Les moteurs à propergol solide de certains lanceurs spatiaux peuvent présenter des oscillations de poussée provoquées par des oscillations de la pression interne du moteur. Il est désormais connu qu'une instabilité hydrodynamique propre à l'écoulement et mise en évidence par une approche de stabilité linéaire, appelée Vortex Shedding Parietal, est le phénomène à l'origine de ces oscillations. Cependant plusieurs questions subsistent quant à l'apparition de ces oscillations. En particulier, on constate que ces oscillations ne sont observées que dans la seconde moitié du tir. On suppose que la transition laminaire-turbulent de l'écoulement joue un rôle dans ce phénomène. Par ailleurs, l'utilisation possible de la géométrie étoilée pour les blocs de propergol de géométrie étoilée oblige à reprendre l'étude de stabilité linéaire pour l'étude de ces oscillations. Cette thèse porte ainsi à la fois sur l'étude de la stabilité linéaire de l'écoulement induit par une géométrie étoilée et sur la transition laminaire-turbulent d'une configuration circulaire. Une solution analytique de l'écoulement au sein d'un conduit à paroi débitante de géométrie étoilée est d'abord obtenue. Le profil de vitesse associé peut présenter des points d'inflexion en fonction de la déformation radiale ou du nombre de Reynolds de l'écoulement. Ensuite les approches de stabilité linéaire locale et biglobale sont appliquées à cette solution. Par rapport au cas circulaire, cette étude de stabilité linéaire met en évidence la possible existence d'un ou plusieurs modes amplifiés. Enfin, une simulation numérique LES de la transition laminaire-turbulent de la configuration du montage VALDO est effectuée. / Solid rocket motors may exhibit thrust oscillations induced by pressure oscillations inside the engine. In the scientific literature, the so-called vortex shedding parietal, a hydrodynamic instability specific to the internal flow, has been proven to be the triggering mechanism through linear stability analyses. However, some questions still remain. These oscillations are observed during the second half of Ariane 5 launches only, the laminar-turbulent transition of the intern flow being expected to play a significant role in that behavior. Additionally, non-circular grain shapes used in some engines may impact the stability study. The present PhD work extends the base flow linear stability studies to star-shaped geometries and investigate transition mechanisms in a circular configuration. Firstly, an analytical expression of the base flow in a duct with a star-shaped cross-section is determined. Wall-normal injection is assumed, which is representative of solid rocket engines. The velocity profile may exhibit an inflection point depending on both the Reynolds number and wall radial deformation. Secondly, both local and biglobal stability analyses are applied to this flow. In contrast to the circular case, the flow may exhibit one or several unstable modes. Lastly, a large eddy simulation of the VALDO experimental test bench is performed. The influence of the acoustic impedance of the outflow boundary condition on the amplitude of pressure oscillations is highlighted.

Submitted by Ellen Silva Gervazoni null (emillen_@hotmail.com) on 2016-08-25T17:45:32Z No. of bitstreams: 1 Disserataçaofinal_EllenGervazoni.pdf: 1426674 bytes, checksum: 25ce3b189028e33485b050b9f7676a94 (MD5) / Approved for entry into archive by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br) on 2016-08-29T19:17:40Z (GMT) No. of bitstreams: 1 gervazoni_es_me_prud.pdf: 1426674 bytes, checksum: 25ce3b189028e33485b050b9f7676a94 (MD5) / Made available in DSpace on 2016-08-29T19:17:40Z (GMT). No. of bitstreams: 1 gervazoni_es_me_prud.pdf: 1426674 bytes, checksum: 25ce3b189028e33485b050b9f7676a94 (MD5) Previous issue date: 2016-06-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Diversos escoamentos de interesse prático são de fluidos viscoelásticos e muitas vezes é desejável saber se estes escoamentos propagam-se no estado laminar ou no turbulento. Embora a hidrodinâmica de fluidos viscoelásticos sejam fortemente afetadas pelo balanço entre forças inerciais e elásticas no escoamento, o efeito da elasticidade sobre a estabilidade de escoamentos inerciais não foi completamente estabelecida. No presente trabalho, estuda-se o que ocorre entre estes dois estados, na transição laminar-turbulenta. Especi- ficamente, é investigada a convecção de ondas de Tollmien-Schlichting para o escoamento incompressível de Poiseuille para um fluido viscoelástico, utilizando a equação constitutiva Oldroyd-B. Para isto, utiliza-se a Simulação Numérica Direta para verificar a estabilidade dos escoamentos de fluidos viscoelásticos a perturbações