Neste trabalho, relatam-se soluções analíticas para as equações da cinética da teoria de difusão de nêutrons. Para a solução das equações da cinética pontual consideram-se seis grupos de precursores de nêutrons atrasados e assume-se reatividade variável como uma função arbitrária do tempo. A ideia principal consiste inicialmente na determinação da solução das equações da cinética pontual com reatividade constante apenas usando os resultados bem conhecidos para a solução de sistemas de equações diferenciais matriciais lineares de primeira ordem com entradas constantes. Com a aplicação do método de Decomposição, é possível transformar as equações da cinética pontual com reatividade variável com o tempo em um conjunto de problemas recursivos semelhantes às equações da cinética pontual com reatividade constante, o que pode ser resolvido diretamente com a técnica mencionada anteriormente. Para ilustração, apresentam-se simulações para as funções com reatividade constante, linear e senoidal, bem como comparações com resultados na literatura. Já com relação às equações da cinética espacial, consideram-se um e seis grupos de precursores de nêutrons atrasados, modelo multigrupo de energia, meio homogêneo e dimensões espaciais bi e tridimensionais. O formalismo do procedimento da solução é geral em relação ao número de grupos de energia, famílias de precursores de nêutrons atrasados e regiões com diferentes composições químicas. O fluxo rápido e térmico e as concentrações de nêutrons atrasados são expandidos em uma série de termos de autofunções que, pela aplicação da técnica da GITT, resulta em uma equação diferencial matricial de primeira ordem semelhante às equações de cinética pontual. Por esse motivo, a solução deste problema transformado segue o formalismo do método da Decomposição aplicado às equações da cinética pontual. Por fim, apresentam-se simulações numéricas e comparações com resultados disponíveis na literatura. / In this work we report analytical solutions for the neutron kinetics diffusion equations. For the solution of the point kinetics equations we consider six groups of delayed neutron precursors and assume that the reactivity is an arbitrary function of time. The main idea initially consists in the determination of the solution of the point kinetics equations with constant reactivity by just using the well-known results of the solution of systems of first-order linear ordinary differential equations in matrix form with constant matrix entries. Applying the decomposition method, we are able to transform the point kinetics equations with time dependent reactivity into a set of recursive problems similar to the point kinetics equations with constant reactivity, which can be directly solved by the above mentioned technique. For illustration, we also report simulations for constant, linear and sinusoidal reactivity time functions of time as well as comparisons with results published in the literature. As for the space kinetics equations we consider six groups of delayed neutron precursors, energy multigroup model, homogeneous media and two and three-dimensional geometries. The solution procedure formalism is general with respect to the number of energy groups, neutron precursor families and regions with different chemical compositions. The fast and thermal flux and the delayed neutron precursors concentrations are expanded in a series in terms of eigenfunctions that, upon insertion into the kinetics equation and upon taking moments, result in a first order linear differential matrix equation with source terms similar to the point kinetics equations. The solution of this transformed problem follows the formalism of the decomposition method applied to the point kinetics equations. We present numerical simulations and comparisons with available results in the literature.

