Control of Gortler Vortices by Means of Wall Deformations and Blowing/Suction

Görtler vortices evolve in boundary layers over concave surfaces as a result of the imbalance between centrifugal forces and radial pressure gradients. Depending on various geometrical and free-stream flow conditions, these instabilities may lead to secondary instabilities and early transition to turbulence. In this thesis, a control algorithm based on the boundary region equations is applied to reduce the strength of the Görtler instabilities by controlling the energy of the fully developed vortices, using either local wall deformations or blowing/suction at the wall. A proportional-integral control scheme is utilized to deform the wall or to provide transpiration velocity, where the inputs are either the wall-normal or streamwise velocity components in a plane that is parallel to the wall. The results show that the control based on wall deformation using wall-normal velocity components is more effective in tempering the vortex during its streamwise growth by almost one or two orders of magnitude

Vortex Formation and Decay: The Scaling of Vortex-Wall Interaction

Das Ziel der vorliegenden Arbeit ist es den Einfluss von Turbulenz und im speziellen der Reynoldszahl ($Re$) auf die Prozesse der Wirbelformation und des Wirbelzerfalls zu untersuchen. Inspiriert von Wirbeln, die bei der Fortbewegung von schwimmenden und fliegenden Tieren auftreten, werden drei charakteristische Merkmale identifiziert, die durch das Zusammenspiel eines Wirbels mit einem beschleunigten Festkörper (z.B. einem Flügel oder einer Flosse) entstehen: eine gekrümmte freie Scherschicht, der Wirbelkern und die Grenzschicht zwischen dem Wirbel und dem beschleunigten Körper. Im Rahmen der Arbeit werden mehrere Experimente und Simulationen vorgestellt, welche diese Merkmale der Wirbel in vereinfachten Konfigurationen reproduzieren und von anderen Effekten isolieren. Dies ermöglicht es den Einfluss der Turbulenz auf besagte Wirbelmerkmale zu quantifizieren. Zunächst wird die Interaktion eines generischen Wirbels mit einer Wand betrachtet. Hierzu wird ein Zylinder, welcher ein Fluid in Starrkörperrotation enthält, schlagartig angehalten. Das Abklingen und der Zerfall der des Starrkörperwirbels wird mithilfe einer direkten numerischen Simulation (DNS) für Reynoldszahlen im Bereich $Re \leq 2.8 \cdot 10^4$ analysiert. Fünf Stufen des Wirbelzerfalls können aufgrund der zugrundeliegenden Strukturen der Strömung charakterisiert werden. Darüber hinaus liefern die Ergebnisse der DNS empirische Skalierungsgesetze, die verschiedene Stufen den Wirbelzerfalls beschreiben. Die Skalierungsgesetze werden anschließend anhand von zwei experimentellen Kampagnen im moderaten ($Re\leq 5.6\cdot 10^5$) und hohen ($Re\leq 4\cdot 10^6$) Reynoldszahlbereich validiert. Anschließend wird die gekrümmte Scherschicht und der Wirbelkern genauer betrachtet. In Experimenten in einem großskaligen Schleppkanal wird eine runde Platte aus der Ruhe beschleunigt. Hierbei liefern Experimente in einem großen Reynoldszahlbereich Erkenntnisse über die Auswirkungen von kleinskaligen Strukturen auf die Wirbelformation. Weiterhin wird die Turbulenz im Wirbel durch Modifikationen der umlaufenden Plattenkante beeinflusst. Inspiriert von in der Natur auftretenden Flossenformen werden wellenartige Strukturen aufgeprägt, welche Strukturen im Bereich ihrer eigenen Wellenlänge in die Strömung einbringen. Sind diese Wellenlängen größer als die Dicke der gekrümmten Scherschicht, wird das Wirbelwachstum beeinflusst und damit die Kraft, die auf die Platte wirkt, modifiziert

Numerical Study on the Flow over a Simplified Vehicle Door Gap – an Old Benchmark Problem Is Revisited

A simplified automobile door gap model, defined at the Third Computational Aeroacoustics (CAA) Workshop on Benchmark Problems (Category 6) was investigated. After a thorough mesh study compressible and incompressible simulations were carried out and various turbulence models were tried. The influence of three dimensional effects and boundary layer thickness effects were examined too. In case of compressible simulations stability problems were encountered with the non-reflective boundary condition of CFX (beta version at the time of the simulations). It was found that for deep cavities incompressible simulations are not applicable. In spite of the diculties a good agreement between measurements and simulations was found when the flow speed was 50m/s. In case of 26.8m/s flow speed it was found that the presence of the upper channel wall, not taken into account by the previous authors simulating this problem plays an important role – a hitherto unexplained peak in the measured spectrum appeared this way in the simulation

Görtler instability and transition in compressible flows

We present a discussion on theoretical, experimental, and computational research studies on Görtler instability and the related transition to turbulence occurring in compressible boundary layers over concave surfaces. We first examine the theoretical results on primary and secondary instabilities, emphasizing the role of receptivity, the mechanism by which external agents, such as freestream fluctuations or wall roughness, act on a boundary layer to trigger Görtler vortices. We review experimental findings obtained from measurements in supersonic and hypersonic wind tunnels and discuss studies employing numerical methods, focusing on the direct numerical simulation approach. The research in these two last sections is surveyed according to the geometrical configuration, from simple concave walls to more complex surfaces of hypersonic vehicles. The experimental investigations have been successful in the visualizations of Görtler vortices, in the measurement of the wall-heat transfer in the transitional region, and in the computation of the Görtler-vortex growth rates, although detailed boundary-layer velocity measurements are still missing. Direct numerical simulations have confirmed instability results emerging from stability theories and revealed nonlinear interactions between Görtler vortices and other disturbances. The established initial-boundary-value receptivity theory can certainly benefit from more advanced experimental measurements, and receptivity results should be used in combination with direct numerical simulations. A major conclusion of our review is therefore that the understanding of Görtler vortices should be pursued by a combined methodology including theoretical analysis based on the receptivity formalism, direct numerical simulation, and experiments. Highly desirable outcomes of such endeavor are the prediction of the location and extension of the transition region, and a model for the transition process. We finally highlight further prospects and challenges on fundamental and applied research on Görtler instability and transition in compressible flows

