Αντικείμενο της παρούσας εργασίας είναι η πρόβλεψη τόσο της κίνησης, αλληλεπίδρασης και παραμόρφωσης δύο φυσαλίδων λόγω μεταβολής της πίεσης στο περιβάλλον ιξώδες υγρό, όσο και της ανοδικής κίνησης μιας φυσαλίδας λόγω άνωσης σε ένα Νευτωνικό ή ιξωδοπλαστικό ρευστό. Για τη μοντελοποίηση των αλληλεπιδρώντων φυσαλίδων, αναπτύχθηκε μιας νέα ελλειπτική μεθόδος κατασκευής του υπολογιστικού πλέγματος προκειμένου να αντιμετωπιστούν επιτυχώς τα ιδιάζοντα σημεία (πόλοι) των φυσαλίδων και οι μεγάλες παραμορφώσεις των διεπιφανειών τους. Με τη μέθοδο αυτή η πύκνωση του πλέγματος περιορίζεται μόνο στις περιοχές που είναι αναγκαίο, μειώνοντας έτσι το υπολογιστικό κόστος και αυξάνοντας την ακρίβεια των υπολογισμών. Για την επίλυση των παρακάτω προβλημάτων χρησιμοποιήθηκε η μέθοδος των μικτών πεπερασμένων στοιχείων κατά Galerkin. Στην περίπτωση των αλληλεπιδρώντων φυσαλίδων έχει εξετασθεί η επίδραση του σχετικού μεγέθους τους, της συχνότητας και του εύρους μεταβολής της επιβαλλόμενης πίεσης και πότε οδηγούν σε έλξη ή άπωση των φυσαλίδων. Στην περίπτωση ελκτικής δύναμης, ακολουθείται η κίνηση και η παραμόρφωσή τους μέχρι του σημείου που έρχονται σε επαφή, όπου αυτό είναι εφικτό. Για τη μελέτη του προβλήματος της φυσαλίδας που ανέρχεται λόγω άνωσης, υποθέτουμε αξονική συμμετρία και μόνιμη κατάσταση. Σύγκριση των προβλέψεών μας για το σχήμα των φυσαλίδων και το πεδίο ροής γύρω τους με προηγούμενα θεωρητικά και πειραματικά αποτελέσματα για Νευτωνικά ρευστά έδειξε άριστη συμφωνία. Στην περίπτωση του ιξωδοπλαστικού ρευστού εξετάστηκαν λεπτομερώς οι παραμορφώσεις των φυσαλίδων σαν συνάρτηση των αριθμών Bingham, Bond και Αρχιμήδη και υπολογίσθηκαν οι συνθήκες υπό τις οποίες είναι δυνατή η παγίδευση της φυσαλίδας μέσα σε αυτό. / The present study deals with the numerical simulation of the motion, interaction and deformation of two bubbles due to variation of the pressure of the ambient Newtonian fluid, and the buoyancy-driven rise of a bubble in a Newtonian or a viscoplastic fluid. A new elliptic mesh generation method is developed in order to deal with the singular points (poles) of the bubbles and the large deformations of their surface. This method permits us to increase the mesh resolution only in the regions that is necessary, decreasing thus the computational cost and increasing the precision of our calculations. The following problems are solved using the mixed finite element/Galerkin method. In the case of the interacting bubbles the effect of their relative size, the frequency and the width of the imposed pressure is examined as well as the conditions that lead in attraction or repulsion of the bubbles. In the case that attractive forces exist, the motion and the deformation of the bubbles followed up to the point that they come in contact, whenever this is possible. In order to study the problem of the bubble that rises due to buoyancy, axial symmetry and steady flow is assumed. Our results for the shape of the bubbles and the flow around them are in very good agreement with previous theoretical and experimental results for Newtonian fluids. The deformations of the bubbles rising in a viscoplastic material are also examined for various values of the Bingham, Bond and Archimedes numbers and the conditions under which entrapment of a bubble is possible are determined.

