No description available.

The research examines how the Bi-Level Integrated System Synthesis decomposition technique can be adapted to perform as the conceptual aeroelastic design tool. The study describes a comprehensive solution of the aeroelastic coupled problem cast in this decomposition format and implementation in an integrated framework. The method is supported by application details of a proof-of-concept high speed vehicle. Physics-based codes such as finite element and an aerodynamic panel method are used to model the high-definition geometric characteristics of the vehicle. A synthesis and sizing code was added to referee the conflicts that arise between the two disciplines. This research's novelty lies in four points. First is the use of physics-based tools at the conceptual design phase to calculate the aeroelastic properties. Second is the projection of flutter and divergence velocity constraint lines in a power loading versus wing loading graph. The mapping of such constraints in a designer's familiar format is a valuable tool for fast examination of the design space. Third is the improvement of the aeroelastic assessment given the time allotted. Until recently, because of extensive computational and time requirements, aeroelasticity was only assessed at the preliminary design phase. This research illustrates a scheme whereby, for the first time, aeroelasticity can be assessed at the early design formulation stages. Forth, this assessment allowed to verify the impact of changing velocity, altitude, and angle of attack and identify robust design space with these three mission properties. The method's application to the quiet supersonic business jet gave a delta shaped wing for the supersonic speed regime. A subsonic case resulted in a high aspect ratio wing. The scaling approach allowed iso-flutter and iso-divergence lines to be plotted. The main effects of velocity, altitude, and angle of attack on these iso-lines were also discussed, as was the identification of robust design space. The response surface surrogate models allowed convergence of the system optimization but questions were posed as to the accuracy of these quadratic models. Other future improvements include the addition of more disciplines and more detailed models.

No description available.

The ongoing process of deregulation in energy markets changes the market from a monopoly into a complex one, in which large utilities and independent power producers are no longer suppliers with guaranteed returns but enterprisers which have to compete. This competence has forced utilities to improve their efficiency. In effect, they must still manage the challenges of physical delivery while operating in a complex market characterized by significant volatility, volumetric uncertainty and credit risk. In such an environment, risk management gains more importance than ever. In order to manage risk, first it must be measured and then this quantified risk must be utilized optimally. Using stochastic programming to construct a model for an energy company in liberalized markets is useful since it provides a generic framework to model the uncertainties and enable decisions that will perform well. However, the resulting stochastic programming problem is a large-scale one and decomposition techniques are needed to solve them.

The increasing emphasis on mass customization, shortened product lifecycles, synchronized supply chains, when coupled with advances in information system, is driving most firms towards make-to-order (MTO) operations. Increasing global competition, lower profit margins, and higher customer expectations force the MTO firms to plan its capacity by managing the effective demand. The goal of this research was to maximize the operational profits of a make-to-order operation by selectively accepting incoming customer orders and simultaneously allocating capacity for them at the sales stage. For integrating the two decisions, a Mixed-Integer Linear Program (MILP) was formulated which can aid an operations manager in an MTO environment to select a set of potential customer orders such that all the selected orders are fulfilled by their deadline. The proposed model combines order acceptance/rejection decision with detailed scheduling. Experiments with the formulation indicate that for larger problem sizes, the computational time required to determine an optimal solution is prohibitive. This formulation inherits a block diagonal structure, and can be decomposed into one or more sub-problems (i.e. one sub-problem for each customer order) and a master problem by applying Dantzig-Wolfe’s decomposition principles. To efficiently solve the original MILP, an exact Branch-and-Price algorithm was successfully developed. Various approximation algorithms were developed to further improve the runtime. Experiments conducted unequivocally show the efficiency of these algorithms compared to a commercial optimization solver. The existing literature addresses the static order acceptance problem for a single machine environment having regular capacity with an objective to maximize profits and a penalty for tardiness. This dissertation has solved the order acceptance and capacity planning problem for a job shop environment with multiple resources. Both regular and overtime resources is considered. The Branch-and-Price algorithms developed in this dissertation are faster and can be incorporated in a decision support system which can be used on a daily basis to help make intelligent decisions in a MTO operation.

