In order to study three-dimensional unsteady turbulent flow fields such as the wakes of bluff bodies, a Digital Particle Image Velocimetry (DPIV) system was developed. This system allows non-intrusive two-dimensional and time varying velocity measurements. Software and hardware modifications necessary to enhance the capabilities of the system were preformed, resulting in increased frequency resolution. However, due to hardware limitations and limitations inherited from the implementation of the method, space resolution is reduced. Subsequently, digital image processing tools to improve the space resolutions were developed. The advantages and limitations of the method for the study of turbulent flows are presented in detail. The developed system is employed in the documentation of time-varying turbulent flow fields. Initially we study the spanwise variation of the near wake of a low-aspect ratio, surface-mounted, circular cylinder piercing a free surface. The asymmetry of the end conditions combined with the natural unsteadiness of the vortex shedding generates a very complex flow filed which is difficult to study with conventional methods. By employing the aforementioned system we are able to reveal a departure of the two-dimensional character of the flow in the form of oblique vortex shedding. The effect of free surface on the vortex formation length and on the vortex reconnection process is documented. Near the free surface the alternate mode of vortex shedding is suppressed, leading to simultaneous shedding of vortices in the wake. Indications of vortex dislocations and change of the vortex axis in order to reconnect to the free surface are observed. Finally, a novel approach of reconstructing the three-dimensional, time -varying volume of the flow field by obtaining simultaneous measurements of Laser Doppler Velocimetry and Particle Image Velocimetry planes is presented. The same field is investigated with focus on the streamwise structures. Three-dimensional streamwise vortical structures are known to exist due to instabilities of plane shear layers. Similar streamwise vortices, also known as braid vortices have been observed in the past in the wake of circular cylinders with symmetric boundary conditions. The present spatio-temporal analysis demonstrated coexistence of two types of streamwise vortices in the wake, bilge and braid type of vortices. These may be due to the three dimensionality introduced by the free surface. In addition, the sufficient time resolution allowed the detection of the primary Von-Karman vortex through a plane of interrogation normal to the free stream, thus revealing the spanwise variation of the vortex shedding and its evolution at different downstream stations. The combination of the effect of the asymmetric boundary conditions with a free surface is investigated by adding one more source of three-dimensionality in terms of inclination of the cylinder axis. Hydrogen-bubble and particle-flow visualizations are preformed in combination with Laser-Doppler Velocimetry measurements. From both qualitative and quantitative results the effects of inclination and Froude number are documented. It is proved that the vortex shedding is suppressed for high values of the Froude number, however the inclination counteracts the vortex suppression and favors the vortex shedding mechanism. In addition, in the region of the no-slip boundary condition the flow is dominated by the effect of the horseshoe vortex. The case of a three-dimensional separated flow over a surface-mounted prism is investigated using a modified version of the system. The character of the separated from the leading edge corner shear layer and the formed separation bubble are documented in space and time along the mid-plane of symmetry of the body. Three different flows corresponding to different Reynolds numbers are studied. The unsteadiness of the flow is presented indicating a pseudo-periodic character. Large-scale, low-frequency oscillations of the shear layer that have been observed in the past using point measurement methods are now confirmed by means of a whole field velocity measurement, technique allowing a holistic view of the flow. In addition, the unsteadiness of the point of reattachment is associated with the flapping of the shear layer and the shedding of vorticity in the wake. Finally, it is demonstrated that the apparent vortex shedding mechanism of such flows is dependent on the interaction of the primary vortex of the separation bubble with a secondary vortex formed by the separation of the reverse flow boundary layer. By performing measurements with such time and space resolution the inadequacy of time averaged or point measurement methods for the treatment of such complex and unsteady flow fields becomes evident. In final case we employ Particle-Image Velocimetry to show the effect of unsteady excitation on two-dimensional separated flow over a sharp edged airfoil. It is proved that such an approach can be used to effectively control and organize the character of the flow, potentially leading to lift increase and drug reduction of bluff bodies / Ph. D.

