A novel on-line capillary rheometer (OLR) was used to examine the shear and extensional characteristics of polyolefin melts during twin screw extrusion (TSE). Comparisons with off-line rheometry were made using a twin-bore capillary rheometer and a modular in-line slit die rheometer (ILR) provided in-line rheometry comparisons. Both capillary rheometers were controlled via PCs running dedicated software, and the extrusion line and ELR were fully instrumented allowing real-time process monitoring to be carried out by IBM compatible PCs via data acquisition hardware and software. The prototype OLR was developed by the re-design of several key features including an instrumented transfer section and capillary die block which facilitated the use of various die geometries. Shear and extensional on-line rheometry of three polyethylenes (linear and branched), and four molecular weight grades of polypropylene were examined, and a direct comparison with off-line capillary rheometry showed a good correlation. The effect of a high loading of filler on two of the polyethylenes was investigated. In-line shear stress and entry pressure measurements showed a reasonable correlation with on-line rheometry. A study of entry flows in the OLR using capillary dies approaching orifice showed non-linearities occurred at very low capillary length to diameter(L:D) ratios, and this was repeatable using off-line rheometry. Predicted zero length entry pressures (Po) were used to estimate apparent extensional viscosity using a number of standard models. Melt instability and capillary wall slip were also investigated using on-line rheometry. Melt pressure and temperature in the twin screw extruder and OLR were monitored at various process conditions to examine the ability of the OLR to condition melt during testing, and the effect of OLR testing on extrusion conditions. Pressure variation in the extruder, OLR and off-line rheometer were compared in order to quantify process noise. The effect of OLR testing on melt rheology and polymer molecular weight were examined using off-line rheometry and gel permeation chromatography(GPC).

Tanto os motores turbo-jato quanto os turbo-fan, são os maiores responsáveis pela geração de ruído durante a decolagem, segmento de subida e de aceleração de uma aeronave. Devido a isto, o problema de ruído em jatos vem sendo intensamente investigado ao longo dos últimos anos. Já na fase do pouso, o slat é uma das fontes de ruído mais importantes. Para este caso, na maioria das aplicações práticas, existe o descolamento da camada limite no intradorso do slat a partir de onde se desenvolve uma camada de mistura. Ainda assim, existem inúmeros aspectos de tais escoamentos que precisam de investigação. Uma abordagem frequentemente feita para o estudo da instabilidade hidrodinâmica e ruído em jatos é o estudo de metade do jato. A estratégia consiste em estudar os fenômenos na camada de mistura, o que é uma aproximação razoável quando o jato tem diâmetro muito grande comparado à espessura da camada cisalhante que se desenvolve nas bordas do jato. Assim, alguns aspectos do ruído gerado pelos modos axi-simétricos de instabilidade são em grande parte reproduzidos. Um aspecto aparentemente jamais estudado antes é o efeito do emparelhamento de vórtices de diferentes geometrias na camada de mistura. Caso o efeito da modulação dos vórtices produzisse um padrão de ruído com características diferentes no emparelhamento, um controle ativo de escoamento por excitação periódica poderia ser usado para reduzir o ruído em jatos. O objetivo do presente trabalho é investigar tal efeito. A idéia é investigar este emparelhamento de vórtices na camada de mistura em desenvolvimento temporal bi-dimensional. Com isto foi possível visualizar um emparelhamento isolado de outros emparelhamentos e sem o efeito Doppler (presente na camada de mistura em desenvolvimento espacial). O método adotado foi a simulação numérica direta (DNS) das equações de Navier Stokes compressíveis na forma não-conservativa escritas na formulação característica. Os resultados mostram que a modulação dos vórtices não produz alteração significativa do ruído gerado no emparelhamento. / Turbo-fan and turbo-jet engines are the most important noise sources during the aircraft take off, climb and acceleration segments. Owing to this fact, the jet flow noise has been studied in the past years. For the landing stage, the slat is an important sound source. In this case, the slat leading edge frequently experiences a boundary layer deattachment causing the development of a mixing layer inside the slot. Nevertheless, there are many aspects of such phenomenon that have not been studied yet. Mixing layers constitutes an usual approach for jet flow instability in aeroacoustics studies. The stategy is to study the mixing layer in order to understand the jet-flow. This strategy becomes better as the ratio between the jet diameter and mixing layer thickness becomes larger. This approach is only reazonable for the jet flow axi-symetric unstable modes. The effect of vortex modulation on the vortex pairing sound production has not been found in the literature. If such effect could cause a significant change in the sound generation patterns, an active flow control system could be developed in order to enhance the jet noise performance. The purpose of the present work was to investigate such effect. It was also possible to observe a single vortex pairing inside a wide domain without the Doppler effect. The strategy was to study the vortex pairing in a bi-dimensional mixing layer under temporal development. The method used was the direct numerical simulation (DNS) of the compressible bidimensional (2D) Navier Stokes equations written in a nonconservative form of the characteristics formulation. The results showed that the vortex modulation did not produce a significant change on the vortex pairing sound.