Estratégias de otimização em tempo real (RTO: Real Time Optimization) são utilizadas para avaliar e determinar as condições ótimas operacionais de uma planta em estado estacionario, maximizando a produtividade econômica do processo sujeita a restrições operacionais. Esse problema de otimização engloba toda a planta e pode ser resolvido utilizando um só modelo para todo o processo que maximize o lucro bruto operacional considerando os preços de mercado das correntes de entrada e saída do processo. No entanto, na prática, essa abordagem centralizada muitas vezes não pode ser aplicada, devido ao tamanho e complexidade do problema de otimização, a que é muito difícil que todas as unidades da planta estejam em estado estacionário ao mesmo tempo e a que as unidades de processo não estão sincronizadas já que em muitos processos não existe armazenamento intermediário. Uma solução é utilizar uma estrutura distribuída, na qual o problema de otimização deve ser decomposto em subproblemas com reduzida complexidade numérica. Tal decomposição, no entanto, exige que o preço das correntes de entrada e saída de cada subproblema sejam adequadamente determinados. Com este proposito, neste trabalho, serão aplicadas técnicas de decomposição em uma unidade de produção de propeno da refinaria REPLAN (Refinaria de Paulínia, São Paulo) da PETROBRAS. Essa unidade será modelada, simulada e otimizada no software orientado a equações EMSO (Environment for Modeling, Simulation and Optimization). Com o objetivo de testar as técnicas de decomposição, a unidade será decomposta em três divisões que são: depropanizadora, deetanizadora e C3 splitter. Mostra-se que duas técnicas tradicionais chamadas de relaxação Lagrangiana e Lagrangeano aumentado não conseguem convergir em uma solução devido a duas causas. A primeira causa é que o processo estudado contém divisões indiferentes, o que significa que não existe dependência linear entre a função objetivo e as restrições complicadoras. A segunda causa é que os subproblemas de otimização que representam cada uma das divisões da unidade têm funções objetivos lineares, neste caso, a restrição ativa de cada subproblema irá ser sempre a capacidade de produção máxima ou mínima de cada divisão e não uma vazão intermediária. Uma técnica alternativa, Pricing Interprocess Streams Using Slack Auctions, também foi aplicada ao processo estudado. Essa técnica define uma folga de recurso entre as correntes 2 intermediárias das divisões e utiliza leilões para ajustar o preço dos produtos intermediários. Mostra-se que esse último abordagem também apresenta problemas na sua aplicação, porque todas as divisões estudadas têm dois produtos diferentes, isso significa que a técnica produzirá sempre a vazão máxima do produto final (vazão que tem preço de mercado) de cada divisão e não assim do produto intermediário (vazão que vai de uma divisão para outra). Identificados os problemas nessas técnicas de decomposição, é proposta uma modificação do algoritmo de relaxação Lagrangeana. Para o qual é considerada uma nova variável denominada limite de produção disponível (LPD) e uma restrição para as vazões de carga de cada uma das divisões, a qual será atualizada a cada iteração. Essa modificação no algoritmo consegue superar os problemas apresentados para a resolução do problema de otimização para a unidade estudada considerando uma estrutura distribuída. / Real time optimization strategies (RTO) are used to evaluate and determine the optimum operating conditions of a plant, maximizing the economic productivity of the process which is subject to operational constraints. This optimization framework encompasses the entire plant, and can be solved using one model for the entire process that maximizes the operating gross profit considering the market prices of input and output stream`s process. However, in practice this centralized approach often cannot be applied due to the size and complexity of the optimization problem. One solution is to use a distributed structure, in which the optimization problem must be broken into sub-problems with reduced numerical complexity. Such decomposition, however, requires that the price of input and output stream of each sub-problem should be adequately determined. With this purpose, in this work, decomposition techniques is applied in a propylene production unit at the refinery REPLAN (Refinaria de Paulínia, São Paulo) owned by PETROBRAS. This unit is modeled, simulated and optimized in an equation oriented software EMSO (Environment for Modeling, Simulation and Optimization). In order to test the decomposition techniques, the unit is decomposed into three divisions, which are depropanizer, deethanizer and C3 splitter. It