<p>Many practical fluid flows involve liquid-particle systems and so there is a need to better understand the mechanism of particle deposition, adhesion, and agglomeration in suspensions, especially in complex geometries with moving boundaries and free surfaces. In this thesis, the nature of the particle-solid interactions and particle-fluid interactions is studied where the above complexities are present, taking into account particle collision, colloidal, and hydrodynamic forces, and two way coupling between the fluid flow and particles. The research is motivated by the industrial examples of: flow of dross particles near the sink roll surface in a galvanizing bath (moving surface), and the flow of particles in slot coating dies (free and moving surfaces). Particle motion and agglomeration play important roles in the example systems chosen for this fundamental 3-D study. Numerical studies of flow of dispersed suspensions makes it possible to understand the effects of flow conditions, particle characteristics, and flow geometry specifications that lead to agglomeration of particles in complex systems, especially where experimental studies are difficult to perform. Often the effects of these conditions are discovered due to process or product failures, rather than through insight into the processing steps.</p> <p>The modeling methodology used in this work is that micron sized spherical particles are tracked in the fluid phase by solution of Newton`s second law of motion for each particle. Fluid phase applies hydrodynamic forces on particles (drag, lift). Body forces, (soft sphere) particle-particle collisions and particle-wall collisions are considered. Particle concentrations are in the dilute regime between 0.01-5%vol. Flow of particles with the fluid phase is a fully coupled formulation in systems with particle concentrations > 1%vol.</p> <p>The thesis is organized around three example problems taken from industry that pose challenging modeling issues. The first involves particle collisions with a moving wall (dross particles in a zinc bath). The second problem includes particle-particle and particle-wall collisions in a turning flow geometry. The third problem, particle dispersion flows in a slot coating die, has the most complexity and includes particle-particle, particle-wall and free surfaces.</p> <p>Dross particle build up on the sink roll inside the zinc bath is an industrial problem that causes significant down time, and where an experimental study of the molten zinc in a bath running at C is difficult to perform. With the aid of computational fluid dynamics, turbulent flow of molten zinc in galvanizing bath is simulated, compared with previous cold model experiments, and coupled with the motion of dross particles around the sink roll. The presence of fixed position hardware and moving sink roll and guide rolls in a bath with dimensions in the orders of meters, and micron sized (20-100 ) dross particles makes this case a complex study. Drag, buoyancy, lift force and soft sphere nonlinear collision is considered in solution of Newton`s law of motion for each particle. Turbulent flow is simulated using a standard model. Simulations show regions on the sink roll where particles are dragged toward the surface of sink roll and have long residence times. These regions have been reported to experience large particle build-ups in the hot-dip galvanizing process.</p> <p>In another study, formation and breakage of agglomerates in a turning flow is studied. Neutrally buoyant particles with concentration of 5%vol are tracked in a fully coupled flow. Particles form agglomerates at the corner, where drag and lift force from the fluid breaks a number of agglomerates. The presence of a moving wall in the turning flow shifts the suspended particle formations toward the inside of channel. Location of particles agglomerates shifts toward the free surface with the presence of free surface at the turning flow.</p> <p>Motion of micron sized spherical particles with 1-4%vol through a slot die coating system is elucidated in a separate study. The system is complex with presence of moving web and free surface. Discrete element method (DEM) for motion of dispersed phase and volume of fluid (VOF) method for solution of continuous phase are integrated in a simulation study. Particles are 2-4 and the flow dimensions of the system are in the order of 100 . Particles experience collision, colloidal and hydrodynamic forces. Coupling between flow of particles and fluid phase is conducted. The results of this study show particle positions on the coating film can be predefined and depends on their initial positions within the feed slot. Particles agglomerate in recirculating regions of the coating gap and follow the streamlines of flow on the moving web. Regions in the coating gap where particles have high residence times (inside the die and near the feed slot edges) have particle agglomerations in the slot die coating system.</p> / Doctor of Philosophy (PhD)

