A realização deste trabalho tem como objetivo fundamental estudar os efeitos dos atuadores de jato sintético no escoamento de uma camada limite desenvolvida sobre uma placa plana e um aerofólio hipotético. A interação dos jatos sintéticos com um escoamento transversal pode conduzir a uma aparente modificação da forma aerodinâmica de corpos rombudos e, dessa forma, fornecer uma maneira de controle da separação na camada limite. Estudos recentes demonstram que tipos diferentes de escoamentos podem ser produzidos pelo atuador dependendo da oscilação da membrana. Um método numérico para solução das equações de Navier-Stokes incompressíveis bidimensionais na formulação vorticidade-velocidade é utilizado neste trabalho. As equações governantes são discretizadas utilizando-se métodos de diferenças finitas compactas de sexta ordem para as derivadas espaciais. A equação de Poisson para a componente da velocidade normal é resolvida por um método iterativo de sobre-relaxação em linhas sucessivas usando um esquema com malha composta para acelerar a convergência. Os resultados de simulações com diferentes valores de freqüência, amplitude e comprimento de fenda foram verificados através de uma análise de Fourier temporal. Através desta análise é verificado qual a melhor situação para se atrasar a separação da camada limite / This work has as a fundamental objective the study of the effects of synthetic jet actuators on the boundary layer flow on a flat plate and on a hypothetical airfoil. The interaction of synthetic jets with transverse flow can lead to an apparent modification in the aerodynamic shape of blunt bodies and, in that way, supply a means of control of transition within the boundary layer. Recent studies demonstrate that different types of flow may be produced by the actuator, depending on the amplitude of oscillation of the membrane. A numerical method for the solution of two-dimensional incompressible Navier-Stokes equations written in vorticity-velocity formulation is used in this work. The spatial derivatives are discretized with a sixth order compact finite differences scheme. The Poisson equation for the normal velocity component is solved by an iterative line successive over relaxation method and uses a multigrid full approximation scheme to accelerate the convergence. The results of simulations with different values of frequency, amplitude and slot length were verified through a temporal Fourier analysis. By way of this analysis it is verified which are the better parameters for the controlled delay of boundary layer separation

A realização deste trabalho tem como objetivo fundamental estudar os efeitos dos atuadores de jato sintético no escoamento de uma camada limite desenvolvida sobre uma placa plana e um aerofólio hipotético. A interação dos jatos sintéticos com um escoamento transversal pode conduzir a uma aparente modificação da forma aerodinâmica de corpos rombudos e, dessa forma, fornecer uma maneira de controle da separação na camada limite. Estudos recentes demonstram que tipos diferentes de escoamentos podem ser produzidos pelo atuador dependendo da oscilação da membrana. Um método numérico para solução das equações de Navier-Stokes incompressíveis bidimensionais na formulação vorticidade-velocidade é utilizado neste trabalho. As equações governantes são discretizadas utilizando-se métodos de diferenças finitas compactas de sexta ordem para as derivadas espaciais. A equação de Poisson para a componente da velocidade normal é resolvida por um método iterativo de sobre-relaxação em linhas sucessivas usando um esquema com malha composta para acelerar a convergência. Os resultados de simulações com diferentes valores de freqüência, amplitude e comprimento de fenda foram verificados através de uma análise de Fourier temporal. Através desta análise é verificado qual a melhor situação para se atrasar a separação da camada limite / This work has as a fundamental objective the study of the effects of synthetic jet actuators on the boundary layer flow on a flat plate and on a hypothetical airfoil. The interaction of synthetic jets with transverse flow can lead to an apparent modification in the aerodynamic shape of blunt bodies and, in that way, supply a means of control of transition within the boundary layer. Recent studies demonstrate that different types of flow may be produced by the actuator, depending on the amplitude of oscillation of the membrane. A numerical method for the solution of two-dimensional incompressible Navier-Stokes equations written in vorticity-velocity formulation is used in this work. The spatial derivatives are discretized with a sixth order compact finite differences scheme. The Poisson equation for the normal velocity component is solved by an iterative line successive over relaxation method and uses a multigrid full approximation scheme to accelerate the convergence. The results of simulations with different values of frequency, amplitude and slot length were verified through a temporal Fourier analysis. By way of this analysis it is verified which are the better parameters for the controlled delay of boundary layer separation

