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In this work Adaptive Polynomial Tabulation (APT) is presented. It is a new approach to solve the initial value chemical rate equation system. In this approach zeroeth, first and second order polynomials are used in real-time to approximate the solution of the initial value chemical rate equation system. The sizes of the local regions encountered for the different orders of polynomial approximation are calculated in real-time. To improve accuracy the chemical state space is partitioned into hypercubes. During calculations the hypercubes accessed by the reactive mixture are divided into adaptive hypercubes depending on the accuracy of the local solution. Mixture initial conditions are stored in the adaptive hypercubes. Around each stored initial condition two concentric ellipsoids of accuracy (EOA) are defined. These include the ISAT and identical EOAs. The time evolution of mixture initial conditions which encounter an identical and ISAT EOA are approximated by zero and first order polynomials respectively. With a certain number of stored initial conditions within an adaptive hypercube, its second order polynomial coefficients are constructed from the stored initial conditions. The time evolution of additional mixture initial conditions that encounter this adaptive hypercube are approximated with second order polynomials. The APT model is simplified by the replacement of the entire set of species mass fractions with a progress variable based on the enthalpy of formation evaluated at 298 K. APT has 3 degrees of freedom which include the progress variable, total enthalpy and pressure. The APT model was tested with a zero dimensional Stochastic Reactor Model (SRM) for HCCI engine combustion. A skeletal n-heptane/toluene mechanism with 148 chemical species and 1281 reactions was used. In the tests, the HCCI engine simulations using APT were in very good agreement with the model calculations using the ODE solver. The cool flame and main ignition events were accurately captured. The major and minor species were also accurately captured by APT. In SRM-HCCI calculations without cyclic variations, a computational speed up factor greater than 1000 was obtained when APT was used for all the operating points considered without significant loss in accuracy. For the SRM-HCCI engine calculations with cyclic variations, APT demonstrated a computational speed up exceeding 12 without significant loss in accuracy.
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.
Diese Dissertation befasst sich mit der numerischen Simulation von Verbrennung sowie Ruß- und NOx-Emissionen in Dieselmotoren.
Für die Rußsimulation wurde das detaillierte Rußmodell von Prof. Dr. F. Mauß angewandt, das auf einer Flamelet-Bibliothek basiert (engl. Flamelet Library of Sources – FLOS). Dabei wird die detaillierte Chemie a priori gelöst und tabelliert, wodurch eine Berücksichtigung von lokalen Chemie- und Turbulenzeffekten bei akzeptablen CPU-Rechenzeiten ermöglicht wird. Unter der berechtigten Annahme, dass die Rußchemie viel langsamer als die turbulenten Längenskalen im Strömungsfeld ist, können Rußreaktionsraten vorausberechnet und in der FLOS tabelliert werden. Des Weiteren wurde ein ähnlich gestaltetes NOx-Modell entwickelt, das auch auf einem Flamelet-Bibliotheksansatz basiert.
Eine große Herausforderung bei der Anwendung von Flamelet-Bibliotheksansätzen ist die Kopplung zum CFD-Code. Eines der Hauptziele dieser Arbeit ist die Entwicklung einer neuen Methode, mit der die Kopplung zum CFD-Code verbessert wird. Der vorgeschlagene Ansatz weist eine weitere Bibliothek auf, in der Temperaturprofile von stationären Flamelets tabelliert sind. Mithilfe dieser zusätzlichen Bibliothek kann das Flamelet ausgewählt werden, das genau den thermodynamischen Bedingungen und der Gemischzusammensetzung in der CFD-Zelle entspricht. Damit wird die Konsistenz zwischen FLOS und CFD-Code hinsichtlich Mischungs-bruch und Temperatur gewährleistet.
Weitere Optimierung der Kopplung zwischen FLOS und dem CFD-Code wurde durch die Berücksichtigung der lokalen Acetylenkonzentration erreicht. Das Rußmodell ist unabhängig von dem in der CFD-Software verwendeten Verbrennungsmodell. Somit werden die Verbrennungsvorgänge in der Gasphase vom Rußmodell nicht beeinflusst. Gleichzeitig wird das Rußmodell von der Gasphasenchemie nicht beeinflusst. Während der stationären Flamelet-Rechnungen ist die lokale Rußoberfläche, von der das Oberflächenwachstum direkt abhängt, nicht bekannt. Aus diesem Grund kann der Acetylenverbrauch durch Rußoberflächenwachstum in der FLOS nicht explizit berechnet werden. Deshalb wurde das Acetylen-Feedback eingeführt: eine Limitierung der Rußoberflächenwachstumsrate, die die lokale Acetylenkonzentration berücksichtigt.