Nesta tese é apresentado um esquema novo de alta resolução upwind (denominado TDPUS-C3) para reconstrução de fluxos numéricos para leis de conservação não lineares e problemas relacionados em DFC. O esquema é baseado nos critérios de estabilidade CBC e TVD e desenvolvido utilizando condições de diferenciabilidade \'C POT. 3\'. Além disso, é realiozada a implementação da associação do esquema TDPLUS-C3 com a modelagem de turbulência RNG \'\\kappa - \\epsilon\'. O propósito é obter soluções numéricas de sistemas hiperbólicos de leis de conservação para dinâmica dos gases e equações de Navier-Stokes para escoamento incompreensível de fluidos newtonianos e não newtonianos (viscoelásticos). Fazendo o uso do esquema TDPUS-C3, a precisão global dos métodos numéricos é verificada acessando o erro em problemas teste (benchmark) 1D e 2D. Um estudo comparativo entre os resultados do esquema TDPUS-C3 e os esquemas upwind convencionais para leis de conservação hiperbólicas complexas é também realizado. A Associação das modelagens numéricas (upwinding mais RNG \'\\kappa - \\epsilon\') é , então, examinada na simulação de escoamentos turbulentos de fluidos newtonianos envolvendo superfícies livres móveis, usando a metodologia URANS. No geral, em termos do comportamento global, concordância satisfatória é observada / In this thesis, a new high-resolution upwind scheme (named TDPUS-C3) for reconstruction of numerical fluxes for nonlinear conservation laws and related CFD problems in presented. The scheme is based on CBC and TVD stability criteria and developed by employing differentiability condictions (\'C POT. 3\'). In additon, the implementation of an association of the TDPUS-C3 scheme with the RNG \'\\kappa - \\epsilon\' turbulence modelling is also performed. The purpose is to obtain numerical solutions of systems of hyperbolic conservation laws for gas dynamics and Navier-Stokes equations for incompressible flow of Newtonian and non-Newtonian (viscoelstic) fluids. By using the TDPUS-C3 scheme, the global accuracy of the numerical methods is verified by assessing the error on 1D and 2D benchmark test cases. A comparative study between the TDPUS-C3 scheme and convectional upwind schemes to solve standard and complex hyperbolic conservation laws is also accomplished. The association of the numerical modelling (upwinding plus RNG \'\\kappa - epsilon\') is then examined in the simulation of turbulent Newtonian fluid flows involving moving free surfaces, by using URANS methodology. Overall, satisfactory agreement is found in terms of the overall behaviour

Três esquemas de captura de descontinuidade são apresentados para simular hiperbólicos de leis de conservação e equações de Navier-Stokes incompressíveis, a saber: FDHERPUS (Five Degree Hermite Upwind Scheme); RUS (Rational Upwind Scheme); e CSPUS (Cubic Spline Polynomial Upwind Scheme). Esses esquemas são baseados nos critérios de estabilidade CBC e TVD e implementados nos contextos das metodologias diferenças finitas e volumes finitos. A precisão local dos esquemas é verificada acessando o erro e a taxa de convergência em problemas testes de referência. Um estudo comparativo entre os esquemas estudados (incluido o WENO5) e o esquema bem estabelecido de van Albada, para resolver leis de conservação lineares e não lineares, é também realizado. O esquema de convecção que fornece melhores resultados em leis de conservação hiperbólicas é então examinado na simulação de escoamentos de fluidos newtonianos com superfícies livres móveis de complexidade crescente; resultados satisfatórios têm sido observados em termos do comportamento global / Three shock capturing schemes for numerical solution of hyperbolic conservation laws and incompressible Navier-Stokes equations are presented, namely: FDHERPUS (Five Degree Hermite Polynomial Upwind Scheme); RUS (Rational Upwind Scheme); and CSPUS ( Cubic Spline Polynomial Upwind Scheme). These schemes are based on CBC and TVD stability criteria and implemented in the context of finite volume methodologies. The local observed accuracy of the schemes is verified by assessing the error and convergence rate on benchmark test cases. A comparative study between the schemes (including WENO5) and the well established van. Albada scheme to solve standard linear and nonlinear hyperbolic conservation laws is also accomplished. The scheme that has provided better results in hyperbolic conservation laws is then examined in the simulation of Newtonian moving free surface flows of increasing complexity, satisfactory agreement has been observed in terms of the overall behavior

Neste trabalho apresenta-se um novo esquema prático tipo upwind de alta resolução, denominado EPUS (Eight-degree Polynomial Upwind Scheme), para resolver numericamente equações de conservação TVD e é implementado no contexto do método das diferenças finitas. O desempenho do esquema é investigado na resolução de sistemas hiperbólicos de leis de conservação e escoamentos incompressíveis complexos com superfícies livres. Os resultados numéricos mostraram boa concordãncia com outros resultados numéricos e dados experimentais existentes / Is this work a new practical high resolution upwinding scheme, called EPUS (Eight-degree Polynomial Upwind Scheme), for the numerical solution of transient convection-dominated conservation equations is present. The scheme is based on TVD stability criterion and is implemented in the context of the finite difference methodology. The performance of the scheme is investigated by solving hyperbolic systems of conservation laws and complex incompressible flows with free surfaces. The numerical results displayed good agreement with other existing numerical and experimental data

