A stochastic model for the dynamics of a limit order book is evaluated and tested on empirical data. Arrival of limit, market and cancellation orders are described in terms of a Markovian queuing system with exponentially distributed occurrences. In this model, several key quantities can be analytically calculated, such as the distribution of times between price moves, price volatility and the probability of an upward price move, all conditional on the state of the order book. We show that the exponential distribution poorly fits the occurrences of order book events and further show that little resemblance exists between the analytical formulas in this model and the empirical data. The log-normal and Weibull distribution are suggested as replacements as they appear to fit the empirical data better.

台灣特殊的兩黨對立政治環境及幾乎每年都會有的固定選舉，使得政治的不確定性深深的影響著國內的投資環境及投資人心態。本研究便是要探討，2002/1/1~2006/1/16 研究期間台灣的投資人在選舉前後的投資行為，是否真如大家所預期的，會受到台灣選舉事件的影響。 本研究首先利用適當的機率密度函數模型及選擇權市場資訊來導出隱含的風險中立密度值。再利用這些風險中立密度值，求出各個選舉事件相對應的機率分配圖形，並透過其機率分配圖形及波動率指數等統計值於投票日前後的變化來觀察某一選舉事件前後投資者的反應。 研究結果發現：1. 選舉事件的發生確實會影響投資者的心理，且投資者會透過選擇權市場有效率的反應預期的未來股價指數分佈情況。2. 越大型、越具爭議且全國性的選舉結果，其選舉期間機率分配圖形及波動率指數具有較高的波動性。3. 一般而言，選舉過後市場不確定因素降低，將使投資者對於股市的預期較為一致和樂觀。而若這個選舉結果使投資者感到意外，因而增加了市場的不確定性，則選後機率分配圖形及波動率指數的改變反而會更為明顯。4. 在此研究下對數常態混合法比傳統的 Black-Scholes 方法產生較低的誤差值，因此就實證的分析上能提供更好的配適。 / This research examines the behavior of investors during election periods from January 1st 2002 to January 6th 2006 in Taiwan. The research includes a few steps. First, we adopted a proper probability density function composed of stock index options data to construct the implied distribution. Then, when changing the whole shape of the risk-neutral implied distribution, the volatility indexes, and the statistics of the implied distribution, we observed investors' response around a specific election event. According to the empirical results, we found that: 1. An election event would influence investors’ behavior, and investors tend to reflect their expectation of future stock index in the option market in an efficient way. 2. The result of a large-scale and more disputed nationwide election will cause a higher fluctuation in both the implied distribution and the volatility index. 3. In general, the factor resulting from investors’ uncertainty of the market is likely to reduce after the election, which makes investors’ relatively unanimous and optimistic expectation of the stock market. However, if this election result surprises investors, their uncertainty of the market will increase, and thus the changes of the implied distribution and the volatility index become quite obvious. 4. The in-sample performance of the lognormal mixtures method employed in the research is considerably better than that of the traditional Black-Scholes model by having a lower root mean squared error.

The probability density function (PDF) approach is a powerful technique for large eddy simulation (LES) based modeling of turbulent reacting flows. In this approach, the joint-PDF of all reacting scalars is estimated by solving a PDF transport equation, thus providing detailed information about small-scale correlations between these quantities. The objective of this work is to further develop the LES/PDF approach for studying flame stabilization in supersonic combustors, and for soot modeling in turbulent flames. Supersonic combustors are characterized by strong shock-turbulence interactions which preclude the application of conventional Lagrangian stochastic methods for solving the PDF transport equation. A viable alternative is provided by quadrature based methods which are deterministic and Eulerian. In this work, it is first demonstrated that the numerical errors associated with LES require special care in the development of PDF solution algorithms. The direct quadrature method of moments (DQMOM) is one quadrature-based approach developed for supersonic combustion modeling. This approach is shown to generate inconsistent evolution of the scalar moments. Further, gradient-based source terms that appear in the DQMOM transport equations are severely underpredicted in LES leading to artificial mixing of fuel and oxidizer. To overcome these numerical issues, a new approach called semi-discrete quadrature method of moments (SeQMOM) is formulated. The performance of the new technique is compared with the DQMOM approach in canonical flow configurations