Stuttgart, Univ., Diss., 2005.

Zugl.: Hannover, Univ., Diss., 2007

Techn. University, Diss., 2003--Berlin.

The key to success in separation of liquid mixtures is the efficient creation and utilization of vapour-liquid contact area. By packing the column with gas-liquid contact devices such as structured packing, the vapour-liquid contact area can be increased. However, the efficiency of these packed columns depends strongly on the local flow behaviour of the liquid and vapour phase inside the packing. The aim of this work was to develop three-dimensional CFD models to study the hydrodynamic behaviour on the corrugated sheets of packing. Different approaches are possible to simplify the problem and to extend it for more complex flow scenarios. In this work, three-dimensional CFD simulations were performed to study the complete fluid-dynamic behaviour. This was performed in two steps. As a first step, the developed model was validated with experimental studies using a simplified geometry i.e., an inclined plate. The three-dimensional Volume-of-Fluid (VOF) model was utilized to study the flow behaviour of the gas-liquid countercurrent flow. The influence of the liquid surface tension was taken into consideration using the Continuum Surface Force (CSF) model. The wetting characteristics of liquids with different viscosity (1 and 5 mPas) and contact angle (70° and 7°) were studied for different flow rates. Three different mixtures (water, water-glycerol (45 wt. %) and silicon-oil (DC5)) were considered. Initially, the rivulet width of experiments and simulations were compared and an error of 5 % maximum was determined. The results were also in good agreement with earlier studies. The percentage of wetting due to changes in flow rate, viscosity and contact angle was compared and discussed. For all tested systems, excellent agreement between the experiments and simulation studies was found. In addition, profiles of the velocity in the film at film flow conditions over a smooth inclined plate obtained from simulations were compared with experimental profiles obtained using a μPIV technique. A detailed sensitivity study was also performed in order to understand the changes in the velocity profiles due to small change in liquid flow rate, temperature and inclination angle. As a next step, the developed model was extended to geometries resembling real corrugated sheets of packing used in industrial applications. In earlier numerical studies of structured packing, geometries were simplified to enable easy meshing and faster computation. In this work, the geometries of corrugated sheets of packing were developed without any simplification and the flow behaviour was studied using the model validated in the first step. The flow behaviour on sheets with different geometrical modifications such as smooth and triangular crimp surfaces as well as perforations on the sheets were numerically studied and quantitatively compared with experimental studies for the three different fluid test systems. The agreement between the simulations and experiments was within an acceptable range for all system. The difference in the interfacial area between the corrugated sheets of a packing with and without perforation was analyzed and the prediction ability of different empirical correlations for the interfacial area available in literature was also compared and discussed. Furthermore, the numerical study was extended to understand the influence of the second corrugated sheet. Studying the flow behaviour between two sheets experimentally is very challenging, especially inside opaque packing. The model proved to be a very suitable tool to study the hold-up of the liquid between two sheets, the change in wetting behaviour due to small change in liquid inlet position. The results are also in good agreement with the earlier experimental studies, where researchers measured the liquid hold-up mainly in the region where two corrugated sheets touch each other. The three-dimensional CFD model was validated to study the flow behaviour on corrugated sheets of packing. The results from the simulations agree very well with findings from the experimental studies in terms of wetting and hold-up.

This work refers to ball-intersections bodies as well as covering, packing, and kissing problems related to balls and spheres in normed spaces. A quick introduction to these topics and an overview of our results is given in Section 1.1 of Chapter 1. The needed background knowledge is collected in Section 1.2, also in Chapter 1. In Chapter 2 we define ball-intersection bodies and investigate special classes of them: ball-hulls, ball-intersections, equilateral ball-polyhedra, complete bodies and bodies of constant width. Thus, relations between the ball-hull and the ball-intersection of a set are given. We extend a minimal property of a special class of equilateral ball-polyhedra, known as Theorem of Chakerian, to all normed planes. In order to investigate bodies of constant width, we develop a concept of affine orthogonality, which is new even for the Euclidean subcase. In Chapter 2 we solve kissing, covering, and packing problems. For a given family of circles and lines we find at least one, but for some families even all circles kissing all the members of this family. For that reason we prove that a strictly convex, smooth normed plane is a topological Möbius plane. We give an exact geometric description of the maximal radius of all homothets of the unit disc that can be covered by 3 or 4 translates of it. Also we investigate configurations related to such coverings, namely a regular 4-covering and a Miquelian configuration of circles. We find the concealment number for a packing of translates of the unit ball.