<div>Free surface flows where the shape of the interface separating two fluids is unknown <i>apriori</i> are an important area of interest in fluid dynamics. The study of free surface flows such as the breakup and coalescence of drops, and thinning and rupture of films lends itself to a diverse range of industrial applications, such as inkjet printing, crop spraying, foam and emulsion stability, and nanolithography, and helps develop an understanding of natural phenomena such as sea spray generation in oceans, or the dynamics of tear films in our eyes. In free surface flows, singularities are commonly observed in nite time, such as when the radius of a thread goes to zero upon pinchoff or when the thickness of a film becomes zero upon rupture. Dynamics in the vicinity of singularities usually lack a length scale and exhibit self-similarity. In such cases, universal scaling laws that govern the temporal behavior of measurable physical quantities such as the thickness of a lm can be determined from asymptotic analysis and veried by high-resolution experiments and numerical simulations. These scaling laws provide deep insight into the underlying physics, and help delineate the regions of parameter space in which certain forces are dominant, while others are negligible. While the majority of previous works on singularities in free-surface flows deal with Newtonian fluids, many fluids in daily use and industry exhibit non-Newtonian rheology, such as polymer-laden, emulsion, foam, and suspension flows.</div><div><br></div><div><div>The primary goal of this thesis is to investigate the thinning and rupture of thin films of non-Newtonian fluids exhibiting deformation-rate-thinning (power-law) rheology due to attractive intermolecular van der Waals forces. This is accomplished by means of intermediate asymptotic analysis and numerical simulations which utilize a robust Arbitrary Eulerian-Lagrangian (ALE) method that employs the Galerkin/Finite-Element Method for spatial discretization. For thinning of sheets of power-law fluids, a signicant finding is the discovery of a previously undiscovered scaling regime where capillary, viscous and van der Waals forces due to attraction between the surfaces of the sheet, are in balance. For thinning of supported thin films, the breakdown of the lubrication approximation used almost exclusively in the past to study such systems, is shown to occur for films of power-law fluids through theory and conrmed by two dimensional simulations. The universality of scaling laws determined for rupture of supported films is shown by studying the impact of a bubble immersed in a power-law fluid with a solid wall.</div></div><div><br></div><div><div>Emulsions, which are ne dispersions of drops of one liquid in another immiscible liquid, are commonly encountered in a variety of industries such as food, oil and gas, pharmaceuticals, and chemicals. Stability over a specied time frame is desirable in some applications, such as the shelf life of food products, while rapid separation into its constituent phases is required in others, such as when separating out brine from crude oil. The timescale over which coalescence of two drops of the dispersed phase occurs is crucial in determining emulsion stability. The drainage of a thin film of the outer liquid that forms between the two drops is often the rate limiting step in this process. In this thesis, numerical simulations are used to decode the role played by fluid inertia in causing drop rebound, and the subsequent increase in drainage times, when two drops immersed in a second liquid are brought together due to a compressional flow imposed on the outer liquid. Additionally, the influence of the presence of insoluble surfactants at the drop interface is studied. It is shown that insoluble surfactants cause a dramatic increase in drainage times by two means, by causing drop rebound for small surfactant concentrations, and by partially immobilizing the interface for large surfactant concentrations.</div></div>

Este trabalho é dedicado à análise e implementação de esquemas "upwind" de alta ordem modernos e o modelo de turbulência k-epsilon padrão no Freeflow-2D; um ambiente integrado para simulação numérica em diferenças finitas de problemas de escoamentos incompressíveis com superfícies livres. O propósito do estudo é a simulação de escoamentos de fluidos newtonianos incompressíveis, bidimensionais, confinados e/ou com superfícies livres e a altos valores do número de Reynolds. O desempenho do código Freeflow-2D atual é avaliada na simulação do escoamento numa expansão brusca e de um jato livre incidindo perpendicularmente sobre uma superfície rígida impermeável. O código é então aplicado na simulação de um jato planar turbulento em uma porção de fluido com superfície livre e estacionário. Os resultados numéricos obtidos são comparados com dados experimentais, soluções analíticas e soluções numéricas de outros trabalhos. / This work is devoted to the analysis and implementation of modern high-order upwind schemes and the standard k-epsilon turbulence model into the Freeflow-2D; a finite difference integrated environment for the numerical simulation of incompressible free surface flow problems. The purpose of this study is the two-dimensional simulation of high-Reynolds incompressible newtonian confined and/or free surface flows. The performance of the current Freeflow-2D code is assessed by applying it to the simulation of flow over a backward facing step and of an impinging free jet onto an impermeable rigid surface. The code is then applied to a turbulent planar jet into a pool. The numerical results are compared with experimental data, analytical solution, and numerical simulations of other works.

