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

Le contrôle de l’instabilité de Rayleigh-Taylor (RT) est crucial pour la fusion par confinement inertiel (FCI) puisque son développement peut compromettre l’implosion et la correcte compression de la cible. En attaque directe, l’énergie fournie par l’irradiation de nombreux faisceaux laser provoque l’ablation de la couche externe de la cible (ablateur) et l’apparition résultante d’un plasma de basse densité en expansion. De ce fait, une très haute pression apparait autour de cette surface, ce qui conduit à l’accélération de la cible vers l’intérieur. On se trouve alors en présence d’un fluide de basse densité qui pousse et accélère le fluide plus dense. C’est une des situations typiques qui favorisent le développement de l’instabilité de RT. Cette thèse développe pour la première fois, dans le contexte de la FCI, une théorie linéaire de stabilité pour des structures à double front d’ablation, qui apparaissent quand des matériaux de nombre atomique modéré sont utilisés comme ablateurs. / The Rayleigh-Taylor instability is a major issue in inertial confinement fusion capable to prevent appropriate target implosions. In the direct-drive approach, the energy deposited by directed laser irradiation ablates off the external shell of the capsule (ablator) into a low-density expanding plasma. This induces a high pressure around the ablating target surface (ablation region) that accelerates the capsule radially inwards. This situation, a low density fluid pushing and accelerating a higher density one, is the standard situation for the development of the Rayleigh-Taylor instability, and therefore a potential source of target compression degradation. For moderate-Z materials, the hydrodynamic structure of the ablation region is made up of two ablation fronts (double ablation front) due to the increasing importance of radiation effects. This thesis develops for the first time a linear stability theory of double ablation fronts for direct-drive inertial confinement fusion targets.

[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.

O som gerado por escoamentos, também conhecido como aeroacústica, tem se tornado cada vez mais importante em áreas industriais diversas desde aviação comercial até aparelhos eletrodomésticos, afetando diretamente os requisitos necessários para o desenvolvimento de novos produtos. Um caso particular é o ruído gerado por válvulas de compressores herméticos de refrigeração, sendo o compressor a principal fonte de ruído em refrigeradores domésticos. O presente trabalho tem por objetivo iniciar o desenvolvimento de uma ferramenta confiável de simulação capaz de auxiliar engenheiros na predição de problemas de aeroacústica, especialmente um que possa no futuro ser utilizado para estudar o ruído gerado pelo escoamento em válvulas de compressores herméticos. Para isso, foi desenvolvido um código para simulação numérica direta de aeroacústica. Utilizou-se processamento paralelo com decomposição de domínio para usar Simulação Numérica Direta em um tempo factível; esquemas de discretização espaciais e temporais de alta ordem para minimizar ao máximo os fenômenos de dissipação e dispersão do escoamento e das ondas acústicas e uma série de tratamentos no domínio como filtragem e estiramento da malha como também condições de contorno características com o intuito de obter uma solução adequada para estudo de aeroacústica. Assim, são apresentadas todas as etapas desenvolvidas no equacionamento, implementação e verificação. A verificação foi realizada segundo um processo matemático formal (Método das Soluções Manufaturadas) com o qual obteve-se que a ordem de precisão dos cálculos era a mesma da ordem formal dos esquemas de discretização utilizados para todas as variáveis. Também obteve-se a mesma concordância para análise do divergente da velocidade, verificando o código para simulação numérica direta de aeroacústica. Posteriormente, foram realizadas simulações de escoamentos compressíveis cisalhantes e seus resultados comparados com dados apresentados em literatura. Também foram calculadas as taxas de amplificação de perturbações e comparadas com a Teoria de Estabilidade Linear. Novamente, foram obtidos resultados satisfatórios nessas etapas, mostrando que a implementação do código DNS está verificada. / Sound generated by flow, known as aeroacoustics, is becoming more important in several industrial areas from commercial aircraft to household appliances, affecting directly the requirements to the development of new products. A particular case is the noise generated by valves of refrigeration hermetic compressors, being the compressor the main noise source in household refrigerators. This work has the goal of initiate the development of a reliable tool able to help engineers to predict aeroacoustics problems, specially one that can be used in the future to study the noise generated by the flow in valves of hermetic compressors. To do so, it was developed a numerical code to perform direct numerical simulation of aeroacoustics. It was used parallel processing with domain decomposition to use Direct Numerical Simulation in a feasible time; high order temporal and spatial discretization schemes to minimize the most the dispersion and dissipation phenomena of the flow field and of the acoustics waves and a series of treatments in the domain as filtering and mesh stretching as well as characteristics boundary conditions aiming a proper solution to study aeroacoustics. Thus, here all the steps developed in the formulation, implementation and verification are presented . The verification was done according to a formal mathematical procedure (Method of Manufactured Solutions) with which was found that the precision order of the calculations was the same of the formal order of the used discretization schemes for all variables. The same agreement was also obtained to the analysis of the divergence of the velocity, verifying the code to direct numerical simulation of aeroacoustics. Posteriorly, it were simulated shear compressible flows and the results were compared to literature data. Also, it were calculated the amplification rates of the disturbances and compared to Linear Stability Theory. Once more, it was obtained satisfactory results in these steps, showing that the implementation of the DNS code is verified.

