The initial stage of liquid phase sintering, involving liquid penetration, agglomerate separation, particle spreading and growth has been investigated in experiments using tungsten heavy alloys. The particle composites used were produced by hot isostatic pressing (HIP) of pure powder mixtures of W-Ni-Fe-(Co). By using different HIP temperatures, volume fractions of tungsten, alloying elements like Cobalt and Sulphur or excluding Iron from the matrix, liquid penetration, agglomerate separation and particle growth conditions were affected. The investigations were performed mainly under microgravity (sounding rockets or parabolic trajectories by airplanes) but at high tungsten particle fractions, short sintering times or at infiltration of solid pure tungsten, they were performed at normal gravity. The liquid penetration of the tungsten agglomerates is explained by initial wetting under non-equilibrium conditions, due to the reaction between the liquid matrix and the particles, and a decrease of interfacial energy. The dissolving of tungsten gives a pressure drop in the penetrating liquid and a driving force for the liquid movement by a suggested parabolic penetration model. For cold worked tungsten, a penetration theory was proposed, where an internal stress release in the penetrated tungsten grains creates space for the advancing liquid. The spreading of the tungsten agglomerates is explained by an interagglomerate melt swelling due to a Kirkendall effect. The liquid matrix undergoes a volume increase since the diffusion rates of Ni-Fe are higher than for W and initial concentration gradients of W and Ni, Fe exists. The suggested model by Kirkendall are also used for an analysis of the interaction behaviour between solid particles and a solidification front and inclusion behaviour in iron base alloys during teeming and deoxidation. The average tungsten particles size decrease initially since part of the tungsten particles is dissolved when the non-equilibrium matrix phase is melting. When equilibrium is reached, the tungsten particles grow in accordance with the Ostwald ripening process by an approximately 1/3 power law. Larger particle fraction of particles showed a higher growth rate, due to shorter diffusion distances between the particles. Cobalt, Sulphur and absence of iron in the matrix were found to increase the growth rate of the tungsten particles due to a higher surface tension between the solid tungsten particles and the matrix melt. / QC 20100528

Deposition of dispersed phase from flowing dispersions onto a substrate surface is of utmost relevance for various industrial processes like fouling of sparingly soluble salts, such as CaCO3 and CaSO4 in heat exchangers and desalination evaporators which tend to form deposits on flow surfaces of tubes or pipelines conveying hard water and in water filtration and purification processes since concentration of CaCO3 in many natural water resources is equal to or greater than the saturation level. The study of deposition is also of intrinsic interest for biophysics and colloid science where vascular calcification i.e. precipitation and deposition of calcium phosphates (hydroxyapatites) in the muscular layer of the blood reduces arterial compliance and promotes congestive heart failure. Experiments were conducted on straight, circular cross section silica tubing of inner di-ameter (ranging from 0.88 mm to3.40 mm) to study the effect of electrostatic interaction and hydrodynamics on the deposition behavior of CaCO3 on silica surface when streams of aqueous solutions of Ca(NO3)2 and Na2CO3 with a concentration of 40.0 g l−1 and 25.9gl−1 respectively flowing at a volumetric flow rate of 1 l h−1 each is mixed to form CaCO3 dispersion which was then transported through silica tubing at a steady volumetric flow rate of 2lh−1. The in situ phenomenology of CaCO3 particles transport, deposition, and evolution of spatial and temporal patterns of the CaCO3 deposition on the silica surface along with the dendritic growth of CaCO3 during the flow was visually documented with the aid of a 100X optical microscope. The study discussed the deposition behavior of dispersed phase of CaCO3 from its aqueous dispersion on the silica tubing during flow and attributed charge inversion from negative to positive of silica surface, due to the adsorption of Na+ formed during precipitation reaction of CaCO3, as a plausible reason for the reversal of electrostatic interaction from attraction between initially negatively charged silica surface and positively charged CaCO3 particles which promoted deposition and subsequent evolution of patterns of CaCO3 deposition on the silica surface during the early stage of experiments to repulsion between finally net positively charged silica surface and positively charged CaCO3 particles which resulted in retarded deposition and subsequent emergence of sparsely adhered CaCO3 agglomerates as localized, limited patches of CaCO3 deposits on the silica surface during the later stage of the experiments