O presente trabalho consiste em uma extensão do sistema FreeFlow-2D para simular escoamentos de fluidos não newtonianos bidimensionais com superfí cies livres, onde o fluido é descrito pelos modelos de Cross ou o modelo ``power-law\'\'. O método numérico empregado é o método GENSMAC. As equações governantes são aproximadas pelo método de diferenças finitas em uma malha deslocada e partículas marcadoras são utilizadas para a visualização do escoamento e localização da superfície livre. Resultados numéricos são apresentados. Em particular, a presente implementação é validada comparando-se a solução numérica com uma solução analítica / This work presents an extention of the Freeflow-2D system to non-Newtonian free surface flows. The governing equations are solved by the finite difference method on a staggered grid. Marker particles are used to describe the fluid providing the location and the visualization of the free surface. The methodology employed is based on the GENSMAC method. The fluid is modelled by the Cross and power-law models. Numerical examples are presented. The code is validated by making a comparison between analytical and numerical solutions

Στόχος της παρούσας διδακτορικής διατριβής είναι η μελέτη χρονικά μεταβαλλόμενων και ασταθών υπό συνθήκες ροών ιξωδοπλαστικών και ιξωδο-ελαστικών ρευστών λόγω της σημασίας που παρουσιάζουν τα υλικά αυτά σε διάφορες βιομηχανικές διεργασίες. Στα πλαίσια της εργασίας αυτής μελετήθηκε αρχικά το πρόβλημα της συμπίεσης ιξωδοπλαστικού ρευστού μεταξύ δύο δίσκων το οποίο είναι ένα βασικό πείραμα ρεολογικού χαρακτηρισμού μη Νευτωνικών υλικών. Η χρονικά μεταβαλλόμενη προσομοίωση επέτρεψε τον προσδιορισμό των σημαντικών διαφορών μεταξύ των δύο εκδοχών του συγκεκριμένου ρεολογικού πειράματος (δίσκοι κινούμενοι υπό σταθερή ταχύτητα ή υπό σταθερή δύναμη) που ήταν αδύνατος με τα προηγούμενα μοντέλα, ενώ παρουσιάζεται και πλήρης παραμετρική μελέτη της διεργασίας αυτής. Το υπόλοιπο μέρος της παρούσας εργασίας αφιερώθηκε στη μελέτη της διεργασίας εκβολής ιξωδοελαστικών υλικών η οποία συναντάται ευρέως στη βιομηχανία μορφοποίησης πολυμερών. Παρουσιάζεται μια πλήρης παραμετρική ανάλυση για την εκβολή ενός ιξωδοελαστικού ρευστού Phan-Tien & Tanner (PTT) από ένα δακτυλιοειδή αγωγό προκειμένου να εξετάσουμε την επίδραση της γεωμετρίας του αγωγού, και των ρεολογικών ιδιοτήτων του ρευστού. Επιπλέον ένα σημαντικό πρόβλημα που εμφανίζεται κατά την εκβολή από ένα κυλινδρικό, επίπεδο ή δακτυλιοειδή αγωγό είναι η εμφάνιση ασταθειών οι οποίες επηρεάζουν σημαντικά την ποιότητα του τελικού προϊόντος. Προκειμένου να διερευνηθεί ο μηχανισμός που προκαλεί την εμφάνιση αυτών των ασταθειών πραγματοποιήθηκε γραμμική ανάλυση ευστάθειας για τη αξονοσυμμετρική και καρτεσιανή δισδιάστατη ροή επικόλλησης-ολίσθησης (stick-slip flow) ενός ρευστού PTT. Γύρω από τη λύση μόνιμης κατάστασης πραγματοποιείται γραμμική ανάλυση ευστάθειας, και υπολογίζονται οι ιδιοτιμές του γενικευμένου προβλήματος με τη βοήθεια της μεθόδου Arnoldi. Έτσι προσδιορίζεται η επίδραση των ιδιοτήτων του υλικού στην ευστάθεια ή μη της ροής. / The purpose of this dissertation is to perform a study on time-dependent and conditionally unstable flows of viscoplastic and viscoelastic fluids because of their importance in various industrial processes. A typical experiment which is used widely for the rheological characterization of non-Newtonian fluids is squeeze flow which is the subject of the first chapter of this dissertation. The time-dependent simulation permitted the determination of the distinct differences between the two versions of this rheological experiment (disks moving with constant velocity or under constant force) which was impossible with the models used up to