Ocean submesoscales are the subject of increasing focus in the oceanographic literature; with instrumentation now more capable of observing them in situ and numerical models now able to reach the resolution required to more fully capture them. Submesoscales are typified by horizontal spatial scales of O(1 − 10) km, vertical scales O(100) m and time-scales of O(1) day and are known to be associated with regions of high vertical velocity and vorticity. Occurring most commonly at density fronts at the ocean surface they can control mixed layer restratification and provide an important control on fluxes between the atmosphere and the deep ocean. This thesis sets out to better understand the fundamental physical processes underpinning submesoscale instabilities using a number of idealised process models. Linear stability analysis complemented by non-linear, high-resolution simulations will be used initially to explore the ways in which submesoscale instabilities in the mixed layer may compete and interact with one another. In particular, we will investigate the way in which symmetric and ageostrophic baroclinic instabilities interact when simultaneously present in a flow, with focus on the growth rates and energetic pathways of previously unexplored dynamic instabilities that arise in this paradigm; three-dimensional, mixed symmetric-baroclinic instabilities. Further, these non-linear simulations will allow us to investigate the transition to dissipative scales that can occur in the classical Eady model via a multitude of small-scale secondary instabilities that result from primary submesoscale instabilities. Finally, observational data, taken aboard the SMILES project cruise to the Southern Ocean, helps to motivate the consideration of a new dynamical paradigm; the Eady model with superimposed high amplitude barotropic jet. Non-linear simulations investigate the extent to which the addition of such a jet is capable of damping submesoscale growth. The causes of this damping are then investigated using linear analysis. With this approach eventually demonstrated as being unable to fully explain growth rate reductions, we introduce a new framework combining potential vorticity mixing by submesoscale instabilities with geostrophic adjustment, which relaxes the flow back to a geostrophic balanced state. This framework will help to explain, conceptually, how non-linear eddies control the linear stability of the flow.

O som gerado por escoamentos, também conhecido como aeroacústica, tem se tornado cada vez mais importante em áreas industriais diversas desde aviação comercial até aparelhos eletrodomésticos, afetando diretamente os requisitos necessários para o desenvolvimento de novos produtos. Um caso particular é o ruído gerado por válvulas de compressores herméticos de refrigeração, sendo o compressor a principal fonte de ruído em refrigeradores domésticos. O presente trabalho tem por objetivo iniciar o desenvolvimento de uma ferramenta confiável de simulação capaz de auxiliar engenheiros na predição de problemas de aeroacústica, especialmente um que possa no futuro ser utilizado para estudar o ruído gerado pelo escoamento em válvulas de compressores herméticos. Para isso, foi desenvolvido um código para simulação numérica direta de aeroacústica. Utilizou-se processamento paralelo com decomposição de domínio para usar Simulação Numérica Direta em um tempo factível; esquemas de discretização espaciais e temporais de alta ordem para minimizar ao máximo os fenômenos de dissipação e dispersão do escoamento e das ondas acústicas e uma série de tratamentos no domínio como filtragem e estiramento da malha como também condições de contorno características com o intuito de obter uma solução adequada para estudo de aeroacústica. Assim, são apresentadas todas as etapas desenvolvidas no equacionamento, implementação e verificação. A verificação foi realizada segundo um processo matemático formal (Método das Soluções Manufaturadas) com o qual obteve-se que a ordem de precisão dos cálculos era a mesma da ordem formal dos esquemas de discretização utilizados para todas as variáveis. Também obteve-se a mesma concordância para análise do divergente da velocidade, verificando o código para simulação numérica direta de aeroacústica. Posteriormente, foram realizadas simulações de escoamentos compressíveis cisalhantes e seus resultados comparados com dados apresentados em literatura. Também foram calculadas as taxas de amplificação de perturbações e comparadas com a Teoria de Estabilidade Linear. Novamente, foram obtidos resultados satisfatórios nessas etapas, mostrando que a implementação do código DNS está verificada. / Sound generated by flow, known as aeroacoustics, is becoming more important in several industrial areas from commercial aircraft to household appliances, affecting directly the requirements to the development of new products. A particular case is the noise generated by valves of refrigeration hermetic compressors, being the compressor the main noise source in household refrigerators. This work has the goal of initiate the development of a reliable tool able to help engineers to predict aeroacoustics problems, specially one that can be used in the future to study the noise generated by the flow in valves of hermetic compressors. To do so, it was developed a numerical code to perform direct numerical simulation of aeroacoustics. It was used parallel processing with domain decomposition to use Direct Numerical Simulation in a feasible time; high order temporal and spatial discretization schemes to minimize the most the dispersion and dissipation phenomena of the flow field and of the acoustics waves and a series of treatments in the domain as filtering and mesh stretching as well as characteristics boundary conditions aiming a proper solution to study aeroacoustics. Thus, here all the steps developed in the formulation, implementation and verification are presented . The verification was done according to a formal mathematical procedure (Method of Manufactured Solutions) with which was found that the precision order of the calculations was the same of the formal order of the used discretization schemes for all variables. The same agreement was also obtained to the analysis of the divergence of the velocity, verifying the code to direct numerical simulation of aeroacoustics. Posteriorly, it were simulated shear compressible flows and the results were compared to literature data. Also, it were calculated the amplification rates of the disturbances and compared to Linear Stability Theory. Once more, it was obtained satisfactory results in these steps, showing that the implementation of the DNS code is verified.

