In this study laminar forced film condensation of vapor flowing in cross-flow direction through the annular space between two concentric cylinders was investigated numerically. To achieve this, governing equations of the vapor and the condensate flow in cross-flow direction between two concentric cylinders were developed. After obtaining the equations in integral forms by using the finite difference technique the vapor boundary layer thicknesses on the inner and outer cylinders and the condensate layer thickness was obtained as a function of the angular position on the cylinders. It was assumed that the condensation took place on the outer surface of the inner cylinder only and the outer cylinder was assumed to be insulated. The computer program developed is capable to calculate the condensate film thickness, vapor boundary layer thickness, the heat flux and the heat transfer coefficient and the interface velocity between the condensate and the vapor layer as a function of the angular position on the cylinders. Effects of changing the free stream velocity flowing in the channel, the radius of the inner cylinder, the temperature difference between the saturated vapor and the wall and the annular space between the concentric cylinders were investigated numerically by using the computer program and the results were presented graphically. Results showed that by increasing the free stream velocity of the vapor in the core, the film thickness decreased and by increasing the radius of the inner cylinder, the temperature difference between the saturated vapor and the wall and the annular space, the film thickness increased.

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FAPEMIG - Fundação de Amparo a Pesquisa do Estado de Minas Gerais / Atualmente nas indústrias é notória a presença de problemas envolvendo a dinâmica dos fluidos com transferência de energia térmica. Neste contexto, problemas onde a transferência de energia térmica ocorre sobre cilindros aquecidos merece um destaque especial. No presente trabalho objetivou-se desenvolver uma análise numérica tridimensional sobre o problema de transferência de energia térmica por convecção natural em cilindros concêntricos na presença de pares discretos de fonte-sumidouro de energia térmica, com ênfase no estudo do regime estável-instável do escoamento (fluido de trabalho ar). O código numérico foi desenvolvido em coordenadas cilíndricas, discretizado utilizando a técnica dos volumes finitos e esquemas temporais e espaciais de segunda ordem, onde o acoplamento pressão velocidade é feito através do método do passo fracionado. Através dos campos de velocidades, de temperatura e de vorticidade obtidos, verificou-se como a transferência de energia térmica é afetada pelas primeiras instabilidades no regime instável. Foi possível também, evidenciar a desestabilização do escoamento estudado, não sendo necessário para tal o uso de uma malha fina. Além disso, os dados obtidos apresentaram uma excelente concordância com os resultados experimentais da literatura, sobretudo no regime estável. / In the current industry, is notorious the presence of problems involving fluid dynamics with heat transfer. In this context, problems where the heat transfer occurs over heated cylinders deserves a special attention. The present work study aimed to develop a three-dimensional numerical analysis of the heat transfer by natural convection in concentric cylinders in the presence of discrete heat source-sink pairs, with emphasis on the study of stable-unstable regime flow (air working fluid). The numerical code was developed in cylindrical coordinates, discretized using the finite volume technique and temporal/ spatial schemes of second order, where the pressure-velocity coupling is done through the fractional step method. Through velocity, temperature and vorticity fields, it was found that the heat transfer is affected by the first instabilities in the unstable regime. It was also possible to verify the destabilization of the flow with a thin mesh. Moreover, the data obtained showed an excellent agreement with the experimental data found in the literature, especially in the stable regime. / Dissertação (Mestrado)

[pt] A superposição de um escoamento circular de Couette e um fluxo com gradiente de pressão axial, através de um espaço anular ocorre em muitas aplicações práticas, tais como: reatores químicos catalíticos, filtros, extratores líquido- líquido, mancais e o fluxo de retorno de lamas de perfuração entre a coluna de perfuração rotatória e a formação rochosa na perfuração de poços produtores de petróleo e gás. As linhas de corrente curvadas do fluxo circular de Couette podem causar uma instabilidade centrífuga que produz vórtices toroidais, conhecidos como vórtices de Taylor. A presença destes vórtices muda as características hidrodinâmicas e a transferência de calor no processo. Em conseqüência, é muito importante ser capaz de prever o aparecimento da instabilidade. A maioria das análises numéricas e experimentais disponíveis na literatura são para fluidos Newtonianos e viscoelásticos (soluções polimericas). Neste trabalho, o efeito das propriedades viscoplásticas de suspensões de altas concentrações neste tipo de escoamento e nas condições críticas para o aparecimento de vórtices são determinadas teoricamente através da solução das equações de conservação. As equações diferenciais foram integradas pelo método de elementos finitos-Galerkin e o sistema de equações algébricas não lineares resultante foi resolvido pelo método de Newton. / [en] The superposition of a circular Couette flow and a pressure- driven axial flow in an annulus occurs in many practical applications, such as catalytic chemical reactors, filtration devices, liquid-liquid extractors, journal bearings, and the return flow of drilling mud between the rotating drill string and the stationary wall in oil and gas well drilling. The curved streamlines of the circular Couette flow can cause a centrifugal instability leading to toroidal vortices, well known as Taylor vortices. The presence of these vortices changes the hydrodynamic and heat transfer characteristics of the process. Therefore, it is very important to be able to predict the onset of instability. Most of the available theoretical and experimental analyses are for Newtonian and viscoelastic (polymeric solutions) liquids. In this work, the effect of the viscoplastic properties of high concentration suspensions on the onset of the Taylor vortices are determined theoretically by solving the conservation equations and searching the critical conditions. The differential equations were solved by the Galerkin / finite element method and the resulting set of non-linear algebraic equations, by Newtons method.