is shown that two traditional techniques called Lagrangian relaxation and augmented Lagrangian cannot converge on a solution due to two causes. The first cause is that the studied process contains indifferent divisions, which means that there is no linear dependence between the objective function and the complicating constraints. The second cause is that the optimization sub-problem that represent each divisions has linear objective functions, in this case, the active constraint of each sub-problem will always be the maximum or minimum production capacity of each division and not an intermediate flow rate. An alternative technique Pricing Interprocess Streams Using Slack Auctions was also applied to the studied process. This technique defines a resource slack between the intermediary streams and use auctions for adjusting the price of intermediary products. It is shown that this technique also presents problems in its applications because all divisions studied has two different products, this means that this technique will always produce the maximum flow rate of the final product (flow rate that has a market price) of each division, and not the intermediate product (flow rate that goes from one division another). Identified problems in these decomposition 4 techniques, the proposed approach extended the Lagrangian relaxation algorithm, in which a new variable called \"available production limit\" (LPD) and a restriction to the feed flow rate from each divisions are considered, which will be updated at every iteration. This change in the algorithm can overcome the issues presented for solving the optimization problem for the unit studied considering a distributed structure.

Estratégias de otimização em tempo real (RTO: Real Time Optimization) são utilizadas para avaliar e determinar as condições ótimas operacionais de uma planta em estado estacionario, maximizando a produtividade econômica do processo sujeita a restrições operacionais. Esse problema de otimização engloba toda a planta e pode ser resolvido utilizando um só modelo para todo o processo que maximize o lucro bruto operacional considerando os preços de mercado das correntes de entrada e saída do processo. No entanto, na prática, essa abordagem centralizada muitas vezes não pode ser aplicada, devido ao tamanho e complexidade do problema de otimização, a que é muito difícil que todas as unidades da planta estejam em estado estacionário ao mesmo tempo e a que as unidades de processo não estão sincronizadas já que em muitos processos não existe armazenamento intermediário. Uma solução é utilizar uma estrutura distribuída, na qual o problema de otimização deve ser decomposto em subproblemas com reduzida complexidade numérica. Tal decomposição, no entanto, exige que o preço das correntes de entrada e saída de cada subproblema sejam adequadamente determinados. Com este proposito, neste trabalho, serão aplicadas técnicas de decomposição em uma unidade de produção de propeno da refinaria REPLAN (Refinaria de Paulínia, São Paulo) da PETROBRAS. Essa unidade será modelada, simulada e otimizada no software orientado a equações EMSO (Environment for Modeling, Simulation and Optimization). Com o objetivo de testar as técnicas de decomposição, a unidade será decomposta em três divisões que são: depropanizadora, deetanizadora e C3 splitter. Mostra-se que duas técnicas tradicionais chamadas de relaxação Lagrangiana e Lagrangeano aumentado não conseguem convergir em uma solução devido a duas causas. A primeira causa é que o processo estudado contém divisões indiferentes, o que significa que não existe dependência linear entre a função objetivo e as restrições complicadoras. A segunda causa é que os subproblemas de otimização que representam cada uma das divisões da unidade têm funções objetivos lineares, neste caso, a restrição ativa de cada subproblema irá ser sempre a capacidade de produção máxima ou mínima de cada divisão e não uma vazão intermediária. Uma técnica alternativa, Pricing Interprocess Streams Using Slack Auctions, também foi aplicada ao processo estudado. Essa técnica define uma folga de recurso entre as correntes 2 intermediárias das divisões e utiliza leilões para ajustar o preço dos produtos intermediários. Mostra-se que esse último abordagem também apresenta problemas na sua aplicação, porque todas as divisões estudadas têm dois produtos diferentes, isso significa que a técnica produzirá sempre a vazão máxima do produto final (vazão que tem preço de mercado) de cada divisão e não assim do produto intermediário (vazão que vai de uma divisão para outra). Identificados os problemas nessas técnicas de decomposição, é proposta uma modificação do algoritmo de relaxação