Polímeros sintéticos ocupam uma posição de grande importância no estilo de vida moderno, servindo como matérias-primas para a construção de uma variedade de utensílios. Apesar do grande número de operações de processamento e produtos disponíveis, o planejamento de produtos e a otimização dos processos de produção raramente constituem-se de tarefas triviais. Isso deve-se ao fato da maioria das operações aplicadas na indústria de processamento de polímeros envolverem geometrias e padrões de escoamento complexos, além da dificuldade intrínseca relacionada ao comportamento reológico complexo de polímeros fundidos ou soluções poliméricas. Devido a estes fatores, o desenvolvimento de técnicas de dinâmica de fluido computacional (computational fluid dynamics – CFD) para a simulação de escoamentos de fluidos poliméricos e etapas de operações de processamento tem sido assunto de numerosos estudos durante as últimas décadas. Sob esta perspectiva, o solver viscoelasticFluidFoam, merece destaque. Ele é capaz de resolver simulações de escoamentos de fluidos viscoelásticos utilizando diferentes equações constitutivas. Contudo, apesar de resultados existentes na literatura apresentarem um bom potencial de aplicação, uma análise extensiva de seu desempenho numérico ainda não foi realizada. Neste contexto, a proposta do presente trabalho é a análise da influência de parâmetros de malha, numéricos e constitutivos no comportamento do solver. As bases para os testes compreendem uma geometria simples – escoamento laminar entre duas placas paralelas – o modelo constitutivo de Oldroyd-B e respectivas soluções analíticas para os campos de velocidade e tensão. Mesmo os testes demonstrando a inegável versatilidade do solver, eles revelam limitações em lidar com algumas configurações de malha e parâmetros constitutivos, principalmente com relação ao refinamento na direção perpendicular ao escoamento, diminuição do número de Reynolds e aumento do número de Weisenberg. Estas limitações podem ser parcialmente contornadas com escolha adequada de parâmetros de relaxação das variáveis e da razão de aspecto dos volumes de controle. Tais dificuldades não estão presentes em simulações de escoamentos de fluidos newtonianos em condições semelhantes, sugerindo que trabalhos futuros devem focar em implementações mais robustas do solver viscoelasticFluidFoam. / Synthetic polymers hold a position of great importance in modern lifestyle, serving as raw materials for the construction of a wide variety of appliances. Despite the large number of processing operations and products available, product planning and optimization of production processes rarely constitute a trivial task. This is due to the fact of operations applied in polymer processing industry involve complex geometries and flow patterns, plus the intrinsic difficulty related to the molten polymers or polymer solutions complex rheological behavior. Because of these factors, the development of techniques of computational fluid dynamics (CFD) for the simulation of flows of polymeric fluids and stages of processing operations has been the subject of numerous studies during the last decades. From this perspective, the viscoelasticFluidFoam solver deserves mention. The solver is capable of resolving simulations of viscoelastic fluid flows using different constitutive equations. However, despite the existing results in the literature present a great potential for application, an extensive analysis of their numerical performance has not been performed yet. The purpose of this paper is to examine the influence of mesh, numerical and constitutive parameters in the behavior of the solver. Bases for the tests comprise a simple geometry – laminar flow between two parallel plates – the constitutive model of Oldroyd-B and its analytical solutions for the velocity and stress fields. Although the tests show the undeniable versatility of the solver, they also reveal limitations in dealing with some mesh settings and constitutive parameters, particularly with respect to refinement in the direction perpendicular to the flow, decreasing in the Reynolds number and increasing in the Weisenberg number. This limitation can be partially circumvented with proper choice of variables relaxation parameters and aspect ratio of the control volumes. Such difficulties are not present in simulations of Newtonian fluids flows under similar conditions, suggesting that future works should focus on more robust implementations of the viscoelasticFluidFoam solver.

付記する学位プログラム名: 京都大学卓越大学院プログラム「先端光・電子デバイス創成学」 / 京都大学 / 新制・課程博士 / 博士(工学) / 甲第23205号 / 工博第4849号 / 新制||工||1757(附属図書館) / 京都大学大学院工学研究科電気工学専攻 / (主査)教授 小林 哲生, 教授 松尾 哲司, 特定教授 中村 武恒 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

Im Folgenden wird die analytische Lösung der eindimensionalen, instationären Wärmeleitungsgleichung mit einer Randbedingung 3. Art gegeben. Die Außentemperatur wird dabei als harmonische Schwingung angenommen. Abhängig von den materialspezifischen Eigenschaften des Bauteils (Wärmeleitfähigkeit, Rohdichte, spezifische Wärmekapazität) kommt es zur Dämpfung und zeitlichen Verschiebung der Temperaturwelle im Bauteil. Die analytische Lösung liefert den raum- und zeitaufgelösten Temperaturverlauf innerhalb des Bauteils. Die analytische Lösung ist primär für die Kalibrierung und Validierung numerischer Approximationsverfahren relevant. Die zeitliche Verfügbarkeit von thermischer Speichermasse ist für die thermische Gebäude- und Raumsimulation von besonderer Wichtigkeit. Daher muss ein numerisches Berechnungsverfahren diese Prozesse gut abbilden können. Die hier gezeigte analytische Lösung kann daher zur Bewertung der Güte der gewählten numerischen Approximation verwendet werden. Zu diesem Zweck werden Ergebnisse beispielhaft für zwei getrennte Konstruktionen angegeben.