não estacionárias. Os resultados numéricos obtidos para escoamentos de fluidos viscoelásticos são comparados com os resultados de escoamentos de fluidos Newtonianos, que já estão bem documentados na comunidade científica. Além disso, uma equação de Orr-Sommerfeld modificada é deduzida para um escoamento viscoelástico utilizando a Teoria de Estabilidade Linear. / Several flows of practical interest are of viscoelastic fluids and it is often desirable to know if these flows are in a laminar or turbulent state. Although the hydrodynamics of viscoelastic fluids are strongly affected by the balance between inertia and elastic forces in the flow, the effect of elasticity on the stability of inertial flows has not been completely established. In this work is studied what happens between these two states, the laminar-turbulent transition. Specifically, it will be investigated the convection of Tollmien-Schlichting waves to incompressible Poiseuille flow of viscoelastic fluid, using the constitutive equation Oldroyd-B. For this, the analysis is carried out by means of Direct Numerical Simulation to verify the stability of the non-stationary disturbances viscoelastic fluids flows. The numerical results obtained for viscoelastic fluids flows are compared with the results of Newtonian fluids flows, which are already well documented in scientific community. In addition, an Orr-Sommerfeld modified equation is deducted for a viscoelastic flow using Linear Stability Theory.

Orientador: Patricio Anibal Letelier Sotomayor / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-08T22:19:55Z (GMT). No. of bitstreams: 1 Rosa_ValeriaMattosda_D.pdf: 1232759 bytes, checksum: e4b5f9dd20a1bb1f521f2972b43bbfaf (MD5) Previous issue date: 2007 / Resumo: Várias soluções das equações de Einstein admitem curvas tipo-tempo fechadas (CTCs). Estudamos o comportamento deste tipo de curva quanto à estabilidade linear. Analisando as CTCs no universo de Gödel, encontramos que elas são linearmente estáveis, assim como as curvas desse tipo encontradas em um exemplo particular de métrica tipo-Gödel com fundo plano. As CTCs que aparecem no modelo contendo uma única corda cósmica girante também apresentam estabilidade linear. Estudamos todos os exemplos conhecidos de soluções das equações de Einstein que possuem geodésicas tipo-tempo fechadas (CTGs). Encontramos que a CTG apresentada pelos autores da solução dos dois perjeons não é linearmente estável, mas obtivemos condições, para os parâmetros desse modelo, sob as quais ela admite outras CTGs e, sob condições mais restritivas, obtivemos CTGs linearmente estáveis. As CTGs apresentadas por Soares em seu modelo topológico e por Grøn e Johannesen em seu modelo da núvem de cordas não possuem estabilidade linear. Já as CTGs de uma das soluções dada por van Stockum foram analisadas e verificamos que são linearmente estáveis. Encontramos CTGs em um exemplo particular de métrica tipo-Gödel com fundo conformemente plano, e estas também são estáveis. Analisamos, também, a deformação provocada pelo buraco negro de Schwarzschild ao ser colocado em um espaço-tempo com uma corda cósmica girante. Encontramos as CTGs desse espaço-tempo e determinamos as condições para que estas sejam estáveis / Abstract: Several solutions of Einstein¿s field equations admit closed timelike curves (CTCs). We study the linear stability of this kind of curve. We analyze the CTCs in Gödel universe and we find that these curves are stable. The same occurs with the CTCs of a particular case of Gödel-type metric with flat background and with CTCs of a model that contains a single spinning cosmic string. We study all known solutions of Einstein¿s equations that contain closed timelike geodesics (CTGs). We find that the CTG presented by Bonnor and Steadman in their model of two Perjeons is not stable under linear perturbations, but we present conditions to have stable CTGs in this model. The CTGs presented by Soares in his topological model and those presented by Grøn and Johannensen in their model of the cloud of strings are not stable. But, analizing the CTGs presented by Steadman in a solution gave by van Stockum, we conclude that these curves are stable. Besides these known CTGs, we find this kind of curve in a particular case of G¨odel-type metric with conformally flat background and we also find that they are stable. We also study the deformation that a Schwarzschild black hole causes in the spacetime of a single spinning cosmic string. We find the CTGs of this new spacetime and we determine conditions to have linear stability / Doutorado / Fisica-Matematica / Doutor em Matemática Aplicada

