Refine
Document Type
- Doctoral thesis (15)
- Master thesis (1)
Has Fulltext
- yes (16)
Is part of the Bibliography
- no (16)
Year of publication
Keywords
- Numerische Strömungssimulation (16) (remove)
Institute
- FG Thermische Energietechnik (3)
- FG Aerodynamik und Strömungslehre (2)
- FG Numerische Strömungs- und Gasdynamik (2)
- FG Thermodynamik / Thermische Verfahrenstechnik (2)
- FG Biotechnologie der Wasseraufbereitung (1)
- FG Chemische Reaktionstechnik (1)
- FG Mechanische Verfahrenstechnik (1)
- FG Numerische Mathematik und Wissenschaftliches Rechnen (1)
- FG Technische Akustik (1)
- FG Technische Mechanik und Fahrzeugdynamik (1)
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.
In the Garu-Tempane area and Tamne River basin of north-eastern Ghana, granitic aquifers supply nearly 80% of annually abstracted groundwater. Rapid and diffuse recharge enters the fractured and weathered Tamnean Plutonic Suite aquifers mainly granitoid, which are the dominant rock types in the study area. However, a greater challenge to the water supply in the area is posed by global climatic changes and overexploitation due to population growth. The semi-arid nature of the area together with the factors mentioned earlier has caused water scarcity, particularly in the dry season and these have affected the livelihoods of the farmers who depend mostly on the groundwater for irrigation and domestic purposes. A promising way to balance water resources in the region is using engineering technology such as managed aquifer recharge (MAR). MAR augments water levels in water-scarce areas and represents a key tool in water supply management.
For this reason, a comprehensive hydrogeological characterization involving the hydrochemistry of the groundwater, groundwater recharge process and residence time using multi-environmental tracers, and a numerical groundwater flow model was developed.
Based on the hydrochemistry results, the water quality index showed that the groundwater is very suitable for drinking. However, about 10.5 % out of the 38 groundwater samples had elevated nitrate concentrations exceeding the permissible WHO drinking water limit. These are mainly agricultural areas, which might have influenced the elevated nitrate concentrations.
Groundwater age dating using sulphur hexafluoride (SF6) and chlorofluorocarbons (CFCs) was used to date shallow groundwater in Ghana for the first time. The results proved that the mean residence time of groundwater was around 30 years, an indication of young groundwater and rapid groundwater renewability. The findings also showed different groundwater ages implying diffused flow systems occurring in the fractured granitic aquifer.
Investigation of the groundwater recharge using stable isotopes of deuterium and oxygen-18 revealed that the main source of groundwater recharge is of meteoric origin. There were little or no contributions from the stream and ponds as they were subjected to evaporative fractionation during the dry season. The White Volta River samples and samples from two big rivers were depleted in heavy isotopes, which suggested a hydraulic connection between them and the groundwater.
The numerical groundwater flow model was used to assess the feasibility of MAR and determine the maximum recharge and abstraction rates. The results showed that the aquifer had enough storage to accommodate enough volumes of floodwater without causing groundwater mounding. This shows that MAR is feasible in augmenting the water levels in the area when irrigation and domestic withdrawals are regulated.
Wind energy is a growing concern over the present awareness of lethal impact of green house gas emission. This energy source has been proven a promising alternative to fossil fuel based energy. Increased onshore wind capacity and decreased amount of low roughness wind sites has inspired the wind energy researchers to explore the possibilities of wind energy from high roughness sites such as urban area. Moreover, exhausted grid capacity between the wind energy producer from remote area and the consumer at city is also a major constrain for wind energy expansion. Driven by such motivation, this thesis has explored possibilities of wind energy conversion from buildings where energy is needed the most. Urban topography is known to be highly turbulent region considering its roughness characteristics.
