Orientador: José Luiz Boldrini / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-16T04:16:02Z (GMT). No. of bitstreams: 1 Souza_FernandoPereirade_D.pdf: 1266767 bytes, checksum: b584f3645886881d382881c8b1ee2d7c (MD5) Previous issue date: 2010 / Resumo: Neste trabalho estudamos quatro modelos do tipo campo de fases para a evolução de processos de solidificação/liquefação de certos materiais, tanto puros quanto ligas binárias, com a possibilidade de movimentação da fase não-sólida. As equações que governam o comportamento de materiais puros incluem a equação para o campo de fases, uma equação para a temperatura e uma equação singular do tipo de Navier- Stokes com um termo do tipo Carman-Kozeni e também um termo do tipo Boussinesq. Para ligas binárias, uma equação extra para a concentração do soluto _e incluída. Para materiais puros, tanto no caso bidimensional quanto no caso tridimensional, provamos a existência de soluções globais no tempo; no caso tridimensional, consideramos um modelo com dissipação mais intensa (não linear) do que no caso bidimensional. Para ligas binárias, obtivemos apenas a existência de soluções locais no tempo. Tais soluções são obtidas da seguinte forma: primeiramente o problema _e penalizado e uma sequência de soluções aproximadas _e obtida usando o teorema do ponto fixo de Leray- Schauder; então, usando argumentos de compacidade, provamos que esta sequência tem um ponto limite, o qual _e uma solução do problema original em um sentido generalizado. / Abstract: In this work we study four phase field models for the evolution of a solidification/liquefaction process of certain pure material or certain binary alloys, with the possibility of motion of the melt phase. The governing equations for pure materials include a phase-field equation, a heat equation and a singular Navier-Stokes system with a term of Carman-Kozeni type and a Boussines type term. For binary alloys, an extra equation for solute concentration is included. For pure materials, both in the two and three-dimensional cases we prove the existence of global in time solutions; in the three-dimensional, we consider a model with stronger (nonlinear) dissipation than in the two-dimensional case. For alloys, both in the two-dimensional and three-dimensional case, we obtain just local in time solutions. These solutions are obtained as follows: firstly the problem is penalized and a sequence of approximate solutions is obtained by using the Leray-Schauder's fixed point theorem; then, by using compactness arguments, we prove that this sequence has a limit point which is a solution of the original problem in a generalized sense. / Doutorado / Equações Diferenciais Parciais / Doutor em Matemática

Orientador: Antonio Marsaioli Junior / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia de Alimentos / Made available in DSpace on 2018-08-04T03:44:11Z (GMT). No. of bitstreams: 1 Berteli_MicheleNenhemy_D.pdf: 3298845 bytes, checksum: ea9c6612c92dcdbe419e972f4ca5e13b (MD5) Previous issue date: 2005 / Doutorado / Doutor em Engenharia de Alimentos

[pt] Neste trabalho é feita uma análise teórica e numérica da evaporação não isotérmica de um líquido contido em um recipiente cilíndrico parcialmente cheio, com paredes adiabáticas. Postula-se que a evaporação acontece em presença de convecção natural impulsionada por diferenças de massa específica, associadas com gradientes de temperatura e composição da mistura. Esta consiste de um gás e o vapor do líquido. Embora a formulação seja geral, o presente trabalho focaliza a evaporação de água para o ar. Estudou-se três situações. Um caso isotérmico, variante do clássico problema de difusão de Stefan, um Caso em que a temperatura do líquido é maior do que a temperatura ambiente e um terceiro caso no qual a temperatura do líquido é menor do que a do ambiente. Duas diferentes condições de contorno foram usadas na abertura do recipiente de modo a explorar a sensibilidade do escoamento às condições no topo. A distância entre a superfície do líquido e o topo variou de duas a dez vezes o raio do recipiente. Duas diferenças de temperatura entre o líquido e o ambiente foram investigadas, 3 graus Celsius e - 2 graus Celsius. O ar ambiente foi considerado como sendo muito seco ou muito úmido. Encontrou-se que, quando a temperatura do líquido é maior do que a temperatura ambiente, a taxa de evaporação alcança valores até quatro vezes maiores do que para o caso isotérmico. Para o caso em que a temperatura do líquido é menor do que a temperatura ambiente, a taxa de evaporação decresce para valores até duas vezes menores do que para o caso isotérmico. / [en] This work reports a theoretical and numerical analysis of the non-isothermal evaporation of a liquid contained in a partially filled cylinder vessel, with adiabatic walls. It is assumed that the evaporation occurs in the presence of natural convection driven by differences in specific mass associated with gradient of temperature and mixture composition. The mixture consist of a gas and the vapor of the evaporating liquid. Although the formulation is general, the specific focus of the present work is on the evaporation of water into air. Three situations were studied. An isothermal case, which is a variant of the classical Stefan diffusion problem, a case where the liquid temperature is higher than the ambient temperature, and a third case in which the liquid temperature is lower than the ambient. Two different boundary conditions were used at the openning of the vessel in a way to explore the sensitivity of the flow to the conditions on the top. The distance between the liquid surface and the top of the vessel varied from two to ten times the vessel radius. Two temperature differences between the liquid and the ambient were investigated, 3 degrees Celsius and - 2 degrees Celsius. The environmental air was considered to be either very dry or very wet. It was found that, when the liquid temperature is higher than the ambient temperature, the rate of evaporation can reach values up to four times larges than that for the isothermal case. For the case where the liquid temperature. is lower than the ambient temperature, the rate of evaporation decreases to values down to half of theisothermal case.

