The dynamical equations of the non-hydrostatic mesoscale model GESIMA are solved numerically on an Arakawa-C grid. Because of the staggered grid most of the prognostic variables and their derivatives have identical local positions. The functional connection between the fluxes and velocities defined at different places is managed by the MacCormack scheme ignoring the local diff erences. The systematic errors are diminished by means of alternate down- and upwind shifting of the fluxes after each time step. A cycle of 8 time steps is necessary to achieve approximately symmetrical conditions because of the shift permutations. Nevertheless, the systematic errors are not completely removed and the iterative calculation of the dynamic pressure is retarded by starting values from eight time steps ago (same permutation of shift directions). Both shortcomings are avoided by a symmetrized MacCormack scheme without the loss of its advantages of handling strong gradients. The new method is based on the symmetrization of the equations with respect to the passive quantities and on the simultaneous calculation of each equation for opposite shift directions of the active variables followed by averaging both increments. The method is tested for a typical example. / Die dynamischen Modellgleichungen des nicht-hydrostatischen mesoskaligen Atmosphärenmodells GESIMA sind numerisch auf einem Arakawa-C-Gitter gelöst. Durch die versetzte Anordnung der Größen auf dem Gitter besitzen die Differenzenquotienten (auf den rechten Seiten) und die prognostizierten Größen (auf den linken Seiten) von vornherein die gleiche lokale Position, allerdings nicht in jedem Fall. Das bisher in GESIMA praktizierte MacCormack-Schema stellt den Zusammenhang zwischen den an verschiedenen Gitterstellen definierten Flüssen und Geschwindigkeiten her, indem die Ortsdifferenz zwischen Fluß- und zugehöriger Geschwindigkeitskomponente ignoriert wird. Zur Verringerung der systematischen Fehler erfolgt die direkte Zuordnung einer Flußkomponente abwechselnd (sequentiell) in einem Zeitschritt zur flußabwärts benachbarten Geschwindigkeitskomponente und im nächsten Zeitschritt zur flußaufwärts benachbarten. Nach Ablauf von jeweils 8 Zeitschritten sind die notwendigen Zuordnungspermutationen der 3 Vektorkomponenten zwecks einer annähernden Symmetrisierung des Verfahrens erreicht. Nachteile des bisherigen Verfahrens sind (a) der nicht vollständige Abbau der jedem Zeitschritt immanenten systematischen Zuordnungsfehler und (b) ein stark erhöhter Rechenaufwand für die iterative Bestimmung des dynamischen Druckes durch einen um 8 Zeitschritte (jeweils gleiche Zuordnungspermutation) zurückliegenden Startwert. Beide Nachteile werden durch ein neues, symmetrisiertes MacCormack-Schema vermieden, ohne daß auf die Vorteile bei der Handhabung starker Gradienten verzichtet werden muß. Das Verfahren beruht (a) auf der Symmetrisierung der lokalen Zuordnung für die passiven Größen innerhalb einer Gleichung (d.h. der nicht durch sie prognostizierten Größen) und (b) auf der simultanen Durchführung der zwei entgegengesetzten Zuordnungsrichtungen für jede der 3 Geschwindigkeitskomponenten innerhalb eines Zeitschrittes mit anschließender Mittelung der beiden Inkremente. Das neue Verfahren wurde anhand eines Beispiels geprüft.

Zwei numerische Verfahren, das Upstream- und das MacCormack-Verfahren, werden im Hinblick auf ihre Eigenschaften bei der Lösung unterschiedlicher Advektionsprobleme verglichen. Das Letzere, welches eine Genauigkeit zweiter Ordnung liefert, wird in den Impulsadvektionsteil des numerischen Strömungsmodells MISKAM implementiert und anhand von Sensitivitätsstudien mit dem Upstream-Verfahren verglichen. Anschließend findet eine Modellevaluierung mit Hilfe von Datensätzen, welche am Hamburger Grenzschichtwindkanal erzeugt wurden, statt. Das Verfahren zeigt bei stabiler thermischer Modellschichtung signifikant veränderte Ergebnisse, deutlich zeigt sich die verringerte numerische Diffusion, vor allem im Bereich von Ecken und Kanten eines Hindernisses. / Two numerical schemes are compared concerning their numerical abilities when solving different advection problems. MacCormack\'s scheme which is of second order accuracy is implemented in the numerical flow model MISKAM in order to calculate the advection of momentum. It is compared to the upstream scheme with the help of sensitivity studies and with a model evaluation using wind tunnel data from the University of Hamburg. The scheme shows for stable thermical stratification significant differences near the edges of obstacles that result mainly from the reduced numerical diffusion which was the major problem when using the upstream scheme.