as well as a three-dimensional supersonic cavity stabilized flame configuration. The SeQMOM approach is shown to predict subfilter statistics accurately compared to the DQMOM approach. For soot modeling in turbulent flows, an LES/PDF approach is integrated with detailed models for soot formation and growth. The PDF approach directly evolves the joint statistics of the gas-phase scalars and a set of moments of the soot number density function. This LES/PDF approach is then used to simulate a turbulent natural gas flame. A Lagrangian method formulated in cylindrical coordinates solves the high dimensional PDF transport equation and is coupled to an Eulerian LES solver. The LES/PDF simulations show that soot formation is highly intermittent and is always restricted to the fuel-rich region of the flow. The PDF of soot moments has a wide spread leading to a large subfilter variance. Further, the conditional statistics of soot moments conditioned on mixture fraction and reaction progress variable show strong correlation between the gas phase composition and soot moments. / text

This thesis is related to the Bit Error Rate (BER) estimation for any digital communication system. In many designs of communication systems, the BER is a Key Performance Indicator (KPI). The popular Monte-Carlo (MC) simulation technique is well suited to any system but at the expense of long time simulations when dealing with very low error rates. In this thesis, we propose to estimate the BER by using the Probability Density Function (PDF) estimation of the soft observations of the received bits. First, we have studied a non-parametric PDF estimation technique named the Kernel method. Simulation results in the context of several digital communication systems are proposed. Compared with the conventional MC method, the proposed Kernel-based estimator provides good precision even for high SNR with very limited number of data samples. Second, the Gaussian Mixture Model (GMM), which is a semi-parametric PDF estimation technique, is used to estimate the BER. Compared with the Kernel-based estimator, the GMM method provides better performance in the sense of minimum variance of the estimator. Finally, we have investigated the blind estimation of the BER, which is the estimation when the sent data are unknown. We denote this case as unsupervised BER estimation. The Stochastic Expectation-Maximization (SEM) algorithm combined with the Kernel or GMM PDF estimation methods has been used to solve this issue. By analyzing the simulation results, we show that the obtained BER estimate can be very close to the real values. This is quite promising since it could enable real-time BER estimation on the receiver side without decreasing the user bit rate with pilot symbols for example.

Commercial fuels are mixtures with large numbers of components. Continuous thermodynamics is a technique for modelling fuel mixtures using a probability density function rather than dealing with each discreet component. The mean and standard deviation of the distribution are then used to model the chemical reactions of the mixture. This thesis develops the necessary theory to apply the technique of continuous thermodynamics to the oxidation reactions of hydrocarbon fuels. The theory is applied to three simplified models of hydrocarbon oxidation: a global one-step reaction, a two-step reaction with CO as the intermediate product, and the four-step reaction of Müller et al. (1992), which contains a high- and a low-temperature branch. These are all greatly simplified models of the complex reaction kinetics of hydrocarbons, and in this thesis they are applied specifically to n-paraffin hydrocarbons in the range from n-heptane to n-hexadecane. The model is tested numerically using a simple constant pressure homogeneous ignition problem using Cantera and compared to simplified and detailed mechanisms for n-heptane. The continuous thermodynamics models are able not only to predict ignition delay times and the development of temperature and species concentrations with time, but also changes in the mixture composition as reaction proceeds as represented by the mean and standard deviation of the distribution function. Continuous thermodynamics is therefore shown to be a useful tool for reactions of multicomponent mixtures, and an alternative to the "surrogate fuel" approach often used at present.

