Numerical Simulation

Nowadays mathematical modeling and numerical simulations play an important role in life and natural science. Numerous researchers are working in developing different methods and techniques to help understand the behavior of very complex systems, from the brain activity with real importance in medicine to the turbulent flows with important applications in physics and engineering. This book presents an overview of some models, methods, and numerical computations that are useful for the applied research scientists and mathematicians, fluid tech engineers, and postgraduate students

Contribution to the definition of non deterministic robust optimization in aeronautics accounting with variable uncertainties

Shape optimization is a largely studied problem in aeronautics. It can be applied to many disciplines in this field, namely efficiency improvement of engine blades, noise reduction of engine nozzles, or reduction of the fuel consumption of aircraft. Optimization for general purposes is also of increasing interest in many other fields. Traditionally, optimization procedures were based on deterministic methodologies as in Hamalainen et al (2000), where the optimum working point was fixed. However, not considering what happens in the vicinity of the defined working conditions can produce problems like loose of efficiency and performance. That is, in many cases, if the real working point differs from the original, even a little distance, efficiency is reduced considerably as pointed out in Huyse and Lewis (2001). Non deterministic methodologies have been applied to many fields (Papadrakakis, Lagaros and Tsompanakis, 1998; Plevris, Lagaros and Papadrakakis, 2005). One of the most extended nondeterministic methodologies is the stochastic analysis. The time consuming calculations required on Computational Fluid Dynamics (CFD) has prevented an extensive application of the stochastic analysis to shape optimization. Stochastic analysis was firstly developed in structural mechanics, several years ago. Uncertainty quantification and variability studies can help to deal with intrinsic errors of the processes or methods. The result to consider for design optimization is no longer a point, but a range of values that defines the area where, in average, optimal output values are obtained. The optimal value could be worse than other optima, but considering its vicinity, it is clearly the most robust regarding input variability. Uncertainty quantification is a topic of increasing interest from the last few years. It provides several techniques to evaluate uncertainty input parameters and their effects on the outcomes. This research presents a methodology to integrate evolutionary algorithms and stochastic analysis, in order to deal with uncertainty and to obtain robust solutions