Nesta tese é analisada a dinâmica de uma partícula relativística se movendo sob a influência de um campo magnético uniforme e uma onda eletrostática e estacionária dada na forma de pulsos periódicos. O mapa que descreve a evolução temporal do sistema é explícito e pode ser considerado como uma versão relativística e magnetizada do mapa padrão clássico. A posição aproximada dos pontos periódicos é calculada analiticamente e com essa informação é possível estudar as ressonâncias primárias. Para o sistema em estudo, observa-se que a maior parte das ressonâncias possui mais de uma cadeia de ilhas. Isso ocorre pois o sistema apresenta um número infinito de termos ressonantes com o mesmo número de rotação e que podem gerar ilhas na mesma posição do espaço de fases. Verifica-se que essa superposição de termos ressonantes faz com que o número de cadeias varie em função dos parâmetros da onda. Para valores de período ou número de onda suficientemente elevados, todas as ressonâncias primárias apresentam duas ou mais cadeias de ilhas no espaço de fases. As ilhas de ressonância primária são utilizadas nesta tese para acelerar partículas de forma regular. Em particular, considera-se a ressonância principal do sistema, para a qual a energia inicial da partícula pode estar muito próxima de sua energia de repouso se os parâmetros da onda forem adequados. Além disso, aplica-se um método de controle do caos para Hamiltonianas quase integráveis que consiste na adição de um termo de controle simples e com baixa amplitude ao sistema. Esse termo de controle cria toros invariantes em todo o espaço de fases que confinam as trajetórias caóticas em pequenas regiões, tornando a dinâmica controlada mais regular. Verifica-se numericamente que o termo de controle reduz drasticamente as regiões caóticas. Além disso, observa-se que o controle do caos e a consequente recuperação de trajetórias periódicas e quase periódicas no espaço de fases podem ser utilizados para melhorar o processo de aceleração regular de partículas. / In this thesis, we analyze the dynamics of a relativistic particle moving under the influence of a uniform magnetic field and a stationary electrostatic wave given as a series of periodic pulses. The map that describes the time evolution of the system is explicit, and it can be considered as a magnetized relativistic version of the classical standard map. We calculate analytically the approximate position of the periodic points and we use this information to study the primary resonances. For the system under study, we observe that most of its resonances exhibit more than one island chain. It occurs because the system presents an infinite number of resonant terms with the same winding number that may generate islands in the same position of phase space. We verify that this superposition of resonant terms makes the number of chains vary as a function of the parameters of the wave. For sufficiently large values of the wave period or wave number, all the primary resonances present two or more island chains in phase space. We use the islands of primary resonances in this thesis to regularly accelerate particles. In particular, we consider the main resonance of the system, for which the initial energy of the particle can be very close to its rest energy if the parameters of the wave are adequate. Furthermore, we apply a method of control of chaos for near-integrable Hamiltonians that consists in the addition of a simple control term with low amplitude to the system. This control term creates invariant tori in the whole phase space that confine the chaotic trajectories to small regions, making the controlled dynamics more regular. We verify numerically that the control term drastically reduces the chaotic regions. Moreover, we observe that the control of chaos and the consequent recovery of periodic and quasiperiodic trajectories in phase space can be used to improve the process of regular particle acceleration.

Orientador: Milton Mori / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica / Made available in DSpace on 2018-08-14T18:54:23Z (GMT). No. of bitstreams: 1 Bastos_JaciCarloSchrammCamara_D.pdf: 4353350 bytes, checksum: 0de3633c8edcc4ae2ec7fc57a3b590d0 (MD5) Previous issue date: 2009 / Resumo: Apresenta-se nesta pesquisa uma análise experimental e numérica do comportamento da fase dispersa em um jato circular bifásico confinado e uma comparação com jato circular bifásico livre. Nas análises experimentais, uma câmara pentagonal em acrílico foi utilizada como sistema de confinamento para a obtenção de perfis axiais e radiais de velocidade média, flutuação de velocidade (RMS) e intensidade de turbulência. Estes dados foram analisados a fim de desenvolver uma análise completa da região desenvolvida do jato. Três diferentes jatos foram utilizados para a alimentação da fase gás no topo da câmara, mas apenas o jato central foi carregado com partículas entre 60 e 90µm de diâmetro. Os outros dois foram utilizados para proporcionar uma maior interação entre as fases no interior da câmara. A técnica óptica Phase Doppler Anemometry (PDA), foi empregada na medição da velocidade instantânea da fase sólida e do diâmetro das partículas nas diferentes posições axiais a partir do bico do jato. Nove casos de estudo distintos são investigados individualmente e, em seguida, comparados entre si. Estes casos fornecem informações importantes sobre o comportamento e o efeito do confinamento dos jatos sobre o transporte macrocóspico e turbulento das partículas entre o centro e as regiões de contorno do jato. As análises numéricas tratam da modelagem matemática tridimensional, turbulenta e transiente do escoamento no jato bifásico confinado. O modelo trata as fases gás e sólida a partir de uma abordagem Euleriana. O fechamento das equações de transporte foi realizado utilizando o modelo de turbulência de duas equações k-e para a fase gás e modelos de turbulência de zero-equação para a fase sólida, e ainda em alguns casos esta última apenas sofreu efeitos turbulentos advindos da fase contínua. A acurácia das previsões do modelo em um jato de partículas confinadas com as características médias no tempo, assim como os coeficientes da correlação de turbulência foram avaliados. Perfis radiais de velocidade média e fração volumétrica das partículas foram capturados em quarenta e dois níveis, subdivididos em nove casos e comparados aos dados experimentais adquiridos. O