No description available.

Flerfasestrømning er av betydning i en lang rekke anvendelser, blant annet i olje- og gassindustrien, i den kjemiske og i prosessindustrien, inkludert i varmepumpende systemer, samt i sikkerhetsanalyse av kjernekraftverk. Denne avhandlingen analyserer modeller for tofasestrømning, og metoder for numerisk løsning av disse modellene. Den er derfor ett bidrag til å utvikle pålitelige ingeniørverktøy for flerfase-anvendelser. Slike verktøy trengs og forventes av ingeniører i industrien. Den tilnærmede Riemann-løseren framsatt av Roe har blitt studert. Roe-skjema for tre ulike modeller for tofasestrømning har blitt implementert i rammen av en standard numerisk algoritme for løsning av hyperbolske bevaringslover. Disse skjemaene har blitt analysert ved hjelp av referanse-regnestykker fra litteraturen, og ved sammenlikning med hverandre. Et Roe-skjema for den fire-liknings ettrykks tofluid-modellen har blitt implementert, og det har blitt vist at en andreordens utvidelse basert på bølge-dekomponering og fluksdifferanse-splitting virker godt, og gir forbedrede resultater sammenliknet med det førsteordens skjemaet. Det har blitt foreslått et Roe-skjema for en fem-liknings totrykks tofluid-modell med trykkrelaksering. Bruken av analoge numeriske metoder for fire-liknings- og fem-liknings-modellene gjorde det mulig med en direkte sammenlikning av en metode med og uten trykkrelaksering. Numeriske eksperiment demonstrerte at de to framgangsmåtene konvergerte til samme resultat, men at den fem-liknings trykkrelakserings-metoden var betydelig mer dissipativ, særlig for kontakt-diskontinuiteter. Videre viste beregninger at selv om fem-liknings-modellen har reelle egenverdier, så produserte den oscillasjoner for tilfeller der fire-liknings-modellen hadde komplekse egenverdier. Et Roe-skjema har blitt konstruert for driftfluks-modellen med generelle lukningslover. Roe-matrisen er helt analytisk for det tilfellet at man kan anvende Zuber-Findlay-slipp-loven som beskriver boblestrømning. Dermed er dette Roe-skjemaet mer effektivt enn tidligere fullt numeriske Roe-skjema for driftfluks-modellen. En isentropisk diskret-nivå-flerfasemodell har blitt presentert. En diskusjon av hvordan man kan ta hensyn til ulike interfase-trykkmodeller har blitt gitt. Med de passende modellene for interfase-trykk og -fart, var samsvaret svært godt mellom diskret-nivå-modellen og det fem-liknings Roe-skjemaet. Multi-steg- (MUSTA) metoden har som siktemål å komme nær oppstrøms-metodene i nøyaktighet, samtidig som den bevarer enkelheten til sentrerte skjema. Her har metoden blitt brukt på driftfluks-modellen. Når antallet steg økes, nærmer resultatene fra MUSTA-metoden seg det man får med Roe-metoden. De gode resultatene til MUSTA-metoden er avhengige av at man bruker et stort nok lokalt grid. Derfor er hovedfordelen med MUSTA-metoden at den er enkel, snarere enn at man sparer regnetid. En karakteristikk-basert metode for å spesifisere grensebetinglser for flerfase-modeller har blitt testet, og funnet å virke godt for transiente problem. / This thesis analyses models for two-phase flows and methods for the numerical resolution of these models. It is therefore one contribution to the development of reliable design tools for multiphase applications. Such tools are needed and expected by engineers in a range of fields, including in the oil and gas industry. The approximate Riemann solver of Roe has been studied. Roe schemes for three different two-phase flow models have been implemented in the framework of a standard numerical algorithm for the solution of hyperbolic conservation laws. The schemes have been analysed by calculation of benchmark tests from the literature, and by comparison with each other. A Roe scheme for the four-equation one-pressure two-fluid model has been implemented, and a second-order extension based on wave decomposition and flux-difference splitting was shown to work well and to give improved results compared to the first-order scheme. The convergence properties of the scheme were tested on smooth and discontinuous solutions. A Roe scheme has been proposed for a five-equation two-pressure two-fluid model with pressure relaxation. The use of analogous numerical methods for the five-equation and four-equation models allowed for a direct comparison of a method with and without pressure relaxation. Numerical experiments demonstrated that the two approaches converged to the same results, but that the five-equation pressure-relaxation method was significantly more dissipative, particularly for contact discontinuities. Furthermore, even though the five-equation model with instantaneous pressure relaxation has real eigenvalues, the calculations showed that it produced oscillations for