Refine
Document Type
- Doctoral thesis (6)
- Habilitation thesis (1)
Has Fulltext
- yes (7)
Is part of the Bibliography
- no (7)
Keywords
- Strömungsmechanik (7) (remove)
Numerical investigation and extension of quadrature-based moment methods for population balances
(2023)
Particulate systems can be described by a number density function (NDF) with respect to a vector of internal coordinates. The evolution of the NDF is governed by the typically high-dimensional population balance equation (PBE). A common approach to reduce the dimensionality of the problem is to solve only for a set of moments instead of the NDF. The derived system of moment equations, however, includes unclosed integral terms that still contain the unknown NDF. One way to close the system of moment equations is to approximate the unclosed integral terms using a Gaussian quadrature computed from the moments. The procedure of taking a set of moments to compute a Gaussian quadrature, which is, in turn, used to close the moment equations, is known as the quadrature method of moments (QMOM). It gave rise to an entire family of methods, the quadrature-based moment methods (QBMMs), which are the primary focus of this work. The presented research can be divided into three major parts. The first part involves the formulation of a common Lagrangian droplet breakup model for QBMMs and the numerical investigation with the QMOM as well as the more sophisticated extended QMOM (EQMOM). The results indicate that the approximations are reasonably accurate when at least six moment equations are solved, with the EQMOM providing no advantages for the investigated configurations. In the second part, a quadrature-based moment model for the effects of fluid turbulence on particle velocities is formulated. The resulting moment equations contain non-smooth integrands that are the source of large errors when using common QBMMs. As an alternative, the Gauss/anti-Gauss QMOM (GaG-QMOM) is proposed that uses the average of a Gaussian and an anti-Gaussian quadrature. Numerical studies show that the GaG-QMOM is able to significantly reduce the previously observed large errors. Another novelty proposed in this context is the modification of the second-order strong-stability preserving Runge-Kutta method to guarantee the preservation of moment realizability in the presence of phase-space diffusion. The third part is concerned with the numerical exploration of the core algorithm of most QBMMs in terms of performance and accuracy. The algorithm consists of, first, computing the recurrence coefficients of the orthogonal polynomials associated with a set of moments, second, solving a symmetric tridiagonal eigenvalue problem to obtain the quadrature nodes and weights, and third, evaluating the integral terms in the moment equations. The results indicate that the contribution of the first step to compute the recurrence coefficients from moments to the overall computational costs is negligible. Instead, the primary focus should be on the fast solution of the eigenvalue problem and, possibly, on the efficient implementation of the moment source term evaluation, which becomes important when second-order processes are considered.
The Taylor-Couette (TC) flow, the flow confined between two concentric independently rotating cylinders, is used as a perfect model to investigate shear flow over concave surfaces and one of the paradigmatic systems of the physics of fluids. In this thesis, an experimental investigation of the turbulent TC flow in a very wide gap geometry with a radius ratio 𝜂 = 0.1 is performed. The physical and dynamic behavior of the flow is studied in a geometry that has rarely been investigated before the current study, which makes this study unique. The study aims to understand the effect of curvature on the TC flow, particularly in cases where the circumferential length of the inner cylinder is smaller than the gap width. The flow is studied in the different rotation regimes: counter-rotating, co-rotating, and purely inner cylinder rotating regimes up to shear Reynolds numbers Re_s≤ 150000. The flow field has been qualitatively studied using visualization techniques. By probing the different flow parameters, familiar coherent TC flow patterns appear, in addition to newly observed patterns we assume only exist for very wide gap TC flows. For a more detailed quantitative study, a time-resolved velocity field measurement has been conducted using the High-speed Particle Image Velocimetry technique through the system end plate. The radial and azimuthal velocity components in the 2D horizontal plane are measured at different axial positions, in order to scan the axial variance of the flow. The recorded flow field is used to compute the angular momentum transport in terms of the quasi-Nusselt number (Nu_ω). The results show a maximum of Nu_ω for low counter-rotating rates of −0.011 ≤ μ_max ≤ −0.0077, which is associated with large-scale structures that span the entire gap. Moreover, the Nu_ω decreases for counter-rotation rates higher than μ_max until it reaches a minimum value and then tends to increase again for higher counter-rotation cases. The space-time behavior of the turbulent flow field for the high counter-rotating cases shows the existence of newly observed patterns next to the outer cylinder wall that propagates inward, enhancing the angular momentum transport and resulting in a second maximum in transport for higher counter-rotating rates. For the pure rotating inner cylinder, the momentum transport scaling with the shear rate Nu_ω ∼ Re_s^α has been studied, and it shows a transition in scaling to 𝛼 = −0.76 for all flows with Re_(s )≥ 25000. This new scaling reveals the transition of the flow from the classical turbulent regime to the ultimate one, where this transition is accompanied by a clear change in the flow behavior. Moreover, the flow in the co-rotating regime and particularly in the centrifugal stable regime (𝜇 > +0.01) is investigated. The Velocity measurements show the presence of disturbed flow near the inner cylinder, where the measured velocity profiles showed a clear deviation from those predicted by laminar flow for flows up to 𝜇 = +0.04.