Dans cette thèse, nous présentons une nouvelle approche pour la simulation numérique des phénomènes électroconvectifs et électro-therrno-convectifs. La principale difficulté réside dans la détermination du champ électrique et de la distribution de densité volurnique de charges électriques. Dans cette approche, des schémas de type TVD (Total Variation Dirninishing) et IDC (ImprovedDeferred Correction) sont utilisées dans la discrétisation des flux convectifs et diffusifs par la méthode des volumes finis. La première partie de cette thèse présente certains aspects numériques liés à l'implémentation de ces schémas. Une approche unifiée pour les schémas convectifs TVD de type borné à haute résolution est présentée et diverses fonctions limiteur sont comparées. Dans une deuxième partie, l'électro-convection entre deux plaques parallèles est simulée. La méthodologie a étéévaluée et validée par la détermination des Critères de stabilité linéaire et non linéaire. Les différents scenarii d'évolution du développement de cette instabilité électroconvective vers l'état chaotique ont été définis. L'effet du mécanisme de diffusion la densité volumique de charge sur la boucle d'hystérésis et sur la structure de l'écoulement est étudié. L'influence du rapport d'aspect de la cavité est analysé. Enfin dans une dernière partie, nous étudions l'électro-thermo-convection lorsque le fluide est soumis simultanément à une injection unipolaire et à un gradient thermique. L'augmentation des transferts de chaleur a été caractérisée. / In this thesis, a numerical approach is presented to simulate the electro- and electro-thermo convection in dielectric liquids. The total variation diminishing (TVD) scheme and improved deferred correction (IDC) scheme are used to compute the convective and diffusive respectively. The aim of TVD scheme is to avoid non-physical oscillations and to capture high gradient of charge density. Some fundarnental aspects related to TVD and LDC schemes are investigated firstly. A unified approach for TVD schemes is explained and various limiter functions are compared. The connection among three methods for diffusive flux computation has been revealed. The original IDC scheme is improved by the application of 2nd order gradient evaluation method.The electro-convection between two parallel plates is then simulated. The methodology was assessed by the determination of the linear and nonlinear stability criterion. By continuously increasing the driving parameter, the successive instabilities and route to chaotic state has been defined. The effects of the diffusion mechanism for the charge density and vertical walls on the hysteresis 100p and the structure are also investigated. The last part is to simuiate electro-thermo-convection when injection and thermal gradient are simultaneously applied. Our solver was verified with a stationary and an overstable stability problem.The case that both heating and injection are from a bottom electrode has been analyzed in details. The neutral stabiliïy curve was reproduced. The existence of nonlinear phenornenon and the structure are highlighted.

We present the first detailed 3D hydrodynamic implicit large eddy simulations of turbulent convection of carbon burning in massive stars. Simulations begin with radial profiles mapped from a carbon-burning shell within a 15M circle dot 1D stellar evolution model. We consider models with 128(3), 256(3), 512(3), and 1024(3) zones. The turbulent flow properties of these carbon-burning simulations are very similar to the oxygen-burning case. We performed a mean field analysis of the kinetic energy budgets within the Reynolds-averaged Navier-Stokes framework. For the upper convective boundary region, we find that the numerical dissipation is insensitive to resolution for linear mesh resolutions above 512 grid points. For the stiffer, more stratified lower boundary, our highest resolution model still shows signs of decreasing sub-grid dissipation suggesting it is not yet numerically converged. We find that the widths of the upper and lower boundaries are roughly 30 per cent and 10 per cent of the local pressure scaleheights, respectively. The shape of the boundaries is significantly different from those used in stellar evolution models. As in past oxygen-shell-burning simulations, we observe entrainment at both boundaries in our carbon-shell-burning simulations. In the large Peclet number regime found in the advanced phases, the entrainment rate is roughly inversely proportional to the bulk Richardson number, Ri(B) (alpha Ri(B)(-alpha) a, 0.5 less than or similar to alpha less than or similar to 1.0). We thus suggest the use of Ri(B) as a means to take into account the results of 3D hydrodynamics simulations in new 1D prescriptions of convective boundary mixing.