Lagrangeana. Para o qual é considerada uma nova variável denominada limite de produção disponível (LPD) e uma restrição para as vazões de carga de cada uma das divisões, a qual será atualizada a cada iteração. Essa modificação no algoritmo consegue superar os problemas apresentados para a resolução do problema de otimização para a unidade estudada considerando uma estrutura distribuída. / Real time optimization strategies (RTO) are used to evaluate and determine the optimum operating conditions of a plant, maximizing the economic productivity of the process which is subject to operational constraints. This optimization framework encompasses the entire plant, and can be solved using one model for the entire process that maximizes the operating gross profit considering the market prices of input and output stream`s process. However, in practice this centralized approach often cannot be applied due to the size and complexity of the optimization problem. One solution is to use a distributed structure, in which the optimization problem must be broken into sub-problems with reduced numerical complexity. Such decomposition, however, requires that the price of input and output stream of each sub-problem should be adequately determined. With this purpose, in this work, decomposition techniques is applied in a propylene production unit at the refinery REPLAN (Refinaria de Paulínia, São Paulo) owned by PETROBRAS. This unit is modeled, simulated and optimized in an equation oriented software EMSO (Environment for Modeling, Simulation and Optimization). In order to test the decomposition techniques, the unit is decomposed into three divisions, which are depropanizer, deethanizer and C3 splitter. It is shown that two traditional techniques called Lagrangian relaxation and augmented Lagrangian cannot converge on a solution due to two causes. The first cause is that the studied process contains indifferent divisions, which means that there is no linear dependence between the objective function and the complicating constraints. The second cause is that the optimization sub-problem that represent each divisions has linear objective functions, in this case, the active constraint of each sub-problem will always be the maximum or minimum production capacity of each division and not an intermediate flow rate. An alternative technique Pricing Interprocess Streams Using Slack Auctions was also applied to the studied process. This technique defines a resource slack between the intermediary streams and use auctions for adjusting the price of intermediary products. It is shown that this technique also presents problems in its applications because all divisions studied has two different products, this means that this technique will always produce the maximum flow rate of the final product (flow rate that has a market price) of each division, and not the intermediate product (flow rate that goes from one division another). Identified problems in these decomposition 4 techniques, the proposed approach extended the Lagrangian relaxation algorithm, in which a new variable called \"available production limit\" (LPD) and a restriction to the feed flow rate from each divisions are considered, which will be updated at every iteration. This change in the algorithm can overcome the issues presented for solving the optimization problem for the unit studied considering a distributed structure.

<p dir="ltr">Matrix decompositions play a pivotal role in matrix computation and applications. While general dense matrix-vector multiplications and linear equation solvers are prohibitively expensive, matrix decompositions offer fast alternatives for matrices meeting specific properties. This dissertation delves into my contributions to two fast matrix multiplication algorithms and one fast linear equation solver algorithm tailored for certain matrices and applications, all based on efficient matrix decompositions. Fast dimensionality reduction methods in spectral clustering, based on efficient eigen-decompositions, are also explored.</p><p dir="ltr">The first matrix decomposition introduced is the "kernel-independent" interpolative decomposition butterfly factorization (IDBF), acting as a data-sparse approximation for matrices adhering to a complementary low-rank property. Constructible in $O(N\log N)$ operations for an $N \times N$ matrix via hierarchical interpolative decompositions (IDs), the IDBF results in a product of $O(\log N)$ sparse matrices, each with $O(N)$ non-zero entries. This factorization facilitates rapid matrix-vector multiplication in $O(N \log N)$ operations, making it a versatile framework applicable to various scenarios like special function transformation, Fourier integral operators, and high-frequency wave computation.