L'objectif principal visé par cette thèse est de modéliser les poutres gonflables en textiles techniques orthotropes. Les approches statiques font l'objet de ce rapport. Avant d'aborder ce problème, nous avons été amenés à identifier tous les paramètres qui ont un effet direct sur les propriétés mécaniques effectives de ces composites. Ainsi, nous avons développé un modèle micro mécanique de prédiction de ces propriétés mécaniques. Le modèle proposé est basé sur l’analyse d'un volume élémentaire représentatif (VER) prenant en compte non seulement les propriétés mécaniques et la. fraction de volume de chaque phase dans le VER mais également leur géométrie et leur architecture. Chaque fil dans le VER a été modélisé comme un matériau isotrope transverse (contenant les fibres et la résine). La méthode dite d’assemblage de cylindres a été utilisée pour l’homogénéisation au niveau des fils. Une deuxième homogénéisation est ensuite réalisée. Elle prend en compte la fraction de volume de chaque constituant (fils de chaîne, fils de trame et résine non prise en compte dans les fils). Le modèle a été validé par des résultats expérimentaux existant dans la littérature. Une élude paramétrique a été menée afin d'étudier les effets des divers paramètres géométriques et mécaniques sur ces propriétés mécaniques. Dans l'analyse structurale, un modèle poutre gonflable 3D de Timoshenko en tissu orthotrope a été proposé. Il prend en compte les non-linéarités géométriques et l'effet de la force suiveuse générée par la pression de gonflage. Les équations d'équilibre non-linéaires dérivent du principe des travaux virtuels en configuration lagrangienne totale. Dans une première approche, une linéarisation a été faite autour de la configuration de référence précontrainte pour obtenir les équations adaptées aux problèmes linéaires. A titre d'exemple, le problème de flexion plane a été abordé. Quatre cas de conditions aux limites ont été traités et les résultats obtenus améliorent les modèles existants dans le cas de tissu isotrope. Les charges de plissage ont été également proposées dans chaque cas traité. Dans une deuxième approche, les équations non-linéaires ont été discrétisées par la méthode des éléments finis. Deux types de solutions ont été alors proposées : les solutions aux problèmes éléments finis linéaires obtenues par une linéarisation des équations discrétisées autour de la configuration de référence précontrainte et les solutions aux problèmes éléments finis non-linéaires réalisées en adoptant une méthode Quasi-Newton sous sa forme incrémentale. A titre d’exemple, la flexion d’une poutre encastrée-libre a été étudiée et les résultats améliorent les modèles théoriques. Le modèle éléments finis non-linéaire a été comparé favorablement à un modèle éléments finis coque mince 3D. Une étude paramétrique a été ensuite effectuée. Elle a porté sur l'influence des propriétés mécaniques et sur de la pression de gonflage sur la réponse de la poutre. Les solutions éléments finis linéaires se sont avérées proches des résultats théoriques linéarisés d'une part et les résultats du modèle éléments finis non-linéaire se sont avérés proches des résultats du modèle linéaire dans le cas des propriétés mécaniques élevées alors que le modèle éléments finis non-linéaire est indispensable pour modéliser ces poutres lorsque les propriétés mécaniques du tissu sont faibles / The main objective of this thesis was to model inflatable beams made frorn orthotropic woven fabric composites. The static aspects were investigated in this report. Before planning to develop these models, it was necessary to know all the parameters which have a direct effect on the effective mechanical properties these composites. Thus, a micro­ mechanical model was performed for predicting the effective mechanical properties. The proposed model was based on the analysis of the representative volume element (RVE). The model took into account not only the mechanical properties and volume fraction of each components in the RVE but also their geometry and architecture. Each yarn in the RVE was modelled as a transversely isotropic material (containing fibres and resin) using the concentric cylinders model (CCIVI). A second volumetric averaging which took into account the volume fraction of each constituent (warp yarn, weft yarn and resin), was performed. The model was validated favorably against experimental available data. A parametric study was conducted in order to investigate the effects of various geometrical and mechanical parameters on the elastic properties of these composites. ln the structural analysis, a 3D Timoshenko airbeam with a homogeneous orthotropic woven fabric (OWF) was addressed. The model took into account the geometrical nonlinearities and the inflation pressure follower force effect. The analytical equilibrium equations were performed using the total Lagrangian form of the virtual work principle. As these equations were nonlinear, in a first approach, a linearization was performed at the prestressed reference configuration to obtain the equations devoted to linearized problems. As example, the bending problem was investigated. Four cases of boundary conditions were treated and the deflections and rotations results improved the existing models in the case of isotropic fabric. The wrinkling load in every case was also proposed. In a second approach, the nonlinear equilibrium equations of the 3DTimoshenko airbeam were discretized by the finite element method. Two finite element solutions were then investigated : finite element solutions for linearized problems which were obtained by the means of the linearization around the prestressed reference configuration of the nonlinear equations and nonlinear finite element solutions which were performed by the use of an optimization algorithm based on the Qua.si-Newton method. As an example, the bending problem of a cantilever inflated beam under concentrated load was considered and the deflection results improve the theoretical models. As these beams are made from fabric, the beam models were validated through their comparison with a 3D thin-shell finite element model. The influence of the material effective properties and the inflation pressure on the beam response was also investigated through a parametric study. The finite element solutions for linearized problems were found to be close to the theoretical linearized results. On the other hand, the results for the nonlinear finite element model were shown to be close to the results for the linearized finite element model in the case of high mechanical properties and the non linear finite element model was used to improve the linearized model when the mechanical properties of the fabric are low