Ultra Wideband (UWB) communication has recently drawn considerable attention from academia and industry. This is mainly owing to the ultra high speeds and cognitive features it could offer. The employability of UWB in numerous areas including but not limited to Wireless Personal Area Networks, WPAN's, Body Area Networks, BAN's, radar and medical imaging etc. has opened several avenues of research and development. However, still there is a disagreement on the standardization of UWB. Two contesting radios for UWB are Multiband Orthogonal Frequency Division Multiplexing (MB-OFDM) and DS-UWB (Direct Sequence Ultra Wideband). As nearly all of the reported research on UWB hasbeen about a very narrow/specific area of the communication system, this thesis looks at the end-to-end performance of an MB-OFDM approach. The overall aim of this project has been to first focus on three different aspects i.e. interference, antenna and propagation aspects of an MB-OFDM system individually and then present a holistic or an end-to-end system analysis finally. In the first phase of the project the author investigated the performance of MB-OFDM system under the effect of his proposed generic or technology non-specific interference. Avoiding the conventional Gaussian approximation, the author has employed an advanced stochastic method. A total of two approaches have been presented in this phase of the project. The first approach is an indirect one which involves the Moment Generating Functions (MGF's) of the Signal-to-Interference-plus-Noise-Ratio (SINR) and the Probability Density Function (pdf) of the SINR to calculate the Average Probabilities of Error of an MB-OFDM system under the influence of proposed generic interference. This approach assumed a specific two-dimensional Poisson spatial/geometric placement of interferers around the victim MB-OFDM receiver. The second approach is a direct approach and extends the first approach by employing a wider class of generic interference. In the second phase of the work the author designed, simulated, prototyped and tested novel compact monopole planar antennas for UWB application. In this phase of the research, compact antennas for the UWB application are presented. These designs employ low-loss Rogers duroid substrates and are fed by Copla-nar Waveguides. The antennas have a proposed feed-line to the main radiating element transition region. This transition region is formed by a special step-generating function-set called the "Inverse Parabolic Step Sequence" or IPSS. These IPSS-based antennas are simulated, prototyped and then tested in the ane-choic chamber. An empirical approach, aimed to further miniaturize IPSS-based antennas, was also derived in this phase of the project. The empirical approach has been applied to derive the design of a further miniaturized antenna. More-over, an electrical miniaturization limit has been concluded for the IPSS-based antennas. The third phase of the project has investigated the effect of the indoor furnishing on the distribution of the elevation Angle-of-Arrival (AOA) of the rays at the receiver. Previously, constant distributions for the AOA of the rays in the elevation direction had been reported. This phase of the research has proposed that the AOA distribution is not fixed. It is established by the author that the indoor elevation AOA distributions depend on the discrete levels of furnishing. A joint time-angle-furnishing channel model is presented in this research phase. In addition, this phase of the thesis proposes two vectorial or any direction AOA distributions for the UWB indoor environments. Finally, the last phase of this thesis is presented. As stated earlier, the overall aim of the project has been to look at three individual aspects of an MB-OFDM system, initially, and then look at the holistic system, finally. Therefore, this final phase of the research presents an end-to-end MB-OFDM system analysis. The interference analysis of the first phase of the project is revisited to re-calculate the probability of bit error with realistic/measured path loss exponents which have been reported in the existing literature. In this method, Gaussian Quadrature Rule based approximations are computed for the average probability of bit error. Last but not the least, an end-to-end or comprehensive system equation/impulse response is presented. The proposed system equation covers more aspects of an indoor UWB system than reported in the existing literature.

В данной работе, основываясь на решении уравнения Фоккера-Планка-Брауна аналитически определена динамическая магнитная восприимчивость обездвиженных магнитных частиц к слабым переменным магнитным полям с учетом межчастичных диполь-дипольных взаимодействий. Полученное решение, а также известные из литературы аналитические и численные данные динамической восприимчивости систем подвижных и обездвиженных взаимодействующих магнитных частиц использовались для моделирования и анализа удельной поглощаемой мощности в зависимости от режимных параметров рассматриваемой системы. / In that work, based on the solution of the Fokker-Planck-Brown equation, the dynamic magnetic susceptibility of immobilized magnetic particles to weak alternating magnetic fields is analytically determined taking into account interparticle dipole-dipole interactions. The solution obtained, as well as the analytical and numerical data of the dynamic susceptibility of systems of moving and immobilized interacting magnetic particles known from the literature, were used to model and analyze the specific loss power depending on the regime parameters of the system under consideration.