cases where the four-equation model had complex eigenvalues. A Roe scheme has been constructed for the drift-flux model with general closure laws. For the case of the Zuber-Findlay slip law describing bubbly flows, the Roe matrix is completely analytical. Hence the present Roe scheme is more efficient than previous fully numerical Roe schemes for the drift-flux model. An isentropic discrete-equation multiphase model has been presented. The incorporation of different interfacial-pressure models was discussed, and examples were given. With the adequate models for the interfacial pressure and velocity, the agreement was very good between the discrete-equation model and the five-equation Roe scheme. The flux-limiter centred (FLIC) scheme was tested for the four-equation two-fluid model. Only the first-order version (FORCE) of the scheme was found to work well, but it was rather diffusive. The purpose of the multi-stage (MUSTA) method is to come close to the accuracy of upwind schemes while retaining the simplicity of centred schemes. Here it has been applied to the drift-flux model. As the number of stages was increased, the results of the MUSTA scheme approached those of the Roe method. The good results of the MUSTA scheme were dependent on the use of a large-enough local grid. Hence, the main advantage of the MUSTA scheme is its simplicity. A multiphase characteristic-based boundary-condition method has been tested, and it was shown to be workable for transient problems.

Es wurde ein neues Zweifluidmodell entwickelt, um Nichtgleichgewichtseffekte in kritischen und nahkritischen Ein-komponenten-Zweiphasenströmungen von anfänglich unter-kühlten oder siedenden Fluiden durch Rohre und Düsen zu untersuchen. Das vorgeschlagene Sechs-Gleichungsmodell besteht aus den phasenbezogenen Erhaltungsgleichungen für Masse und Impuls, der Bilanzgleichung für die thermische Energie der flüssigen Phase sowie einer zusätzlichen Transport-gleichung für die volumetrische Blasenanzahl. Zur Lösung des Systems aus partiellen Differentialgleichungen wird ein semi-implizites Finite-Differenzen-Zeitschrittverfahren angewendet. Die Schließung des Gleichungssystems wird durch Einbindung thermodynamischer Beziehungen und konstitutiver Gleichungen, die den strömungsformabhängigen Impuls-, Wärme- und Stofftransport beschreiben, erreicht. Für Strömungssysteme mit spontaner Entspannungsverdampfung aus dem rein flüssigen Zustand (Flashing) werden verschiedene Keimbildungsmodelle eingesetzt, die den Anfangszustand der verzögerten Dampfbildung beschreiben. Auf diese Weise werden thermodynamische Nichtgleichgewichtszustände als Folge von Zuständen mit für die Aktivierung von Keimstellen benötigtem Energieüberschuß, eingeschränkt vorhandener Phasengrenzfläche sowie begrenzter Wärmeübertragung zwischen den Phasen betrachtet. Abweichungen vom fluid-dynamischen Gleichgewicht (Phasenschlupf) ergeben sich aufgrund unterschiedlicher Trägheitseigenschaften und verschieden stark ausgeprägter mechanischer Kopplung zwischen den Phasen. Die mit diesem Modell erhaltenen numerischen Ergebnisse stimmen gut mit experimentellen Werten für Zweiphasen-strömungen mit unterschiedlichen Eintrittsbedingungen und Kanalgeometrien überein. / A new two-fluid flow model has been developed in order to examine non-equilibrium effects in critical and near-critical one-component two-phase flows of initially subcooled or saturated fluids through pipes and nozzles. The six-equation model proposed consists of the phasic conservation equations of mass and momentum, the liquid thermal energy, and of an additional transport equation for the bubble number density. To solve for the unknowns of the system of partial differential equations, a semi-implicit finite difference time-marching method is utilized. The closure of the set of equations is accomplished by thermodynamic relationships and additional constitutive equations describing momentum transport, interphase heat, and mass transfer which account for different flow regimes. For fluid flow systems undergoing a sudden change of phase from the pure liquid state (flashing), distinct nucleation models are included to describe the initial state of delayed vapor generation. In this way thermal non-equilibrium states are considered to be the consequence of excessive energy states required to activate nucleation sites, of restricted interfacial area and limited heat transfer between the phases. Deviation from fluid-dynamic equilibrium (phasic slip) results from different inertial properties and from distinct strength of mechanical coupling between the phases. The numerical results obtained with this model agree quite well with experimental data for two-phase flows with various inlet conditions and channel geometries.