No description available.

[pt] O presente trabalho apresenta o método de varredura de valores iniciais para a solução de problemas não-similares de camada limite, aplicado a uma cunha em convecção mista. É feita uma análise dos efeitos da força de empuxo nas características de transferência de calor e atrito, na superfície da cunha submetida a um escoamento laminar em convecção forçada. Os casos analisados referem-se a temperatura uniforme na superfície e a fluxo de calor uniforme através da superfície. Apresentam-se resultados numéricos para a placa vertical e a cunha em 120 graus celsius (problema similar), os quais foram comparados com os disponíveis na literatura, apresentando-se excelente concordância. Ainda são apresentados resultados para a cunha em 90 graus celsius e em 180 graus Celsius. Os resultados foram obtidos para o número de Prandtl 0,7 em uma larga faixa do parâmetro de não-similaridade (0 a 100 para temperatura uniforme e 0 a 5 para fluxo de calor uniforme). Em geral, verifica-se que para ambos os casos estudados de condições da superfície, o coeficiente de atrito local e o número de Nusselt local aumentam com o aumento da força de empuxo para o escoamento ajudado e diminuem com o aumento da força de empuxo para o escoamento ajudado e diminuem com o aumento da força de empuxo para o escoamento oposto. Verifica-se também que os efeitos de convecção natural diminuem com o aumento do ângulo da cunha. Compara-se, por fim os resultados de transferência de calor entre os dois casos estudados. O método possibilita a obtenção de resultados com o uso de um microcomputador PC AT-286 com o co-processador matemático, sem o uso de dupla precisão. As tolerâncias utilizadas para a convergência são as mesmas dos resultados disponíveis na literatura. Adicionalmente, o tempo computacional necessário para a obtenção das soluções foi bastante reduzido. Para toda a faixa de variação do parâmetro de não-similaridade, o equacionamento utilizado foi o mesmo, baseado em parâmetros de correlação para convecção forçada em uma superfície plana com injeção de massa, com ótima concordância com resultados disponíveis na literatura. / [en] The present work introduces a method for searching initial values, to solve non-similar Boundary Layer problems. The new method has been applied to the problem of mixed convection on a Wedge. An analysis is performed to study the effects of buoyancy force on the heat transfer and friction characteristics of laminar forced convection flow which is either maintained at a uniform temperature or subjected to a uniform temperature or subjected to a uniform heat flux. Numerical results are presented for Prandtl number of 7,0 over a wide range of values of the buoyancy force parameters (0 to 100 for uniform temperature and 0 to 5 for uniform heat flux). The results for the vertical plate and for the similar wedge (120 graus celsius) Have been compared with solutions availabein the literature, showing an excellent agreement. In addition, solutions for the 90 degree celsius wedge and for the flat wall (180 degree celsius are also obtained. In general, it is found that for both surface heating conditions, the local friction factor and the local Nusselt number increase with increasing bouyancy force for assisting flow and decrease with inscreasing bouyancy force for opposing flow. Further, the effects of the buoyancy force on these two quantities are found to diminish as the angle of the wedge increases. A comparison is also made of the results beteween the case of uniform wall temperature and the case of uniform surface heat flux. The method turns possible to obtain results with the use of a microcomputer PC AT-286 with a Math co-processor, discarding the use of double precision. The tolerances for convergence are the same as the results available in the literature. The necessary computacional time to get the solution was greatly reduced. For the entire range of the buoyancy force parameter, the governing equations are the same, based upon forced convection parameters. To illustrate the flexibility of the method, the surface mass trasnfer problem of uniform injection (blowing) in a flat plate under forced cnvection, has been solved and the results compared with the available ones in the literature.