We consider both a long-wave model and a first-order weighted-residual integral boundary layer (WIBL) model in the investigation of thin film flow down a topographical incline whilst under the effects of a normal electric field. The liquid is assumed to be a perfect dielectric, although is trivially extended to the case of a perfect conductor. The perfect dielectric case with no topography includes a simple modified electric Weber number which incorporates the relative electrical permittivity constant into itself. Linear stability analysis is carried out for both models, and critical Reynolds numbers which depend on the electric Weber number and the capillary number are produced. Regions of stability, convective instability and absolute instability are then determined for both models in terms of our electric Weber number and Reynolds number parameters in the case of no topography. Time-dependent simulations are produced to corroborate the aforementioned regions and investigate the effect of normal electric field strength in addition to sinusoidal and rectangular topographical amplitude on our system for various domain sizes. For the time-dependent simulations we find strong agreement with the linear stability analysis, and the results suggest that the inclusion of a normal electric field may have some stabilising properties in the long-wave model which are absent in the case of a flat wall, for which the electric field is always linearly destabilising. This stabilising effect is not observed for the same parameters in the WIBL model with a sinusoidal wall, although a similar effect is noticed in the WIBL model with a rectangular wall. We also investigate the simultaneous effect of domain size, wall amplitude and electric field strength on the critical Reynolds numbers for both models, and find that increasing the electric field strength can make large-amplitude sinusoidal topography stabilising rather than destabilising for the long-wave model. Continuation curves of steady solutions and bifurcation diagrams are also produced, and comparisons between the two models are made for various parameter values, which show excellent agreement with the literature. Subharmonic branches and time-periodic solutions are additionally included, similarly showing very good agreement with the literature.