No description available.

[pt] O atual esgotamento de campos de petróleo tradicionais tem aumentado a demanda pela produção e transporte óleos não convencionais, que podem possuir uma alta viscosidade dinâmica. Neste contexto, o estudo do escoamento simultâneo de gás e óleos viscosos em tubulações é de grande importância para a indústria de Óleo e Gás. Simulações numéricas uni-dimensionais desempenham um papel essencial nestes estudos, especialmente aquelas baseadas no Modelos de Dois-Fluidos 1D, cuja solução numérica em malhas refinadas consiste na Metodologia de Captura de Regimes. O propósito deste trabalho é utilizar esta abordagem para reproduzir dados experimentais de escoamentos óleo viscoso-gás em golfadas e estratificado ondulado em um duto horizontal em escala laboratorial. Para aprimorar os resultados desta metodologia, dados experimentais foram usados conjuntamente com um procedimento de otimização e uma versão simplificada do Modelos de Dois-Fluidos 1D para criar duas novas expressões para o fator de atrito interfacial, as quais mostraram maior eficiência que correlações padrão da literatura. O efeito da introdução da pressão dinâmica, difusão axial de quantidade de movimento e tensão interfacial dinâmica no Modelo de Dois-Fluidos 1D foi analisado. Resultados de gradiente de pressão e de fração volumétrica de líquido (histogramas, valores médios e perfis transientes) foram comparados com dados experimentais. Observou-se, com o auxílio de análises de boa-colocação, que a pressão dinâmica e as novas expressões para o fator de atrito interfacial fornecem resultados satisfatórios. / [en] The current depletion of traditional oil fields is increasing the demand for the production and transport of unconventional oils, which might possess a high dynamic viscosity. In this context, the study of the simultaneous flow of gas and viscous oils in pipelines is of paramount importance for the Oil and Gas industry. One-dimensional numerical simulations play a key role in such studies, especially the ones based on the 1D Two-Fluid Model, whose numerical solution in fine meshes consists in the Regime Capturing Methodology. The purpose of this work is to use this approach for reproducing the experimental data of isothermal slug and stratified wavy viscous oil-gas flows in a horizontal laboratory-scale pipe. For improving the results of the methodology, experimental data were used together with an optimization procedure and a simplified version of the 1D Two-Fluid Model for successfully creating two new expressions for the interfacial friction factor, which showed better efficiency than standard literature correlations. The effect of introducing a dynamic pressure, axial momentum diffusion and dynamic interfacial shear in the 1D Two-Fluid Model was examined. Results of pressure gradient and liquid holdup (histograms, mean values and transient profiles) were compared against experimental data. It was seen, with the aid of well-posedness analyses, that the dynamic pressure and the new expressions for the interfacial shear stress provided satisfactory results.