Model-H is used to describe structures found in the phase separation in films of binary liquid mixture that have a surface that is free to deform and also may energetically prefer one of the components. The film rests on a solid smooth substrate that has no preference for any component. On the one hand the study focuses on static aspects by investigating steady states that are characterised by their concentration and film height profiles. A large variety of such states are systematically analysed by numerically constructing bifurcation diagrams in dependence of a number of control parameters. The numerical method used is based on minimising the free energy functional at given constraints within a finite element method for a variable domain shape. The structure of the bifurcation diagrams is related to the symmetry properties of the individual solutions on the various branches. On the other hand the full time dependent model-H is linearised about selected steady states, in particular, the laterally invariant, i.e.\ layered states. The resulting dispersion relations are discussed and related to the corresponding bifurcation points of the steady states. In general, the results do well agree and confirm each other. The described analysis is performed for a number of important cases whose comparison allows us to gain an advanced understanding of the system behaviour: We distinguish the critical and off-critical case that correspond to zero and non-zero mean concentration, respectively. In the critical case the investigation focuses on (i) flat films without surface bias, (ii) flat films with surface bias, (iii) height-modulated films without surface bias, and (iv) height-modulated films with surface bias. Each case is analysed for several mean film heights and (if applicable) energetic bias at the free surface using the lateral domain size as main control parameter. Linear stability analyses of layered films and symmetry considerations are used to understand the structures of the determined bifurcation diagrams. For off-critical mixtures our study is more restricted. There we consider height-modulated films without and with surface bias for several mean film heights and (if applicable) energetic bias employing the mean concentration as main control parameter.

Στόχος της παρούσας διδακτορικής διατριβής είναι η μελέτη χρονικά μεταβαλλόμενων και ασταθών υπό συνθήκες ροών ιξωδοπλαστικών και ιξωδο-ελαστικών ρευστών λόγω της σημασίας που παρουσιάζουν τα υλικά αυτά σε διάφορες βιομηχανικές διεργασίες. Στα πλαίσια της εργασίας αυτής μελετήθηκε αρχικά το πρόβλημα της συμπίεσης ιξωδοπλαστικού ρευστού μεταξύ δύο δίσκων το οποίο είναι ένα βασικό πείραμα ρεολογικού χαρακτηρισμού μη Νευτωνικών υλικών. Η χρονικά μεταβαλλόμενη προσομοίωση επέτρεψε τον προσδιορισμό των σημαντικών διαφορών μεταξύ των δύο εκδοχών του συγκεκριμένου ρεολογικού πειράματος (δίσκοι κινούμενοι υπό σταθερή ταχύτητα ή υπό σταθερή δύναμη) που ήταν αδύνατος με τα προηγούμενα μοντέλα, ενώ παρουσιάζεται και πλήρης παραμετρική μελέτη της διεργασίας αυτής. Το υπόλοιπο μέρος της παρούσας εργασίας αφιερώθηκε στη μελέτη της διεργασίας εκβολής ιξωδοελαστικών υλικών η οποία συναντάται ευρέως στη βιομηχανία μορφοποίησης πολυμερών. Παρουσιάζεται μια πλήρης παραμετρική ανάλυση για την εκβολή ενός ιξωδοελαστικού ρευστού Phan-Tien & Tanner (PTT) από ένα δακτυλιοειδή αγωγό προκειμένου να εξετάσουμε την επίδραση της γεωμετρίας του αγωγού, και των ρεολογικών ιδιοτήτων του ρευστού. Επιπλέον ένα σημαντικό πρόβλημα που εμφανίζεται κατά την εκβολή από ένα κυλινδρικό, επίπεδο ή δακτυλιοειδή αγωγό είναι η εμφάνιση ασταθειών οι οποίες επηρεάζουν σημαντικά την ποιότητα του τελικού προϊόντος. Προκειμένου να διερευνηθεί ο μηχανισμός που προκαλεί την εμφάνιση αυτών των ασταθειών πραγματοποιήθηκε γραμμική ανάλυση ευστάθειας για τη αξονοσυμμετρική και καρτεσιανή δισδιάστατη ροή επικόλλησης-ολίσθησης (stick-slip flow) ενός ρευστού PTT. Γύρω από τη λύση μόνιμης κατάστασης πραγματοποιείται γραμμική ανάλυση ευστάθειας, και υπολογίζονται οι ιδιοτιμές του γενικευμένου προβλήματος με τη βοήθεια της μεθόδου Arnoldi. Έτσι προσδιορίζεται η επίδραση των ιδιοτήτων του υλικού στην ευστάθεια ή μη της ροής. / The purpose of this dissertation is to perform a study on time-dependent and conditionally unstable flows of viscoplastic and viscoelastic fluids because of their importance in various industrial processes. A typical experiment which is used widely for the rheological characterization of non-Newtonian fluids is squeeze flow which is the subject of the first chapter of this dissertation. The time-dependent simulation permitted the determination of the distinct differences between the two versions of this rheological experiment (disks moving with constant velocity or under constant force) which was impossible with the models used up to now, while a complete parametric analysis of this process is presented. The rest of this work focuses in the important problem of the extrusion process of a viscoelastic fluid, which is frequently encountered in the polymer industry. A complete parametric analysis is presented for the extrusion of a Phan-Thien Tanner (PTT) fluid from an annular die in order to examine the effect of the die geometry and the rheological properties of the fluid on this process. Moreover, it is widely known that during the extrusion from a cylindrical, planar or an annular die various flow instabilities may arise affecting significantly the quality of the final product. In order to investigate the mechanism, which causes the appearance of these instabilities, a linear stability analysis is performed for the cylindrical or planar stick-slip flow of a PTT fluid. The stability analysis is performed around the steady state solution and the eigenvalues of the generalized problem are calculated using the Arnoldi algorithm. With this method the effect of the various rheological properties of the fluid on the stability of the flow is determined.