Wind energy yield from urban aerodynamics is a vast arena of experimental research. Within the time frame of the thesis period and available opportunities, a brief description about the wind energy assessment modelling approach from urban flow was outlined. There are several possibilities of wind energy yield from the built structure, but only building integrated duct was focused in this thesis.
Time-averaged and global wind speed on the building integrated ducts, flow around the buildings was measured from wind tunnel and numerical analysis. Available wind energy yield and turbulence present in the locations measured from the flow was calculated based on the wind tunnel data and summarized with the pros and cons of the particular geometry. Elliptical duct configuration was found to achieve maximum energy yield from the omnidirectional free stream flow. However, simple rectangular duct configuration was determined as most efficient and optimized considering its simplicity, financial feasibility and relative energy yield with other duct configuration. The thesis also showed that on roof configuration is also very promising for wind energy exploration from the omnidirectional free stream flow.
Necessary recommendations were made based on available result for future development of the research approach. Scope and opportunities was mentioned. This investigation has proved that it is possible to extract limited amount of wind energy from building augmented ducts using concentrator effect of the building exterior. Thus, the thesis concluded that the wind energy yield from building augmented ducts using the concentrator effect of the building exterior is a promising renewable energy source.
Electrostatic precipitators (ESPs) belong to the most efficient devices for control of particle emissions in the process industry and environmental technologies in general. The operating principle of ESPs, relying on particle precipitation by electrical charging, leads to an enhanced turbulent motion by electrohydrodynamic (EHD) effects within the gaseous working fluid passing through the ESP. This enhanced turbulence is generally considered detrimental to the separation efficiency, because the additional shear forces acting on the collection electrodes promote re-entrainment of already precipitated particles. Further, the enhanced turbulent cross mixing diminishes the transport of charged particles by electric forces directed towards the collection electrodes. In other industrial applications however, many process units that are based on heat or mass transport would benefit from enhanced turbulent mixing. These include heat exchangers for energy recuperation or evaporation and absorption units such as flue gas scrubbers. A combination of these with an ESP possibly allows for versatile new applications in the process industry.
The motivation of this thesis is to study the effects of electrohydrodynamically generated motions onto the turbulent cross mixing within gaseous flows over a wide parameter space including variations in geometry and operating conditions. In order to do so, the influence of EHD effects on the three major transport properties, i.e. thermal energy, mass and momentum, were experimentally investigated. Based on analogies caused by similar transport mechanisms, the experimental results were compared despite different methods being used. In order to help with the comparison a simplified eddy viscosity model is applied.
The study for each transport property was conducted with a different setup of a tube type ESP. These setups include axial and radial pressure drop measurements to quantify the momentum transport, a self-built local heat transfer sensor to determine heat transfer coefficients and a wetted wall-column to study the enhancement of mass transport phenomena. Experiments on momentum and heat transport include a large variation of different geometries and operating variables such as discharge electrode design, tube diameter, flow velocity, as well as magnitude and polarity of operating voltage. In addition, selected measurements with aerosol particles were conducted, to gain additional insights on the effects of EHD induced turbulence generation by particle bound space charge compared to ion bound space charge in clean gas flows.
The results do not only provide transport coefficients for the hands-on application by plant designers, but also feature numerous experimental data that can be used as reference values for ongoing research in the numerical simulation of electrohydrodynamically enhanced flow and therefore significantly increase the available amount of data provided by current literature.
A local algebraic simulation model was developed, to determine the characteristic length scales for dispersed phases. This model includes the Ishii- Zuber drag model, the lift, the wall lubrication force and the turbulent dispersion force as well. It is based on the Algebraic Interface Area Density (AIAD) model from the Helmholtz Zentrum Dresden Rossendorf (HZDR), which provides the morphology detection and the free surface drag model. The developed model is in agreement with the current state of knowledge based on an examination of the theory and of state of science models for interface momentum transfer.