The GeoFlow (Geophysical Flow) experiment on the International Space Station (ISS) and the AtmoFlow (Atmospherical Flow) experiment are designed to study convective processes under microgravity conditions in the spherical gap geometry. By applying a high voltage field between two concentric spherical shells and utilizing a dielectric working fluid it is possible to maintain an artificial radial force field that is comparable to a planetary gravitational field. This makes it possible to study convection such as known from the Earth's outer core, the Earth's mantle, or planetary atmospheres. The radial force field is based on the dielectrophoretic effect and is described by thermo-electro hydrodynamics (TEHD). This habilitation thesis presents a comprehensive view on modeling TEHD and the numerical simulation of the governing equations with a focus on GeoFlow and AtmoFlow. The GeoFlow experiment investigated thermal convection with and without dielectric (internal) heating under long-time micro-gravity conditions on the ISS. This unique experimental setup consisted of a bottom heated and top cooled spherical gap, filled with the silicon oil M5 or 1-Nonanol. Rotation, varying voltage, and temperature differences across the gap could be applied, to spread the experimental parameter space. The main focus of GeoFlow was the investigation of flow properties such as the convective onset, the transition from laminar to turbulent flows, and the influence of rotation on convection. Experimental outcomes were compared with theoretical and numerical results via advanced post-processing techniques. This includes pattern recognition algorithms and statistical evaluation of the numerical simulations. The TEHD model was validated on the onset of convection through linear stability analysis, on properties of columnar cells and global convective structures such as regular laminar flows. It is shown that TEHD based convection is comparable with Rayleigh-Benard convection and that is can be described by the quasi-normal approximation. For rotating cases and low super-criticalities the Proudman-Taylor theorem dominated the fluid flow which resulted in global columnar cells. In summary, the presented TEHD model is able to explain certain aspects of convective flows observed in GeoFlow. It is the first validation for such a model at all stages. The AtmoFlow experiment is based on GeoFlow but is designed to investigate global cells and planetary waves which are known from planetary atmospheres. Its unique feature are the atmospheric-like boundary conditions. Understanding the interaction between atmospheric circulation and a planet's climate, be it Earth, Mars, Jupiter, or a distant exoplanet, contributes to various fields of research such as astrophysics, geophysics, fluid physics, and climatology. AtmoFlow is currently under construction and is planned for operation on the ISS in 2024.
PEM water electrolysis is a clean technology for hydrogen production. In spite of its many advantages, the costs of the conventional PEM electrolysis cell makes it commercially less competitive vis-à-vis its peers. An alternative cell design has been proposed which has up to a 25 % costs advantage over the conventional cell. In this alternative cell design, the flow channel plate which bears the most costs in the conventional cell design has been replaced with a 3-D Porous Transport Layer (PTL) structure. It has however, been observed that the conventional cell by far out performs the low cost cell at high current density operations, due to increased mass transport limitation in the later. Industrial and commercial hydrogen production efforts are focused towards high current density operation (> 3 A/cm²), so the alternative cell design must be optimized for mass transport limitation.
PEM water electrolysis is a clean technology for hydrogen production. In spite of its many advantages, the costs of the conventional PEM electrolysis cell makes it commercially less competitive vis-à-vis its peers. An alternative cell design has been proposed which has up to a 25 % costs advantage over the conventional cell. In this alternative cell design, the flow channel plate which bears the most costs in the conventional cell design has been replaced with a 3-D Porous Transport Layer (PTL) structure. It has however, been observed that the conventional cell by far out performs the low cost cell at high current density operations, due to increased mass transport limitation in the later. Industrial and commercial hydrogen production efforts are focused towards high current density operation (> 3 A/cm²), so the alternative cell design must be optimized for mass transport limitation.