This thesis details the ACTIVE campaign in the tropics of northern Australia during 2005-2006 (based in Darwin). The focus of the campaign was to find the influence of tropical convection on the aerosol and chemical content of the Tropical Tropopause Layer [TTL] and the cirrus cloud cover in the area, which is important for the global energy budget. This study details the background climatology of the Darwin region with statistical categorisation of the trace gases and particles. The TTL had regions of extremely high aerosol number concentration, much higher than that of the PBL. The 10 to 1000 nm particle concentrations were as high as 25,000 cm-3 and 100 to 1000 nm were as high as 1000 cm-3. High aerosol concentrations were usually found in cloud-free conditions; cloudy regions were typically low in aerosol number. Wind data and trajectories (BADC) were used to find the origin of the high particle concentrations. Aerosols were found to be nucleating in outflow regions of convective anvils. SO2 oxidation to H2SO4 is a widely accepted mechanism for nucleation. A binary mechanism (H2O-H2SO4), with SO2 as the precursor, was found to be inadequate in explaining the nucleation and growth rates -- tested using an aerosol sectional model. However, it was found, via back trajectory analysis, that the climatology of Darwin was influenced by local and long-range sources, including advection from Indonesia and the Tropical Warm Pool. These distant sources could have introduced condensable matter, with aerosol precursor properties (certain organic compounds). The aerosol model found a condensable precursor concentration of at least 300 pptv was necessary to replicate the observations.

When a gas undergoes an exothermic reaction in a closed vessel, spatial temperature gradients can develop. If these gradients become sufficiently large, the resulting buoyancy forces will move the gas, i.e. there is natural convection. The nature of the resulting flow is determined by the Rayleigh number, Ra = (β g ΔT L^3) / (κ ν). The evolution of such a system will depend on the interactions of natural convection, diffusion of both heat and chemical species, and chemical reaction. This study is concerned with a gas-phase system undergoing Sal'nikov's reaction: P → A → B, in the presence of natural convection. This kinetic scheme is used as a simplified representation of a cool flame, which is a feature of the low temperature combustion of a hydrocarbon vapour. Sal'nikov's reaction is one of the simplest to display thermokinetic oscillations, such as those seen in cool flames. The behaviour of Sal'nikov's reaction in the presence of natural convection was investigated using a combination of analytical and numerical techniques. First, a numerical model was developed to compute the temperature, velocity and concentrations when a simple exothermic reaction occurs in a spherical batch reactor, the results of which could be compared with previous experimental measurements. Subsequently, a scaling analysis of Sal'nikov's reaction proceeding in a spherical reactor was performed. This yielded significant insight into the general behaviour of this and similar systems. The forms of the analytical scales were confirmed through comparison with the results from numerical simulations. These scales were used to predict how the system responds to changes in certain key process variables, such as the pressure and the size of the reactor. It was shown that the behaviour of this system is governed by the ratios of the characteristic timescales for diffusion, reaction and natural convection. These ratios were used to define a regime diagram describing the system. The behaviour in different parts of this regime diagram was characterised and regions in which oscillations occur were identified.

La fenêtre pariéto-dynamique est un système « passif » de récupération de chaleur. Son principe de fonctionnement consiste à faire circuler l’air neuf de ventilation entre les lames de verre avant son introduction dans le volume habitable. Une partie de la chaleur traversant les vitrages est alors récupérée par l’écoulement d’air. La fenêtre Paziaud® est une fenêtre pariéto-dynamique particulière, composée de trois vitrages séparés par des lames d’air ventilées qui forment un conduit en U. Alors que la mise en place d’un système de ventilation double flux est complexe dans un contexte de réhabilitation, ce type de fenêtre présente une alternative intéressante moyennant un surcoût d’environ 20% par rapport à une fenêtre double vitrage classique mais permettant une récupération de chaleur non négligeable.Afin de caractériser les performances de la fenêtre Paziaud®, des études numériques et expérimentales ont été entreprises et ont confirmé le potentiel du dispositif. Par ailleurs, la prise en compte de ce genre de système dans les codes de simulation thermique des bâtiments n’est pas satisfaisante. Pour répondre à ce besoin, ont été développés plusieurs modèles simplifiés basés sur un bilan thermique représentable par analogie électrique. Une attention particulière a été portée sur le traitement des échanges convectifs dans les lames d’air. Les résultats ont permis de valider un modèle simplifié, qui pourra être utilisé par la suite dans un code de thermique de l’habitat. / The ventilated window is a passive system of heat recovery. It draws fresh air circulating between window’s glasses from the outside to the inside. A part of the heat which crosses the glasses is then recovered by the air flow. The Paziaud® window is composed of three glasses separated by ventilated air spaces in U-shape. While the implementation of a double-flow ventilation system for the housing retrofitting is complex, this Paziaud® window costs only 20% more than a conventional double-glazed window but improves significantly the heat recovery.In order to study the performance of the Paziaud® window, numerical and experimental works have been undertaken and have confirmed the potentiality of such windows. However, a thermal code able to take into account the heat exchange is not available for such system. Considering this lack of simulations, several simplified models based on electrical analogy have been developed. Particular attention is paid to the convective exchange process in the ventilated air spaces. The numerical results could validate a simplified thermal model which can be integrated to the building codes.