A presente pesquisa tem como objetivo realizar um estudo teórico e desenvolver simulações computacionais envolvendo a dinâmica de sistemas gás-sólido. O foco principal do trabalho é a modelagem do particulado através da análise das forças de contato entre partículas de materiais granulares utilizando modelos contínuos baseados na mecânica dos solos e na teoria cinética dos escoamentos granulares (sistemas grandes com muitas partículas, formulação Euleriana - Volumes Finitos) e modelos discretos baseados nas características físicas dos materiais (sistemas intermediários e número limitado de partículas, formulação Lagrangeana - Método dos Elementos Discretos). Investigam-se os modelos existentes na literatura com intuito de melhorar os modelos contínuos e discretos baseados na interação entre as partículas que caracterizam a dinâmica do particulado em sistemas gás-sólido. Propõe-se uma nova abordagem para a determinação do coeficiente de rigidez da mola baseada em uma equivalência entre os modelos lineares e não-lineares. Utiliza-se o código fonte MFIX para realizar simulações computacionais da dinâmica de sistemas gás-sólido, analisando o processo de fluidização, mistura e segregação de partículas, influência das correlações de arrasto, e análise das forças de contato entre as partículas através do novo método para a determinação do coeficiente de rigidez da mola . Os resultados obtidos são comparados com dados numéricos e experimentais da literatura. / The purpose of the present study is to perform a theoretical study and develop numerical simulations involving dynamic in gas-solid systems. The focus of the work is the modeling of particulate matter using continuous models based on soil mechanics and the kinetic theory of granular flows (large systems with many particles, Eulerian formulation - Finite Volume) and discrete models based on physical characteristics of the particles (intermediate systems and limited number of particles, Lagrangian formulation - Discrete Element Method). It is proposed a new approach to determine the normal spring stiffness coefficient of the linear model through the numerical solution for the overlap between particles in non-linear models. The linear spring stiffness is determined using an equivalence between the linear and the non-linear models. It is used the MFIX computational code to perform numerical simulations of the dynamics of gas-solid systems. It is analyzed the processes of fluidization, mixing and particle segregation and the influence of drag correlations. The proposed approach for normal spring stiffness coefficient is applied in the numerical simulations of two problems: single freely falling particle and bubbling fluidized bed. The results were compared with numerical and experimental data from literature.

Foram desenvolvidos estudos de modelagem e simulação numérica de escoamentos bifásicos gás-sólido na coluna ascendente de leitos fluidizados circulantes utilizando um modelo Euleriano de duas fases separadas. O sistema de equações diferenciais parciais conservativas governantes foi obtido através de um procedimento tradicional. Ambas as fases foram assumidas como meio contínuo. Aplicou-se o procedimento de médias estatísticas de Euler, enfatizando a obtenção dos modelos hidrodinâmicos A e B desenvolvidos no IIT/ANL. Realizou-se análise comparativa de correlações para transferência de quantidade de movimento na interface. Discutiu-se a formulação de condições de contorno apropriadas. As equações diferenciais parciais médias foram discretizadas em volumes de controle Eulerianos. As equações de continuidade foram resolvidas implicitamente. As equações de quantidade de movimento foram resolvidas através de um procedimento explícito-implícito. Foram desenvolvidas simulações numéricas para uma coluna ascendente típica de leitos fluidizados circulantes. Desenvolveu-se análise paramétrica da influência de vários aspectos físicos e matemáticos sobre o escoamento. Avaliou-se resultados de simulação através de metodologia de identificação e caracterização de estruturas coerentes. Estudou-se o efeito da função de arrasto na interface sobre os processos dinâmicos que caracterizam estas estruturas coerentes. Foram realizados estudos numéricos de turbulência a partir de resultados de simulação direta. Várias conclusões e recomendações para futuros trabalhos foram propostas com base nas análises realizadas. Foram apresentadas algumas considerações gerais relativas a aspectos críticos na modelagem e simulação com modelo das duas fases separadas. / Studies were carried out on modeling and numerical simulation of gas-solid two-phase flows in the riser of circulating fluidized beds using an Eulerian two-fluids model. The system of conservative partial differential governing equations was derived through a traditional procedure. Both phases were assumed as a continuum. The Euler averaging procedure was applied emphasizing the derivation of the so called hydrodynamic models A and B developed at IIT/ANL. A comparative analysis was performed among correlations for momentum transfer at the interface. The formulation of suitable boundary conditions was discussed. The average partial differential conservative equations were discretized on Eulerian control volumes. The continuity equations were solved implicitly. The momentum equations were solved through an explicit-implicit procedure. Numerical simulation was performed for a typical circulating fluidized bed riser. A parametric analysis was carried out regarding the influence on the flow of various physical and mathematical aspects. Results of simulation were evaluated through a methodology of identification and characterization of coherent structures. The effect of the interface drag function on dynamic features of those coherent structures was addressed. Numerical studies on turbulence were performed from results of direct simulation. Several conclusions and recommendations for future work were put forward on the basis of the performed analyses. Some general considerations were presented regarding critical features of modeling and simulation through Eulerian two-fluids models.