Cette thèse a pour objectif d'améliorer la compréhension de la dynamique d'une interaction entre une onde de choc droite ou oblique et une couche limite laminaire ou turbulente. En particulier, nous nous sommes intéressés aux mécanismes responsables de l'apparition d'oscillations auto-entretenues basses fréquences. Ce phénomène survient dans de nombreux cas applicatifs comme dans des entrées d'air d'avions supersoniques, autour d'un profil d'aile en régime transsonique et au sein de tuyère en régime de sur-détente. La première partie de ce mémoire traite des différentes études réalisées pour déterminer la phénoménologie de ce type de dynamique. Dans un deuxième temps, nous expliquons la stratégie retenue pour effectuer notre étude qui consiste à développer un outil d'étude des instabilités, adapté à des écoulements turbulents présentant une interaction entre une onde de choc et une couche limite. Le développement d'un outil CFD linéarisé couplé à une méthode de résolution d'un problème aux valeurs propres par une approche dite sans matrice ou de « time-stepping », a permis la réalisation d'une telle étude. Après une étape de validation de notre outil, nous avons étudié des cas d'écoulements présentant une interaction entre une onde de choc et une couche limite. Trois cas en particulier ont été traités. Le premier cas correspond à une interaction entre une onde de choc oblique impactant une couche limite laminaire se développant sur une plaque plane. Ce cas est généralement qualifié dans la littérature de cas de « réflexion de choc ». Nous montrons qu'un tel écoulement est globalement stable et que sa dynamique peut être caractérisée par des mécanismes de réceptivité et par la réponse de l'écoulement vis-à-vis de perturbations extérieures. Les deux autres cas abordés dans ce travail ont été le cas d'un écoulement transsonique autour d'un profil d'aile de type NACA0012 en régime d'entrée en tremblement aérodynamique et un cas de tuyère transsonique plane de type Sajben en régime de sur-détente. Dans le premier cas, l'analyse de stabilité nous permet de mettre en évidence le phénomène de « buffet » sur le profil NACA0012, ce qui montre que le phénomène est lié à une instabilité globale linéaire . Dans le second cas, l'analyse de stabilité ne permet pas d'expliquer le phénomène auto-entretenues basses fréquences, et montre que l'écoulement est linéairement globalement stable. Dans ce cas, la dynamique est convective, transitoire et pilotée par des mécanismes de réceptivité. / The general purpose of this study is to provide a better understanding of the dynamics of an interaction between a shock wave and a laminar or turbulent boundary layer. In particular, we were interested in mechanisms responsible for the emergence of low-frequency self-sustained oscillations. This phenomenon arises in numerous industrial cases as in air inlets of supersonic aircrafts, around a profile of wing in transonic regime and within over-extended nozzle. The first part of this report handles various studies carried out to determine the phenomenology of this kind of dynamics. Secondly, we explain the strategy adopted to make our study which consists in developing a tool of study of the instabilities adapted to turbulent flows including an interaction between a shock wave and a boundary layer. The development of a linearized CFD tool coupled with a method of resolution of a eigenvalue problem by a free-matrix approach ( " time-stepping " approach), allowed the realization of such a study. After a stage of validation of our tool, we studied cases of flows including an interaction between a shock wave and a boundary layer. Three cases in particular were handled. The first case corresponds to an interaction enter an oblique shock wave impacting on a laminar boundary layer developing on a flat plate. This case is generally qualified in the literature of case as " reflected shock wave". We show that such a flow is globally stable and that the dynamics of such a flow behaves as a selective noise amplifier, the dynamic is mainly driven by receptivity mechanisms and by the response of upstream white nose disturbance. Two other cases have been studied on this work, the case of a transonic flow around a profile wing of NACA0012 type around the onset of buffet phenomenon and the case of transonic nozzle of Sajben type on over-extended regime. In the first case, the global stability analysis allows us to highlight the buffet phenomenon of on the profile NACA0012, what shows that the phenomenon is linked to a linear global instability. In the second case, the analysis of stability does not allow to explain the self-sustained low frequencies phenomenon, and shows that the flow is linearly globally stable. In this case, the dynamics is convective, passing and piloted by receptivity mechanisms.