This new simulation model was tested on three different experiments. Two experiments can be found in the literature, the Fabre 1987 and the Hewitt 1987 experiment. And the third simulation is based on a steam drum experiment. This steam drum experiment is designed with ERK Eckrohrkessel GmbH internals and was developed to examine the droplet mass flow out of the turbulent separation stage.
The implementation of all models and tests was performed using Ansys CFX. The first analysis was carried out to reproduce a wavy stratified flow to examine the effects of different simulation model set-ups according to the velocity and kinetic energy profiles, as well as the pressure drop gradient and the water level measured by Fabre 1987. The second analysis was a proof on concept for reproducing the vertical flow pattern by an experiment from Hewitt 1987. The third simulation analysed the water distribution in the steam drum and feeding pipes system as well as the droplet carryover into the gas phase in the turbulent separation region of the drum.
These simulations have shown, that the accuracy of the particle distribution model in interaction with the drag and non-drag forces is able to reproduce horizontal and vertical flow patterns. Higher deviations are recognised for the liquid volume fraction close above the interface. Generally, simulations can now be performed to optimise industrial steam drum designs.
Beschleunigung der Verdichterkennfeldberechnung mithilfe von Methoden des maschinellen Lernens
(2021)
In der heutigen Triebwerksentwicklung ist die Verwendung komplexer und zeitaufwändiger numerischer Strömungssimulationsverfahren (3D-CFD) unerlässlich. Dies gilt auch und insbesondere für den Bereich der Verdichterkennfeldberechnung, welcher viele zeitintensive 3D-CFD Berechnungen benötigt. Dabei sind zur qualitativen Beurteilung eines Verdichterentwurfs sowohl Betriebspunkte wie, Reiseflug, Start und Landung, hinreichend genau abzubilden, als auch die kritischen, den Verdichterarbeitsbereich limitierenden Betriebsgrenzen Pumpen und Sperren zu detektieren. Bisherige Arbeiten zur automatisierten Verdichterkennfeldberechnung basieren auf strukturierten Berechnungen von verschiedenen Drehzahllinien, auf welchen jeweils isoliert Pump- und Sperrgrenze gesucht werden. Durch die Beschränkung auf einzelne Drehzahlen wird jedoch nicht der gesamte Charakter des Kennfeldes erfasst, so dass unbekannte Betriebsbereiche aus linearer Interpolation abgeleitet werden müssen. Ein zusätzlicher Nachteil solcher auf einzelne Drehzahllinien fixierten Methoden ist ihre geringe Parallelisierbarkeit.
Der Fokus dieser Arbeit liegt daher auf der Entwicklung eines effizienten Verfahrens zur Erfassung des gesamten Verdichterkennfeldes. Die zwei wesentlichen Anforderungen an das Verfahren sind erstens die Reduktion der Anzahl der notwendigen CFD-Berechnungen zur hinreichend genauen Beschreibung des Verdichterkennfeldes sowie zweitens die Beschleunigung jeder einzelnen 3D-CFD-Berechnung. Zu diesem Zweck wird zur Kennfeldberechnung eine Strategie vorgeschlagen, welche sich von der üblichen strukturierten Berechnung einzelner Drehzahllinien löst und stattdessen mit unstrukturierten, zufällig bestimmte Stützstellen arbeitet. Dabei wird ein zweiphasiges Verfahren entwickelt, bei dem zunächst die Pump- und Sperrlinien in ihrer Gesamtheit mit einer iterativen, hoch parallelisierbaren, auf Support-Vector-Machine beruhenden Strategie bestimmt werden. Als nächster Schritt wird mit Methoden der statistischen Versuchsplanung eine ausreichende Dichte von Stützstellen innerhalb der Betriebsgrenzen des Verdichters generiert. Abschließend werden auf Basis aller verwendeten Stützstellen Antwortflächen für Verdichterdruckverhältnis, Wirkungsgrad und Eintrittsmassenstrom aufgebaut.