This work seeks to understand the source of, and to eliminate the mass transport losses in the alternative cell design to get it performing at least as good as the conventional cell at current densities up to 5 A/cm². A 2-D non-isothermal semi-empirical fully-coupled models of both cell designs have been developed and experimentally validated. The developed validated models were then used as tools to simulate and predict the best operating conditions, design parameters and micro-structural properties of the PTL at which the mass transport issues in the alternate cell will be at its minimum, at high current densities. The models are based on a multi-physics approach in which thermodynamic, electrochemical, thermal and mass transport sub-models are coupled and solved numerically, to predict the cell polarization and individual overpotentials, as well as address heat and water management issues. The most unique aspect of this work however, is the development of own semi-empirical equations for predicting the mass transport overpotential imposed by the gas phase (bubbles) at high current densities. For the very first time, calculated polarization curves up to 5 A/cm² have been validated by own experimental data. The results show that, the temperature and pressure, water flowrate and thickness of the PTL are the critical parameters for mitigating mass transport limitation. It was found that, for the size of the cells studied (25 cm² active area each), when both cells are operating at the same temperature of 60 °C, alternative design will have a comparable performance to the conventional designed cell even at 5 A/cm² current density when; the operating pressure is ≥ 5 bar, the feed water flowrate is ≥ 0.024l/min∙cm², PTL porosity is 50 %, PTL pore size is ≥ 11 µm and PTL thickness is 0.5 mm. At these operating, design and micro-structural conditions, the predicted difference between the polarizations of both cells will be only ~10 mV at 5 A/cm² operating current density.
Investigations of high Reynolds number pipe flow is up to now a great challenge due to the complex mechanisms which appear in pipe flow turbulence. Hence, suitable experimental facilities are necessary to resolve turbulent dynamics and therewith to provide the knowledge for the understanding of such a simple shear flow. For this reason the recent thesis deals with conceptual design and setup of a new high Reynolds number pipe test facility further on named CoLaPipe - Cottbus Large Pipe. It also comprises first investigations on pipe flow obtained from the new CoLaPipe, which can be classified into 1.)calibration measurements to put the facility into service and 2.)continuative measurements to provide experimental results helping to understand pipe flow.
The first results within the CoLaPipe show that this new experimental facility is suitable to investigate turbulence at high Reynolds numbers, where this conclusion can be drawn from intensive investigations on the development length of the flow either for natural and artificial transition. From further experiments on the evaluation of the wall friction velocity using different estimation methods great difficulties and variations in the calculated values are obtained. These deviations are directly related to the scaling behavior of the mean and fluctuating velocity, which is also shown within this thesis and intensively discussed.
Among the discussion of the setup of the new CoLaPipe and the first experimental results this thesis contains a broad literature review with the focus on high and very high Reynolds numbers. Nevertheless, pipe flow at low and moderate Reynolds numbers is described as well.
Single-use Bioreaktoren sind im biopharmazeutischen Umfeld etabliert und werden heute vor allem im F&E-Bereich sowie bei der klinischen Produktion von biopharmazeutischen Produkten eingesetzt. Für die Herstellung solcher Produkte werden vielfach die single-use Bioreaktoren von Sartorius Stedim Biotech (UniVessel® SU und der BIOSTAT® STR) und Thermo Scientific (S.U.B.) genutzt, deren Eignung auf Basis ihrer Strömungseigenschaften in dieser Arbeit diskutiert wird. Hierfür wird sowohl eine grundlegende als auch eine erweiterte, örtlich und zeitlich betrachtende verfahrenstechnische Charakterisierung durchgeführt. Die für Zellkulturbioreaktoren verfahrenstechnisch relevanten Parameter, wie der spezifische Leistungseintrag, die Mischzeit, der Sauerstoffübergang werden durch etablierte, experimentelle Methoden bis zu einem Maßstab von 50 L bestimmt. Mittels der örtlichen und