Cette thèse présente la Simulation des Grandes Echelles (LES) de l’injection, de la pulvérisation et de la cavitation dans un injecteur pour les applications liées aux moteurs à combustion interne. Pour la modélisation de l’atomisation, on utilise le modèle ELSA (Eulerian Lagrangian Spray Atomization). Le modèle résout la fraction volumique du combustible liquide ainsi que la densité de surface d’interface liquide-gaz pour décrire le processus complet d’atomisation. Dans cette thèse, l’écoulement à l’intérieur de l’injecteur est également pris en compte pour une étude ultérieure de l’atomisation. L’étude présente l’application du modèle ELSA à un injecteur Diesel typique, à la fois dans le contexte de RANS et de LES.Le modèle est validé à l’aide de données expérimentales disponibles dans Engine Combustion Network (ECN). Le modèle ELSA, qui est normalement conçu pour les interfaces diffuses (non résolues), lorsque l’emplacement exact de l’interface liquide-gaz n’est pas pris en compte, est étendu pour fonctionner avec une formulation de type Volume of Fluid (VOF) de flux à deux phases, où l’interface est explicitement résolu. Le couplage est réalisé à l’aide de critères IRQ (Interface Resolution Quality), qui prennent en compte à la fois la courbure de l’interface et la quantité modélisée de la surface de l’interface. Le modèle ELSA est développé en premier lieu en considérant les deux phases comme incompressibles. L’extension à la phase compressible est également brièvement étudiée dans cette thèse. Il en résulte une formulation ELSA compressible qui prend en compte la densité variable de chaque phase. En collaboration avec l’Imperial College de Londres, la formulation de la fonction de densité de probabilité (PDF) avec les champs stochastiques est également explorée afin d’étudier l’atomisation. Dans les systèmes d’injection de carburant modernes, la pression locale à l’intérieur de l’injecteur tombe souvent en dessous de la pression de saturation en vapeur du carburant, ce qui entraîne une cavitation. La cavitation affecte le flux externe et la formulation du spray. Ainsi, une procédure est nécessaire pour étudier le changement de phase ainsi que la formulation du jet en utilisant une configuration numérique unique et cohérente. Une méthode qui couple le changement de phase à l’intérieur de l’injecteur à la pulvérisation externe du jet est développée dans cette thèse. Ceci est réalisé en utilisant le volume de formulation de fluide où l’interface est considérée entre le liquide et le gaz; le gaz est composé à la fois de vapeur et d’airambiant non condensable. / This thesis presents Large Eddy Simulation (LES) of fuel injection, atomization and cavitation inside the fuel injector for applications related to internal combustion engines. For atomization modeling, Eulerian Lagrangian Spray Atomization (ELSA) model is used. The model solves for volume fraction of liquid fuel as well as liquid-gas interface surface density to describe the complete atomization process. In this thesis, flow inside the injector is also considered for subsequent study of atomization. The study presents the application of ELSA model to a typical diesel injector, both in the context of RANS and LES. The model is validated with the help of experimental data available from Engine Combustion Network (ECN). The ELSA model which is normally designed for diffused (unresolved) interfaces, where the exact location of the liquid-gas interface is not considered, is extended to work with Volume of Fluid (VOF) type formulation of two phase flow, where interface is explicitly resolved. The coupling is achieved with the help of Interface Resolution Quality (IRQ) criteria, that takes into account both the interface curvature and modeled amount of interface surface. ELSA model is developed first considering both phases as incompressible, the extension to compressible phase is also briefly studied in this thesis, resulting in compressible ELSA formulation that takes into account varying density in each phase. In collaboration with Imperial College London, the Probability Density Function (PDF) formulation with Stochastic Fields is also explored to study atomization. In modern fuel injection systems, quite oftenthe local pressure inside the injector falls below the vapor saturation pressure of the fuel, resulting in cavitation. Cavitation effects the external flow and spray formulation. Thus, a procedure is required to study the phase change as well as jet formulation using a single and consistent numerical setup. A method is developed in this thesis that couples the phase change inside the injector to the external jet atomization. This is achieved using the volume of fluid formulation where the interface is considered between liquid and gas; gas consists of both the vapor and non condensible ambient air.

