to be efficient and was verified experimentally. The ROM characterizes the dynamics of the system accurately as compared with the computational model. The simulations using the full computational model showed that the closed-loop system is robust and superior to the open-loop system in the regulation of fiber diameter. The modeling and control methods can be applied to the design optimization and parameter regulation of the high-speed large-preform draw processes as well as other manufacturing processes that involve similar thermal-fluid transports.

A suspension flow model based on the "suspension balance" approach has been developed. This work modifies the model to allow the solution of suspension flows under general flow conditions. This requires the development of a frame-invariant constitutive model for the particle stress which can take into account the spatially-varying local kinematic conditions. The mass and momentum balances for the bulk suspension and particle phase are solved numerically using a finite volume method. The particle stress is based upon the computed rate of strain and the local kinematic conditions. A nonlocal stress contribution corrects the continuum approximation of the particle phase for finite particle size effects. Local kinematic conditions are accounted through the local ratio of rotation to extension in the flow field. The coordinates for the stress definition are the local principal axes of the rate of strain field. The developed model is applied to a range of problems. (i) Axially-developing conduit flows are computed using both the full two-dimensional solution and the more computationally efficient "marching" method. The model predictions are compared to experimental results for cross-stream particle concentration profiles and axial development lengths. (ii) Model predictions are compared to experiments for wide-gap circular Couette flow of a concentrated suspension in a shear-thinning liquid. With minor modification, the suspension flow model predicts the major trends and results observed in this flow. (iii) Comparisons are made to experiments for an axisymmetric contraction-expansion. Model predictions for a two-dimensional planar contraction flow test the influence of model formulation. The variation of the magnitude of an isotropic particle normal stress with local kinematic conditions and anisotropy in the in-plane normal stresses are both explored. The formulation of the particle phase stress is found to have significant effects on the solid fraction and velocity. (iv) Finally, for a rectangular piston-driven flow and an obstructed channel flow, a "computational suspension dynamics" study explores the effect of particle migration on the bulk flow field, system pressure drop and particle phase composition.

Dielectric Barrier Discharge (DBD) excimer lamp is a very attractive source for Ultraviolet (UV) radiation. It has a number of advantages compared to the mercury lamp which is the main lamp used in the industry for UV production. Some of these advantages are instant UV radiation (no warm-up period), narrow UV spectrum, longer life times and simple construction. The DBD UV lamp can be used in number of applications like water disinfection, Plasma Display Panels (PDP) and surface treatment in the semiconductor industry. Yet, the full industrial application of this lamp still faces some problems mainly related to finding the optimum electrical driver to maximize the efficiency of such a lamp. This includes the type of the electrical waveform to generate and the power electronic driver to produce it. In this thesis, firstly a physically based circuit model for the DBD lamp using the Finite Volume Method (FVM) is developed. This model provides the electrical and optical characteristics of the lamp. Using this model the sensitivity of the lamp efficiency to the proposed electrical waveform has been determined. Secondly, the order of this FVM model has been reduced to obtain a model which is used in the design procedure of the proposed driver. Since the DBD lamp has a capacitive nature, a current controlled driver is proposed in this thesis as opposed to most of the published drivers which are voltage controlled drivers. The design of this driver is intended to enhance the electrical to optical efficiency of the lamp and therefore enhancing the overall efficiency of the system. The driver topology permits direct control of the peak lamp current and the operating frequency of the supplied current to the DBD lamp. The width of the current pulses is determined by the transformer magnetizing inductance and the lamp capacitance. Experimental results of the proposed driver connected to a XeCl DBD lamp are presented to validate the performance of the driver and to prove the concept of such a current controlled driver. The proposed driver performance is compared to a voltage source driver which was also implemented. The proposed driver produced higher overall system efficiency but at the expense of a reduction in the driver efficiency as compared to the voltage source driver. The complete system, which consists of the developed FVM based model and the equivalent circuit of the proposed driver, was simulated and the results were compared to the experimental results to validate the accuracy of the developed model for the DBD lamp.

A Large Eddy-Simulation code, based on a mesh transparent algorithm, for hybrid unstructured meshes is presented to deal with complex geometries that are often found in engineering flow problems. While tetrahedral elements are very effective in dealing with complex geometry, excessive numerical diffusion often affects results. Thus, prismatic or hexahedral elements are preferable in regions where turbulence structures are important. A second order reconstruction methodology is used since an investigation of a higher order method based upon Lele's compact scheme has shown this to be impractical on general unstructured meshes. The convective fluxes are treated with the Roe scheme that has been modified by introducing a variable scaling to the dissipation matrix to obtain a nearly second order accurate centred scheme in statistically smooth flow, whilst retaining the high resolution TVD behaviour across a shock discontinuity. The code has been parallelised using MPI to ensure portability. The base numerical scheme has been validated for steady flow computations over complex geometries using inviscid and RANS forms of the governing equations. The extension of the numerical scheme to unsteady turbulent flows and the complete LES code have been validated for the interaction of a shock with a laminar mixing layer, a Mach 0.9 turbulent round jet and a fully developed turbulent pipe flow. The mixing layer and round jet computations indicate that, for similar mesh resolution of the shear layer, the present code exhibits results comparable to previously published work using a higher order scheme on a structured mesh. The unstructured meshes have a significantly smaller total number of nodes since tetrahedral elements are used to fill to the far field region. The pipe flow results show that the present code is capable of producing the correct flow features. Finally, the code has been applied to the LES computation of the impingement of a highly under-expanded jet that produces plate shock oscillation. Comparison with other workers' experiments indicates good qualitative agreement for the major features of the flow. However, in this preliminary computation the computed frequency is somewhat lower than that of experimental measurements.