zeitlich auflösenden numerischen Strömungsmechanik (engl.: Computational Fluid Dynamics, CFD) werden Prozessgrößen verglichen und detaillierte Strömungsverläufe beschrieben. Die experimentelle Betrachtung des Strömungsverhaltens und der Fluidgeschwindigkeiten sowie der Vergleich der experimentell und numerisch erhaltenen verfahrenstechnischen Parameter dienen der Validierung der CFD-Modelle bis zum 50 L Maßstab. Auf Basis der validierten CFD-Modelle erfolgt die numerische Bestimmung der verfahrenstechnischen Parameter für die unterschiedlichen single-use Bioreaktoren bis zu den jeweiligen maximalen Arbeitsvolumen von 1000 L (BIOSTAT® STR) bzw. 2000 L (S.U.B.). Aufgrund der verfahrenstechnischen Parameter sind die betrachteten single-use Kultivierungssysteme vergleichbar mit konventionellen Zellkulturbioreaktoren (aus Glas oder Edelstahl) und zeigen eine Skalierbarkeit auf. Eine detailliertere Betrachtung zur Maßstabsübertragung basiert auf den Mischzeit und den mittleren, lokalen Schergradienten. Beide Parameter zeigen eine Abhängigkeit zur Reaktor- und Rührergeometrie, zum spezifischen Leistungseintrag und zum Volumen, wodurch sich deren Bestimmung durch die Etablierung zweier Gleichungen für die aufgeführten single-use Bioreaktoren realisieren lässt. Die numerisch erhaltenen verfahrenstechnischen Parameter werden schließlich für die Prozessauslegung und -entwicklung eines Modellprotein-Produktionsprozesses mit CHO-Zellen herangezogen. Das üblicherweise eingesetzte Kriterium einer Maßstabsübertragung - der spezifische Leistungseintrag - zeigt dabei nur bedingt erfolgversprechende Ergebnisse für die Prozessauslegung auf. Hingegen werden mit den numerischen Mischzeiten und den mittleren, lokalen Schergradienten als Kriterien zur Maßstabsübertragung wesentlich höhere maximale Lebendzelldichten erhalten. Zusätzlich sind die gemessenen maximalen Lebendzellzahlen für die Labor- und Pilotmaßstäbe reproduzierbar. Des Weiteren wird für die Prozessentwicklung die Quantität der Proteinexpression des biphasischen Produktionsprozesses (mit CHO XM 111-10 Zellen) herangezogen. Nach der Proteininduktion mittels eines etablierten single-use Crossflow-Verfahrens werden Proteinkonzentrationen bis 60 U/mL gemessen. Die aus den Produktionsprozessen gewonnenen Resultate lassen dabei auf die vorteilhafte Nutzung der single-use Bioreaktoren von Sartorius Stedim Biotech schließen und zeigen die Möglichkeit einer CFD-basierten Prozessauslegung auf. Die numerische Herangehensweise kann resultierend auch als Grundlage für weitere moderne Produktionsprozesse, wie beispielsweise für die Stammzellexpansionen, dienen.
Gekoppelte fluidmechanische Modelle für Desinfektionsvorgänge und deren Effizienz in UV-Reaktoren
(2005)
Ziel der Dissertation ist es, mikrobiologische, biophysikalische, optische und fluidmechanische Ansätze von einem theoretischen Standpunkt derart zu vereinen, dass für den betreffenden Anwendungsfall mit einem durchgängigen Rechengang der optimale UV-Reaktor dimensioniert werden kann. Ein solches die Einzeldisziplinen verbindendes Modell erhält die Bezeichnung Gekoppeltes Fluidmechanisches Modell (GFM) bzw. wenn weitere Gesichtspunkte eine Rolle spielen Gekoppelte Fluidmechanische Modelle. Dieses Ziel wurde durch die Formulierung und die Aufstellung der entsprechenden Gleichungssysteme erreicht. Für diesen Zweck wurden aufbauend auf dem Erkenntnisstand der Einzeldisziplinen die adäquaten Ergebnisse und Modellansätze ausgewählt und mathematisch erprobt. Eine repräsentative Auswahl der derzeit in der Bundesrepublik Deutschland seitens der Industrie verwendeten UV-Reaktorkonstruktionen wurden untersucht und bewertet. Die im Rahmen der Arbeit entwickelten Gekoppelten Fluidmechanische Modelle (GFM) wurden unter dem Aspekt eines theoretischen Modellreaktors und einer konkreten technischen Anwendung (Praxisreaktor) sowie deren Erweiterung durch die Variation eines Konstruktionsparameters, in numerische Berechnungen getestet. Vorliegende meßtechnische in der Praxis des Betriebs von Schwimmbädern gewonnene Ergebnisse dienten als experimenteller Hintergrund. Der Inhalt der Arbeit ist derart aufbereitet, dass die Ansätze und Verfahrensvorschläge für die Einbindung in ein existierendes CFD-software-Paket geeignet sind oder in einer kombinierten Form genutzt und angewendet werden können (spread-sheet-Lösung). Während der Analyse wurde eine Klassifizierungsmethode entwickelt, die sich auf den technischen Details der Reaktorkonstruktionen und auf den in diesen verwendeten Plasma - Strahlungsquellen gründet.