On s'intéresse dans ce travail au problème de propagation acoustique dans des guides à parois traitées avec des matériaux absorbants à réaction localisée ou non localisée en présence d'écoulement. En effet, dans les systèmes industriels comme les turboréacteurs d'avions, les silencieux d'échappement et les systèmes de ventilation, le bruit est le plus souvent canalisé vers l'extérieur par des guides de géométries plus ou moins complexes. Une étude des guides d'ondes permet donc de prédire et de comprendre les phénomènes physiques tels que la réfraction, la convection, l'absorption et l'atténuation des ondes. Dans l'étude des guides d'ondes, on considère souvent qu'ils sont infiniment longs afin de s'affranchir de certains phénomènes (réflexion par exemple) à leurs extrémités. Résoudre le problème de propagation dans les guides infinis par la méthode des éléments finis nécessite de tronquer le domaine infini par des frontières artificielles sur lesquelles des conditions limites transparentes doivent être écrites. Dans ce travail, les conditions limites transparentes sont écrites sous forme d'un opérateur Dirichlet-to-Neumann (DtN) basé sur une décomposition de la pression acoustique sur la base des modes propres du guide étudié tout en prenant en compte l'influence des paramètres comme l'écoulement et le traitement acoustique avec des matériaux absorbants. La propagation acoustique dans le guide est régie par un modèle scalaire basé sur l'équation de Helmholtz et les matériaux absorbants utilisés sont des matériaux absorbants d'impédance locale Z et des matériaux poreux. Nous nous sommes intéressés en particulier aux matériaux poreux ? squelette rigide que l'on modélise par un fluide équivalent car la propagation acoustique dans ces matériaux est aussi gouvernée par l'équation de Helmholtz comme dans un milieu fluide. Des résultats d'étude de la propagation acoustique dans des guides rectilignes uniformes traités en présence d'un écoulement uniforme ont permis de valider la méthode développée pour tronquer les domaines infinis. L'étude a aussi été menée avec succés pour des guides non uniformes traités en présence d'un écoulement potentiel. / Our concern in this work is the problem of acoustic propagation in guides lined with locally or non locally reacting materials with the presence of mean fluid flow. In several industrial systems such as aircraft jet engines, mufflers exhaust and ventilation systems, noise is mostly channeled outside by guides of more or less complex geometries. A study of waveguides makes it possible to predict and understand the physical phenomena such as refraction, convection, absorption and wave attenuation. In waveguides studies, guides are often considered infinitely long to get rid of some phenomena (reflection for example) at their ends. Solving the problem of acoustic propagation in infinite guides by finite element method requires to truncate the infinite domain by artificial boundaries on which transparent boundary conditions must be written. In this work, the transparent boundary conditions are written as a Dirichlet-to-Neumann (DtN) operators based on sound pressure decomposition on the eigenmodes basis of the studied guide by taking into account the influence of parameters such as flow and acoustic liners in the guide walls. Acoustic propagation in the guide is governed by a model based on the scalar Helmholtz equation and the used liners are locally reacting materials of local impedance Z and porous materials. In this study, we focused particularly rigid porous materials modelized by an equivalent fluid because the acoustic propagation in these materials is also governed by the Helmholtz equation as in a fluid medium. Results of studies of acoustic propagation in uniform straight lined guides with a uniform flow allowed to validate the method developed to truncate infinite domains. The study was also done successfully for non uniform lined guides with a potential mean flow.