Nous présentons de nouveaux schémas numériques pour l'approximation de problèmes de diffusion hétérogène et anisotrope sur des maillages généraux. Sous des hypothèses correspondant aux cas industriels, nous montrons qu'un premier schéma, qui est centré sur les mailles, possède un petit stencil et converge dans le cas de tenseurs discontinus. La preuve de la convergence repose sur des propriétés de consistance des gradients discrets issus du schéma. Dans une seconde partie, nous proposons des méthodes de correction non linéaire du schéma initial pour obtenir le principe du maximum. L'efficacité de ces schémas est étudiée sur des tests numériques ayant fait l'objet de bancs d'essais d'une grande variété de schémas de volumes finis. Les comparaisons avec les schémas volumes finis classiques montrent l'apport de ces schémas en termes de précision. Nous montrons ainsi le bon comportement de ces schémas sur des maillages déformés, et le maintien de la précision des schémas non-linéaires, alors que les oscillations ont été supprimées / We present a new scheme for the discretization of heterogeneous anisotropic diffusion problems on general meshes. With light assumptions, we show that the algorithm can be written as a cell-centered scheme with a small stencil and that it is convergent for discontinuous tensors. The key point of the proof consists in showing both the strong and the weak consistency of the method. Besides, we study non-linear corrections to correct the FECC scheme, in order to satisfy the discrete maximum principle (DMP).The efficiency of the scheme is demonstrated through numerical tests of the 5th & 6th International Symposium on Finite Volumes for Complex Applications - FVCA 5 & 6. Moreover, the comparison with classical finite volume schemes emphasizes the precision of the method. We also show the good behaviour of the algorithm for nonconforming meshes. In addition, we give some numerical tests to check the existence for the non-linear FECC schemes

Les ondes de batillage générées par l’avancement des bateaux détruisent les rives des voies navigables et accélèrent les phénomènes d’érosion aussi bien au niveau des berges qu’au niveau du fond du canal. Leurs caractéristiques cinématiques dépendent de la vitesse, de l’enfoncement, du chargement du bateau et également de la profondeur de la voie navigable. En outre, les masses d’eau accélérées par l’immersion des bateaux et par leur système propulsif, induisent la remise en suspension d’une grande quantité de sédiments et provoquent l’érosion du fond de la voie navigable.Dans cette thèse, un modèle numérique 3D est présenté pour simuler la génération de ces ondes de batillage. Ce modèle, basé sur les équations de Navier-Stokes (RANS), a été couplé à un modèle d’advection-diffusion 3D pour caractériser la répartition et le mode de transport sédimentaire au passage du bateau. Ce couplage est mis en oeuvre avec prise en compte des effets des hélices du système propulsif du bateau. / Ship-generated waves in restricted waterways lead to the stream banks erosion and cause environmental damage which harms fish, plants, benthos, plankton, etc. They also alter the channel morphology because of the resuspension and transport of bed material by accelerated flows caused by moving-ships. The magnitude of these waves depends mainly on the geometrical and kinematical parameters of the convoy.The objective of this study is to predict the relationship between these geometrical and kinematical parameters and the amplitude of ship-generated waves as well as the water plane drawdown. Numerical simulations are conducted by solving the 3-dimensional Navier-Stokes equations along with the k-ε model for turbulent processes. The results are compared firstly with the empirical models and secondly with experimental measurements performed by the French Compagnie Nationale of Rhône (CNR). The exitance of the propeller increases the sediment in suspension. Therefore, the relationships between the re-suspended sediments and the advancing speeds of the convoy, the wakes generated by the moving convoy, as well as the number of barges are studied by adding 3D advection-diffusion equation and a propeller model.