Transition to turbulence and flow control are studied by means of numerical simulations for different simple shear flows. Linear and non-linear optimisation methods using the Lagrange multiplier technique are employed. In the linear framework as objective function the standard disturbance kinetic energy is chosen and the constraints involve the linearised Navier–Stokes equations. We consider both the optimal initial condition leading to the largest disturbance energy growth at finite times and the optimal time-periodic forcing leading to the largest asymptotic response for the case of the flat plate boundary layer excluding the leading edge. The optimal disturbances for spanwise wavelengths of the order of the boundary layer thickness are streamwise vortices exploiting the lift-up mechanism to create streaks. For long spanwise wavelengths it is the Orr mechanism combined with the amplification of oblique wave packets that is responsible for the disturbance growth. Also linear optimal disturbances are computed around a leading edge and the effect of the geometry is considered. It is found that two-dimentional disturbances originating upstream, relative to the leading edge of the plate are inefficient at generating a viable disturbance, while three dimentional disturbances are more amplified. In the non-linear framework a new approach using ideas from non-equilibrium thermodynamics is developed. We determine the initial condition on the laminar/turbulent boundary closest to the laminar state. Starting from the general evolution criterion of non-equilibrium systems we propose a method to optimise the route to the statistically steady turbulent state, i.e. the state characterised by the largest entropy production. This is the first time information from the fully turbulent state is included in the optimisation procedure. The method is applied to plane Couette flow. We show that the optimal initial condition is localised in space for realistic flow domains, while the disturbance visits bent streaks before breakdown. Feedback control is applied to the bypass-transition scenario with high levels of free-stream turbulence. The flow is the flat-plate boundary layer. In this scenario low frequency perturbations enter the boundary layer and streamwise elongated disturbances emerge due to non-modal growth. The so-called streaky structures are growing in amplitude until they reach high enough energy levels and break down into turbulent spots via their secondary instability. When control is applied in the form of wall blowing and suction, the growth of the streaks is delayed, which implies a delay of the whole transition process. Additionally, a comparison with experimental work is performed demonstrating a remarkable agreement in the disturbance attenuation once the differences between the numerical and experimental setup are reduced. Open-loop control with wall travelling waves by means of blowing and suction is applied to a separating boundary layer. For downstream travelling waves we obtain a mitigation of the separation of the boundary layer while for upstream travelling waves a significant delay in the transition location accompanied by a modest reduction of the separated region. / QC 20110518

The study of turbulence has been dominated historically by a bottom-up approach, with a much stronger emphasis on the physical structure of flows than on that of the dynam- ical state space. Turbulence has traditionally been described in terms of various visually recognizable physical features, such as waves and vortices. Thanks to recent theoretical as well as experimental advancements, it is now possible to take a more top-down approach to turbulence. Recent work has uncovered non-trivial equilibria as well as relative periodic orbits in several turbulent systems. Furthermore, it is now possible to verify theoretical results at a high degree of precision, thanks to an experimental technique known as Particle Image Velocimetry. These results squarely frame moderate Reynolds number Re turbulence in boundary shear flows as a tractable dynamical systems problem. In this thesis, I intend to elucidate the finer structure of the state space of moderate Re wall-bounded turbulent flows in hope of providing a more accurate and precise description of this complex phenomenon. Computation of new undiscovered equilibria, relative equilibria, and their heteroclinic connections provide a skeleton upon which a numerically accurate description of turbulence can be framed. The behavior of the equilibria under variation of Reynolds number and cell aspect ratios is also examined. It is hoped that this description of the state space will provide new avenues for research into nonlinear control systems for shear flows as well as quantitative predictions of transport properties of moderate Re fluid flows.