Das FLOS-Modell und die neu entwickelten Ansätze wurden mit dem CFD-Code STAR-CD© gekoppelt. Das resultierende CFD-Paket wurde für dieselmotorische Verbrennungs- und Emissionssimulation eingesetzt. Der Schwerpunkt der numerischen Untersuchungen lag auf dem Einfluss der AGR-Rate und der Einspritzstrategie auf die Verbrennung und die dabei entstehenden Ruß- und NOx-Emissionen. In diesem Kontext wurde über die Qualität des CFD-Setups und der Verbrennungssimulation diskutiert, die für eine zuverlässige Rußsimulation erforderlich ist. Die Simulationsergebnisse wurden mit experimentellen und diagnostischen Daten verglichen und zeigen eine sehr gute Übereinstimmung für die im Rahmen dieser Arbeit untersuchten Betriebspunkte. Diese Ergebnisse zeigen das Potenzial der verbrennungs-motorischen CFD-Simulation hinsichtlich Brennverfahrensoptimierung auf.
The environmental emergency has led to the development of new combustion technologies. In this context, flameless combustion (FC in this manuscript) offers the prospect of a less polluting and more efficient technology. In FC, combustion is strongly diluted with recirculated burnt gases. Consequently the oxygen content is reduced and temperature peaks are smoothed, yielding reduced heat release. These conditions dramatically reduce the conditions of NO pollutant formation and increase the efficiency of the combustion process. Being FC a relatively new technology, it still needs optimization and R&D, which can be expensive and time consuming. Potentially, CFD can reduce both the financial costs as well as the R&D projects length. The context in which this thesis is inserted is exactly the numerical modeling of FC, by using Large Eddy Smulations for its better prediction of the turbulent ternary mixing (fuel - burnt gases -air), compared to RANS. This work has been divided into two main parts. In the first, combustion in FC has been investigated by means of a new tabulated combustion model initially written in the context of the EC-KIAI project and developed and adapted to FC in this thesis. The model uses diluted homogeneous reactors DHR to simulate FC and it was developed to account for under adiabatic enthalpy losses and the ternary mixing typical of FC. The model was firstly validated on a non-premixed flame academical configuration called Flame D and subsequently on a real FC combustor from the work of Verissimo et al. The results obtained for these configurations are quite correct although some discrepancies in CO prediction are observed. In the second part of the thesis, the NO pollutant modeling in FC is investigated. With this aim, the Diffusion Flame - NO relaxation approach DF-NORA was developed. It consists in tabulating the NO relaxation towards equilibrium of the NO source term in a flamelet structure. As done in the first part, the model was first validated on Flame D and then employed in a real FC configuration. Results are quite satisfactory in both config- urations. The encouraging results obtained in this work open the possibility of applying the proposed developments to real industrial configurations in the future.
Development of a hierarchically detailed chemical reaction mechanism from C₃ to C₅ hydrocarbons
(2022)
The oxidation of fuel molecules can be described by using a reaction mechanism, a tool that combines thermodynamic and transport properties with reaction rates to predict the behavior and sub-products at different temperatures, pressures and equivalence ratios. A detailed reaction mechanism helps to understand the fuel-specific pollutant formation process. The aim of this doctoral thesis is to generate a hierarchically-detailed chemical reaction mechanism from C3 to C5 hydrocarbons that can be used to understand the reaction decomposition pathways for different fuels at high temperature regime, e.g. propene, propane, butane isomers, butene isomers and pentene isomers. A new nomenclature based in the IUPAC rules, has been developed and implemented as part of this work. The naming follows the order of priority for choosing a principal characteristic group. These naming rules and some examples are explained here. As starting point for this investigation, the chemical model presented in Schenk et al. (2013) has been used. Thermodynamic data for sensitive species from C3 chemistry were revised and updated. Updates in reaction rates for n-butane (C4H10) and iso-butane (C4H10-Me2) are shown. The chemistry of the butene (C4H8) isomers have been revised and a correction taking into account the H-atom allyl abstraction is implemented. Laminar flame speeds and ignition delay times for the different isomers are presented and discussed together with experiments in similar conditions for burner-stabilized flame for the three butene and butane isomers.
The high-temperature chemistry for branched and linear C5H10 species is implemented in the model. 2-Methyl-2-butene (C5H10-D2Me2) is the most interesting isomer because 9 of its 10 C-H atoms are in allylic position and it is compared to n-Pentane as an example of a linear molecule. The validation of a burner-stabilized flame, ignition delay time, and laminar flame speed experiments for these fuels are presented and discussed. The compilation strategy was used and it aims to continuously increase the number and type of targets for mechanism validation.