The dynamical equations of the non-hydrostatic mesoscale model GESIMA are solved numerically on an Arakawa-C grid. Because of the staggered grid most of the prognostic variables and their derivatives have identical local positions. The functional connection between the fluxes and velocities defined at different places is managed by the MacCormack scheme ignoring the local diff erences. The systematic errors are diminished by means of alternate down- and upwind shifting of the fluxes after each time step. A cycle of 8 time steps is necessary to achieve approximately symmetrical conditions because of the shift permutations. Nevertheless, the systematic errors are not completely removed and the iterative calculation of the dynamic pressure is retarded by starting values from eight time steps ago (same permutation of shift directions). Both shortcomings are avoided by a symmetrized MacCormack scheme without the loss of its advantages of handling strong gradients. The new method is based on the symmetrization of the equations with respect to the passive quantities and on the simultaneous calculation of each equation for opposite shift directions of the active variables followed by averaging both increments. The method is tested for a typical example. / Die dynamischen Modellgleichungen des nicht-hydrostatischen mesoskaligen Atmosphärenmodells GESIMA sind numerisch auf einem Arakawa-C-Gitter gelöst. Durch die versetzte Anordnung der Größen auf dem Gitter besitzen die Differenzenquotienten (auf den rechten Seiten) und die prognostizierten Größen (auf den linken Seiten) von vornherein die gleiche lokale Position, allerdings nicht in jedem Fall. Das bisher in GESIMA praktizierte MacCormack-Schema stellt den Zusammenhang zwischen den an verschiedenen Gitterstellen definierten Flüssen und Geschwindigkeiten her, indem die Ortsdifferenz zwischen Fluß- und zugehöriger Geschwindigkeitskomponente ignoriert wird. Zur Verringerung der systematischen Fehler erfolgt die direkte Zuordnung einer Flußkomponente abwechselnd (sequentiell) in einem Zeitschritt zur flußabwärts benachbarten Geschwindigkeitskomponente und im nächsten Zeitschritt zur flußaufwärts benachbarten. Nach Ablauf von jeweils 8 Zeitschritten sind die notwendigen Zuordnungspermutationen der 3 Vektorkomponenten zwecks einer annähernden Symmetrisierung des Verfahrens erreicht. Nachteile des bisherigen Verfahrens sind (a) der nicht vollständige Abbau der jedem Zeitschritt immanenten systematischen Zuordnungsfehler und (b) ein stark erhöhter Rechenaufwand für die iterative Bestimmung des dynamischen Druckes durch einen um 8 Zeitschritte (jeweils gleiche Zuordnungspermutation) zurückliegenden Startwert. Beide Nachteile werden durch ein neues, symmetrisiertes MacCormack-Schema vermieden, ohne daß auf die Vorteile bei der Handhabung starker Gradienten verzichtet werden muß. Das Verfahren beruht (a) auf der Symmetrisierung der lokalen Zuordnung für die passiven Größen innerhalb einer Gleichung (d.h. der nicht durch sie prognostizierten Größen) und (b) auf der simultanen Durchführung der zwei entgegengesetzten Zuordnungsrichtungen für jede der 3 Geschwindigkeitskomponenten innerhalb eines Zeitschrittes mit anschließender Mittelung der beiden Inkremente. Das neue Verfahren wurde anhand eines Beispiels geprüft.