Dans cette thèse, on a étudié l’évolution de l’interface par électro-osmose entre deux couches de fluides dans un canal microfluidique. Les applications de ce problème concernent le mélange et le transport, sans contact avec des actionneurs, de fluides en micro-canal. De nombreuses questions restent toutefois posées lorsque le champ est oscillant en temps, notamment vis à vis de la stabilité de l'interface entre les deux fluides. Une analyse de stabilité linéaire basée sur une perturbation à l’interface a été réalisée pour un film mince d'électrolyte sous des champs électriques continus (constants) et alternatifs (dépendant du temps). Une analyse asymptotique avec une hypothèse de grande longueur d’onde des équations d'Orr-Sommerfeld a été appliquée afin de déterminer les seuils de stabilité paramétriques d'un film mince aqueux. L’accent a été mis sur les effets de la tension de surface, de la pression de disjonction pour l'interaction gaz-liquide-substrat, de l'amplitude et de la fréquence du champ électrique appliqué, ainsi que du potentiel zêta du substrat et de la surface libre. Une analyse comparative des profils de vitesse de l’état de base avec et sans contraintes de Maxwell à l’interface, a montré que les gradients de vitesse étaient importants à l'interface liquide-liquide avec les contraintes de Maxwell. De tels gradients sont essentiels à l'instabilité interfaciale sous l’action d’un champ électrique périodique car ils peuvent atténuer ou amplifier les ondes à l’interface. Parallèlement, un dispositif expérimental a été conçu et monté afin de caractériser l’écoulement électroosmotique dans un micro-canal rectangulaire. Avec l'aide d'une analyse PTV (« Particle Tracking Velocimetry »), les distributions de vitesse ont été obtenues et comparées aux prédictions théoriques. Cette comparaison a permis d’estimer le potentiel zêta du PDMS utilisé, valeur conforme à la valeur indiquée dans la littérature. / Since the past decade, use of electro-osmotic flow (EOF) as an alternative flow mechanism in microdevices is becoming more popular due to its less bulky and low maintenance system design. However, one of the biggest shortcomings for its usage in mainstream applications is that it requires the concerned liquid to be electrically conductive. One idea can be to use the flow of conductive fluids to transport non-conductive liquids passively via interfacial shear transfer. Such an idea can has numerous applications in a wide range of fields like bio-chemical processing (e.g. lab-on-a-chip reactors, mixers, etc.), to oil extraction from porous rock formations. One of the significant characteristics of micro-scale flows is high surface to volume ratio, which significantly highlights the role of multi-phase interfaces in such dynamics. The presence of a fluid-fluid interface in an EOF necessitates the characterization of the parameters responsible for hydrodynamic instability of such systems. The present work focuses on the role of steady and time-dependent electric stress (Maxwell stress), capillary force and disjoining pressure on fluid-fluid interfacial instability. A linear stability analysis of interfacial perturbation was performed for a thin film of electrolyte under DC and AC electric fields. Through long wave asymptotic analysis of the Orr-Sommerfeld equations, parametric stability thresholds of a thin aqueous film explored. Further, a set of experiments were performed in order to characterize the EOF in a rectangular microchannel. With the help of a Particle Tracking Velocimetry analysis, velocity distributions were obtained which agreed well to the theoretical values. This was further used to estimate PDMS zeta potential, which was found to be within the reported values in the existing literature. Liquid-liquid interfacial deformation was also explored under a time-periodic EOF and a wide range of the magnitudes of capillary force, and diffusive and convective transport.