The influence of operation parameters on the drying of spherical porous particles containing a mixture of solvents evaporating into nitrogen in a continuously worked vibrated fluid-bed dryer was studied. A simulation based on the analytical solution to heat and mass transfer equations was applied and modifications were suggested.   Four different ternary liquid mixtures were selected: Acetone-Chloroform-Methanol (ACM), Ethanol- 2-propanol-Water (EIpW), Water-Ethanol-Ethyl Acetate (WEEa) and Ethanol-Methylethylketone- Toluene (EMekT). For the solid, physical properties of Pyrex was used.   Comparison of composition- and temperature- profiles indicated that there is no resistance against heat transfer within the solid and that the heat transfer is much faster than mass transfer.   Selectivity diagrams were drawn. The results indicated that selectivity is an important parameter in predicting the drying behavior.   The retention ratio was studied as performance parameter. Its variation was studied in response to changes in operation parameters, including gas velocity and temperature, as well as solid temperature and particle size.   A  modification  to  the  model  was  examined  by  assuming  a  liquid-content-dependent  diffusion resistance factor. It was observed that implementing such an assumption yields decreased values for retention ratios.   The  effect  of  vibration  on  heat  and  mass  transfer  coefficients  was  included  using  a  correlation suggested by Sbrodov and the resulting effect on retention ratio was examined. / Inverkan   av   driftparameter  på  torkning  av   sfäriska  porösa  partiklar  som   innehåller lösningsmedelblandningar som avdunstar i kväve i en kontinuerligt viberande fluidbädd-tork studerades.  En  simuleringsmodell  baserad  på  den  analytiska  lösningen  till  värme-  och materieöverföringsekvationerna användes och ändringar föreslogs.   Fyra  olika  tärnar  vätskeblandningar  valdes:  aceton-kloroform-metanol(ACM),  etanol-2- propanolvatten,(EIpW),     vatten-etanol-etylacetat     (WEEa)     och     etanol-metyletylketon- toluen(EMekT). För den fasta fasen användes fysikaliska egenskaper liknande Pyrex.   Sammansättnings-  och  temperatur-profiler  visade  att  det  inte  finns  något  motstånd  mot värmeöverföring  i  den  fasta  fasen  och  att  värmeöverföringen  sker  mycket  snabbare  än materieöverförningen.   Selektivitetsdiagram ritades. Resultaten indikerar att selektivititen är en viktig parmeter för att förutsäga beteendet vid torkning.   Retentionsförhållandet  användes  som  ett  prestandamått.  Dess  variation  med  avseende  på förändringar av  driftsparmetrar,  bland  annat  gasen  hastighet  och  temperatur  samt  den  fasta  fasens temperatur och partikelstorlek, studerades.   En modifiering av modellen undersöktes genom att införa en vätskehalts-beroende faktor för diffusionsmotståndet. Detta minskade värdena på retentionsförhållandena.   Vibrationens inverkan på värme- och materieöverföring infördes genom att använda Sbrodov samband, och den resulterande effekten på retentionsförhållandet observerades.

<p>Most of the attention to the seismic performance of tunnels has been devoted to shear waves propagating in a direction perpendicular to the tunnel axis, with motion perpendicular to the tunnel axis, causing the so-called “ovaling or racking response”. Body waves, however, can travel through the ground and intersect the tunnel at different angles, thus inducing a complex seismic response that requires a comprehensive understanding of all modes of deformation. This study provides analytical solutions to capture the behavior of the liner and the surrounding ground, for a deep circular tunnel subjected to body waves, for all five possible modes of deformation: (i) axial compression-extension; (ii) transverse compression-extension; (iii) ovaling; (iv) axial shear; and (v) axial bending or snaking. The main assumptions used to derive the analytical solutions include: (i) the tunnel is deep and very long and has a circular cross section; (ii) the ground and the support are homogeneous and isotropic, and their response remains elastic; (iii) the interface between the ground and the liner is either no-slip or full-slip; (iv) the pseudo-static approach, i.e. inertia forces can be neglected, is acceptable to estimate seismic deformations; (v) for the transverse compression-extension and ovaling deformation modes, plane strain conditions in the direction of the tunnel axis apply at any cross section; and (vi) for the axial compression-extension and axial bending deformation modes, the wavelength of the seismic motions is much larger than the tunnel radius. Two and three-dimensional numerical simulations with the finite element codes ABAQUS, for static drained/undrained loading and dynamic drained loading conditions, and MIDAS GTS NX, for dynamic undrained loading conditions, are carried out to validate the analytical solutions and further investigate the seismic response of the tunnel. All the comparison results show good agreement between the analytical and numerical solutions.</p> <p>Dynamic amplification effects on the tunnel cross section are studied for the axial compression-extension, transverse compression-extension, and axial bending deformation modes, through a set of dynamic time-history models where the input frequency of the far-field seismic motion is changed. The results reveal the limits of the analytical solutions, in the form of minimum wavelength-to-tunnel diameter (/D) ratios such that the errors are less than twenty percent, including: (i) 25 (drained) and 20 (undrained) for axial compression-extension; (ii) 25 (drained) and 12.5 (undrained) for transverse compression- extension; and (iii) 7.5 (unsupported tunnel), 7.5 (supported tunnel with no-slip interface), and 12.5 (supported tunnel with full-slip interface) for axial bending or snaking. These ratios are also the limits of applicability of quasi-static (instead of dynamic) numerical simulations to estimate the seismic behavior of the liner and the surrounding ground.</p>