Zwei numerische Verfahren, das Upstream- und das MacCormack-Verfahren, werden im Hinblick auf ihre Eigenschaften bei der Lösung unterschiedlicher Advektionsprobleme verglichen. Das Letzere, welches eine Genauigkeit zweiter Ordnung liefert, wird in den Impulsadvektionsteil des numerischen Strömungsmodells MISKAM implementiert und anhand von Sensitivitätsstudien mit dem Upstream-Verfahren verglichen. Anschließend findet eine Modellevaluierung mit Hilfe von Datensätzen, welche am Hamburger Grenzschichtwindkanal erzeugt wurden, statt. Das Verfahren zeigt bei stabiler thermischer Modellschichtung signifikant veränderte Ergebnisse, deutlich zeigt sich die verringerte numerische Diffusion, vor allem im Bereich von Ecken und Kanten eines Hindernisses. / Two numerical schemes are compared concerning their numerical abilities when solving different advection problems. MacCormack\''s scheme which is of second order accuracy is implemented in the numerical flow model MISKAM in order to calculate the advection of momentum. It is compared to the upstream scheme with the help of sensitivity studies and with a model evaluation using wind tunnel data from the University of Hamburg. The scheme shows for stable thermical stratification significant differences near the edges of obstacles that result mainly from the reduced numerical diffusion which was the major problem when using the upstream scheme.

Made available in DSpace on 2016-06-02T20:00:13Z (GMT). No. of bitstreams: 1 DissHCS.pdf: 4511102 bytes, checksum: 84bb283da6e13fbfe8cb44f55ab48ca7 (MD5) Previous issue date: 2004-12-16 / Nowadays, the quest for solutions to urban problems that affect population quality of life cannot ignore the concepts of inundation and flood in urban areas, which are frequently seen in a number of cities within the country and, whenever reaching crowded areas, bring considerable damage that is, on its turn, irreparable due to the loss of human lives. The proposed methodology was reached with the objective of providing a computational tool to outline areas with higher or lower risk of flood for planning a draining system and urban use. The hydrodynamic propagation model has been developed by using the MacCormack explicit scheme, making it possible to be applied to urban channels. In the case of inundations, corresponding plates and sections are recorded for further generating the inundation preliminary map with the aid of a topographic software. Tests focused on hydrodynamic propagation in a real channel, stream of the Retiro Saudoso, in the city of Ribeirão Preto, state of São Paulo, having a map representing a estimative flooding area. The final outcome of this work might be used as part of a decision-making support system for authorities to estimate and to map flood along a channel. / A busca de soluções para os problemas urbanos que afetam a qualidade de vida das populações não pode prescindir, atualmente, dos conceitos de inundações e enchentes em áreas urbanas, que são freqüentes em várias cidades do país, que quando atingem áreas densamente ocupadas, provocam prejuízos consideráveis, os quais em muitos casos são irreparáveis através da perda de vidas humanas. Com o objetivo de fornecer uma ferramenta computacional para delimitar áreas de maior ou menor risco de ocorrência de enchentes, para uso urbano e planejamento do sistema de drenagem chegou-se a metodologia proposta. Desenvolveuse o modelo de propagação hidrodinâmica utilizando o esquema explicito MacCormack, possibilitando sua aplicação a canais urbanos. Na ocorrência de inundações as lâminas e as seções correspondentes são registradas para posteriormente, gerar-se o mapa preliminar de inundação com o auxílio de um software topográfico. Os testes tiveram como ênfase a propagação hidrodinamica em um canal real, córrego do Retiro Saudoso, na cidade de Ribeirão Preto SP, tendo como produto um mapa representando uma área estimada de inundação. O resultado final deste trabalho pode ser utilizado como parte de um sistema de apoio de decisões para as autoridades no que se refere à inundação, uma vez que o programa pode ser aplicado para estimar e mapear a inundação ao longo de um canal.