Zur Reduktion der Rechenzeit jeder einzelnen 3D-CFD Rechnung werden unterschiedliche Methoden zur Erzeugung von Startlösungen betrachtet. In diesem Rahmen werden Initialisierungsansätze aus reduzierten Strömungsmodellen und aus der Superposition von bereits bekannten Strömungslösungen auf Basis der Methode der Proper-Orthogonal-Decomposition (POD) untersucht.
Als Validierung wird abschließend das entwickelte Verfahren zur Kennfeldberechnung in Kombination mit dem POD-Initialisierungsansatz erfolgreich auf die Analyse eines 4.5- stufigen Forschungsverdichters angewendet.
This thesis is an attempt to assess some of the effects that electroquasistatic body forces exert on turbulent internally forced convective flows. In order to do that, a stochastic turbulence model is employed, namely, the One-Dimensional Turbulence (ODT) model.
The reduced dimensionality of ODT demands a reduction of the Navier-Stokes equations (and in this case, also the Maxwell equations), into a 1-D system. This is done by performing an asymptotic analysis in terms of the nondimensional numbers of the flow. Also, a validation step due to the relative novel character of the cylindrical ODT formulation is done for an incompressible and constant properties flow regime and a variable density flow regime. The validation is presented for both the temporal (T-ODT) and a novel spatial (S-ODT) formulation in both planar and cylindrical geometries. Results in the constant property case show that wall normal (and radial) profiles, in both the T-ODT and S-ODT formulations, show good agreement with each other and to the data of Direct Numerical Simulations (DNSs). For the evaluated variable density heated pipe flow, gradients at the wall can be better reproduced with S-ODT.
After validating the model, ODT is applied first into a planar configuration which emulates the flow in a wire-plate Electrostatic Precipitator (ESP). For this flow, the additional input energy due to the electroquasistatic body force has an effect on the modification of the bulk velocity, and subsequently, the skin friction coefficient. Some qualitative DNS trends are confirmed with ODT, such as the localized increase of the Reynolds stress, as a consequence of increased eddy activity close to the discharge electrodes. Next, the results of ODT simulations in a cylindrical wire-tube ESP are presented. Here, ODT results are compared to experimental results. ODT results for global integral quantities such as the streamwise pressure gradient and the Nusselt number enhancement ratio are able to match in a reasonable way the experimental results. The competing relevance between the EHD contribution to turbulence by momentum, and by affecting the temperature and density due to the Joule heating effect is also analyzed, showing the leading order relevance of the former one. Specifically for the Nusselt number results, the sensitivity of the EHD flow to transition effects is shown to be very significant.
This thesis may open the door to a vast new field of phenomena which can not only serve for the further validation of the ODT model against DNSs or experiments, but also for the real use of ODT in applications which are so far inaccessible for traditional DNSs.
Sophisticated engine knock modeling supports the optimization of the thermal efficiency of spark ignition engines. For this purpose the presented work introduces the resonance theory (Bradley and co-workers, 2002) for three-dimensional Reynolds-Averaged Navier-Stokes (RANS) and for the zero-dimensional Spark Ignition Stochastic Reactor Model (SI-SRM) simulations. Hereby, the auto-ignition in the unburnt gases is investigated directly instead of the resulting pressure fluctuations. Based on the detonation diagram auto-ignition events can be classified to be in acceptable deflagration regime or possibly turn to a harmful developing detonation.
Combustion is modeled using detailed chemistry and formulations for turbulent flame propagation. The use of detailed chemistry caters for the prediction of physical and chemical properties, such as the octane rating, C:H:O-ratio or dilution. For both models, the laminar flame speed is retrieved from surrogate specific look-up tables compiled using the reaction mechanism for Ethanol containing Toluene Reference Fuels by Seidel (2017). In the fresh gas zone, the scheme is used for auto-ignition prediction. For this purpose, the G-equation coupled with a Well-Stirred-Reactor model is applied in RANS. In analogy, in the SI-SRM the combustion is modeled using a two zone model with stochastic mixing between the particles.