Tanto os motores turbo-jato quanto os turbo-fan, são os maiores responsáveis pela geração de ruído durante a decolagem, segmento de subida e de aceleração de uma aeronave. Devido a isto, o problema de ruído em jatos vem sendo intensamente investigado ao longo dos últimos anos. Já na fase do pouso, o slat é uma das fontes de ruído mais importantes. Para este caso, na maioria das aplicações práticas, existe o descolamento da camada limite no intradorso do slat a partir de onde se desenvolve uma camada de mistura. Ainda assim, existem inúmeros aspectos de tais escoamentos que precisam de investigação. Uma abordagem frequentemente feita para o estudo da instabilidade hidrodinâmica e ruído em jatos é o estudo de metade do jato. A estratégia consiste em estudar os fenômenos na camada de mistura, o que é uma aproximação razoável quando o jato tem diâmetro muito grande comparado à espessura da camada cisalhante que se desenvolve nas bordas do jato. Assim, alguns aspectos do ruído gerado pelos modos axi-simétricos de instabilidade são em grande parte reproduzidos. Um aspecto aparentemente jamais estudado antes é o efeito do emparelhamento de vórtices de diferentes geometrias na camada de mistura. Caso o efeito da modulação dos vórtices produzisse um padrão de ruído com características diferentes no emparelhamento, um controle ativo de escoamento por excitação periódica poderia ser usado para reduzir o ruído em jatos. O objetivo do presente trabalho é investigar tal efeito. A idéia é investigar este emparelhamento de vórtices na camada de mistura em desenvolvimento temporal bi-dimensional. Com isto foi possível visualizar um emparelhamento isolado de outros emparelhamentos e sem o efeito Doppler (presente na camada de mistura em desenvolvimento espacial). O método adotado foi a simulação numérica direta (DNS) das equações de Navier Stokes compressíveis na forma não-conservativa escritas na formulação característica. Os resultados mostram que a modulação dos vórtices não produz alteração significativa do ruído gerado no emparelhamento. / Turbo-fan and turbo-jet engines are the most important noise sources during the aircraft take off, climb and acceleration segments. Owing to this fact, the jet flow noise has been studied in the past years. For the landing stage, the slat is an important sound source. In this case, the slat leading edge frequently experiences a boundary layer deattachment causing the development of a mixing layer inside the slot. Nevertheless, there are many aspects of such phenomenon that have not been studied yet. Mixing layers constitutes an usual approach for jet flow instability in aeroacoustics studies. The stategy is to study the mixing layer in order to understand the jet-flow. This strategy becomes better as the ratio between the jet diameter and mixing layer thickness becomes larger. This approach is only reazonable for the jet flow axi-symetric unstable modes. The effect of vortex modulation on the vortex pairing sound production has not been found in the literature. If such effect could cause a significant change in the sound generation patterns, an active flow control system could be developed in order to enhance the jet noise performance. The purpose of the present work was to investigate such effect. It was also possible to observe a single vortex pairing inside a wide domain without the Doppler effect. The strategy was to study the vortex pairing in a bi-dimensional mixing layer under temporal development. The method used was the direct numerical simulation (DNS) of the compressible bidimensional (2D) Navier Stokes equations written in a nonconservative form of the characteristics formulation. The results showed that the vortex modulation did not produce a significant change on the vortex pairing sound.