[pt] Uma investigação da capacidade de previsão de modelos de turbulência baseados na modelagem estatística clássica e de grandes escalas é apresentada. A modelagem estatística clássica de turbulência (média de Reynolds) foi analisada, através da solução de escoamentos complexos, como, por exemplo, o escoamento turbulento em degrau (backstep). Especial atenção foi dada aos modelos kapa-epsilon de baixo Reynolds e as variantes renormalizadas (RNG). O comportamento dos vários termos da equação da energia cinética turbulenta na região da parede foram analisados em detalhes, especialmente o termo de difusão de pressão. Avaliou-se a importância da correta modelagem do termo de difusão de pressão sobre as predições dos modelos de baixo número de Reynolds, nas regiões de recirculação. Alguns modelos, propostos na literatura para o termo de difusão de pressão, foram também avaliados teórica e numericamente. A capacidade de previsão da metodologia de simulação de grandes escalas (LES por Large Eddy Simulation) também foi realizada. O desempenho do modelo de Smagorinsky para prever escoamentos limitados por fronteiras sólidas foi avaliado do ponto de vista computacional. Utilizou-se o método de volumes finitos para integrar tanto as equações médias de Reynolds quanto as equações LES. O escoamento turbulento em canal foi resolvido de modo bidimensional e tridimensional. Já o escoamento em degrau (backstep) foi resolvido exclusivamente de modo bidimensional, enquanto o escoamento em um duto de seção quadrada foi simulado de modo tridimensional. Os resultados foram comparados com aqueles obtidos pelos modelos de baixo Reynolds, analisando-se a relação custo-benefício. / [en] An investigation of turbulence models prediction capacity based on classical statistical modeling and large eddy simulation (LES) is presented. The classical statistical modeling (average of Reynolds) was analyzed, by investigating the solution of complex flows, as, for example, the turbulent flow past a backwardfacing- step (backstep). Special attention was given to low Reynolds number k-e models and models derived by renormalization group theory (RNG). The behavior of the different terms in the turbulent kinetic energy equation in the near wall region was examined in details, specially the pressure diffusion term. It was evaluated the importance of the correct modeling of the pressure diffusion term on the predictions of the low Reynolds number models, in recirculating flows. A few models, proposed in the literature for the pressure diffusion term, were also evaluated theoretically and numerically. The prediction capacity of large eddy simulation (LES) technique was also investigated. The ability of Smagorinsky model to predict complex limited wall flows was analyzed from a computational standpoint. The finite-volume method was employed to integrate both the Reynolds average and LES equations. The fully developed turbulent channel flow was solved in two- dimensional and three-dimensional numerical simulations. The turbulent flow over a backward-facing-step was computed exclusively in a twodimensional manner, while the fully developed turbulent flow in a straight square duct was simulated in a three-dimensional manner. The results were compared with those obtained by the low Reynolds models, analyzing the cost-benefit relation.

Este trabalho tem como propósito investigar como a variação geométrica de determinados parâmetros envolvidos na construção de uma geometria bifurcada de seção circular, em forma de Y, afeta a resistência ao escoamento, tanto de fluidos newtonianos como não newtonianos. As geometrias estudadas foram construídas utilizando-se o princípio do Design Construtal. Os parâmetros variados foram a relação entre os comprimentos dos dutos pais e filhos, a relação entre os diâmetros dos mesmos dutos, e o ângulo central da estrutura em forma de Y. Para as relações geométricas lineares foram utilizados os valores de 0,5; 0,6; 0,7; 0,8; 0,9 e 1, enquanto para os ângulos, foram utilizados os valores de 155°, 135°, 115°, 95°, 75°, 45°, 25° e 10°. Os fluidos utilizados foram do tipo newtoniano e não newtoniano, dentre estes últimos, foram estudados fluidos pseudoplásticos e dilatantes. O trabalho foi realizado através de simulações numéricas, implementadas com a utilização do software comercial Ansys Fluent, o qual resolve as equações governantes através do método dos volumes finitos. As malhas utilizadas foram do tipo poliédrica. Os resultados indicam que há uma diferença em relação ao que se espera da literatura para as relações entre os diâmetros e os comprimentos. A Lei Hess-Murray indica que estas relações ótimas seriam de 2-1/3 para as relações entre os diâmetros e comprimentos. No presente trabalho, foram determinadas relações entre os diâmetros próximas de 0,6, e entre os comprimentos, iguais a 1. Os ângulos ótimos ficaram localizados no intervalo entre 100° e 135°. / This work aims to investigate how the geometric variation of certain parameters involved in the construction of a bifurcated Y-shaped circular cross-section geometry affects the flow resistance of both Newtonian and non-Newtonian fluids. The geometries studied were constructed using the Constructal Design principle. The parameters were the relationship between the lengths of the daughter and parent ducts, the relationship between the diameters of the same ducts, and the central angle of the Y-shaped structure. For the linear geometric relations, values of 0.5; 0.6; 0.7; 0.8; 0.9 and 1 where used, for the angles, the values of 155 °, 135 °, 115 °, 95°, 75 °, 45 °, 25 ° and 10 ° were used. The fluids used were of the Newtonian and non-Newtonian type, among the latter, pseudo plastic and dilatant fluids were studied. The work was carried out through numerical simulations, implemented with the commercial software Ansys Fluent, which solves the governing equations through the finite volume method. The meshes used were of the polyhedral type. The results indicate that there is a difference in relation to what is expected from the literature for the relationships between diameters and lengths. The Hess-Murray Law indicates that these optimal relations would be 2-1/3 for the relationships between diameters and lengths. In the present work, relationships between the diameters close to 0,6 were found and s equal to 1 between the lengths. The optimum angles were located in the range between 100 ° and 135 °.