[ES] El proyecto ESTiMatE nace con el objetivo de mejorar la precisión de las predicciones de hollín para la reducción de emisiones y una mayor sostenibilidad ambiental en la aviación. Para ello es crucial comprender a fondo fenómenos que influyen en la formación de hollín, incluyendo atomización del combustible, mezcla, combustión y formación de emisiones. La presente tesis, como parte del proyecto, se centra en el primer paso para caracterizar las spray flames, el proceso de atomización del líquido. Existen modelos empíricos para ello, pero el objetivo de este trabajo es desarrollar un nuevo modelo fenomenológico a través de simulaciones de alta fidelidad. Se propone acoplar este modelo a los códigos PRECISE-UNS y Alya para inyectar gotas en simulaciones Lagrangianas, reproduciendo de forma efectiva las características clave de atomización primaria en la formación del spray. Realizar estudios sobre la configuración anular de atomizadores prefilming airblast es un gran desafío, por lo que los esfuerzos se han enfocado en la configuración plana como alternativa que proporciona información valiosa. El KIT ha hecho contribuciones notables en este sentido al desarrollar un banco de pruebas de configuración plana, generando una base de datos extensa con resultados que abarcan diversos fluidos de trabajo y condiciones de operación para validar los cálculos. Esta tesis investiga la atomización primaria en estos dispositivos con un enfoque computacional a través de simulaciones eDNS con el código PARIS Simulator. Se utilizan simulaciones VOF-DNS del borde del atomizador para obtener información, y simulaciones LES monofásicas precursoras que permiten tener en cuenta la turbulencia del gas en la entrada. No obstante, se han propuesto dos metodologías derivadas a partir de eDNS, extendiéndola con simulaciones LES bifásicas adicionales. La primera de ellas impone un espesor y velocidad constantes para la película líquida en la entrada, pero sus valores medios se obtienen procesando las nuevas simulaciones LES bifásicas. Esta metodología ha sido validada para una condición de operación de referencia, representativa del reencendido en altitud. La segunda, introduce un espesor y velocidad variables de la película líquida, constituyendo una condición de contorno más realista. Se han realizado dos estudios diferentes. Por un lado, utilizando la primera metodología, se realizó un estudio paramétrico para investigar el impacto de la velocidad media del gas y las propiedades del fluido en la formación de estructuras líquidas. Al variar estos parámetros se observan diferencias en los mecanismos de ruptura basadas en M como en la literatura. La base para un modelo fenomenológico se ha establecido utilizando estos resultados y puede extenderse con más condiciones de operación siguiendo la metodología descrita. Por otra parte, se ha realizado una comparación entre ambas metodologías para considerar la influencia de la historia de la película de combustible en la atomización primaria. En este estudio, al mejorar las condiciones de contorno a la entrada, se ha reproducido con éxito la fenomenología presente en los experimentos, al contrario que con la eDNS estándar. Se ha propuesto una nueva técnica de postprocesado para caracterizar las estructuras líquidas. Los métodos habituales detectan gotas en un dominio 3D, pero solamente detectan ligamentos en una proyección 2D utilizando optimización de funciones algebraicas. Sin embargo, este nuevo método es capaz de encontrar gotas y ligamentos en 3D mediante OpenCV. También ha sido validado con resultados de la literatura. Con todo, la tesis ha sentado las bases para el desarrollo de modelos específicos de atomización airblast mediante simulaciones de alta fidelidad, contribuyendo a una mejor predicción de los fenómenos de inyección, atomización, evaporación, mezcla y combustión de aeromotores que permita realizar un diseño más eficiente de éstos hacia una movilidad aérea sostenible. / [CA] El projecte ESTiMatE naix amb l'objectiu de millorar la precisió de les prediccions de sutge per a la reducció d'emissions i una major sostenibilitat ambiental en l'aviació. Per això, és crucial comprendre a fons fenòmens que influeixen en la formació de sutge, incloent atomització del combustible, mescla, combustió i formació d'emissions. La present tesi, com a part del projecte, se centra en el primer pas per caracteritzar les spray flames, el procés d'atomització del líquid. Existeixen alguns models empírics per això, però l'objectiu d'aquest treball és desenvolupar un nou model fenomenològic a través de simulacions d'alta fildelitat. Es proposa acoblar aquest model als codis PRECISE-UNS i Alya per injectar gotes en simulacions Lagrangianes, reproduint de manera efectiva les característiques clau d'atomització primària en la formació de l'spray. Realitzar estudis sobre la configuració anul·lar d'atomitzadors prefilming airblast és un gran desafiament, per la qual cosa els investigadors han enfocat els seus esforços en la configuració plana com alternativa que proporciona informació valuosa. El KIT ha fet contribucions notables en aquest sentit en desenvolupar un banc de proves de configuració plana, generant una base de dades extensa amb resultats que abasten diversos fluids de treball i condicions d'operació per a validar els càlculs. Esta tesi investiga l'atomització