The key to success in separation of liquid mixtures is the efficient creation and utilization of vapour-liquid contact area. By packing the column with gas-liquid contact devices such as structured packing, the vapour-liquid contact area can be increased. However, the efficiency of these packed columns depends strongly on the local flow behaviour of the liquid and vapour phase inside the packing. The aim of this work was to develop three-dimensional CFD models to study the hydrodynamic behaviour on the corrugated sheets of packing. Different approaches are possible to simplify the problem and to extend it for more complex flow scenarios. In this work, three-dimensional CFD simulations were performed to study the complete fluid-dynamic behaviour. This was performed in two steps. As a first step, the developed model was validated with experimental studies using a simplified geometry i.e., an inclined plate. The three-dimensional Volume-of-Fluid (VOF) model was utilized to study the flow behaviour of the gas-liquid countercurrent flow. The influence of the liquid surface tension was taken into consideration using the Continuum Surface Force (CSF) model. The wetting characteristics of liquids with different viscosity (1 and 5 mPas) and contact angle (70° and 7°) were studied for different flow rates. Three different mixtures (water, water-glycerol (45 wt. %) and silicon-oil (DC5)) were considered. Initially, the rivulet width of experiments and simulations were compared and an error of 5 % maximum was determined. The results were also in good agreement with earlier studies. The percentage of wetting due to changes in flow rate, viscosity and contact angle was compared and discussed. For all tested systems, excellent agreement between the experiments and simulation studies was found. In addition, profiles of the velocity in the film at film flow conditions over a smooth inclined plate obtained from simulations were compared with experimental profiles obtained using a μPIV technique. A detailed sensitivity study was also performed in order to understand the changes in the velocity profiles due to small change in liquid flow rate, temperature and inclination angle. As a next step, the developed model was extended to geometries resembling real corrugated sheets of packing used in industrial applications. In earlier numerical studies of structured packing, geometries were simplified to enable easy meshing and faster computation. In this work, the geometries of corrugated sheets of packing were developed without any simplification and the flow behaviour was studied using the model validated in the first step. The flow behaviour on sheets with different geometrical modifications such as smooth and triangular crimp surfaces as well as perforations on the sheets were numerically studied and quantitatively compared with experimental studies for the three different fluid test systems. The agreement between the simulations and experiments was within an acceptable range for all system. The difference in the interfacial area between the corrugated sheets of a packing with and without perforation was analyzed and the prediction ability of different empirical correlations for the interfacial area available in literature was also compared and discussed. Furthermore, the numerical study was extended to understand the influence of the second corrugated sheet. Studying the flow behaviour between two sheets experimentally is very challenging, especially inside opaque packing. The model proved to be a very suitable tool to study the hold-up of the liquid between two sheets, the change in wetting behaviour due to small change in liquid inlet position. The results are also in good agreement with the earlier experimental studies, where researchers measured the liquid hold-up mainly in the region where two corrugated sheets touch each other. The three-dimensional CFD model was validated to study the flow behaviour on corrugated sheets of packing. The results from the simulations agree very well with findings from the experimental studies in terms of wetting and hold-up.