diâmetro médio das partículas utilizado nas simulações foi de 75µm e as velocidades iniciais utilizadas variam entre 3 e 11m/s no jato central. O modelo matemático previu um escoamento desenvolvido semelhante ao que foi encontrado experimentalmente. / Abstract: It is presented in this research an experimental and numerical analisys of the dispersed phase behavior in a circular confined two-phase jet and a comparison with circular free two-phase jet. In the experimental analysis, a pentagonal plexiglass chamber was used as confined system for the axial and radial profiles investigation of mean velocity, fluctuation velocity known as RMS velocity and turbulence intensity. These data were analyzed in order to develop a complete analysis in the developed region of the jet. Three different nozzles were used to feed the gas phase at the top of the chamber, but just the central nozzle was loaded with particles between 60 and 90µm of diameter. The other two were used to increase the interaction between the phases in the chamber. An optical technique known as Phase Doppler Anemometry was used to measure the instantaneous velocity of the solid phase and particle diameter in different axial positions of the jet nozzle. Nine different cases of study are investigated individually and then compared among each other. These cases provide important information about the jets behavior and the confinement effect on the macrocospic and turbulent transport of particles between the jet center and the jet contour regions. The numerical analysis deals with three-dimensional, turbulent and transient mathematical modeling of a confined two-phase jet flow. The model treats the gas and the solid phases from an Eulerian approach. The closure of the transport equations have been accomplished by using the k-e turbulence model for the gas phase and the zero-equation turbulence model for the solid phase, and in some cases the latter suffered turbulent effects occuring only from the continuos phase. The accuracy of the model predictions in a particle-laden confined jet with the characteristics as well as turbulence correlation coefficients have been evaluated. Radial mean velocity profiles for the solid phase were computed on forty two axial levels, subdivided in nine cases and compared to the obtained experimental data. The mean particle diameter used in the simulations was 75µm and the initial velocities used vary between 3 and 11m/s. The mathematical model predicted a flow development similar to that found experimentally. / Doutorado / Desenvolvimento de Processos Químicos / Mestre em Engenharia Química

Le tube à onde progressive (TOP) est un dispositif où un faisceau d’électrons se déplaçant sur l’axe d’une hélice interagit avec les ondes électromagnétiques propagées par cette hélice. Il est le siège de nombreuses instabilités : des oscillations (génération d’ondes hyperfréquences parasites), mais aussi des instabilités du faisceau qui ont pour conséquence une dissipation parasite due à l'interception du faisceau par l'hélice. L’objectif de cette thèse est de développer une formulation hamiltonienne au problème permettant des modèles approchés plus compacts, plus précis et plus complets. Après l'avoir exposée, nous présentons un schéma numérique contenant notre modèle discret pour la simulation du TOP. Ce modèle discret a été mis au point pour tenir compte des conditions d'adaptation et de changements de géométrie. Le couplage avec les électrons met en jeu des champs de base simples, et le modèle tient compte de la charge d'espace. Différentes méthodes d'intégration numérique sont développées, dont nous comparons l'efficacité. Nous comparons ce modèle discret avec divers modèles d'amplification des ondes à froid, dont le modèle actuellement utilisé chez Thales pour la conception des tubes ({texttt{MVTRAD}}). Nous montrons aussi que les modèles d'amplification des ondes à froid à deux ou trois dimensions comme {texttt{MVTRAD}} ou {texttt{BWIS}} (prenant en compte les ondes inverses) ne respectent pas nécessairement l'équation de Maxwell-Faraday, contrairement au nôtre. Enfin, nous comparons notre modèle discret de circuit et le modèle d'amplification des ondes à froid dans le cas d'un faisceau linéaire. / A traveling-wave tube (TWT) is a device where an electron beam traveling along the axis of a helix interacts with the electromagnetic waves propagated by this helix. It is sensitive to many instabilities : oscillators (generating noise microwave), but also beam instabilities that generate a noise dissipation due to the interception of the beam by the helix. The aim of this thesis is to find a Hamiltonian formulation of the problem to allow more compact, more accurate and more complete approximate models. Having found one, we start to develop a numerical scheme containing our discrete model for the simulation of TOP. This discrete model has been developed to take into account the tapering sections, geometry changes and adaptations. The coupling with electrons involves simple functions of space, and the model takes space charge into account. Different methods of numerical integration are developed, of which we compare the efficiency. We compared the discrete model with various cold waves amplification models, especially with the model currently used at Thales for the design of their tubes ({texttt{MVTRAD}}). Moreover, we showed that two- or three-dimensional cold wave amplification models like {texttt{MVTRAD}} or {texttt{BWIS}} (which takes into account the backward waves) fail to respect the Maxwell-Faraday equation, contrary to ours. Finally we made a comparison between our circuit discrete model and the amplification model of cold waves in the case of a linear beam.