The thesis is focused on the investigation of Rayleigh-Bénard problem in an extended setting approximating the conditions in the Earth's mantle. The aim is to evaluate the influence of depth- and temperature- dependent material parameters, dissipation, adiabatic heating/cooling and heat sources on the qualitative characteristics of thermal convection. We identify the critical values of dimensionless parameters that determine the onset of convection and characterize the dominating convection patterns in marginally supercritical states. These issues are addressed by the application of linear stability analysis and weakly non-linear analysis. It has been found that the character of convection differ substantially from the standard case of Rayleigh-Bénard convection. Powered by TCPDF (www.tcpdf.org)

<div>The growing need to improve the power density of compact thermal systems necessitates developing new techniques to modulate the convective heat transfer efficiently. In the present research, acoustic streaming is evaluated as a potential technology to achieve this objective. Numerical simulations using the linearized and fully non-linear Navier-Stokes equations are employed to characterize the physics underlying this process. The linearized Navier-Stokes equations accurately replicate the low-frequency flow unsteadiness, which is used to find the optimal control parameters. Local and global stability analysis tools were developed to identify the modes with a global and positive heat transfer effect.</div><div><br></div><div>High-fidelity numerical simulations are performed to evaluate the effect of the excitation at selected frequencies, directed by the linear stability analysis, on the heat and momentum transport in the flow. Results indicate that, under favorable conditions, superimposing an acoustic wave, traveling along with the flow, can <i>resonate</i> within the domain and lead to a significant heat transfer enhancement with minimal skin friction losses. Two main flow configurations are considered; at the fixed Reynolds number Re_b=3000, in the supersonic case, 10.1% heat transfer enhancement is achieved by an 8.4% skin friction increase; however, in the subsonic case, 10% enhancement in heat transfer only caused a 5.3% increase to the skin friction. The deviation between these two quantities suggests a violation of the Reynolds analogy. This study is extended to include a larger Reynolds number, namely Re_b=6000 at M_b=0.75 and a similar response is observed. The effect of excitation amplitude and frequency on the resonance, limit-cycle oscillations, heat transfer, and skin friction are also investigated here.</div><div><br></div><div>Applying acoustic waves normal to the flow in the spanwise direction disrupts the near-wall turbulent structures that are primarily responsible for heat and momentum transport near the solid boundary. Direct numerical simulations were employed to investigate this technique in a supersonic channel flow at M_b=1.5 and Re_b=3000. The external excitation is applied through a periodic body force in the spanwise direction, mimicking loudspeakers placed on both walls that are operating with a 180^o phase shift. By keeping the product of forcing amplitude A_f and pulsation period (<i>T</i>) constant, spanwise velocity perturbations are generated with a similar amplitude at different frequencies. Under this condition, spanwise pulsations at <i>T</i>=20 and <i>T</i>=10 show up to 8% reduction in Nusselt number as well as the skin friction coefficient. Excitation at higher or lower frequencies fails to achieve such high level of modulations in heat and momentum transport processes near the walls.<br> <br>In configurations involving a spatially-developing boundary layer, a computational setup that includes laminar, transitional, and turbulent regions inside the domain is considered and the impact of acoustic excitation on this flow configuration has been characterized. Large-eddy simulations with dynamic Smagorinsky sub-grid scale modeling has been implemented, due to the excessive computational cost of DNS calculations at high-Reynolds numbers. The optimal excitation frequency that resembles the mode chosen for the fully-developed case has been identified via global stability analysis. Fully non-linear simulations of the spatially-developing boundary layer subjected to the excitation at this frequency reveal an interaction between the <i>pulsations</i> and the perturbations originated from the tripping which creates a re-laminarization zone traveling downstream. Such technique can locally enhance or reduce the heat transfer along the walls.<br></div>

Reaction-diffusion models have been widely successful in explaining a large variety of patterning phenomena in biology ranging from embryonic development to cancer growth and angiogenesis. Firstly proposed by Alan Turing in 1952 and applied to a simple two-component system, reaction-diffusion models describe spontaneous spatial pattern formation, driven purely by interactions of the system components and their diffusion in space. Today, access to unprecedented amounts of quantitative biological data allows us to build and test biochemically accurate reaction-diffusion models of intracellular processes. However, any increase in model complexity increases the number of unknown parameters and thus the computational cost of model analysis. To efficiently characterize the behavior and robustness of models with many unknown parameters is, therefore, a key challenge in systems biology. Here, we propose a novel computational framework for efficient high-dimensional parameter space characterization of reaction-diffusion models. The method leverages the $L_p$-Adaptation algorithm, an adaptive-proposal statistical method for approximate high-dimensional design centering and robustness estimation. Our approach is based on an oracle function, which describes for each point in parameter space whether the corresponding model fulfills given specifications. We propose specific oracles to estimate four parameter-space characteristics: bistability, instability, capability of spontaneous pattern formation, and capability of pattern maintenance. We benchmark the method and demonstrate that it allows exploring the ability of a model to undergo pattern-forming instabilities and to quantify model robustness for model selection in polynomial time with dimensionality. We present an application of the framework to reconstituted membrane domains bearing the small GTPase Rab5 and propose molecular mechanisms that potentially drive pattern formation.

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