</p><p dir="ltr">The second matrix decomposition accelerates matrix-vector multiplication for computing multi-dimensional Jacobi polynomial transforms. Leveraging the observation that solutions to Jacobi's differential equation can be represented through non-oscillatory phase and amplitude functions, the corresponding matrix is expressed as the Hadamard product of a numerically low-rank matrix and a multi-dimensional discrete Fourier transform (DFT) matrix. This approach utilizes $r^d$ fast Fourier transforms (FFTs), where $r = O(\log n / \log \log n)$ and $d$ is the dimension, resulting in an almost optimal algorithm for computing the multidimensional Jacobi polynomial transform.</p><p dir="ltr">An efficient numerical method is developed based on a matrix decomposition, Hierarchical Interpolative Factorization, for solving modified Poisson-Boltzmann (MPB) equations. Addressing the computational bottleneck of evaluating Green's function in the MPB solver, the proposed method achieves linear scaling by combining selected inversion and hierarchical interpolative factorization. This innovation significantly reduces the computational cost associated with solving MPB equations, particularly in the evaluation of Green's function.</p><p dir="ltr"><br></p><p dir="ltr">Finally, eigen-decomposition methods, including the block Chebyshev-Davidson method and Orthogonalization-Free methods, are proposed for dimensionality reduction in spectral clustering. By leveraging well-known spectrum bounds of a Laplacian matrix, the Chebyshev-Davidson methods allow dimensionality reduction without the need for spectrum bounds estimation. And instead of the vanilla Chebyshev-Davidson method, it is better to use the block Chebyshev-Davidson method with an inner-outer restart technique to reduce total CPU time and a progressive polynomial filter to take advantage of suitable initial vectors when available, for example, in the streaming graph scenario. Theoretically, the Orthogonalization-Free method constructs a unitary isomorphic space to the eigenspace or a space weighting the eigenspace, solving optimization problems through Gradient Descent with Momentum Acceleration based on Conjugate Gradient and Line Search for optimal step sizes. Numerical results indicate that the eigenspace and the weighted eigenspace are equivalent in clustering performance, and scalable parallel versions of the block Chebyshev-Davidson method and OFM are developed to enhance efficiency in parallel computing.</p>

[ES] El principal desafío en los motores turbina de gas empleados en aviación reside en aumentar la eficiencia del ciclo termodinámico manteniendo las emisiones contaminantes por debajo de las rigurosas restricciones. Ésto ha conllevado la necesidad de diseñar nuevas estrategias de inyección/combustión que operan en puntos de operación peligrosos por su cercanía al límite inferior de apagado de llama. En este contexto, el concepto Lean Direct Injection (LDI) ha emergido como una tecnología prometedora a la hora de reducir los óxidos de nitrógeno (NOx) emitidos por las plantas propulsoras de los aviones de nueva generación. En este contexto, la presente tesis tiene como objetivos contribuir al conocimiento de los mecanismos físicos que rigen el comportamiento de un quemador LDI y proporcionar herramientas de análisis para una profunda caracterización de las complejas estructuras de flujo de turbulento generadas en el interior de la cámara de combustión. Para ello, se ha desarrollado una metodología numérica basada en CFD capaz de modelar el flujo bifásico no reactivo en el interior de un quemador LDI académico mediante enfoques de turbulencia U-RANS y LES en un marco Euleriano-Lagrangiano. La resolución numérica de este problema multi-escala se aborda mediante la descripción completa del flujo a lo largo de todos los elementos que constituyen la maqueta experimental, incluyendo su paso por el swirler y entrada a la cámara de combustión. Ésto se lleva a cabo través de dos códigos CFD que involucran dos estrategias de mallado diferentes: una basada en algoritmos de generación y refinamiento automático de la malla (AMR) a través de CONVERGE y otra técnica de mallado estático más tradicional mediante OpenFOAM. Por un lado, se ha definido una metodología para obtener una estrategia de mallado óptima mediante el uso del AMR y se han explotado sus beneficios frente a los enfoques tradicionales de malla estática. De esta forma, se ha demostrado que la aplicabilidad de las herramientas de control de malla disponibles en CONVERGE como el refinamiento fijo (fixed embedding) y el AMR son una opción muy interesante para