Lecithin wird unter anderem zur Steuerung der rheologischen Eigenschaften von Lebensmittelsuspensionen wie zum Beispiel Schokolade eingesetzt. In erster Linie findet dabei Sojalecithin Verwendung, wogegen die Wirkungen von Lecithinen aus Sonnenblumen oder Raps unzureichend dokumentiert sind. Anhand von Untersuchungen an Modellsuspensionen werden Wirkungsbeziehungen von Lecithin auf mikrostruktureller Ebene beleuchtet, um Ursachen für dessen Funktionalität in ölbasierten Suspensionen abzuleiten. Darüber hinaus erfolgt ein Vergleich der Wirkung von Soja-, Raps- und Sonnenblumenlecithin auf rheologische, sensorische und morphologische Eigenschaften von Schokolade. Rheologische Untersuchungen an Zucker/Öl- und Glaskugel/Öl-Suspensionen verdeutlichen den Einfluss der Suspensionsbestandteile auf die Wirkung von Lecithin in ölbasierten Suspensionen. Sedimentationsanalysen an Zucker/Öl-Suspensionen zeigen, dass die Reduktion der rheologischen Parameter mit der Senkung des Sedimentvolumens und einer verstärkt polydispersen Sedimentation einhergeht. Glaskugel/Öl-Suspensionen bilden im Vergleich zu Zucker/Öl-Suspensionen ein deutlich kompakteres Sediment, was auf geringer ausgeprägte Interaktionen zwischen den Glaspartikeln hindeutet und durch Untersuchungen mittels Rasterkraftmikroskop bestätigt wird. Die Anreicherung des Dispersionsmediums mit Lecithin führt zur Adsorption von grenzflächenaktiven Molekülen an der fest/flüssig-Grenzfläche und reduziert die adhäsiven Kräfte zwischen Zuckeroberflächen. In Zucker/Sojaöl-Suspensionen zeigen die Phospholipide Phosphatidsäure, Phosphatidylcholin und Phosphatidylethanolamin im Vergleich zu Sojalecithin eine geringer ausgeprägte Funktionalität bei kleinen Phospholipidkonzentrationen. Soja-, Raps- und Sonnenblumenlecithine besitzen in dunkler und in milchhaltiger Schokoladenmasse lediglich hinsichtlich ihrer Wirkung auf die Fließgrenze leichte Unterschiede. Die Präparate zeigen keine verallgemeinerbaren Wirkunterschiede auf die Fettkristallmorphologie und die Textur von gelagerter dunkler und milchhaltiger Schokolade. Des Weiteren lassen sensorische Untersuchungen keine signifikant ausgeprägte Präferenz für dunkle oder milchhaltige Schokolade erkennen, wenn die Probe mit Soja-, Raps- oder Sonnenblumenlecithin versetzt wird. Die Ergebnisse zeigen, dass die Reduktion der adhäsiven Kräfte zwischen Zuckerpartikeln eine Ursache für die Senkung der rheologischen Parameter und des Sedimentvolumens von Zucker/Öl-Suspensionen darstellt. Außerdem ist zu erkennen, dass bei geringen Phospholipidkonzentrationen synergetische Effekte zwischen unterschiedlichen grenzflächenaktiven Substanzen zu einem Anstieg der Funktionalität des eingesetzten Präparates führen können. Darüber hinaus ist festzustellen, dass Soja-, Raps- und Sonnenblumenlecithin die rheologischen, sensorischen und morphologischen Eigenschaften von Schokolade in gleichem Maß beeinflussen. / Lecithin is used in the food industry, for example to control the rheological properties of oil-based suspensions, such as chocolate. First and foremost, soybean lecithin is used, whereas the effects of possible alternatives, such as lecithin from sunflower or canola, are still insufficient documented. On the basis of model suspensions the effect of lecithin on the microstructural level will be investigated to derive causes of the functionality of the surfactant in oil-based suspensions. Additionally, a comparison is made regarding the effects of soybean lecithin, canola lecithin and sunflower lecithin on the rheological and morphological properties as well as on sensory characteristics of chocolate. Rheological studies illustrate the influence of the suspension components to the action of lecithin in oil-based suspensions. While, in sugar/oil-suspensions, lecithin reduces apparent viscosity and yield stress, the effect of the surfactant in glass sphere/oil-suspensions depends on the dispersion medium. Sedimentation analyses of sugar/oil-suspensions show that the reduction of the rheological parameters coincides with the reduction of the sediment volume and an increased polydisperse sedimentation. The sediment of glass sphere/oil-suspensions is more compact in comparison to sugar/oil-suspensions, indicating less pronounced interactions between glass spheres. Investigations using atomic force microscopy show the less pronounced interactions between glass spheres. While