京都大学 / 新制・課程博士 / 博士(理学) / 甲第24390号 / 理博第4889号 / 新制||理||1699(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 大木谷 耕司, 教授 並河 良典, 准教授 竹広 真一 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

<p>Different techniques have been employed through the years to predict hydrodynamic instabilities on high speed liquid jets. In this work, a local linear stability analysis (LSA) has been chosen to estimate streamwise wavelengths on the jet surface near the jet exit.  Data for 0.24 to 0.5 diameters downstream in a high speed water jet issuing into air, given by Reynolds number based momentum thickness between 240 and 600, for validation of the method.  </p> <p>The hypothesis is: near the exit of the jet nozzle, for high speed liquid jets, the local velocity profile evolves based on the momentum thickness and, because of large inertia effects, the flow may be considered as inviscid for instability purposes. Therefore, the approach in this work is based on the Rayleigh equation and with the momentum thickness scaling, both non-dimensional and dimensional values of the most unstable wavelengths are obtained.</p> <p>The key aspect of the  approach is the relevance of the momentum thickness as the scaling factor for calculation purposes on dimensional values of wavelengths.</p> <p>Also, a hyperbolic tangent velocity profile is assumed for the Linear Stability Analysis based on the Rayleigh equation. Numerical restrictions and comparisons, using the Riccati transformation, are specified and described in detail to generalize this approach.</p> <p>Results show that analytical estimates of the most unstable streamwise wavelengths are close to the experimental measurements published by Portillo et al. in 2011.  The agreement using this new approach is often within the experimental uncertainty.</p> <p><br></p>

Turbulent swirling flows are important in many applications including gas turbines, furnaces and cyclone dust separators among others. Although the mean flow fields have been relatively well studied, a complete understanding of the flow field including its dynamics has not been achieved. The work contained in this dissertation attempts to shed further light on the behavior of turbulent swirling flows, especially focused on the dynamic behavior of a turbulent swirling flow encountering a sudden expansion. Experiments were performed in a new isothermal turbulent swirling flow test facility. Two geometrical nozzle configurations were studied. The \cb\ nozzle configuration exhibits a cylindrical \cb\ in the center of the nozzle. The free vortex nozzle configuration is obtained when the cylindrical \cb\ is removed. Detailed laser velocimeter measurements were performed to map out the flow field near the sudden expansion of the 2.9" (ID) nozzle leading to the 7.4" (ID) downstream section. In addition to presenting detailed flow profiles for both nozzle and downstream flow fields, representative frequency spectra of the flow dynamics are presented. Along with the flow time histories and histograms, the wide variety of dynamic behavior was thus described in great detail. The dynamics observed in the experiment can be classified into three main categories: coherent and large scale motion, intermittent motion and coherent periodic motion. Free vortex geometry flows, in the parameter space of the experiments (Swirl number = 0 - 0.21), exhibited mostly coherent and large scale motion. The spectra in these cases were broadband with very light concentration of spectral energy observed in some specific cases. Center--body geometry flows exhibited all three categories of flows as swirl strength was increased from zero. Flows with little or no swirl exhibited broad--band spectra similar to those for the free vortex geometry. Intermediate swirl levels resulted in a large amount of low frequency energy which, with the aid of the time histories, was identified as a large scale intermittence associated with radial movement of the annular jet as it enters the sudden expansion. Large swirl levels resulted in high magnitude coherent oscillations concentrated largely just downstream of the sudden expansion. Linear stability analysis was used to help in the interpretation of the observed dynamics. Although, as implemented here (using the parallel flow assumption), the analysis was not successful in quantitatively matching the experimentally observed dynamics, significant insight into the physical mechanisms of the observed dynamics was obtained from the analysis. Specifically, the coherent oscillations observed for larger swirl levels were able to be described in terms of the interaction between the inner and outer shear layers of the flow field. / Ph. D.