Lagrange Multiplier-Based Optimal Control Technique for Streak Attenuation in High-Speed Boundary Layers

High-amplitude freestream turbulence and surface roughness elements can excite a laminar boundary-layer flow sufficiently to cause streamwise-oriented vortices to develop. These vortices resemble elongated streaks having alternate spanwise variations of the streamwise velocity. Downstream, the vortices “wobble” through an inviscid secondary instability mechanism and, ultimately, transition to turbulence. We formulate an optimal control algorithm to suppress the growth rate of the streamwise vortex system. Considering a high-Reynolds-number asymptotic framework, we reduce the full compressible Navier–Stokes equations to the nonlinear compressible boundary-region equations. We then implement the method of Lagrange multipliers via an appropriate transformation of the original constrained optimization problem into an unconstrained form to obtain the disturbance equations in the form of the adjoint compressible boundary-region equations (ACBREs) and corresponding optimality conditions. Numerical solutions of the ACBRE approach for high-supersonic and hypersonic flows reveal a significant reduction in the kinetic energy and wall shear stress for all considered configurations. We present contour plots to demonstrate the qualitative effect of increased control iterations. Our results indicate that the primary vortex instabilities gradually flatten in the spanwise direction thanks to the ACBRE algorithm. Previous articl

Azimuthal Variation of Instabilities Generated on a Flared Cone by Laser Perturbations

To study the azimuthal development of boundary-layer instabilities, a controlled, laser-generated perturbation was created in the freestream of the Boeing/U.S. Air Force Office of Scientific Research Mach 6 Quiet Tunnel. The freestream perturbation convected downstream in the wind tunnel to interact with a flared-cone model. The flared cone is a body of revolution bounded by a circular arc with a 3 m radius. Pressure transducers were used to measure a wave packet generated in the cone boundary layer by the freestream perturbation. Nine of these sensors formed three stations of azimuthal arrays and were used to determine the azimuthal variation of the wave packets in the boundary layer. The freestream laser-generated perturbation was positioned upstream of the model in three different configurations: along the centerline axis, offset from the centerline axis by 1.5 mm, and offset from the centerline axis by 3.0 mm. When the freestream perturbation was offset from the centerline of a flared cone with a 1.0 mm nose radius, a larger wave packet was generated on the side toward which the perturbation was offset. As a result, transition occurred earlier on that side. The offset perturbation did not have as large of an effect on the boundary layer of a nominally sharp flared cone

Étude et modélisation du phénomène de croissance transitoire et de son lien avec la transition Bypass au sein des couches limites tridimensionnelles

The transition from a laminar to a turbulent flow strongly modifies the boundary layer properties. Understanding the mechanisms leading to transition is crucial to reliably predict aerodynamic performances. For boundary layers subjected to high levels of external disturbances, the natural transition due to the amplification of the least stable mode is replaced by an early transition, called Bypass transition. This is the result of non-normal mode interactions that lead to a phenomenon of transient growth of disturbances. These disturbances are known as Klebanoff modes and take the form of streamwise velocity streaks. This thesis aims at understanding this linear mechanism of transient growth and quantifying its influence on the classical modal amplification of disturbances. This is done by computing the so-called optimal perturbations, i.e. the initial disturbances that undergo maximum amplification in the boundary layer. These optimal perturbations are first determined for two-dimensional compressible boundary layers developing over curved surfaces. In particular, we show that Klebanoff modes naturally evolve towards Görtler vortices that occur over concave walls. Three-dimensional boundary layers are then considered. In such configurations, transient growth provides an initial amplitude to crossflow vortices. Finally, applying the tools developed in this thesis to new flow cases such as swept wings provides further understanding of the phenomenon of transient growth for realistic geometries.Le passage du régime laminaire au régime turbulent s’accompagne d’importantes modifications des propriétés physiques de la couche limite. La détermination précise de la transition est donc cruciale dans de nombreux cas pratiques. Lorsque la couche limite se développe dans un environnement extérieur faiblement perturbé, la transition est gouvernée par l’amplification du mode propre le moins stable. Lorsque l’intensité des perturbations extérieures augmente, des interactions multimodales entraînent une amplification transitoire des perturbations. Ce phénomène peut conduire à une transition prématurée, appelée transition Bypass. Les perturbations prennent alors la forme de stries longitudinales de vitesse appelées modes de Klebanoff. L’objectif de cette thèse est d’étudier ce mécanisme linéaire de croissance transitoire et son influence sur l’amplification modale classique des perturbations. Cela passe par la détermination des perturbations les plus amplifiées au sein de la couche limite, appelées perturbations optimales. Ces perturbations optimales sont d’abord calculées pour des couches limites bidimensionnelles et compressibles se développant sur des surfaces courbes. En particulier, on montre que les modes de Klebanoff évoluent vers les tourbillons de Görtler qui se forment sur des parois concaves. Le cas plus général de couches limites tridimensionnelles est ensuite envisagé. Pour de telles configurations, la croissance transitoire fournit une amplitude initiale aux instabilités transversales. Enfin, l’application des outils développés dans cette thèse fournit de nouveaux résultats pour des cas d’écoulements autour de géométries réalistes comme une aile en flèche