A multiscale strategy for fouling prediction and mitigation in gas turbines

Gas turbines are one of the primary sources of power for both aerospace and land-based applications. Precisely for this reason, they are often forced to operate in harsh environmental conditions, which involve the occurrence of particle ingestion by the engine. The main implications of this problem are often underestimated. The particulate in the airflow ingested by the machine can deposit or erode its internal surfaces, and lead to the variation of their aerodynamic geometry, entailing performance degradation and, possibly, a reduction in engine life. This issue affects the compressor and the turbine section and can occur for either land-based or aeronautical turbines. For the former, the problem can be mitigated (but not eliminated) by installing filtration systems. For what concern the aerospace field, filtration systems cannot be used. Volcanic eruptions and sand dust storms can send particulate to aircraft cruising altitudes. Also, aircraft operating in remote locations or low altitudes can be subjected to particle ingestion, especially in desert environments. The aim of this work is to propose different methodologies capable to mitigate the effects of fouling or predicting the performance degradation that it generates. For this purpose, both hot and cold engine sections are considered. Concerning the turbine section, new design guidelines are presented. This is because, for this specific component, the time scales of failure events due to hot deposition can be of the order of minutes, which makes any predictive model inapplicable. In this respect, design optimization techniques were applied to find the best HPT vane geometry that is less sensitive to the fouling phenomena. After that, machine learning methods were adopted to obtain a design map that can be useful in the first steps of the design phase. Moreover, after a numerical uncertainty quantification analysis, it was demonstrated that a deterministic optimization is not sufficient to face highly aleatory phenomena such as fouling. This suggests the use of robust or aggressive design techniques to front this issue. On the other hand, with respect to the compressor section, the research was mainly focused on the building of a predictive maintenance tool. This is because the time scales of failure events due to cold deposition are longer than the ones for the hot section, hence the main challenge for this component is the optimization of the washing schedule. As reported in the previous sections, there are several studies in the literature focused on this issue, but almost all of them are data-based instead of physics-based. The innovative strategy proposed here is a mixture between physics-based and data-based methodologies. In particular, a reduced-order model has been developed to predict the behaviour of the whole engine as the degradation proceeds. For this purpose, a gas path code that uses the components’ characteristic maps has been created to simulate the gas turbine. A map variation technique has been used to take into account the fouling effects on each engine component. Particularly, fouling coefficients as a function of the engine architecture, its operating conditions, and the contaminant characteristics have been created. For this purpose, both experimental and computational results have been used. Specifically for the latter, efforts have been done to develop a new numerical deposition/detachment model.Le turbine a gas sono una delle pricipali fonti di energia, sia per applicazioni aeronautiche che terrestri. Proprio per questa ragione, esse sono spesso costrette ad operare in ambienti non propriamente puliti, il che comporta l’ingestione di contaminanti solidi da parte del motore. Le principali implicazioni di questo problema sono spesso sottovalutate. Le particelle solide presenti nel flusso d’aria che il motore ingerisce durante il suo funzionamento possono depositarsi o erodere le superfici interne della macchina, e portare a variazioni alla sua aerodinamica, quindi a degrado di performance e, molto probabilmente, alla diminuzione della sua vita utile. Questo problema aflligge sia la parte del compressore che la parte della turbina, e si manifesta sia in applicazioni terrestri che aeronautiche. Per quanto riguarda la prima, la questione può essere mitigata (ma non eliminata) dall’installazione di sistemi di filtraggio all’ingresso della macchina. Per le applicazioni aeronautiche invece, i sistemi di filtraggio non possono essere utilizzati. Questo implica che il particolato presente ad alte quote, magari grazie ad eventi catastrofici quali eruzioni vulcaniche, o a basse quote, quindi ambienti deseritic, entra liberamente nella turbina a gas. Lo scopo principale di questo lavoro di tesi, è quello di proporre differenti metodologieallo scopo di mitigare gli effetti dello sporcamento o predirre il degrado che esso comporta nelle turbine a gas. Per questo scopo, sia la parte del compressore che quella della turbina sono state prese in considerazione. Per quanto riguarda la parte turbina, saranno presentate nuove guide progettuali volte al trovare la geometria che sia meno sensibile possibile al problema dello sporcamento. Dopo di ciò, i risultati ottenuti verranno trattati tramite tecniche di machine learning, ottenendo una mappa di progetto che potrà essere utile nelle prime fasi della progettazione di questi componenti. Inoltre, essendo l’analisi fin qui condotta di tipo deterministico, un’analisi delle principali fonti di incertezza verrà eseguita con l’utilizzo di tecniche derivanti dall’uncertainty quantification. Questo dimostrerà che l’analisi deterministica è troppo semplificativa, e che sarebbe opportuno spingersi verso una progettazione robusta per affrontare questa tipologia di problemi. D’altro canto, per quanto concerne la parte compressore, la ricerca è stata incentrata principalmente sulla costruzione di uno strumento predittivo, questo perchè la scala temporale del degrado dovuto alla deposizione a "freddo" è molto più dilatata rispetto a quella della sezione "calda". La trategia proposta in questo lavoro di tesi è un’insieme di modelli fisici e data-driven. In particolare, si è sviluppato un modello ad ordine ridotto per la previsione del comportamento del motore soggetto a degrado dovuto all’ingestione di particolato, durante un’intera missione aerea. Per farlo, si è generato un codice cosiddetto gas-path, che modella i singoli componenti della macchina attraverso le loro mappe caratteristiche. Quest’ultime vengono modificate, a seguito della deposizione, attraverso opportuni coefficienti di degrado. Tali coefficienti devono essere adeguatamente stimati per avere una corretta previsione degli eventi, e per fare ciò verrà proposta una strategia che comporta l’utilizzo sia di metodi sperimentali che computazionali, per la generazione di un algoritmo che avrà lo scopo di fornire come output questi coefficienti

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Contribution to the Definition of Non Deterministic Robust Optimization in Aeronautics Accounting with Variable Uncertainties

Shape optimization is a largely studied problem in aeronautics. It can be applied to many disciplines in this field, namely efficiency improvement of engine blades, noise reduction of engine nozzles, or reduction of the fuel consumption of aircraft. Optimization for general purposes is also of increasing interest in many other fields. Traditionally, optimization procedures were based on deterministic methodologies as in Hamalainen et al (2000), where the optimum working point was fixed. However, not considering what happens in the vicinity of the defined working conditions can produce problems like loose of efficiency and performance. That is, in many cases, if the real working point differs from the original, even a little distance, efficiency is reduced considerably as pointed out in Huyse and Lewis (2001) Non deterministic methodologies have been applied to many fields (Papadrakakis, Lagaros and Tsompanakis, 1998; Plevris, Lagaros and Papadrakakis, 2005). One of the most extended nondeterministic methodologies is the stochastic analysis. The time consuming calculations required on Computational Fluid Dynamics (CFD) has prevented an extensive application of the stochastic analysis to shape optimization. Stochastic analysis was firstly developed in structural mechanics, several years ago. Uncertainty quantification and variability studies can help to deal with intrinsic errors of the processes or methods. The result to consider for design optimization is no longer a point, but a range of values that defines the area where, in average, optimal output values are obtained. The optimal value could be worse than other optima, but considering its vicinity, it is clearly the most robust regarding input variability. Uncertainty quantification is a topic of increasing interest from the last few years. It provides several techniques to evaluate uncertainty input parameters and their effects on the outcomes. This research presents a methodology to integrate evolutionary algorithms and stochastic analysis, in order to deal with uncertainty and to obtain robust solutions

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008