now, while a complete parametric analysis of this process is presented. The rest of this work focuses in the important problem of the extrusion process of a viscoelastic fluid, which is frequently encountered in the polymer industry. A complete parametric analysis is presented for the extrusion of a Phan-Thien Tanner (PTT) fluid from an annular die in order to examine the effect of the die geometry and the rheological properties of the fluid on this process. Moreover, it is widely known that during the extrusion from a cylindrical, planar or an annular die various flow instabilities may arise affecting significantly the quality of the final product. In order to investigate the mechanism, which causes the appearance of these instabilities, a linear stability analysis is performed for the cylindrical or planar stick-slip flow of a PTT fluid. The stability analysis is performed around the steady state solution and the eigenvalues of the generalized problem are calculated using the Arnoldi algorithm. With this method the effect of the various rheological properties of the fluid on the stability of the flow is determined.

Nesta tese é apresentado um esquema novo de alta resolução upwind (denominado TDPUS-C3) para reconstrução de fluxos numéricos para leis de conservação não lineares e problemas relacionados em DFC. O esquema é baseado nos critérios de estabilidade CBC e TVD e desenvolvido utilizando condições de diferenciabilidade \'C POT. 3\'. Além disso, é realiozada a implementação da associação do esquema TDPLUS-C3 com a modelagem de turbulência RNG \'\\kappa - \\epsilon\'. O propósito é obter soluções numéricas de sistemas hiperbólicos de leis de conservação para dinâmica dos gases e equações de Navier-Stokes para escoamento incompreensível de fluidos newtonianos e não newtonianos (viscoelásticos). Fazendo o uso do esquema TDPUS-C3, a precisão global dos métodos numéricos é verificada acessando o erro em problemas teste (benchmark) 1D e 2D. Um estudo comparativo entre os resultados do esquema TDPUS-C3 e os esquemas upwind convencionais para leis de conservação hiperbólicas complexas é também realizado. A Associação das modelagens numéricas (upwinding mais RNG \'\\kappa - \\epsilon\') é , então, examinada na simulação de escoamentos turbulentos de fluidos newtonianos envolvendo superfícies livres móveis, usando a metodologia URANS. No geral, em termos do comportamento global, concordância satisfatória é observada / In this thesis, a new high-resolution upwind scheme (named TDPUS-C3) for reconstruction of numerical fluxes for nonlinear conservation laws and related CFD problems in presented. The scheme is based on CBC and TVD stability criteria and developed by employing differentiability condictions (\'C POT. 3\'). In additon, the implementation of an association of the TDPUS-C3 scheme with the RNG \'\\kappa - \\epsilon\' turbulence modelling is also performed. The purpose is to obtain numerical solutions of systems of hyperbolic conservation laws for gas dynamics and Navier-Stokes equations for incompressible flow of Newtonian and non-Newtonian (viscoelstic) fluids. By using the TDPUS-C3 scheme, the global accuracy of the numerical methods is verified by assessing the error on 1D and 2D benchmark test cases. A comparative study between the TDPUS-C3 scheme and convectional upwind schemes to solve standard and complex hyperbolic conservation laws is also accomplished. The association of the numerical modelling (upwinding plus RNG \'\\kappa - epsilon\') is then examined in the simulation of turbulent Newtonian fluid flows involving moving free surfaces, by using URANS methodology. Overall, satisfactory agreement is found in terms of the overall behaviour