Verallgemeinerungen bekannter Existenz- und Eindeutigkeitsaussagen für gebietsfüllende Kreispackungen. Für jedes beschränkte, einfach zusammenhängende Gebiet und für jeden zulässigen Komplex existiert eine gebietsfüllende, verallgemeinerte Kreispackung, die einer beliebigen der folgenden Normalisierungen genügt. alpha-beta-gamma: drei Randkreise sind je einem Randpunkt (Primende) zugeordnet alpha-gamma: ein Kreis mit fixem Mittelpunkt und ein Randkreis mit zugeordnetem Primende alpha-beta: zwei Kreise mit fixen Mittelpunkten Bedingungen werden angegeben, unter welchen die aufgeführten Normalisierungen eindeutige Lösungen implizieren, welche zudem stetig von den Normalisierungsparametern abhängen. Ist der Alpha-Kreis ein innerer Kreis, dann wird gezeigt, dass die alpha-beta Normalisierung im Allg. keine Eindeutigkeit liefert. Bedingungen werden aufgeführt, die nicht-entartete Lösungen (klassische Kreispackungen) garantieren. Alle Beweise sind möglichst elementar und unabhängig von existierenden Kreispackungs-Ergebnissen. / Existing existence and uniqueness results in the field of domain filling circle packings are generalized. For every bounded, simply connected domain, for every admissible complex, and under any of the following normalizations it is shown that there is a domain filling generalized circle packing. alpha-beta-gamma: three boundary disks are each associated with a boundary point (prime end) alpha-gamma: one disk with fixed center and one boundary disk with associated prime end alpha-beta: two disks with fixed centers Conditions are given under which the stated normalizations yield unique solutions, which then depend continuous on some normalization parameters. For the special case of an interior alpha disk it is shown that the alpha-beta normalization does not yield uniqueness in general. Several conditions are stated that guarantee non-degenerate solutions (classical circle packings). All proofs are kept as elementary as possible and independent of existing circle packing results.

This work refers to ball-intersections bodies as well as covering, packing, and kissing problems related to balls and spheres in normed spaces. A quick introduction to these topics and an overview of our results is given in Section 1.1 of Chapter 1. The needed background knowledge is collected in Section 1.2, also in Chapter 1. In Chapter 2 we define ball-intersection bodies and investigate special classes of them: ball-hulls, ball-intersections, equilateral ball-polyhedra, complete bodies and bodies of constant width. Thus, relations between the ball-hull and the ball-intersection of a set are given. We extend a minimal property of a special class of equilateral ball-polyhedra, known as Theorem of Chakerian, to all normed planes. In order to investigate bodies of constant width, we develop a concept of affine orthogonality, which is new even for the Euclidean subcase. In Chapter 2 we solve kissing, covering, and packing problems. For a given family of circles and lines we find at least one, but for some families even all circles kissing all the members of this family. For that reason we prove that a strictly convex, smooth normed plane is a topological Möbius plane. We give an exact geometric description of the maximal radius of all homothets of the unit disc that can be covered by 3 or 4 translates of it. Also we investigate configurations related to such coverings, namely a regular 4-covering and a Miquelian configuration of circles. We find the concealment number for a packing of translates of the unit ball.

Bei der Rektifikation werden heute zunehmend Füllkörperkolonnen mit geordneten Packungen eingesetzt. Die Maldistribution, ein bislang ungelöstes Problem in Füllkörperkolonnen, wirkt sich negativ auf die Stoffaustauschleistung aus. Zur Verringerung der Maldistribution wird zwischen den Packungssektionen mehrfach die Rücklaufflüssigkeit gesammelt und erneut gleichmäßig über den Kolonnenquerschnitt verteilt. Diese Neuverteilung realisieren Zwischenverteiler, die somit einen Großteil der Kolonnenhöhe beanspruchen und damit die Investitions- und Betriebskosten erheblich erhöhen. Hauptursache für die Bauhöhe der Zwischenverteiler ist der Wunsch nach einem vollständigen Konzentrationsausgleich vor der Neuverteilung. Um die Kolonnenhöhe zu verringern und dennoch die gleiche Trennleistung zu erreichen, mangelt es den Anlagenbauern bislang an einer praktikablen Lösung. Entgegen der bisherigen Lehrbuchmeinung wird in dieser Arbeit die Bedeutung des vollständigen Konzentrationsausgleich grundsätzlich in Frage gestellt. Es erfolgen deshalb theoretische und experimentelle Untersuchungen für ein besseres Verständnis der Neuverteilung der Rücklaufflüssigkeit und deren Auswirkung auf die Trennleistung. Durch Modifizierung des klassischen Zwei-Kolonnen-Modells gelingt es, den Einfluss der Maldistribution, der Dampfquervermischung und der hydraulisch gleichmäßigen Flüssigkeitsneuverteilung mit und ohne vollständigen Konzentrationsausgleich numerisch zu simulieren. Die Überprüfung der Simulationsmodelle erfolgt an einer Pilotkolonne mit einem inneren Durchmesser von 1 m. Die Kolonne ist mit Sulzer MellapakPlus 752.Y ausgerüstet und als Testgemisch dient trans-/cis-Dekalin. Im Ergebnis zeigt sich, dass vor allem der hydraulische Ausgleich erforderlich ist und es praktisch keinen Unterschied zwischen vollständigen und unvollständigen Konzentrationsausgleich bei sonst gleichen Betriebsbedingungen gibt. Überlegungen für deutlich flachere Verteilerkonstruktionen werden vorgestellt.