The electrical properties, in particular the U–I characteristics, current and voltage signal shapes within the pulse, are important parameters for the understanding of the processes taking place in the pulsed glow discharge (PGD). The electrical properties are also closely related to the analytical performance of the PGD such as sputtering rates, crater shapes and emission yields. Moreover, the dependence of the U–I plots on the density of the discharge gas can be used to estimate the gas temperature. This result is relevant for the analysis of thermally fragile samples. Nevertheless, there is a lack of PGD studies where the current and voltage signals are considered in detail. Therefore, this article is dedicated to the electrical properties of PGD. The influence of the PGD parameters (duty cycle and pulse duration) on the electrical properties is examined. The results highlight the optimum parameters for particular analytical applications. The question, whether direct current (dc) and radio frequency (rf) discharges behave similarly is also discussed and all experiments are performed for both modes. The comparative studies reveal strong similarities between dc and rf pulsed discharges. / Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.

<div>The current study is aimed at developing a well-posed and objective, i.e., frame invariant, Eulerian one-dimensional (1D) Two-Fluid Model (TFM) to predict flow regime transition from dispersed to clustered bubbly and slug flow for vertical adiabatic two-phase flows. Two-phase flows in general are characterized by local material wave or void fraction wave instabilities and flow regime transitions are one of the important consequences of these instabilities. The physical mechanism of wake entrainment for clustering of dispersed bubbles is proposed, leading to formation of bubble clusters and Taylor bubbles. The focus of the work is on simulation of the local interfacial structures for bubble clusters and Taylor bubbles, using a well-posed, unstable and non-linearly bounded 1D Shallow Water TFM.</div><div><br></div><div>The first part of the current study investigates the dynamic behavior of the well posed 1D mechanistic TFM obtained from the averaging approach of Ishii [1], due to wake entrainment instability. For this, a 1D Shallow Water TFM derived from the 1D mechanistic TFM is used, which retains the same dynamic behavior as that of the latter at short wavelengths and the required wake entrainment force is derived mechanistically. Three stability approaches are followed to study the dynamic behavior of the 1D Shallow Water TFM: characteristics, dispersion analysis, and nonlinear numerical simulations. An in-house code is used for the 1D numerical simulations of the growth of void fraction waves due to wake entrainment. The simulation results are validated with the experimental data of Cheng and Azzopardi [2] and Song et al. [3] To conclude the first part, the 1D results of the two-equation Shallow Water TFM are carried over to the complete four-equation TFM for quasi 1D simulations using the commercial CFD code of ANSYS Fluent.</div><div><br></div>As an alternative to the mechanistic approach, which is based on Newtonian mathematics, a variational approach based on Lagrangian and Hamiltonian mathematics is used in the second part of the thesis. While the mechanistic approach operates in terms of forces acting on the two-phase mixture, the variational approach operates in terms of energies of the two-phase system. To derive the equations of motion using the variational approach, the extended Hamilton principle of least action is applied to the Lagrangian density of the two-phase mixture. One of the appealing features<br>17<br>of this procedure is that the derived equations of motion are objective (Geurst [4]), in particular the added mass terms.<br>Thus, the second part of the current study focuses on deriving an objective, well-posed and unstable 1D TFM as well as developing a constitutive model for the wake entrainment effect using the variational method. Additional momentum transfer terms present in both the liquid phase and gas phase momentum equations, which render the variational TFM objective, are discussed. The variational method is then used to derive the 1D Shallow Water TFM using the fixed flux assumption. The conservative interfacial momentum transfer terms require formulation of the inertial coupling between the phases. Potential flow theory is first used to derive the inertial coupling coefficient for a single bubble and then for a pair of bubbles to consider interaction between the two bubbles. Then, a lumped parameter model is used to derive the inertial coupling coefficient for the wake entrainment effect. A local drag coefficient is obtained for the non-conservative interfacial drag force from the experimental data using kinematic approximation, i.e., force balance between drag and gravity. The linear and non-linear stability analyses are used to address the stability of the 1D variational Shallow Water TFM. The presence of appropriate short-wave physics makes the 1D Shallow Water TFM hyperbolic well-posed and kinematically unstable. Finally, numerical simulations are performed to demonstrate the development of void fraction waves due wake entrainment. The growth of void fraction waves is non-linearly bounded, i.e., Lyapunov stable. The simulation results are compared with the experimental data to validate the propagation properties of void fraction waves for bubble clusters and Taylor bubbles. This work illustrates the short-wave two-phase flow simulation capability of the TFM for the bubbly to slug flow regime transition.