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Este trabalho estuda o fenômeno de evaporação rápida em jatos de líquidos superaquecidos ou metaestáveis numa região 2D. O fenômeno se inicia, neste caso, quando um jato na fase líquida a alta temperatura e pressão, emerge de um diminuto bocal projetando-se numa câmara de baixa pressão, inferior à pressão de saturação. Durante a evolução do processo, ao cruzar-se a curva de saturação, se observa que o fluido ainda permanece no estado de líquido superaquecido. Então, subitamente o líquido superaquecido muda de fase por meio de uma onda de evaporação oblíqua. Esta mudança de fase transforma o líquido superaquecido numa mistura bifásica com alta velocidade distribuída em várias direções e que se expande com velocidades supersônicas cada vez maiores, até atingir a pressão a jusante, e atravessando antes uma onda de choque. As equações que governam o fenômeno são as equações de conservação da massa, conservação da quantidade de movimento, e conservação da energia, incluindo uma equação de estado precisa. Devido ao fenômeno em estudo estar em regime permanente, um método de diferenças finitas com modelo estacionário e esquema de MacCormack é aplicado. Tendo em vista que este modelo não captura a onda de choque diretamente, um segundo modelo de falso transiente com o esquema de \"shock-capturing\": \"Dispersion-Controlled Dissipative\" (DCD) é desenvolvido e aplicado até atingir o regime permanente. Resultados numéricos com o código ShoWPhasT-2D v2 e testes experimentais foram comparados e os resultados numéricos com código DCD-2D v1 foram analisados. / This study analyses the rapid evaporation of superheated or metastable liquid jets in a two-dimensional region. The phenomenon is triggered, in this case, when a jet in its liquid phase at high temperature and pressure, emerges from a small aperture nozzle and expands into a low pressure chamber, below saturation pressure. During the evolution of the process, after crossing the saturation curve, one observes that the fluid remains in a superheated liquid state. Then, suddenly the superheated liquid changes phase by means of an oblique evaporation wave. This phase change transforms the liquid into a biphasic mixture at high velocity pointing toward different directions, with increasing supersonic velocity as an expansion process takes place to the chamber back pressure, after going through a compression shock wave. The equations which govern this phenomenon are: the equations of conservation of mass, momentum and energy and an equation of state. Due to its steady state process, the numerical simulation is by means of a finite difference method using the McCormack method of Discretization. As this method does not capture shock waves, a second finite difference method is used to reach this task, the method uses the transient equations version of the conservation laws, applying the Dispersion-Controlled Dissipative (DCD) scheme. Numerical results using the code ShoWPhasT-2D v2 and experimental data have been compared, and the numerical results from the DCD-2D v1 have been analysed.

Ce travail de thèse concerne l’étude des écoulements de fluides gazeux compressibles laminaires subsonique-supersonique dans une tuyère de type convergent-divergent. Les écoulements étudiés sont à nombres de Reynolds modérés et s’affranchissent de l’hypothèse de condition adiabatique de paroi couramment utilisée afin de mieux prendre en compte les phénomènes de transfert de chaleur par convection et rayonnement avec le milieu extérieur. Cette étude des phénomènes de transferts conjugués a permis de déterminer le comportement dynamique simultané du fluide et de la paroi de la tuyère. Enfin, compte tenu des niveaux élevés de températures mis en jeu dans ces systèmes, une analyse concernant le comportement thermomécanique de l’ensemble de la structure de paroi avec des matériaux monocouches et multicouches a été réalisé. De nombreuses configurations géométriques, propriétés physiques et conditions aux limites sur le fluide et la paroi ont été analysées. Les résultats présentés montrent, la structure des écoulements à travers les iso-contours de vitesses, des nombres de Mach, des pressions dans le fluide, des températures dans le fluide et dans la paroi ainsi que les déformations et les contraintes de la paroi qui résultent des couplages thermomécaniques. Une analyse des performances de la tuyère, en termes de force de poussée et de coefficient de débit spécifique, est largement discutée dans ce travail. / This work concerns the study of flows of compressible gaseous laminar subsonic-supersonic nozzle in a convergent-divergent type. The flows are studied to moderate Reynolds numbers and free themselves from the assumption of adiabatic wall conditions commonly used to better take into account the phenomena of heat transfer by convection and radiation with the external environment. This study combined transfer phenomena was determined simultaneously the dynamic behavior of the fluid and the wall of the nozzle. Finally, given high levels of temperatures at stake in these systems, an analysis of the thermomechanical behavior of the entire wall structure with monolayer and multilayer materials was performed. Many geometric configurations, physical properties and boundary conditions on the fluid and the wall were analyzed. The results presented show the structure of the flow through the iso-contours of speed, Mach numbers, pressures in the fluid, temperatures in the fluid and in the wall as well as the deformations and stresses resulting from the wall thermomechanical couplings. A performance analysis of the nozzle, in terms of thrust coefficient and specific yield, is widely discussed in this work.