Questions that were answered in the dissertation: Which process is suitable to desulphurize biogas knowing that chemical absorption will be used to separate CO2? Which absorption solvent is suitable to separate CO2 from concentrated gases such as biogas at atmospheric pressure? What properties of the selected solvent, namely aqueous diglycolamine (DGA), are already known? How to determine solvent properties such as equilibrium CO2 solubility under absorption and desorption conditions using simple, but robust apparatuses? What values do solvent properties such as density, viscosity and surface tension take at various DGA contents and CO2 loadings? How do primary alkanolamine content and CO2 loading influence solvent properties? What is the optimal DGA content in the solvent? What is the optimal desorption temperature at atmospheric pressure? How can equilibrium CO2 solubility in aqueous DGA solvents be simulated? What is the uncertainty in the results? How to debottleneck an absorber and increase its gas-treating capacity? How to determine the optimal lean loading of the absorption solvent? What are the characteristics of the absorption process that uses aqueous DGA as the solvent to separate CO2 from biogas and is more energy efficient and safer than the state-of-the-art processes? How to quantitatively compare the hazards of absorption solvents? What is the disposition of the German population towards hazards from biogas plants? What are the favourable and adverse environmental impacts of biomethane? / Fragen, die in der Dissertation beantwortet wurden: Welches Verfahren ist zur Entschwefelung von Biogas geeignet, wenn die chemische Absorption zur CO2-Abtrennung genutzt wird? Welches Absorptionsmittel ist geeignet, um CO2 aus konzentrierten Gasen, wie Biogas, bei atmosphärischem Druck abzutrennen? Welche Eigenschaften des ausgewählten Absorptionsmittels, wässriges Diglykolamin (DGA), sind bereits bekannt? Wie wird die CO2-Gleichgewichtsbeladung unter Absorptions- und Desorptionsbedingungen mit einfachen und robusten Laborapparaten bestimmt? Welche Werte nehmen die Absorptionsmitteleigenschaften wie Dichte, Viskosität und Oberflächenspannung bei verschiedenen DGA-Gehalten und CO2-Beladungen? Wie werden die Absorptionsmitteleigenschaften durch den Primäramin-Gehalt und die CO2-Beladung beeinflusst? Was ist der optimale DGA-Gehalt im Absorptionsmittel? Was ist die optimale Desorptionstemperatur bei atmosphärischem Druck? Wie wird die CO2-Gleichgewichtsbeladung im wässrigen DGA simuliert? Welche Ungenauigkeit ist zu erwarten? Wie wird eine Absorptionskolonne umgerüstet, um die Kapazität zu erweitern? Wie wird die optimale CO2-Beladung des Absorptionsmittels am Absorbereintritt (im unbeladenen Absorptionsmittel) bestimmt? Was sind die Prozesseigenschaften eines Absorptionsverfahrens, das wässriges DGA als Absorptionsmittel nutzt sowie energieeffizienter und sicherer als Verfahren auf dem Stand der Technik ist? Wie kann das Gefahrenpotenzial von Absorptionsmittel quantitativ verglichen werden? Wie werden Gefahren aus einer Biogasanlage durch die deutsche Bevölkerung wahrgenommen? Welche positive und negative Umweltauswirkung hat Biomethan?