interactions (adhesive forces) are detectable between sugar surfaces dispersed in oil, no interactions can be determined between glass surfaces. The enrichment of the dispersion medium with lecithin results in the adsorption of the surfactants at the sugar surface and reduces the adhesive forces. In sugar/soybean oil suspensions and at low phospholipid concentrations the results indicate a less pronounced functionality of the individual phospholipids, phosphatidylcholine, phosphatidylethanolamine and phosphatidic acid in comparison to soybean lecithin. In dark chocolate and milk chocolate soybean lecithin, canola lecithin and sunflower lecithin reduces apparent viscosity at low to medium shear rate in the same way. In contrast, small differences in terms of their effect on the yield stress are observed. The lecithins do not show differences regarding their impact on fat crystal morphology and texture of stored dark chocolate and milk chocolate. Furthermore, in sensory studies, no significant preference differences were detectable in case of dark chocolate or milk chocolate containing soybean lecithin, canola lecithin or sunflower lecithin. The results show that the reduction of the adhesive forces between sugar particles causes the reduction of rheological parameters and the sediment volume of sugar/oil-suspensions. Furthermore, at low phospholipid concentrations possible synergistic effects between different surfactants can lead to an increase of the functionality of suractants. Additionally it can be concluded that soybean lecithin, canola lecithin and sunflower lecithin affect the rheological and morphological properties as well as the sensory characteristics of chocolate in equal measure.

In meiner Doktorarbeit untersuche ich ein Kac-artiges Vielteilchen-Modell, das eine Beschreibung von plastischen Verformungen ohne Verwendung einer Referenz-Konfiguration ermöglicht. Im Rahmen des Modells wird die Verformung eines Körpers durch Angabe von Atompositionen beschrieben. Es wird eine Mesoskala zwischen der Mikroskala der Atom-Atom Abstände und der Makroskala des Körpers eingeführt. Um jeden Punkt wird die Konfiguration auf dieser Mesoscala mit einem Bravais-Gitters approximiert. Die Matrix, die dieses Gitter aufspannt, wird als Argument eines elastischen Energiefunktionals verwendet. Auf diese Weise wird ein Energiefunktional definiert, das die Eigenschaften des Systems festlegt. Im Ersten Teil meiner Doktorarbeit analysiere ich das Modell im Fall das eine Referenz-Konfiguration lokal existiert. Ich schätze die Energiedichte einer solchen Konfiguration mit einer Störungsrechung von oben ab und erhalte eine obere Schranke für die Energiebarriere für plastische Relaxation in zwei Dimensionen. Im zweiten Teil untersuche ich Möglichkeiten Lagrange-Koordinaten im Rahmen des Modells zu konstruieren. Ich beweise, dass für zwei Punkte deren Abstand klein genug sind und die bestimmte Regularitätseigenschaften erfüllen, die Gitterparameter der approximierenden Bravais-Gitter bis auf eine Reparametrisierung nahe beieinander liegen müssen. Dies erlaubt diskrete Ketten von regulären Punkten zur Definition von Homotopieklassen zu benutzen die mit verallgemeinerten Burgers-Vektoren charakterisiert werden. Es ist mit dieser Technik auch möglich die Kernenergie von Versetzungen nach unten abzuschätzen. Schließlich passe ich eine Methode kontinuierliche Lagrange-Koordinaten, die von L. Mugnai und S. Luckhaus entwickelt wurden, an das Model an und verbessere sie dergestalt, dass ich die Energiedichte mit Hilfe eines Funktionales der Lagrange-Koordinaten nach unten abschätzen kann. / I study a Kac-type many particle model that allows a reference-free description of plastic deformation.In the framework of the model the state of the body is given by a set of atom position. The typical atom-atom distance is the microscopic scale. The size of the body is the macroscopic scale. Around each point a lattice is fitted to the configuration on a mesoscopic scale. The lattice parameters are used as an argument of a non-linear elasticity energy functional. Hence, this procedure allows to define an free-energy functional of a particle configuration. In the first part of my thesis I analyze the model in the case that a reference configuration exists locally. I bound the energy-density of such a configuration from above with a pertubative calculation and obtain an upper