RANS is used to develop the knock classification methodology and to analyze in detail location, size and shape of the auto-ignition kernels. RANS estimates the ensemble average of the process and therefore cannot reproduce a developing detonation. Hence, Large Eddy Simulation (LES) is used to verify the methodology. Studies using wide ranges of surrogates with different octane rating and cycle-to-cycle variations are carried out using the computationally efficient SI-SRM. Cyclic variations are predicted based on stochastic mixing, stochastic heat transfer to the wall, varying exhaust gas recirculation composition and imposed probability density functions for the inflammation time and the scaling of the mixing time retrieved from RANS.
The methodology is verified for spark timing and octane rating. It is shown that the surrogate formulation has an important impact on knock prediction.
RANS is suitable to predict the mean strength of auto-ignition in the unburnt gas if the thermodynamic and chemical state of the ignition kernel is analyzed instead of the pressure gradients. The probability of the transition to knocking combustion can be determined. Good agreement between RANS and SI-SRM are obtained. The combination of both tools gives insights of local effects using RANS and the distribution of auto-ignition in the whole pressure range of an operating point using SI-SRM with reasonable computationally cost for development purposes.
Die vorliegende Doktorarbeit betrachtet den erosiven Verschleiß von Laval-Düsen für den pneumatischen Stofftransport. Dazu wurden 3D-CFD-Simulationen der Gas-Partikel-Strömung auf Basis des Softwarepaketes OpenFOAM durchgeführt und ein kompressibler 2-Wege-gekoppelter sowie 4-Wege-gekoppelter Strömungslöser entwickelt. Zusätzlich wurden die Partikelmethoden von OpenFOAM erheblich erweitert. So sind z.B. zusätzliche stochastische Methoden für die Partikel-Partikel und Partikel-Wand-Kollisionen (Sommerfeld & Huber, 1999) mit einer erweiterten translatorischen und rotatorischen Impulserhaltung implementiert worden. Die auf die disperse Phase wirkenden fluidmechanischen Kräfte sind die Widerstandskraft nach Henderson (1976), die Kraft durch Druck- und Spannungstensor sowie die Auftriebskraft. Der erosive Verschleiß wird wahlweise mit dem Tabakoff-Modell (Grant & Tabakoff, 1973) und dem Oka-Modell (Oka et al., 2005; Oka & Yoshida, 2005) berechnet.
Diese Arbeit entstand in Zusammenarbeit mit dem HKW Cottbus, welches im Rauchgasreinigungssystem Laval-Düsen für den pneumatischen Abtransport von Asche verwendet. Aufgrund der hohen Gas- und Partikel-Geschwindigkeiten und der Kontur der Düsen sind diese massiv durch Erosion geschädigt worden. Dadurch haben diese ihre Funktion als Blende verloren, was eine Schädigung weiterer Komponenten des Rauchgasreinigungssystems zur Folge hatte.
Zur Validierung des numerischen Strömungslösers wurde das Experiment von Kumar et al. (1983) ausgewählt und ein qualitativ vergleichbares Ergebnis generiert (60% des experimentellen Werts). Das charakteristische Verschleißbild des Experiments stellt sich nur unter Verwendung eines stochastischen Partikel-Wand-Kollisionsmodells mit hoher Wandrauigkeit ein. Im Fall glatter Wände ist der erosive Verschleiß insgesamt geringer und es verschiebt sich das Maximum der lokalen Erosionsrate.
Aufbauend auf diesen Erkenntnissen ist sowohl die Kontur der Laval-Düse des HKW Cottbus modifiziert worden als auch das Material der Düsenwandung von 13CrMo44-Stahl zu Siliziumcarbid-Keramik geändert worden. Die numerischen Simulationen des 4-Wege-gekoppelten Strömungslösers zeigen, dass sich das lokale Maximum der Verschleißrate im kritischen Bereich der Düsenkehle auf 1.5 % des Ausgangswerts reduziert und zugleich von der Düsenkehle weg verschiebt.