afrontar este tipo de problemas multi-escala. Los resultados destacan una optimización del uso de los recursos computacionales y una mayor precisión en las simulaciones realizadas con la metodología presentada. Por otro lado, el uso de herramientas CFD se ha combinado con la aplicación de técnicas de descomposición modal avanzadas (Proper Orthogonal Decomposition and Dynamic Mode Decomposition). La identificación numérica de los principales modos acústicos en la cámara de combustión ha demostrado el potencial de estas herramientas al permitir caracterizar las estructuras de flujo coherentes generadas como consecuencia de la rotura de los vórtices (VBB) y de los chorros fuertemente torbellinados presentes en el quemador LDI. Además, la implementación de estos procedimientos matemáticos ha permitido tanto recuperar información sobre las características de la dinámica de flujo como proporcionar un enfoque sistemático para identificar los principales mecanismos que sustentan las inestabilidades en la cámara de combustión. Finalmente, la metodología validada ha sido explotada a través de un Diseño de Experimentos (DoE) para cuantificar la influencia de los factores críticos de diseño en el flujo no reactivo. De esta manera, se ha evaluado la contribución individual de algunos parámetros funcionales (el número de palas del swirler, el ángulo de dichas palas, el ancho de la cámara de combustión y la posición axial del orificio del inyector) en los patrones del campo fluido, la distribución del tamaño de gotas del combustible líquido y la aparición de inestabilidades en la cámara de combustión a través de una matriz ortogonal L9 de Taguchi. Este estudio estadístico supone un punto de partida para posteriores estudios de inyección, atomización y combus / [CA] El principal desafiament als motors turbina de gas utilitzats a la aviació resideix en augmentar l'eficiència del cicle termodinàmic mantenint les emissions contaminants per davall de les rigoroses restriccions. Aquest fet comporta la necessitat de dissenyar noves estratègies d'injecció/combustió que radiquen en punts d'operació perillosos per la seva aproximació al límit inferior d'apagat de flama. En aquest context, el concepte Lean Direct Injection (LDI) sorgeix com a eina innovadora a l'hora de reduir els òxids de nitrogen (NOx) emesos per les plantes propulsores dels avions de nova generació. Sota aquest context, aquesta tesis té com a objectius contribuir al coneixement dels mecanismes físics que regeixen el comportament d'un cremador LDI i proporcionar ferramentes d'anàlisi per a una profunda caracterització de les complexes estructures de flux turbulent generades a l'interior de la càmera de combustió. Per tal de dur-ho a terme s'ha desenvolupat una metodología numèrica basada en CFD capaç de modelar el flux bifàsic no reactiu a l'interior d'un cremador LDI acadèmic mitjançant els enfocaments de turbulència U-RANS i LES en un marc Eulerià-Lagrangià. La resolució numèrica d'aquest problema multiescala s'aborda mitjançant la resolució completa del flux al llarg de tots els elements que constitueixen la maqueta experimental, incloent el seu pas pel swirler i l'entrada a la càmera de combustió. Açò es duu a terme a través de dos codis CFD que involucren estratègies de mallat diferents: una basada en la generación automàtica de la malla i en l'algoritme de refinament adaptatiu (AMR) amb CONVERGE i l'altra que es basa en una tècnica de mallat estàtic més tradicional amb OpenFOAM. D'una banda, s'ha definit una metodologia per tal d'obtindre una estrategia de mallat òptima mitjançant l'ús de l'AMR i s'han explotat els seus beneficis front als enfocaments tradicionals de malla estàtica. D'aquesta forma, s'ha demostrat que l'aplicabilitat de les ferramente de control de malla disponibles en CONVERGE com el refinament fixe (fixed embedding) i l'AMR són una opció molt interessant per tal d'afrontar aquest tipus de problemes multiescala. Els resultats destaquen una optimització de l'ús dels recursos computacionals i una major precisió en les simulacions realitzades amb la metodologia presentada. D'altra banda, l'ús d'eines CFD s'ha combinat amb l'aplicació de tècniques de descomposició modal avançades (Proper Orthogonal Decomposition and Dynamic Mode Decomposition). La identificació numèrica dels principals modes acústics a la càmera de combustió ha demostrat el potencial d'aquestes ferramentes al permetre caracteritzar les estructures de flux coherents generades com a conseqüència del trencament dels vòrtex (VBB) i dels raigs fortament arremolinats presents al cremador LDI. A més, la implantació d'estos procediments matemàtics ha permès recuperar informació sobre les característiques de la