bound for the energy barrier of plastic deformation for dimension two. In the second part I explore the possibility to construct Lagrangian coordinates in the framework of the model. I prove that for two points that are close to each other and that fulfill certain regularity assumptions the fitted lattice parameters are close to each other up to a reparametrisation. This allows to use discrete chains of regular points for homotopy type arguments and define a generalized Burgers vector as a topological quantity. I also use this method to get a lower bound for the core energy of a dislocation. Finally, I adapt a method to construct continuous Lagrangian coordinates presented in by L.Mugnai and S.Luckhaus to my model and improve it to a point where I can use a functional of these Lagrangian coordinate as a lower bound for the energy of the model.

The transport or the separation of solid particles or droplets suspended in a fluid flow is a common task in mechanical and process engineering. To improve machinery and physical processes (e.g. for coal combustion, reduction of NO_x and soot) an optimization of complex phenomena by simulation applying the fundamental conservation equations is required. Fluid-particle flows are characterized by the ratio of density of the two phases gamma=rho_P/rho_F, by the Stokes number St=tau_P/tau_F and by the loading in terms of void and mass fraction. Those numbers (Stokes number, gamma) define the flow regime and which relevant forces are acting on the particle. Dependent on the geometrical configuration the particle-wall interaction might have a heavy impact on the mean flow structure. The occurrence of particle-particle collisions becomes also more and more important with the increase of the local void fraction of the particulate phase. With increase of the particle loading the interaction with the fluid phase can not been neglected and 2-way or even 4-way coupling between the continous and disperse phases has to be taken into account. For dilute to moderate dense particle flows the Euler-Lagrange method is capable to resolve the main flow mechanism. An accurate computation needs unfortunately a high number of numerical particles (1,...,10^7) to get the reliable statistics for the underlying modelling correlations. Due to the fact that a Lagrangian algorithm cannot be vectorized for complex meshes the only way to finish those simulations in a reasonable time is the parallization applying the message passing paradigma. Frank et al. describes the basic ideas for a parallel Eulererian-Lagrangian solver, which uses multigrid for acceleration of the flow equations. The performance figures are quite good, though only steady problems are tackled. The presented paper is aimed to the numerical prediction of time-dependend fluid-particle flows using the simultanous particle tracking approach based on the Eulerian-Lagrangian and the particle-source-in-cell (PSI-Cell) approach. It is shown in the paper that for the unsteady flow prediction efficiency and load balancing of the parallel numerical simulation is an even more pronounced problem in comparison with the steady flow calculations, because the time steps for the time integration along one particle trajectory are very small per one time step of fluid flow integration and so the floating point workload on a single processor node is usualy rather low. Much time is spent for communication and waiting time of the processors, because for cold flow particle convection not very extensive calculations are necessary. One remedy might be a highspeed switch like Myrinet or Dolphin PCI/SCI (500 MByte/s), which could balance the relative high floating point performance of INTEL PIII processors and the weak capacity of the Fast-Ethernet communication network (100 Mbit/s) of the Chemnitz Linux Cluster (CLIC) used for the presented calculations. Corresponding to the discussed examples calculation times and parallel performance will be presented. Another point is the communication of many small packages, which should be summed up to bigger messages, because each message requires a startup time independently of its size. Summarising the potential of such a parallel algorithm, it will be shown that a Beowulf-type cluster computer is a highly competitve alternative to the classical main frame computer for the investigated Eulerian-Lagrangian simultanous particle tracking approach.