Οι μερικές διαφορικές εξισώσεις (ΜΔΕ), σε πολλές περιπτώσεις πρακτικού ενδιαφέροντος, δέχονται μια επίλυση μέσω της "μεθόδου ομοιότητας". Σε αντίθεση με τη γνωστή μέθοδο του χωρισμού των μεταβλητών, η μέθοδος ομοιότητας βασίζεται σε έναν εύστοχο συνδυασμό των μεταβλητών, μετατρέποντας την αρχική ΜΔΕ σε μια συνήθη διαφορική εξίσωση (ΣΔΕ) μιας και μοναδικής συνδυασμένης μεταβλητής. Η μετατροπή αυτή όχι μόνο αποτελεί το πλέον καθοριστικό βήμα προς τη ζητούμενη λύση αλλά ταυτόχρονα μας αποκαλύπτει και πολλά χαρακτηριστικά από την ουσιαστική φύση του ίδιου του προβλήματος. Στην παρούσα διπλωματική εργασία μελετάμε μερικά αντιπροσωπευτικά παραδείγματα της μεθόδου από τη Μηχανική των Ρευστών, όπως το "πρώτο πρόβλημα του Stokes" (περί της ροής πάνω από μια οριζόντια πλάκα που μέσω μιας ξαφνικής ώθησης τίθεται σε μια ευθύγραμμη ομαλή κίνηση) και το "πρόβλημα του Blasius" περί του συνοριακού στρώματος. Τέλος, στο πλαίσιο του βασικού ερωτήματος πότε ένα πρόβλημα ΜΔΕ δέχεται μια λύση ομοιότητας και πότε όχι, θα συζητήσουμε και το "δεύτερο πρόβλημα του Stokes", περί της ροής πάνω από μια οριζόντια πλάκα που ταλαντώνεται περιοδικά από τα αριστερά προς τα δεξιά και αντίστροφα. Αυτό το πρόβλημα αποτελεί ένα αντιπαράδειγμα για την καθολικότητα της μεθόδου, δείχνοντας ότι αυτή δεν εφαρμόζεται όταν υπάρχουν προκαθορισμένες χωρικές ή χρονικές κλίμακες στο σύστημα. / --

This thesis considers the hydrodynamic instability and optimal forcing of a number of incompressible flow cases. In the first part, the instabilities of three problems that are of great interest in energy and aerospace applications are studied, namely a Blasius boundary layer subject to localized wall-suction, a Falkner–Skan–Cooke boundary layer with a localized surface roughness, and a pair of helical vortices. The two boundary layer flows are studied through spectral element simulations and eigenvalue computations, which enable their long-term behavior as well as the mechanisms causing transition to be determined. The emergence of transition in these cases is found to originate from a linear flow instability, but whereas the onset of this instability in the Blasius flow can be associated with a localized region in the vicinity of the suction orifice, the instability in the Falkner–Skan–Cooke flow involves the entire flow field. Due to this difference, the results of the eigenvalue analysis in the former case are found to be robust with respect to numerical parameters and domain size, whereas the results in the latter case exhibit an extreme sensitivity that prevents domain independent critical parameters from being determined. The instability of the two helices is primarily addressed through experiments and analytic theory. It is shown that the well known pairing instability of neighboring vortex filaments is responsible for transition, and careful measurements enable growth rates of the instabilities to be obtained that are in close agreement with theoretical predictions. Using the experimental baseflow data, a successful attempt is subsequently also made to reproduce this experiment numerically. In the second part of the thesis, a novel method for computing the optimal forcing of a dynamical system is developed. The method is based on an application of the inverse power method preconditioned by the Laplace preconditioner to the direct and adjoint resolvent operators. The method is analyzed for the Ginzburg–Landau equation and afterwards the Navier–Stokes equations, where it is implemented in the spectral element method and validated on the two-dimensional lid-driven cavity flow and the flow around a cylinder. / <p>QC 20171124</p>