Current climate models have a limited ability to increase spatial resolution because numerical stability requires the time step to decrease. I describe initial experiments with two independent but complementary strategies for attacking this "time barrier". First I describe computational experiments exploring the performance improvements from overlapping computation and communication on hybrid parallel computers. My test case is explicit time integration of linear advection with constant uniform velocity in a three-dimensional periodic domain. I present results for Fortran implementations using various combinations of MPI, OpenMP, and CUDA, with and without overlap of computation and communication. Second I describe a semi-Lagrangian method for tracer transport that is stable for arbitrary Courant numbers, along with a parallel implementation discretized on the cubed sphere. It shows optimal accuracy at Courant numbers of 10-20, more than an order of magnitude higher than explicit methods. Finally I describe the development and stability analyses of the time integrators and advection methods I used for my experiments. I develop explicit single-step methods with stability up to Courant numbers of one in each dimension, hybrid explicit-implict methods with stability for arbitrary Courant numbers, and interpolation operators that enable the arbitrary stability of semi-Lagrangian methods.

The materials that exhibit martensite transformation have very important applications in engineering, and the microstructures of the materials play a key role foraffecting their mechanical behavior in macroscope. Therefore many attentions havebeen drawn for studying the related problems. This work focuses on the motion oftwin boundaries. Three questions are being asked: how is a twin boundary is nucleated in a homogenous (untwinned) material? After the twin boundary is nucleated,how is its motion initiated? How fast does it move? This study provides an atomisticunderstanding for these three questions. Linear stability analysis is firstly applied to capture the initiation of motion of atwin boundary. When a twin boundary is about to move, the lowest eigenvalue of thesystem Hessian drops to zero. And the corresponding eigenvector predicts accuratelythe way in which the twin boundary is going to move. The same idea is applied toinvestigate how motion of an irrational twin boundary is initiated. Atomic modelsof irrational twin boundaries are constructed by employment of continuum models,provided that the point group of rotations which relate two variants is extended toany rotations in plane. The zero eigenvectors reveal the complicated behavior ofmotion of irrational twin boundaries. The problem of nonuniqueness of kinetic relations proposed by Schwetlick andZimmer is solved in a thermoelasticity framework. By calculating the net heat fluxcrossing the phase boundary which is carried by the phonons, a unique kinetic relationcan be determined. Finally, a nonlocal criterion for nucleation of twin boundariesis proposed. By checking the stiffness of each unit cell evaluated with respect to asingle variable that represents the displacement along the unit cell diagonal direction,locations and the orientations of nucleated twin boundaries can be predicted.

Alors qu'il est bien connu que le phénomène d'instabilité de Faraday est une manifestation d'ondes de gravité capillaire, son comportement lorsque les effets capillaires et gravitationnels disparaissent reste inexploré théoriquement et expérimentalement. Une étude expérimentale et théorique détaillée est réalisée pour comprendre la physique de ce phénomène dans une petite cavité rectangulaire où la proximité des murs entraîne des contraintes considérables sur les parois latérales. Un couple de liquides binaires est utilisé avec une faible tension interfaciale pour une interface presque plate. Le contrôle thermique de ce système de fluide est utilisé pour diminuer la force capillaire et d’étudier ainsi les instabilités de Faraday dans les fluides miscibles où la tension interfaciale s’annule. Afin de prendre en compte les effets gravitationnels, l'expérience a été réalisée dans des campagnes de vols paraboliques. Pour l'approche théorique, une analyse de stabilité linéaire est effectuée à l'aide d'équations de Navier-Stokes dans un système de fluide visqueux incompressible et newtonien. Ceci est réalisé grâce à une méthode de Fourier-Floquet résultant en un problème aux valeurs propres. Les comparaisons montrent des différences non négligeables. Les équations sont ensuite résolues en incluant des effets d'amortissement visqueux pour compenser les contraintes des parois latérales. Les fluides binaires ont fourni une option commode pourchanger le coefficient de tension interfaciale en augmentant la température jusqu’à la température critique, ce qui a permis de passer d’un système de fluides non miscibles à celui des fluides miscibles tout en restant au-dessous de la température d’ébullition. Le taux d'amortissement visqueux linéaire est mesuré expérimentalement. La correction des calculs théoriques en prenant en compte le taux d'amortissement visqueux a permis une amélioration nette des résultats et donc de mieux comprendre la prédiction de l'amplitude critique expérimentale pour les modes sous-harmonique et harmonique. / While it is well known that the phenomenon of Faraday instability is a manifestation of vibrational acceleration, its behaviour when both the capillary and gravitational effects vanish, remains unexplored theoretically and experimentally. A detailed experimental and theoretical study is performed to understand the physics of this phenomenon in small rectangular geometry where the proximity of wall results in considerable sidewall stresses. A novel binary liquids system is utilized with low interfacial tension for a near flat interface. Thermal control of fluid system is utilized for achieving reduction in capillary force with study of miscible fluids where interfacial tension reduces to almost zero. In order to discriminate between gravity and capillarity effects, experiments were performed in parabolic flight campaigns. . For the theoretical approach a linear stability analysis is performed through Navier-Stokes equations in a Newtonian incompressible viscous fluid system. This is achieved through a Fourier Floquet method resulting into an eigenvalue problem. Equations are solved by including viscous damping effects for compensating sidewall stresses. Experimentally binary fluids provided a convenient option of changing the coefficient of interfacial tension by temperature control and going through immiscible to miscible system without change of liquid charge. Viscous damping rate is determined experimentally by measuring the linear damping rate. The correction in the theoretical calculations with the viscous damping rate helped in achieving a better understanding of the prediction of the experimental critical amplitude for sub-harmonic and harmonic modes.