The transport or the separation of solid particles or droplets suspended in a fluid flow is a common task in mechanical and process engineering. To improve machinery and physical processes (e.g. for coal combustion, reduction of NO_x and soot) an optimization of complex phenomena by simulation applying the fundamental conservation equations is required. Fluid-particle flows are characterized by the ratio of density of the two phases gamma=rho_P/rho_F, by the Stokes number St=tau_P/tau_F and by the loading in terms of void and mass fraction. Those numbers (Stokes number, gamma) define the flow regime and which relevant forces are acting on the particle. Dependent on the geometrical configuration the particle-wall interaction might have a heavy impact on the mean flow structure. The occurrence of particle-particle collisions becomes also more and more important with the increase of the local void fraction of the particulate phase. With increase of the particle loading the interaction with the fluid phase can not been neglected and 2-way or even 4-way coupling between the continous and disperse phases has to be taken into account. For dilute to moderate dense particle flows the Euler-Lagrange method is capable to resolve the main flow mechanism. An accurate computation needs unfortunately a high number of numerical particles (1,...,10^7) to get the reliable statistics for the underlying modelling correlations. Due to the fact that a Lagrangian algorithm cannot be vectorized for complex meshes the only way to finish those simulations in a reasonable time is the parallization applying the message passing paradigma. Frank et al. describes the basic ideas for a parallel Eulererian-Lagrangian solver, which uses multigrid for acceleration of the flow equations. The performance figures are quite good, though only steady problems are tackled. The presented paper is aimed to the numerical prediction of time-dependend fluid-particle flows using the simultanous particle tracking approach based on the Eulerian-Lagrangian and the particle-source-in-cell (PSI-Cell) approach. It is shown in the paper that for the unsteady flow prediction efficiency and load balancing of the parallel numerical simulation is an even more pronounced problem in comparison with the steady flow calculations, because the time steps for the time integration along one particle trajectory are very small per one time step of fluid flow integration and so the floating point workload on a single processor node is usualy rather low. Much time is spent for communication and waiting time of the processors, because for cold flow particle convection not very extensive calculations are necessary. One remedy might be a highspeed switch like Myrinet or Dolphin PCI/SCI (500 MByte/s), which could balance the relative high floating point performance of INTEL PIII processors and the weak capacity of the Fast-Ethernet communication network (100 Mbit/s) of the Chemnitz Linux Cluster (CLIC) used for the presented calculations. Corresponding to the discussed examples calculation times and parallel performance will be presented. Another point is the communication of many small packages, which should be summed up to bigger messages, because each message requires a startup time independently of its size. Summarising the potential of such a parallel algorithm, it will be shown that a Beowulf-type cluster computer is a highly competitve alternative to the classical main frame computer for the investigated Eulerian-Lagrangian simultanous particle tracking approach.

Gas-solid fluidized bed reactors are widely applied in chemical and energy industries, and their design and scale-up are virtually empirical, extremely expensive and time consuming. This scenario has motivated the development of alternative theoretical tools, and two-fluid modeling, where gas and particulate are both treated as interpenetrating continuum phases, has appeared as a most promising approach. Owing to the large domains to be resolved in real-scale fluidized bed reactors, only filtered modeling approaches are feasible, and closure models become necessary to recover sub-grid effects that are filtered by the very coarse numerical grids that are imposed owing to computational limitations. Those closure models, which in hydrodynamic formulations account for filtered interphase momentum exchanges and filtered and residual stresses in the phases, can be derived from results of highly resolved simulations (HRS) performed over small size domains under refined numerical grids. One widely practiced approach consists of applying two-fluid modeling under micro-scale defined closures, generally known as microscopic two-fluid modeling. This approach includes microscopic closures for solid phase stresses derived from the kinetic theory of granular flows (KTGF), which accounts for kinetic-collisional effects only, and is adequate to dilute flows. Otherwise, the conventional KTGF does not account for interparticle friction effects, and its application to dense flow conditions is quite questionable. In this work a literature available modified version of KTGF is applied which also accounts for interparticle friction, and highly resolved