primària en aquests dispositius amb un enfocament computacional a través de simulacions eDNS emprant el codi PARIS Simulator. S'utilitzen simulacions VOF-DNS de la vora de l'atomitzador per a obtindre informació, i simulacions LES monofàsiques precursores que permeten tindre en compte la turbulència del gas a l'entrada. No obstant això, s'han proposat dues noves metodologies derivades a partir de eDNS, estenent-la amb simulacions LES bifàsiques addicionals. La primera d'elles imposa una grossària i velocitat constants per a la pel·lícula líquida en l'entrada, però els seus valors mitjans s'obtenen processant les noves simulacions LES bifàsiques. Aquesta metodologia ha sigut validada per a una condició d'operació de referència, representativa de la reencesa en altitud. La segona, introduïx una grossària i velocitat variables de la pel·lícula líquida, constituint una condició de contorn més realista. S'han realitzat dos estudis diferents. D'una banda, utilitzant la primera metodologia, es va realitzar un estudi paramètric per a investigar l'impacte de la velocitat mitjana del gas i les propietats del fluid en la formació d'estructures líquides. En variar estos paràmetres s'observen diferènciesen els mecanismes de ruptura basades en M com a la literatura. La base per a un model fenomenològic s'ha establit utilitzant aquests resultats i pot estendre's amb més condicions d'operació seguint la metodologia descrita. D'altra banda, s'ha realitzat en paral·lel una comparació entre totes dues metodologies per a considerar la influència de la història de la pel·lícula de combustible en l'atomització primària. En aquest estudi, en millorar les condicionsde contorn a l'entrada, s'ha reproduït amb èxit la fenomenologia present en els experiments, al contrari que amb la eDNS estàndard. S'ha proposat una nova tècnica de postprocessament per a caracteritzar les estructures líquides. Els mètodes habituals detecten gotes en un domini 3D, però solament detecten lligaments en una projecció 2D utilitzant optimització de funcions algebraiques. No obstant això, aquest nou mètode és capaç de trobar gotes i lligaments en 3D mitjançant la llibrería OpenCV. També ha sigut validat amb resultats de la literatura. Amb tot, la tesi ha establit les bases per al desenvolupament de models específics d'atomització airblast mitjançant simulacions d'alta fidelitat, contribuïnt a una millor predicció dels fenòmens d'injecció, atomització, evaporació, mescla i combustió dels aeromotors que permeta realitzar un disseny més eficient dels mateixos cap a una mobilitat aèria sostenible. / [EN] The project ESTiMatE emerges aiming to enhance the precision of soot predictions leading to reduced emissions and improved environmental sustainability in aviation. To achieve this, it is crucial to thoroughly understand various phenomena that influence soot formation, including fuel atomization, mixing, combustion, and subsequent emissions formation. The present thesis, as part of the project, focuses in the first step to characterize spray flames, the liquid atomization process. There exist some empirical models to characterize atomization, but the objective of this specific work package is to develop a new phenomenological model through high-fidelity simulations instead of empirical results. This model is proposed to be coupled to the PRECISE-UNS and Alya codes to inject droplets in Lagrangian simulations, effectively reproducing the key features of the primary atomization process on the spray formation. Conducting fundamental studies on the annular configuration of prefilming airblast atomizers is challenging, so researchers have directed their attention towards planar configurations as an alternative that can provide valuable insights. The KIT has made notable contributions in this regard by developing a dedicated planar test rig, generating a substantial database of results encompassing various working fluids and operating conditions for validation. This thesis investigates primary atomization in these devices with a computational approach using eDNS within the PARIS Simulator code. VOF-DNS simulations of the atomizing Edge are performed to obtain useful data, and precursor one-phase LES simulations in order to account for gas inflow turbulence at the DNS inlet. Nevertheless, two methodologies have been derived from eDNS, extending it with additional precursor two-phase LES simulations. The first one, imposes constant liquid film thickness and velocity at the DNS inlet, but their mean values are obtained processing the new two-phase LES simulations. It has been validated for a reference operating condition, representative of altitude relight. The second one, introduces variable liquid film thickness and velocity instead, constituting a more realistic boundary condition for the DNS. Two different studies have been conducted in this regard. On the one hand, using the former methodology, a parametric study was performed to investigate the impact of mean gas velocity and fluid properties on the formation of liquid structures. By varying these parameters differences on the breakup mechanisms are observed based on M as found in the literature. The basis for a phenomenological model has been established using these results, and it can be extended with more operating conditions following the described methodology. On the other hand, a comparison