Studying the coupling between buoyancy-driven instabilities and chemical reactions is not only relevant to fundamental research, but has also recently gained increased interest because of its relevance to CO$_2$ sequestration in subsurface geological zones. This technique aims to limit the emissions of CO$_2$ to the atmosphere, with a view to mitigating climate change. When injected in e.g. a saline aquifer, CO$_2$ dissolves into the brine occupying the geological formation, thereby increasing the density of the aqueous phase. This increase of density upon dissolution leads to a denser fluid boundary layer rich in CO$_2$ on top of less dense fluid in the gravity field, which drives dissolution-driven convection. This process, also called convective dissolution, accelerates the transport of dissolved CO$_2$ to the host phase and thus improves the safety of CO$_2$ sequestration. The same kind of instability can develop in other contexts involving the dissolution of a phase A into a host phase, such as solid dissolution or transfer between partially miscible liquids. In this context, the goal of our thesis is to understand how chemical reactions coupled to dissolution-driven convection affect the dynamics of the dissolving species A in the host solution. To do so, we introduce a general reaction of the type A + B $rightarrow$ C where A, B and C affect the density of the aqueous solution. We theoretically analyze the influence of the relative physical properties of A, B and C on the convective dynamics. Our theoretical analysis uses a reaction-diffusion-convection model for the evolution of solute concentration in a host fluid solvent occupying a porous medium. First, we quantify the characteristic growth rate of the perturbations by using a linear stability analysis. Thereby we show that a chemical reaction can either accelerate or slow down the development of convection, depending on how it modifies the density profile that develops in the reactive solution. In addition, new dynamics are made possible by differential diffusion effects. Then, by analyzing the full nonlinear dynamics with the help of direct numerical simulations, we calculate the dissolution flux into the host phase. In particular, the dissolution flux can be amplified when convection develops earlier, as CO$_2$ is then transported faster away from the interface. Finally, we compare these theoretical and numerical predictions with results of laboratory experiments and discuss the possible implications of this study for CO$_2$ sequestration. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

We computationally explore the dynamics of superconductivity near the superheating field in two ways. First, we use a finite element method to solve the time-dependent Ginzburg-Landau equations of superconductivity. We present a novel way to evaluate the superheating field Hsh and the critical mode that leads to vortex nucleation using saddle-node bifurcation theory. We simulate how surface roughness, grain boundaries, and islands of deficient Sn change those results in 2 and 3 spatial dimensions. We study how AC magnetic fields and heat waves impact vortex movement. Second, we use automatic differentiation to abstract away the details of deriving the equations of motion and stability for Ginzburg-Landau and Eilenberger theory. We present calculations of Hsh and the critical wavenumber using linear stability analysis.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第18933号 / 工博第3975号 / 新制||工||1612(附属図書館) / 31884 / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 木村 亮, 教授 勝見 武, 准教授 木元 小百合 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