Rock masses may present remarked geostatic stress anisotropy and anisotropic material properties; thus, the tunnel alignment with the geostatic principal stress directions and with the axes of material anisotropy is unlikely. Nevertheless, tunnel design often neglects those misalignments and; yet, the misalignment effects were unknown. In this doctoral research, tunnels under complex anisotropic conditions were modelled analytically and numerically with 3D nonlinear Finite Element Method (FEM). When the tunnel misaligns with the geostatic principal stress directions, anti-symmetric axial displacements and shear stresses are induced around the tunnel. Analytical solutions for misaligned shallow and deep tunnels in isotropic elastic ground are provided. The analytical solutions were validated with 3D FEM analyses. Near the face, the anti-symmetric axial displacements are partially constrained by the tunnel face, producing asymmetric radial displacements and stresses. The asymmetric radial displacements at the face can be divided into a rigid body displacement of the tunnel cross-section and anti-symmetric radial displacements. Those asymmetries may affect the rock-support interaction and the plastic zone developed around the tunnel. In anisotropic rock masses, the tunnel misalignment with the axes of material anisotropy also produces anti-symmetric axial displacements and stresses around the tunnel. It occurs because when the tunnel is not aligned with the principal material directions, the in-plane stresses are coupled with the axial displacements (i.e. the compliance matrix is fully populated). Thus, tunnels in anisotropic rock mass not aligned with the geostatic principal stresses and with the axes of material anisotropy are substantially more complex than tunnels not aligned with the principal stress directions in isotropic rock mass. An analytical solution for misaligned tunnels in anisotropic rock mass is provided. It was observed that the relative orientation of the geostatic principal stresses with respect to the axes of material anisotropy plays an important role. The axial displacements produced by far-field axial shear stresses and by the rock mass anisotropy may compensate each other; thus, axial and radial displacements around the tunnel are reduced. On the other hand, those anti-symmetric axial displacements may be amplified; thus, the ground deformations are increased. Asymmetric radial and axial deformations, and asymmetric spalling of the tunnel walls are commonly observed on tunnels in anisotropic rock masses. The tunnel misalignment with the geostatic principal stress directions and with the axes of material anisotropy could be associated with those phenomena that, so far, are not well comprehended

No description available.

The present work seeks to fully investigate, describe and characterize the distinct flow regimes existing within a mixing vessel at various rotational speeds. This investigation is computational in nature and simulates the flow within a baffled tank containing a Rushton turbine of the standard configuration. For a Re based on impeller diameter and blade rotational speed (Re â ¡ Ï ND2/μ) the following flow regimes were identified and investigated in detail: Reverse/reciprocating flows at very low Re (<10); stalled flows at low Re (â 10); laminar pumping flow for higher Re and transitional pumping flow (10 squared < Re <10 to the 4th). For the three Re numbers 1, 10 and 28, it was found that for the higher Re number (28), the flow exhibited the familiar outward pumping action associated with radial impellers under turbulent flow conditions. However, as the Re number decreases, the net radial flow during one impeller revolution was reduced and for the lowest Re number a reciprocating motion with negligible net pumping was observed. In order to elucidate the physical mechanism responsible for the observed flow pattern at low Re, the forces acting on a fluid element in the radial direction were analyzed. Based on this analysis, a simplified quasi-analytic model of the flow was developed that gives a satisfactory qualitative, as well as quantitative representation of the flow at very low Re. Investigation of the transitional flow regime (Re â 3000) includes a compilation and characterization of ensemble and turbulent quantities such as the Reynolds stress components, dissipation length η and time scales Ï , as well a detailed investigation of the near-impeller flow and trailing vortex. Calculation and compilation of all terms in the turbulent kinetic energy transport equation was performed (including generation and the illusive turbulent pressure work). Specifically, the most important transport mechanism was turbulent convection/diffusion from the impeller disk-plane/trailing vortex region. Mean flow transport of turbulent kinetic energy was primarily towards the impeller disk-plane and radially outward from the trailing vortex region. The turbulent pressure work was found to partially counteract turbulent convection. Turbulent dissipation followed by turbulent viscous work were found to be the least important mechanism responsible for turbulent transport with both terms being maximized within the vortex region and at the disk-plane down-stream from the vortices. / Ph. D.

The analytical solution of a given inhomogeneous boundary value problem of a linear, elliptic, inhomogeneous partial differential equation and a set of inhomogeneous mixed Dirichlet- and Neumann-type boundary conditions is derived in the present paper. In the context of elasticity theory, the problem arises for a non-conservative symmetric ansatz and an extended constitutive law shown earlier. For convenient user application, the scalar function expressed in cylindrical coordinates is primarily obtained for the general case before being expatiated on a special case of linear boundary conditions.