Convection set up in a fluid due to the presence of two components of differing diffusivities is known as double diffusive convection. Double diffusive convection is observed in nature, in oceans, in the formation of certain columnar rock structures and in stellar interiors. The major engineering applications of double diffusive convection are in the fields metallurgy and alloy solidification in casting processes. The two components may be any two substances which affect the density of the fluid, heat and salt being the pair found most commonly in nature. Depending upon the initial stratifications of the two components, double diffusive convection can be set up in either the diffusive mode or the finger mode. In this thesis, the linear stability of a double diffusive system prone to finger instability has been studied in the presence of temporally varying non-linear background profiles of temperature and salinity. The motivation for the present study is to bridge the gap between existing theories, which mainly concentrate on linear background profiles independent of time, on the one hand and experiments and numerical simulations, which have time dependent step-like non-linear background profiles, on the other. The general stability characteristics of a double diffusive system with step-like background profiles have been studied using the standard normal mode method. The background temperature and salinity profiles are assumed to follow the hyperbolic tangent function, since it has a step-like character. The sharpness of the step can be altered by changing a suitable parameter in the hyperbolic tangent function. It is found that changing the degree of non-linearity of the background profile of one of the components keeping the background profile of the other component linear affects the growth rate, Wave number and the form of the disturbances. In general, increasing the degree of nonlinearity of background salinity profile makes the system more unstable and results in a reduction in the vertical extent of the disturbances. On the other hand, increasing the degree of non-linearity of the background temperature profile with the salinity profile kept linear results in a reduction in the growth rate and increase in the wave number. The form of the disturbance may change due to enhanced modal competition between the gravest odd and even modes in this case. The method of normal modes inherently assumes that the background profiles of temperature and salinity are independent of time and hence, it cannot be used for studying the stability of systems with time varying background profiles. A pseudo-similarity method has been used to handle such background profiles. Initial steps of temperature and salinity diffuse according to the error function form, and hence, the case of error function background profiles has been studied in detail. Taking into account the time-dependence of background profiles has been shown to significantly change the wave number and the incipient flux ratio. The dependence of the critical wave number (kc) on the thermal Rayleigh number (RaT ) can be determined analytically and is found to change from kc ~ Ra T1/4 for linear background profiles to kc ~ Ra T1/3 for error function profiles. The region of instability in the Rp (density stability ratio) space is found to increase from 1 ≤ R ρ ≤ r−1 for linear background profiles to 1 ≤ Rρ < r−3/2 for error function background profiles, where T denotes the ratio of the diffusivity of the slower diffusing component to that of the faster diffusing one. A parametric study covering a wide range of parameter values has been carried out to determine the effect of the parameters density stability ratio (Rp), diffusivity ratio (ρ ) and Prandtl number (Pr) on the onset time, critical wavenumber and the incipient flux ratio. The wide range of governing parameters covered here is beyond the scope of experimental and numerical studies. Such a wide range can be covered by theoretical approaches alone. It has been shown that the time of onset of convection determines the thicknesses of the temperature and salinity boundary layers, which in turn determine the width of salt fingers. Finally, the theoretical predictions of salt finger widths have been shown to be in agreement with the results of two dimensional numerical simulations of thermohaline system.

New methodologies and concepts for developing compact and energy efficient automotive exhaust systems have been studied. This originates in the growing concern for global warming, to which road transportation is a major contributor. The focus has been on commercial vehicles—most often powered by diesel engines—for which the emission legislation has been dramatically increased over the last decade. The emissions of particulates and nitrogen oxides have been successfully reduced by the introduction of filters and catalytic converters, but the fuel consumption, which basically determines the emissions of carbon dioxides, has not been improved accordingly. The potential reduction of fuel consumption by optimising the exhaust after-treatment system (assuming fixed after-treatment components) of a typical heavy-duty commercial vehicle is ~4%, which would have a significant impact on both the environment and the overall economy of the vehicle. First, methodologies to efficiently model complex flow duct networks such as exhaust systems are investigated. The well-established linear multiport approach is extended to include flow-acoustic interaction effects. This introduces an effective way of quantifying amplification and attenuation of incident sound, and, perhaps more importantly, the possibility of predicting nonlinear phenomena such as self-sustained oscillations—whistling—using linear models. The methodology is demonstrated on T-junctions, which is a configuration well known to be prone to self-sustained oscillations for grazing flow past the side branch orifice. It is shown, and validated experimentally, that the existence and frequency of self-sustained oscillations can be predicted using linear theory. Further, the aeroacoustics of T-junctions are studied. A test rig for the full determination of the scattering matrix defining the linear three-port representing the T-junction is developed, allowing for any combination of grazing-bias flow. It is shown that the constructive flow-acoustic coupling not only varies with the flow configuration but also with the incidence of the acoustic disturbance. Configurations where flow from the side branch joins the grazing flow are still prone to whistling, while flow bleeding off from the main branch effectively cancels any constructive flow-acoustic coupling. Two silencer concepts are evaluated: first the classic Herschel-Quincke tube and second a novel modified flow reversal silencer. The Herschel-Quincke tube is capable of providing effective attenuation with very low pressure loss penalty. The attenuation conditions are derived and their sensitivity to mean flow explained. Two implementations have been modelled using the multiport methodology and then validated experimentally. The first configuration, where the nodal points are composed of T-junctions, proves to be an example where internal reflections in the system can provide sufficient feedback for self-sustained oscillation. Again, this is predicted accurately by the linear theory. The second implementation, with nodal points made from Y-junctions, was designed to allow for equal flow distribution between the two parallel ducts, thus allowing for the demonstration of the passive properties of the system. Experimental results presented for these two configurations correlate well with the derived theory. The second silencer concept studied consists of a flow reversal chamber that is converted to a resonator by acoustically short-circuiting the inlet and outlet ducts. The eigenfrequency of the resonator is easily shifted by varying the geometry of the short circuit, thus making the proposed concept ideal for implementation as a semi-active device. Again the concept is modelled using the multiport approach and validated experimentally. It is shown to provide significant attenuation over a wide frequency range with a very compact design, while adding little or no pressure loss to the system. / QC 20110208