dinàmica del flux i proporcionar un enfocament sistemàtic per tal d'identificar els principals mecanismes que sustenten les inestabilitats a la càmera de combustió. Finalment, la metodologia validada ha sigut explotada a traves d'un Diseny d'Experiments (DoE) per tal de quantificar la influència dels factors crítics de disseny en el flux no reactiu. D'aquesta manera, s'ha avaluat la contribución individual d'alguns paràmetres funcionals (el nombre de pales del swirler, l'angle de les pales, l'amplada de la càmera de combustió i la posició axial de l'orifici de l'injector) en els patrons del camp fluid, la distribució de la mida de gotes del combustible líquid i l'aparició d'inestabilitats en la càmera de combustió mitjançant una matriu ortogonal L9 de Taguchi. Aquest estudi estadístic és un bon punt de partida per a futurs estudis de injecció, atomització i combustió en cremadors LDI. / [EN] Aeronautical gas turbine engines present the main challenge of increasing the efficiency of the cycle while keeping the pollutant emissions below stringent restrictions. This has led to the design of new injection-combustion strategies working on more risky and problematic operating points such as those close to the lean extinction limit. In this context, the Lean Direct Injection (LDI) concept has emerged as a promising technology to reduce oxides of nitrogen (NOx) for next-generation aircraft power plants In this context, this thesis aims at contributing to the knowledge of the governing physical mechanisms within an LDI burner and to provide analysis tools for a deep characterisation of such complex flows. In order to do so, a numerical CFD methodology capable of reliably modelling the 2-phase nonreacting flow in an academic LDI burner has been developed in an Eulerian-Lagrangian framework, using the U-RANS and LES turbulence approaches. The LDI combustor taken as a reference to carry out the investigation is the laboratory-scale swirled-stabilised CORIA Spray Burner. The multi-scale problem is addressed by solving the complete inlet flow path through the swirl vanes and the combustor through two different CFD codes involving two different meshing strategies: an automatic mesh generation with adaptive mesh refinement (AMR) algorithm through CONVERGE and a more traditional static meshing technique in OpenFOAM. On the one hand, a methodology to obtain an optimal mesh strategy using AMR has been defined, and its benefits against traditional fixed mesh approaches have been exploited. In this way, the applicability of grid control tools available in CONVERGE such as fixed embedding and AMR has been demonstrated to be an interesting option to face this type of multi-scale problem. The results highlight an optimisation of the use of the computational resources and better accuracy in the simulations carried out with the presented methodology. On the other hand, the use of CFD tools has been combined with the application of systematic advanced modal decomposition techniques (i.e., Proper Orthogonal Decomposition and Dynamic Mode Decomposition). The numerical identification of the main acoustic modes in the chamber have proved their potential when studying the characteristics of the most powerful coherent flow structures of strongly swirled jets in a LDI burner undergoing vortex breakdown (VBB). Besides, the implementation of these mathematical procedures has allowed both retrieving information about the flow dynamics features and providing a systematic approach to identify the main mechanisms that sustain instabilities in the combustor. Last, this analysis has also allowed identifying some key features of swirl spray systems such as the complex pulsating, intermittent and cyclical spatial patterns related to the Precessing Vortex Core (PVC). Finally, the validated methodology is exploited through a Design of Experiments (DoE) to quantify the influence of critical design factors on the non-reacting flow. In this way, the individual contribution of some functional parameters (namely the number of swirler vanes, the swirler vane angle, the combustion chamber width and the axial position of the nozzle tip) into both the flow field pattern, the spray size distribution and the occurrence of instabilities in the combustion chamber are evaluated throughout a Taguchi's orthogonal array L9. Such a statistical study has supposed a good starting point for subsequent studies of injection, atomisation and combustion on LDI burners. / Belmar Gil, M. (2020). Computational study on the non-reacting flow in Lean Direct Injection gas turbine combustors through Eulerian-Lagrangian Large-Eddy Simulations [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/159882 / TESIS