In dieser Doktorarbeit ist im Gegensatz zu vergleichbaren numerischen Studien eine Validierung des Strömungslösers an experimentellen Daten durchgeführt worden. Zudem ist die Bedeutung der Partikel-Partikel-Kollisionen und der Wandrauigkeiten für die Berechnung des erosiven Verschleißes bei Laval-Düsen aufgezeigt worden.
In der vorliegenden Arbeit werden die Modellierung und die numerische Simulation von Strömung, Wärme- und Stofftransport zur Abbildung eines Trocknungsprozesses von Braunkohlepartikeln in einer blasenbildenden Wirbelschicht behandelt. Hierbei wird das Euler-Euler Two Fluid Model zugrunde gelegt und die Beschreibung des Fließverhaltens der Feststoffphase mittels der Kinetic Theory of Granular Flow realisiert. Ausgehend von einem Überblick zum aktuellen Stand der Forschung wird der Bedarf nach einer geeigneten Konfiguration von Modellparametern und Submodellen hinsichtlich der Strömungsmodellierung sowie nach der Implementierung eines Trocknungsmodells abgeleitet und als Zielsetzung formuliert.
Experimentelle Voruntersuchungen an einer Wirbelschichtanlage im Labormaßstab schaffen die Datenbasis für die spätere Validierung des Modells. Dabei erfolgt zunächst eine Betrachtung einzelner Zustandspunkte von diskontinuierlichen Trocknungsprozessen, um die darin auftretenden, strömungstechnischen Veränderungen zu quantifizieren. Zur Bewertung werden die makroskopischen Eigenschaften sowie Charakteristiken meso- und mikroskaliger Strömungstrukturen herangezogen, die sich aus der Analyse von Druckfluktuationen ergeben. Des Weiteren werden die Trocknungsverläufe mehrerer Chargen für verschiedene Betriebsparameter aufgezeichnet.
In einem ersten Untersuchungsschwerpunkt werden ausschließlich strömungsmechanische Aspekte fokussiert. Auf Basis umfangreicher Sensitivitätsanalysen zu den Einflüssen der rheologisch relevanten Parameter, der Impulsaustauschfunktion einschließlich der Partikelsphärizität und der Randbedingungen für Behälterwand und Gaseinlass, sowie durch Vergleiche mit den experimentellen Daten wird eine Parameterkonfiguration des Strömungsmodells vorgeschlagen. Die damit erzielten Ergebnisse sind insgesamt zufriedenstellend und geben die beobachteten Veränderungen im Trocknungsprozess korrekt wieder. Ursachen für bestehende Abweichungen zum Experiment werden diskutiert.
Im zweiten Untersuchungsschwerpunkt wird der gesamte Trocknungsprozess betrachtet. Hierzu werden Wärme- und Stofftransportmechanismen innerhalb des Modells berücksichtigt, wobei die eigens implementierte Trocknungskinetik auf Ebene der Partikel ansetzt. Die Einflüsse der Sphärizität und zwei verschiedener Formulierungen zur Berechnung der Wärme- und Stoffübergangskoeffizienten werden untersucht. Für den favorisierten Parametersatz werden die Simulationen mit einem expliziten Vorwärtsverfahren gekoppelt, wodurch die Trocknungsverläufe auf makroskopischer Zeitskale approximiert und somit mit den experimentellen Daten verglichen werden können. Es wird gezeigt, dass das vorgeschlagene Gesamtmodell die Trocknungsverläufe bei niedrigen bis mäßigen Leerrohrgeschwindigkeiten zuverlässig abbilden kann. Auftretende Diskrepanzen werden diskutiert und weiterer Entwicklungsbedarf abgeleitet.