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• W2115963227 abstract "Population balance systems model the interaction of the surrounding medium and the particles which are described by the particle size distribution (PSD). This way of modeling results in a system of partial differential equations where the incompressible Navier–Stokes equations for the fluid velocity and pressure are coupled to convection-diffusion equations for species concentration and the system temperature, and a transport equation for the PSD. The equation for the PSD may even contain an integral operator that models, e.g., the aggregation of the particles. Whereas the flow field, the concentration of dissolved species, and temperature are defined in a three-dimensional spatial domain, the PSD depends also on the internal coordinates, which are used to describe additional properties of the particles (e.g., diameter, volume). In particular, uni-variate and bi-variate population balance models are based on oneand two-dimensional geometrical characterizations of the individual particles (diameter, volume, or main axis in the case of anisotropic particles), resulting in four-dimensional (4D) and five-dimensional (5D) population balance systems. There are several classes of numerical methods for solving population balance systems. With the ongoing rise of computer power, the option of using direct discretizations for simulating those systems becomes more and more interesting since these discretizations do not introduce an additional error by circumventing the solution of the higher-dimensional equation for PSD, like momentum-based methods or operator-splitting schemes. In this thesis, it is shown for uni-variate population balance systems that for an appropriate choice of the unknown model parameters in aggregation kernel good agreements can be achieved between the experimental data and the numerical results computed by the numerical methods. A mixed finite difference/finite volume method is used for discretizing the PSD equation in the case of bi-variate population balance systems. In this case, it is demonstrated that even in the class of direct discrerizations, different numerical methods lead to qualitatively different numerical solutions. Zusammenfassung. Populationsbilanzsysteme modellieren die Wechselwirkung zwischen Teilchen, welche durch ihre Partikelgrosenverteilung beschrieben sind, und ihrem umgebenden Medium. Aus mathematischer Sicht fuhrt das auf ein gekoppeltes System von partiellen Differentialgleichungen. Die inkompressible Navier–Stokes– Gleichungen, welche die Fluidgeschwindigkeit und den Druck beschreiben, sind hier an Konvektions–Diffusions–Gleichungen, welche die Konzentration der Spezies sowie die Temperatur des Systems modellieren und an eine Transportgleichung fur die Beschreibung der Partikelgrosenverteilung gekoppelt. Die Gleichung fur die Partikelgrosenverteilung kann sogar einen Integraloperator enthalten, der zum Bespiel die Aggregation von Partikeln modelliert. Das Stromungsfeld, die Konzentration der gelosten Spezies und die Temperatur des Systems sind in einem dreidimensionalen Gebiet definiert. Die Partikelgrosenverteilung hangt daruber hinaus von den internen Koordinaten ab, welche zusatzliche Eigenschaften der Partikel (z. B. Durchmesser, Volumen) beschreiben. Insbesondere sind univariate und bivariate Populationsbilanzmodelle dadurch gekennzeichet, dass sie eine einoder zweidimensionale geometrische Charakterisierung der einzelne Partikel darstellen (Durchmesser, Volumen der Teilchen oder Hauptachse von anisotropen Teilchen). Dies resultiert in vierdimensionale (4D) und funfdimensionale (5D) Populationsbilanzsysteme. Zur numerischen Losung von solchen Systemen konnen verschiedene Klassen von Methoden genutzt werden. Mit dem Anstieg der Rechenleistung werden direkte Diskretisierungen fur die Simulation zunehmend interessanter. Solche direkten Schemata haben gegenuber Momentenmethoden oder Operator-Splitting-Methoden den Vorteil, dass kein zusatzlicher Fehler durch die Dimensionsreduktion entsteht. Fur univariate Populationsbilanzsysteme wird in der Arbeit gezeigt, dass unter Benutzung von geeigneten Modellparametern fur den Aggregationskern gute Ubereinstimmungen zwischen den numerischen Resultaten und den experimentellen Messungen erzielt werden konnen. Fur die Diskretisierung der Partikelgrosenverteilung fur bivariate Populationsbilanzsysteme wird ein gemischtes Finite–Differenzen/Finite–Volumen–Verfahren benutzt. In diesem Fall wird gezeigt, dass sogar direkte Diskretisierungsmethoden zu qualitativ unterschiedlichen Losungen fuhren konnen. Acknowledgment. First of all, I would like to express my deep gratitude to Prof. Dr. Volker John, my research supervisor, for his patient guidance, enthusiastic encouragement, remarkable suggestions, and useful critiques throughout my PhD project. I also deeply appreciate the help of all my colleagues from the research group Numerical Mathematics and Scientific Computing of Weierstrass Institute for Applied Analysis and Stochastic. Special thanks should be given to Alfonso Caiazzo, Andre Fiebach, Hartmut Langmach, and Ellen Schmeyer for their valuable and constructive advices during the planning and development of this research work. My grateful thanks are also extended to Gabi Blatermann and to the research group secretary Marion Lawrenz for their enormous support and kindness. Furthermore, I would like to thank also Prof. Dr. Sundmacher and his working group for the good collaboration as well as for many valuable discussions concerning the field of process engineering. Special thanks should be given to the former PhD student Cristian Borchert. Also, I would like to thank the Bundesministerium fur Bildung und Forschung (BMBF) for the financial support. Of course, I am overwhelmingly grateful to all my friends for their optimistic encouragements. Especially, I would like to express my deepest gratitude to my extraordinary friends, Claudiu Serban, Claudia Bivolaru, Carmen Iovan, Ligia Iovan, Monika Honsel, Oliver Schirra, and Dirk Voltz for being a consistent mental support during this period. I would like to thank also my friend, Jocelyn Polen, for her immediate help in checking the language of some parts of this thesis. Finally, I would like to express my deep obligation to my parents, Ionelia Muja and Constantin Suciu, my sister, Denisa Walder, for their love and encouragements over the years and to my nephew, Kevin Walder, for his ever shining smile of kindness and love. Berlin, May 2013 Oana Carina Suciu." @default.
• W2115963227 created "2016-06-24" @default.
• W2115963227 creator A5074747649 @default.
• W2115963227 date "2014-01-01" @default.
• W2115963227 modified "2023-09-27" @default.
• W2115963227 title "Numerical methods based on direct discretizations for uni- and bi-variate population balance systems" @default.
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