[pt] O processo de revestimento por rotação é caracterizado pelo uso de cilindros girantes para controlar a espessura e aplicar uma fina camada de líquido em um substrato em movimento. A não ser a baixas velocidades dos cilindros, o escoamento bi-dimensional na região de formação dos filmes sobre cada cilindro é instável e o padrão observado experimentalmente consiste em um escoamento tri-dimensional e periódico na direção transversal ao substrato. Esta instabilidade pode limitar a velocidade máxima do processo se a camada líquida depositada sobre o substrato tem que ser uniforme. Para líquidos Newtonianos, a estabilidade deste escoamento é determinada pela competição de forças viscosas e capilares: a instabilidade ocorre acima de um número de capilaridade máximo. Apesar da maioria dos líquidos utilizados em processos de revestimento serem não Newtonianos, as análises disponíveis deste escoamento se limitam a estudos de líquidos Newtonianos. O comportamento não Newtoniano do líquido pode alterar completamente a natureza do escoamento perto da superfície livre; quando pequenas quantidades de polímeros flexíveis de alto peso molecular estão presentes, a instabilidade na direção transversal ocorre a velocidades muito mais baixas, quando comparado ao caso Newtoniano. Os mecanismos responsáveis pela instabilidade a baixas velocidades ainda não são completamente compreendidos. Este escoamento viscoelástico com superfície livre é analisado neste trabalho através de duas equações constitutivas diferenciais, o modelo de Oldroyld-B e o modelo de FENE-P. As equações de conservação de massa, quantidade de movimentos acopladas com os modelos constitutivos, e as equações não-lineares de mapeamento que transformam o problema de superfície livre em um problema de valor de contorno foram resolvidas pelo método de elementos finitos DEVSS-G/SUPG. O sistema de equações algébricas não linear foi resolvido pelo método de Newton com continuação por pseudo-comprimento de arco. Os resultados mostram como o campo de tensão muda com o aumento do número de Weissenberg (elasticidade do líquido), levando a formação de uma camada limite de tensão elástica na superfície livre e tensões elásticas compressivas na direção transversal, que podem explicar o aparecimento da instabilidade a baixas velocidades. Este trabalho também apresenta a formulação de estabilidade linear para escoamentos viscoelásticos com superfícies livres. O modelo dá origem a um problema de auto-valor generalizado, que foi resolvido pelo método de GMRES (ARPACK). Os auto-valores dominantes da matriz Jacobiana indicam a estabilidade do escoamento. Esta formulação foi testada em três escoamentos distintos: escoamento em uma cavidade de tampa móvel, piscina de líquido estática e um escoamento de Couette (simples de cisalhamento). / [en] Roll coating is distinguished by the use of one or more gaps between rotating cylinders to meter and apply a liquid layer to a substrate. Except at low speed, the film splitting flow that occurs in forward roll coating is three-dimensional and results in more or less regular stripes in the machine direction. This instability can limit the speed of the process if a smooth film is required as a final product. For Newtonian liquids, the stability of the film-split flow is determined by the competition of capillary forces and viscous forces: the onset of meniscus nonuniformity is market by a critical value of the capillary number. Although most of the liquids coated industrially are polymeric solutions and dispersions, that are not Newtonian, most of previous theoretical analyses of film splitting flows dealt only with Newtonian liquids. Non-Newtonian behavior can drastically change the nature of the flow near the free surface; when minute amounts of flexible polymer are present, the onset of the three-dimensional instability occurs at much lower speeds than in the Newtonian case. the mechanisms responsible for the early onset of this flow instability is not well understood. This free surface coating flow is analyzed here with differential constitutive models, the Oldroyld-B and the FENE-P equations. The continuity, momentum equations coupled with the constitutive models, and the non-linear mapping equations that transform the free boundary problem into a fixed boundary problem are solved by Newton s method with pseudo-arc-length continuation. The results show how the stress field changes with Weisenberg number, leading to the formation of an elastic boundary layer near the free surface and compressive elastic stresses in the crss-flow direction that may explain the onset of the ribbing instability at the smaller Capillary numbers when viscoelastic liquids are used. This work also presents the formulation for linear stanility analysis of viscoelastic free surface flows. The model leads to a generalized eigenproblem that is solved here using the Arnoldi s method with the software (ARPACK). The leading eigenvalues of the Jacobian Matrix indicate the stability of the flow. The formulation is tested in three different flows: lid-driven cavity, static liquid pool and a couette flow.