Este trabalho estuda o fenômeno de evaporação rápida em jatos de líquidos superaquecidos ou metaestáveis numa região 2D. O fenômeno se inicia, neste caso, quando um jato na fase líquida a alta temperatura e pressão, emerge de um diminuto bocal projetando-se numa câmara de baixa pressão, inferior à pressão de saturação. Durante a evolução do processo, ao cruzar-se a curva de saturação, se observa que o fluido ainda permanece no estado de líquido superaquecido. Então, subitamente o líquido superaquecido muda de fase por meio de uma onda de evaporação oblíqua. Esta mudança de fase transforma o líquido superaquecido numa mistura bifásica com alta velocidade distribuída em várias direções e que se expande com velocidades supersônicas cada vez maiores, até atingir a pressão a jusante, e atravessando antes uma onda de choque. As equações que governam o fenômeno são as equações de conservação da massa, conservação da quantidade de movimento, e conservação da energia, incluindo uma equação de estado precisa. Devido ao fenômeno em estudo estar em regime permanente, um método de diferenças finitas com modelo estacionário e esquema de MacCormack é aplicado. Tendo em vista que este modelo não captura a onda de choque diretamente, um segundo modelo de falso transiente com o esquema de \"shock-capturing\": \"Dispersion-Controlled Dissipative\" (DCD) é desenvolvido e aplicado até atingir o regime permanente. Resultados numéricos com o código ShoWPhasT-2D v2 e testes experimentais foram comparados e os resultados numéricos com código DCD-2D v1 foram analisados. / This study analyses the rapid evaporation of superheated or metastable liquid jets in a two-dimensional region. The phenomenon is triggered, in this case, when a jet in its liquid phase at high temperature and pressure, emerges from a small aperture nozzle and expands into a low pressure chamber, below saturation pressure. During the evolution of the process, after crossing the saturation curve, one observes that the fluid remains in a superheated liquid state. Then, suddenly the superheated liquid changes phase by means of an oblique evaporation wave. This phase change transforms the liquid into a biphasic mixture at high velocity pointing toward different directions, with increasing supersonic velocity as an expansion process takes place to the chamber back pressure, after going through a compression shock wave. The equations which govern this phenomenon are: the equations of conservation of mass, momentum and energy and an equation of state. Due to its steady state process, the numerical simulation is by means of a finite difference method using the McCormack method of Discretization. As this method does not capture shock waves, a second finite difference method is used to reach this task, the method uses the transient equations version of the conservation laws, applying the Dispersion-Controlled Dissipative (DCD) scheme. Numerical results using the code ShoWPhasT-2D v2 and experimental data have been compared, and the numerical results from the DCD-2D v1 have been analysed.

Ce travail de thèse concerne l'étude des écoulements de fluides gazeux compressibles laminaires subsonique-supersonique dans une tuyère de type convergent-divergent. Les écoulements étudiés sont à nombres de Reynolds modérés et s'affranchissent de l'hypothèse de condition adiabatique de paroi couramment utilisée afin de mieux prendre en compte les phénomènes de transfert de chaleur par convection et rayonnement avec le milieu extérieur. Cette étude des phénomènes de transferts conjugués a permis de déterminer le comportement dynamique simultané du fluide et de la paroi de la tuyère. Enfin, compte tenu des niveaux élevés de températures mis en jeu dans ces systèmes, une analyse concernant le comportement thermomécanique de l'ensemble de la structure de paroi avec des matériaux monocouches et multicouches a été réalisé. De nombreuses configurations géométriques, propriétés physiques et conditions aux limites sur le fluide et la paroi ont été analysées. Les résultats présentés montrent, la structure des écoulements à travers les iso-contours de vitesses, des nombres de Mach, des pressions dans le fluide, des températures dans le fluide et dans la paroi ainsi que les déformations et les contraintes de la paroi qui résultent des couplages thermomécaniques. Une analyse des performances de la tuyère, en termes de force de poussée et de coefficient de débit spécifique, est largement discutée dans ce travail.