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.
This thesis is a combined work of understanding the high temperature oxidation chemistry of cycloalkanes viz. methylcyclohexane based on previously developed cyclohexane and extending it to generate the larger n-propylcyclohexane chemical kinetic mechanism. The detailed kinetic reaction mechanism model for the oxidation of 1-hexene previously developed has been added to account for the ring opening of cyclohexane forming 1-hexene. As an update to the publication, preference of allylic H-abstractions from 1-hexene has been taken into account and retro-ene reaction producing propene has been added. The complete model is composed of 329 species and 2065 reactions with 3796 reversible elementary reactions. Further, these models have been validated against different experiments such as shock tubes, jet stirred reactors and laminar flames to cover full range of temperatures, pressures and equivalence ratios making the models comprehensive and was found to be adequate to satisfactorily reproduce the experimental data. The allylic radicals (C₆H₁₁-D1R3) preferred abstractions from 1-hexene improves the C₆H₁₁ profiles in the 1-hexene model. But it also influences the otherwise isomerization path of C₆H1₁₁-D1R6 to CYC₆H₁₁ (Cyclohexyl radical) which would further form cyclohexene (CYC₆H₁₀). It is observed that CYC₆H₁₀ profiles in 1-hexene flames and cyclohexane speciation are over-predicted. The major decomposition pathway of the cycloalkanes is through H-abstractions on the ring. The path which leads towards ring opening to form olefin is observed for cyclohexane and methylcyclohexane but is very low. The fulvene pathway influence on benzene profiles of 1-hexene is obvious but do not seem to affect the cycloalkanes. This infers there are other benzene formation pathways in cycloalkanes. Some possible pathways would be the dehydrogenation of dienes and dehydrogenation of cyclo-olefins.
Within this thesis, a detailed multicomponent gasoline surrogate reaction scheme was developed and reduced to a four component scheme of skeletal size. The main target is to cover the most important features for typical spark ignited (SI) combustion - flame propagation, emission formation and the tendency to auto ignite and subsequently cause engine knock. To achieve this a variable mechanism concept was developed to include sub models for different fuels as needed. Using this approach a detailed mechanism describing the oxidation of n-heptane, iso-octane, toluene and ethanol was compiled and compared against various experiments published in literature. Furthermore, correlations were developed to suggest four component gasoline surrogates based on typical fuel data sheets. The correlation method is validated against measurements in Cooperative Fuel Research (CFR) engine from various groups and further compared against correlations between octane numbers (ON) and predicted 0D ignition delay times. These correlations are used to identify and discuss the impact of the uncertainty of two reactions on ignition delay time of a multicomponent fuel. To be able to reduce the detailed scheme in a time efficient way existing reduction concepts where improved and applied to different schemes and targets. Since various reduction techniques are available, an optimal sequence of those was worked out. Using this sequence of reduction steps two multicomponent schemes were compiled: one scheme for the prediction of laminar flame speeds and one for the prediction of major emissions and auto-ignition. To underline that the suggested reduction procedure is universal it was also applied to n-heptane as single fuel surrogate for diesel fuel and to a large two component fuel from another work group.
Im Rahmen dieser Arbeit wurde ein Berechnungsmodell zur thermisch-geometrischen Dimensionierung eines kontinuierlich arbeitenden Druck-Wirbelschicht-Verdampfungs-Trockners mit Tauchheizflächen für polydisperse Braunkohle erstellt. Zunächst wurde auf Basis experimenteller Ergebnisse eine strukturell optimierte Grundgleichung zur Beschreibung des zeitlichen Feuchteverlaufes entwickelt. Dabei wurden die Besonderheiten des Trocknungsgutes (z.B. die Polydispersität und die Ausbildung einer Gleichgewichtsfeuchte) berücksichtigt. Mit Hilfe der für den Trockner aufgestellten Energiebilanzen wurde ein Modell zur Beschreibung des zeitlichen Verdampfungstrocknungsverlaufes entwickelt. Dabei wurde auch der Einfluss des Druckes in den Subgleichungen und Stoffwertberechnungen berücksichtigt. (Der Überdruck ist einer der Hauptunterschiede der DDWT zu zahlreichen anderen Trocknungsverfahren). Weiterführend wurde unter Anwendung der Gleichungen zur Beschreibung der wirbelschicht-bedingten asymmetrischen Verweilzeitverteilung ein Gesamtmodell – das Trockner-Auslegungs-Modell (TRAM) – entwickelt und die Modellarchitektur detailliert beschrieben.
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.