No description available.

Since the past decade, use of electro-osmotic flow (EOF) as an alternative flow mechanism in microdevices is becoming more popular due to its less bulky and low maintenance system design. However, one of the biggest shortcomings for its usage in mainstream applications is that it requires the concerned liquid to be electrically conductive. One idea can be to use the flow of conductive fluids to transport non-conductive liquids passively via interfacial shear transfer. Such an idea can has numerous applications in a wide range of fields like bio-chemical processing (e.g. lab-on-a-chip reactors, mixers, etc.), to oil extraction from porous rock formations. One of the significant characteristics of micro-scale flows is high surface to volume ratio, which significantly highlights the role of multi-phase interfaces in such dynamics. The presence of a fluid-fluid interface in an EOF necessitates the characterization of the parameters responsible for hydrodynamic instability of such systems. The present work focuses on the role of steady and time-dependent electric stress (Maxwell stress), capillary force and disjoining pressure on fluid-fluid interfacial instability. A linear stability analysis of interfacial perturbation was performed for a thin film of electrolyte under DC and AC electric fields. Through long wave asymptotic analysis of the Orr-Sommerfeld equations, parametric stability thresholds of a thin aqueous film explored. Further, a set of experiments were performed in order to characterize the EOF in a rectangular microchannel. With the help of a Particle Tracking Velocimetry analysis, velocity distributions were obtained which agreed well to the theoretical values. This was further used to estimate PDMS zeta potential, which was found to be within the reported values in the existing literature. Liquid-liquid interfacial deformation was also explored under a time-periodic EOF and a wide range of the magnitudes of capillary force, and diffusive and convective transport.

Diese numerische Arbeit untersucht, wie sich die laminar-turbulente Transition in der Grenzschicht einer ebenen Platte mit elektromagnetischen Kräften verzögern lässt. Erzeugt von einer Elektroden-Magnet-Anordnung in der Platte wirken jene Kräfte im wandnahen Bereich der Strömung. Sie sind wandparallel sowie stromab gerichtet und besitzen zwei Parameter, die Amplitude und die Eindringtiefe. Zwei- und dreidimensionale Direkte Numerische Simulationen, Grenzschichtgleichungslöser sowie lineare Stabilitätsanalyse werden eingesetzt, um zwei Ansätze der Transitionsverzögerung zu verfolgen: Zum einen die aktive Wellenauslöschung, bei der ankommende Grenzschichtinstabilitäten von gegenphasig angeregten Wellen bis zu 97% ausgelöscht werden. Zum anderen können elektromagnetische Kräfte die Grenzschicht beschleunigen und so zu deutlich stabilieren Grenzschichtprofilen führen. Über evolutionäre Optimierung wurde eine räumliche Verteilung von Eindringtiefe und Kraftamplitude gefunden, die den Energieeinsatz minimiert und gleichzeitig laminare Strömung sicherstellt; dennoch bliebt die energetische Effizienz der Beeinflussung unter Eins. / This numerical work investigates how electromagnetic forces may delay laminar-turbulent transition of a flat plate boundary layer. Generated by an array of electrodes and magnets flush mounted in the wall, those forces act within the wall-near flow. They are oriented in wall-parallel, downstream direction and are characterized by two parameters, namely amplitude and penetration depth. Two- and three-dimensional Direct Numerical Simulations, numerical solutions of boundary layer equations and linear stability analysis are applied to study two possible ways of transition delay: first, the so-called active wave cancellation, where an anti-wave cancels incoming boundary layer instabilities by up to 97%. A second option is have electromagnetic forces accelerate the boundary layer, thereby modifying its mean velocity profile for greatly enhanced stability. Using evolutionary optimization, a spatial distribution of force amplitude and penetration depth was obtained that maintains laminar flow while minimizing electrical power consumption of the actuator. However, the energetic efficiency of actuation remains less than unity.