La première partie concerne les interactions acoustique-vorticité dans les écoulements cisaillés linéaires incompressibles, qui peuvent être décomposés en la somme d’une partie hyperbolique et d’une partie rotation solide. L’écoulement de Couette en est un exemple. En utilisant la démarche non-modale , les équations d’évolution de perturbations compressibles se réduisent à une EDO de dimension trois en temps, qui dépend d’un paramètre adimensionné ε représentant le rapport entre le taux de cisaillement de l’écoulement et la fréquence des perturbations. Pour ε faible, la méthode WKB permet d’exhiber naturellement trois modes (deux modes acoustiques et un mode de vorticité) et permet de mettre en évidence des couplages entre ces modes. Ces couplages sont exponentiellement faible en 1/ε, et ne peuvent être pris en compte par une méthode asymptotique. Ils semblent être liés à la partie hyperbolique de l’écoulement. La seconde partie traite de la réflexion d'une onde par une surface de géométrie complexe. Une transformation conforme permet de transformer une frontière complexe en une frontière plane, mais fait apparaître des coefficients non constants dans les équations en volume. Celles-ci sont résolues au moyen de la méthode de la matrice d’impédance multimodale qui ramène le problème à une équation de Riccati pour la matrice d’impédance. Une méthode pour trouver des géométries admettant des modes piégés est proposée. Puis la méthode de résolution est appliquée à la modélisation de la couche limite visqueuse d’un fluide oscillant au contact d’une surface complexe périodique. Une solution perturbative est proposée. La présence de zones de recirculation est étudiée. / The first part is a study of the interactions between acoustic and vorticity perturbations in linear incompressible shear flows, which can decomposed as a sum of a hyperbolic part and of a rigid rotation part. The plane Couette flow is an example of such flows. By using the non-modal approach, the equations governing the evolution of compressible perturbations reduce to an ODE of dimension three in time, which depends on a dimensionless parameter ε representing the ratio between the shear rate of the flow and the frequency of the perturbations. For small ε values, the WKB method allows us to exhibit naturally three modes (two acoustic modes and one vorticity mode) and to highlight couplings between these modes. These couplings are exponentially small in 1/ε, and cannot be taken into account by an asymptotic method. They seem to be linked to the hyperbolic part of the flow.The second part deals with the reflection of a wave by a geometrically complex surface. A conformal mapping allows us to transform a complex boundary into a plane boundary, but makes appear varying coefficients in the bulk equations. These equations are then solved with the multimodal impedance matrix method, which reduce the problem to a Riccati equation for the impedance matrix. A method to find geometries allowing for the existence of trapped modes is proposed. Then the solving method is applied to the modeling of the viscous boundary layer of a fluid oscillating near a periodical rough surface. A perturbative solution is proposed. The presence of recirculation areas is studied.

A novel on-line capillary rheometer (OLR) was used to examine the shear and extensional characteristics of polyolefin melts during twin screw extrusion (TSE). Comparisons with off-line rheometry were made using a twin-bore capillary rheometer and a modular in-line slit die rheometer (ILR) provided in-line rheometry comparisons. Both capillary rheometers were controlled via PCs running dedicated software, and the extrusion line and ELR were fully instrumented allowing real-time process monitoring to be carried out by IBM compatible PCs via data acquisition hardware and software. The prototype OLR was developed by the re-design of several key features including an instrumented transfer section and capillary die block which facilitated the use of various die geometries. Shear and extensional on-line rheometry of three polyethylenes (linear and branched), and four molecular weight grades of polypropylene were examined, and a direct comparison with off-line capillary rheometry showed a good correlation. The effect of a high loading of filler on two of the polyethylenes was investigated. In-line shear stress and entry pressure measurements showed a reasonable correlation with on-line rheometry. A study of entry flows in the OLR using capillary dies approaching orifice showed non-linearities occurred at very low capillary length to diameter(L:D) ratios, and this was repeatable using off-line rheometry. Predicted zero length entry pressures (Po) were used to estimate apparent extensional viscosity using a number of standard models. Melt instability and capillary wall slip were also investigated using on-line rheometry. Melt pressure and temperature in the twin screw extruder and OLR were monitored at various process conditions to examine the ability of the OLR to condition melt during testing, and the effect of OLR testing on extrusion conditions. Pressure variation in the extruder, OLR and off-line rheometer were compared in order to quantify process noise. The effect of OLR testing on melt rheology and polymer molecular weight were examined using off-line rheometry and gel permeation chromatography(GPC). / Rosand Precision Ltd. and Raychem Ltd.

In this thesis I investigate a number of problems in the nonlinear stability of density stratified plane Couette flow. I begin by describing the history of transient growth phenomena, and in particular the recent application of adjoint based optimisation to find nonlinear optimal perturbations and associated minimal seeds for turbulence, the smallest amplitude perturbations that are able to trigger transition to turbulence. I extend the work of Rabin et al. (2012) in unstratified plane Couette flow to find minimal seeds in both vertically and horizontally sheared stratified plane Couette flow. I find that the coherent states visited by such minimal seed trajectories are significantly altered by the stratification, and so proceed to investigate these states both with generalised Koopman mode analysis and by stratifying the self-sustaining process described by Waleffe (1997). I conclude with an introductory problem I considered that investigates the linear Taylor instability of layered stratified plane Couette flow, and show that the nonlinear evolution of the primary Taylor instability is not coupled to the form of the linearly unstable mode, in contrast to the Kelvin-Helmholtz instability, for example. I also include an appendix in which I describe joint work conducted with Professor Neil Balmforth of UBC during the 2015 WHOI Geophysical Fluid Dynamics summer programme, investigating stochastic homoclinic bifurcations.