simulations are performed for dense flow conditions in order to evaluate the effects of friction over relevant filtered parameters (namely effective drag coefficient, filtered and residual stresses). Ranges of domain average solid volume fractions and gas Reynolds numbers are considered (macro-scale conditions) embracing dense gas-solid fluidized flows from suspensions up to pneumatic transport. The MFIX open source code is used in all the simulations, which are performed over 2D periodical domains for a unique monodisperse particulate. The HRS results (i.e. meso-scale flow fields) are filtered over regions compatible with grid sizes in large scale simulations, and the relevant filtered parameters of concern are derived and classified by ranges of other filtered parameters taken as independent variables (filtered solid volume fraction, filtered slip velocity, and filtered kinetic energy of solid velocity fluctuations, which are referred to as markers). Results show that the relevant filtered parameters of concern are well correlated to all of those filtered markers, and also to all of the imposed macro-scale conditions. Otherwise, interparticle friction showed no significant effects over any filtered parameter. It is recognized that this issue clearly requires further investigation notably regarding the suitability of the markers that were assumed for classifying the filtered results. The current work is intended as a contribution for future developments of more accurate closure models for large scale simulations of gas-solid fluidized flows. / Reatores de leito fluidizado de escoamento gás-sólido são largamente utilizados nas indústrias química e de energia, e o seu projeto e escalonamento são virtualmente empíricos, extremamente caros e demorados. Este cenário tem motivado o desenvolvimento de ferramentas teóricas alternativas, e a modelagem de dois fluidos, onde gás e particulado são ambos tratados com fases contínuas interpenetrantes, tem surgido como uma aproximação muito promissora. Devido aos grandes domínios a serem resolvidos em reatores de leito fluidizado de escala real, apenas aproximações de modelagem filtradas são viáveis, e modelos de fechamento tornam-se necessários para recuperar efeitos sub-malha que são filtrados pelas malhas numéricas grosseiras que são impostas devido as limitações computacionais. Estes modelos de fechamento, que em formulações hidrodinâmicas respondem principalmente por trocas de momentum filtradas entre fases e tensões filtradas e residuais nas fases, podem ser obtidos de resultados de simulações altamente resolvidas (SAR) realizadas em domínios de dimensões reduzidas sob malhas numéricas refinadas. Uma aproximação largamente praticada consiste na aplicação de modelagem de dois fluidos sob fechamentos definidos na micro-escala, genericamente conhecida como modelagem microscópica de dois fluidos. Esta aproximação inclui fechamentos microscópicos para tensões da fase sólida obtidos da teoria cinética dos escoamentos granulares (TCEG), que considera apenas efeitos cinéticos-colisionais, e é adequada para escoamentos diluídos. Por outro lado, a TCEG convencional não leva em conta efeitos de fricção interpartículas, e sua aplicação para condições densas de escoamento é bastante questionável. Neste trabalho aplica-se uma versão modificada da TCEG disponível na literatura que também leva em conta fricção interpartículas, e simulações altamente resolvidas são realizadas para condições de escoamentos densos visando avaliar os efeitos da fricção sobre os parâmetros filtrados relevantes (coeficiente de arrasto efetivo, tensões filtradas e residuais). Considera-se faixas de frações volumétricas de sólido e números de Reynolds do gás médios no domínio (condições de macro-escala) abrangendo escoamentos gás-sólido fluidizados densos desde suspensões até transporte pneumático. O código aberto MFIX é utilizado em todas as simulações, que foram executadas sobre domínios periódicos 2D para um único particulado monodisperso. Os resultados das SAR (i.e., campos de escoamento de meso-escala) foram filtrados sobre regiões compatíveis com tamanhos de malha praticados em simulações de grandes escalas, e os parâmetros filtrados relevantes de interesse são calculados e classificados por faixas de outros parâmetros filtrados tomados como variáveis independentes (fração volumétrica de sólido filtrada, velocidade de deslizamento filtrada, e energia cinética das flutuações de velocidade da fase sólida filtrada, que são referidos como marcadores). Os resultados mostram que os parâmetros filtrados relevantes de interesse são bem correlacionados com todos os marcadores, e também com todas as condições de macro-escala impostas. Por outro lado, a fricção interpartículas não mostrou efeitos significativos sobre qualquer parâmetro filtrado. Reconhece-se que este aspecto claramente requer investigações adicionais, notadamente com respeito à adequação dos marcadores que foram considerados para classificação dos resultados filtrados. O trabalho corrente é posto como uma contribuição para o desenvolvimento futuro de modelos de fechamento mais acurados para simulações de grandes escalas de escoamentos gás-sólido fluidizados.