between both methodologies has been carried out in parallel, in order to account for the influence of film history on the primary atomization process. In this study, by improving the inlet boundary conditions, the phenomenology observed in the experiments has been succesfully reproduced, unlike with the standard eDNS. A novel post-processing technique for characterizing liquid structures has been proposed. Usual post-processing methods detect droplets in a 3D domain, but only detect ligaments in a top view 2D projection of it using algebraic functions optimization. However, this new method is able to find both droplets and ligaments as well as its 3D properties using the Open Computer Vision Library (OpenCV) instead. It has been also validated with the results in the literature. Overall, the thesis has laid the foundations for the development of specific airblast atomization models through the use of high-fidelity simulations,contributing to a better prediction of the injection, atomization, evaporation, mixing and combustion phenomena in aero engines, enabling a more efficient design towards sustainable air mobility. / Moreno Montagud, C. (2024). Computational Modelling of the Primary Atomization in Aero Engine Airblast Atomizers through a DNS Approach [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/211359

In dieser Arbeit betrachten wir das Strömungs-Diffusions-(Reaktions)-Problem für passive Markerteilchen, die in zweidimensionalen laminaren Strömungsmustern mit geringem thermischem Rauschen gelöst sind. Der deterministische Fluss umfasst Zellen in Form von Quadraten oder Katzenaugen. In ihnen tritt Rotationsbewegung auf. Einige der Strömungen bestehen aus wellenförmigen Bereichen mit gerader Vorwärtsbewegung. Alle Systeme sind entweder periodisch oder durch Wände begrenzt. Eine untersuchte Familie von Strömungen interpoliert kontinuierlich zwischen Reihen von Wirbeln und Scherflüssen. Wir analysieren zahlreiche numerische Simulationen, die bisherige theoretische Vorhersagen bestätigen und neue Phänomene offenbaren. Ohne Rauschen sind die Teilchen in einzelnen Bestandteilen des Flusses für immer gefangen. Durch Hinzufügen von schwachem thermischen Rauschen wird die normale Diffusion für lange Zeiten stark verstärkt und führt zu verschiedenen Diffusionsarten für mittlere Zeiten. Mit Continuous-Time-Random-Walk-Modellen leiten wir analytische Ausdrücke in Übereinstimmung mit den numerischen Ergebnissen her, die je nach Parametern, Anfangsbedingungen und Alterungszeiten von subdiffusiver bis superballistischer anomaler Diffusion für mittlere Zeiten reichen. Wir sehen deutlich, dass einige der früheren Vorhersagen nur für Teilchen gelten, die an der Separatrix des Flusses starten - der einzige Fall, der in der Vergangenheit ausführlich betrachtet wurde - und dass das System zu vollkommen anderem Verhalten in anderen Situationen führen kann, einschließlich einem Schwingenden beim Start im Zentrum einesWirbels nach einer gewissen Alterungszeit. Darüber hinaus enthüllen die Simulationen, dass Teilchenreaktionen dort häufiger auftreten, wo sich die Geschwindigkeit der Strömung stark ändert, was dazu führt, dass langsame Teilchen von schnelleren getroffen werden, die ihnen folgen. Die umfangreichen numerischen Simulationen, die für diese Arbeit durchgeführt wurden, mussten jetzt durchgeführt werden, da wir die Rechenleistung dafür besitzen. / In this thesis, we consider the advection-diffusion-(reaction) problem for passive tracer particles suspended in two-dimensional laminar flow patterns with small thermal noise. The deterministic flow comprises cells in the shape of either squares or cat’s eyes. Rotational motion occurs inside them. Some of the flows consist of sinusoidal regions of straight forward motion. All systems are either periodic or are bounded by walls. One examined family of flows continuously interpolates between arrays of eddies and shear flows. We analyse extensive numerical simulations, which confirm previous theoretical predictions as well as reveal new phenomena. Without noise, particles are trapped forever in single building blocks of the flow. Adding small thermal noise, leads to largely enhanced normal diffusion for long times and several kinds of diffusion for intermediate times. Using continuous time random walk models, we derive analytical expressions in accordance with numerical results, ranging from subdiffusive to superballistic anomalous diffusion for intermediate times depending on parameters, initial conditions and aging time. We clearly see, that some of the previous predictions are only true for particles starting at the separatrix of the flow - the only case considered in depth in the past - and that the system might show a vastly different behavior in other situations, including an oscillatory one, when starting in the center of an eddy after a certain aging time. Furthermore, simulations reveal that particle reactions occur more frequently at positions where the velocity of the flow changes the most, resulting in slow particles being hit by faster ones following them. The extensive numerical simulations performed for this thesis had to be done now that we have the computational means to do so. Machines are powerful tools in order to gain a deeper and more detailed insight into the dynamics of many complicated dynamical and stochastic systems.