A novel fuzzy system named as 2-way fuzzy system is developed by combining the intuitionistic fuzzy set theory with the fuzzy systems theory. The developed system is used in modelling and minimizing uncertainty and inconsistency. Uncertainty is the width of the interval introduced by the independent assignment of membership and nonmembership functions of the intuitionistic fuzzy sets / and inconsistency is the violation of the consistency inequality in this assignment. The uncertainty and inconsistency is reduced through a 2 phase training. An evaluation of the degree of reduction of inconsistency is carried out at the end of the rst phase of training by forming the shadowed set patterns of the membership and nonmembership functions. The system is further trained for a second phase in order to reduce uncertainty. There are three dierent methods developed for the stability analysis of fuzzy systems. The rst method is based on the approximating sequences technique, and the design turns into an optimal control problem. In the sec ond analysis, describing function of a 2-way fuzzy system is evaluated analytically, and a systematic design approach is developed using describing function technique. The last analysis technique employs the Lie algebra theory in the stability analysis of Takagi-Sugeno fuzzy systems. The theoretical results are simulated on an application system, which is a exible-joint robot arm system.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This study had as main objective to perform the modeling and analysis of transient stability of a typical electric power system. The second goal, also important, was to assess the feasibility of using ATP (Alternative Transients Program) as a computer tool for simulation of transient stability. The system focused here is comprised of nine busses with three generators, one hydraulic and the other two with thermal characteristics. All the system machines were equipped with voltage regulators and speed governor in ATP software. The technical issues studied here refer to the analysis of system stability after a disturbance, such as: three-phase short-circuit, load loss and generation outage. The results show that ATP software performs satisfactorily the transient stability analysis. This fact can also be proved by comparing the results obtained from ATP with those from simulations with PSAT (Power System Analysis Toolbox). For this purpose some adjustments were necessary in the graphical results since ATP works in time domain while PSAT program operates in the frequency domain. / Este trabalho teve como principal objetivo realizar a modelagem e a análise da estabilidade transitória de um sistema elétrico de potência típico. O segundo objetivo, também importante, consistiu em avaliar a viabilidade de se utilizar o ATP (Alternative Transients Program) como uma ferramenta computacional para simulação de estabilidade transitória. O sistema aqui enfocado é composto por nove barramentos com três unidades geradoras, uma com característica hidráulica e as outras duas com características térmicas. Todas as máquinas do sistema foram equipadas com reguladores de tensão e velocidade no programa ATP. As questões técnicas estudadas aqui se referem à análise da estabilidade do sistema após uma perturbação, sendo elas: falta trifásica, perda de carga e saída de geração. Os resultados mostram que o software ATP realiza satisfatoriamente a análise de estabilidade transitória. Este fato pode também ser comprovado pela comparação dos resultados obtidos com o ATP com aqueles provenientes de simulações com o PSAT (Power System Analysis Toolbox). Para este propósito foi necessário realizar alguns ajustes nos resultados gráficos já que ATP trabalha no domínio do tempo enquanto que o programa PSAT opera no domínio da frequência, tais como: transformação de alguns gráficos fornecidos pelo ATP em pu. / Mestre em Ciências

>Magister Scientiae - MSc / In this thesis, we investigate the HIV/AIDS epidemic in a population which experiences a significant flow of immigrants. We derive and analyse a math- ematical model that describes the dynamics of HIV infection among the im- migrant youths and intervention that can minimize or prevent the spread of the disease in the population. In particular, we are interested in the effects of public-health education and of parental care.We consider existing models of public-health education in HIV/AIDS epidemi-ology, and provide some new insights on these. In this regard we focus atten-tion on the papers [b] and [c], expanding those researches by adding sensitivity analysis and optimal control problems with their solutions.Our main emphasis will be on the effect of parental care on HIV/AIDS epidemi-ology. In this regard we introduce a new model. Firstly, we analyse the model without parental care and investigate its stability and sensitivity behaviour.We conduct both qualitative and quantitative analyses. It is observed that in the absence of infected youths, disease-free equilibrium is achievable and is asymptotically stable. Further, we use optimal control methods to determine the necessary conditions for the optimality of intervention, and for disease eradication or control. Using Pontryagin’s Maximum Principle to check the effects of screening control and parental care on the spread of HIV/AIDS, we observe that parental care is more effective than screening control. However, the most efficient control strategy is in fact a combination of parental care and screening control. The results form the central theme of this thesis, and are included in the manuscript [a] which is now being reviewed for publication. Finally, numerical simulations are performed to illustrate the analytical results.

Master thesis deals with a computing simulation of two props turbines lines. The thesis output is gaining maximum possible load, at which a commencement of deformation stability critical state for various geometrical imperfections has not arisen yet. The calculation has been done by FEM in two different ways: linear solution (using a calculation conversion into eigenbuckling) and nonlinear solution (using a FEM deformation option). Result analysis compares both methods outcomes. Safety factor for the props operation has been proposed taking into consideration known influences on operating state.