The effects of vortices on the propagation of acoustic waves are numerous, from simple convection effects to instabilities in the acoustic phenomena, including absorption,<p>reflection and refraction effects. This work focusses on the effects of mean flow<p>vorticity on the acoustic propagation. First, a theoretical background is presented<p>in chapters 2-5. This part contains: (i) the fluid dynamics and thermodynamics<p>relations; (ii) theories of sound generation by turbulent flows; and (iii) operators taken<p>from scientific literature to take into account the vorticity effects on acoustics. Later,<p>a family of scalar operators based on total enthalpy terms are derived to handle mean<p>vorticity effects of arbitrary flows in acoustics (chapter 6). Furthermore, analytical<p>solutions of Pridmore-Brown’s equation are featured considering exponential boundary<p>layers whose profile depend on the acoustic parameters of the problem (chapter 7).<p>Finally, an extension of Pridmore-Brown’s equation is formulated for predicting the<p>acoustic propagation over a locally-reacting liner in presence of a boundary layer of<p>linear velocity profile superimposed to a constant cross flow (chapter 8).<p> / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

Determining the hydrodynamic force acting on bubbles and particles moving parallel to a wall in a shear flow is a problem of fundamental importance, as this configuration is involved in a variety of technical and natural systems. The presence of the wall tends to increase the drag force, and more importantly causes a transverse lift force acting on the body. This thesis focuses on extending the current capability in predicting drag and lift forces on spherical bubbles and particles translating in a linear shear flow, primarily in the vicinity of a wall, and obtaining quantitative insight into the interaction mechanisms at work in the context of finite sphere Reynolds number. The investigations are performed through direct numerical simulation (DNS) using an accurate finite volume method. The first part of the thesis summarizes all expressions for the drag and lift forces available in the literature. A comprehensive review of existing results from analytical, experimental, and direct numerical simulation studies is given. The available correlations are critically assessed by comparison to data from these studies. Based on the comparison, recommendations are given which correlations to use including some new proposals, and gaps in the data are identified. The second part aims to fill the gaps mentioned above by means of DNS. Specifically, the three-dimensional flow around a non-rotating sphere translating steadily in a wall-bounded linear shear flow is investigated by solving the full Navier-Stokes equations. Numerical results and analytical expressions are combined to provide accurate semi-empirical expressions for the drag and lift forces at arbitrary Reynolds number and separation distance. Present numerical results help to rationalize and quantify the various mechanisms at work and the ways they interact. From a practical point of view, they also result in several closure models for the drag correction and transverse force, which are necessary inputs in the point-particle based Eulerian-Lagrangian simulations or in Eulerian-Eulerian simulations based on the interpenetrating continua concept.:1 INTRODUCTION 1.1 Background 1.2 Underlining mechanisms 1.3 State of the art 1.4 Motivation, goal and outline of the thesis 2 STATE OF THE ART 2.1 Statement of the problem 2.2 Overview of literatures 2.3 Unbounded linear shear flow 2.4 Linear shear flow with the wall lying in the inner region 2.5 Stagnant flow with the wall lying in the outer region 2.6 Linear shear flow with the wall lying in the outer region 2.7 Conclusions 3 NUMERICAL APPROACH AND PRELIMINARY TESTS 3.1 Numerical approach 3.2 Preliminary tests 4 CLEAN SPHERICAL BUBBLE IN WALL-BOUNDED FLOW 4.1 Characteristics of the flow field and fundamental mechanisms 4.2 Hydrodynamic forces on the bubble: fluid at rest at infinity 4.3 Hydrodynamic forces on the bubble: linear shear flow 4.4 Conclusions 5 RIGID SPHERE IN WALL-BOUNDED FLOW 5.1 Characteristics of the flow field and fundamental mechanisms 5.2 Hydrodynamic forces on the sphere: fluid at rest at infinity 5.3 Hydrodynamic forces on the sphere: Linear shear flow 5.4 Conclusions 6 CONCLUSIONS AND FUTURE WORK 6.1 Summary and conclusions 6.2 Future work 7 REFERENCE