BOUNDARY LAYER ON FLAT PLATE WITH LEADING EDGE PATTERNS

Ph.DDOCTOR OF PHILOSOPH

Low order modelling of flow-control techniques for turbulent skin-friction reduction

In the present thesis a linearized formulation of the Navier-Stokes equations is used to study two main subjects: the generation of near-wall streaks in turbulent boundary layers and the response of turbulent wall-bounded flows to streamwise-travelling waves of spanwise oscillations of the bounding walls. For the purposes of the present work, these oscillations of the wall have been considered as a flow control mechanism. A mathematical model, based on a velocity-vorticity formulation linearized around a turbulent mean base flow, is adopted to simulate the fluid flow equations. A hybrid spectral-finite differences solver has been employed to numerically implement the linearized system. A review on turbulent streak generation is presented and the concepts of exponential growth, algebraic growth and viscous dissipation of small-scale perturbations are linked to the concept of transient growth. Mechanisms of generation of near-wall streaks are explored using a large set of sources of excitation for the linearized Navier- Stokes equations (LNSE). Two types of sources, here labelled as Excitation Mechanisms (EM), are employed: a body-force source and an initial condition. The selection of parameters for the excitation mechanisms is performed based on the definition of a multi-step optimization problem. The different EMs studied consist of a restricted number of parameters, and therefore can be considered as a Low Order Model (LOM) for the generation of streaks. It is shown that both types of EM produce satisfactory results for the streak generation process evaluated in terms of experimentally expected optimal spanwise scales. Finally, a large set of numerical experiments are conducted to evaluate the response of the LNSE with optimised EM, to the flow control by a spanwise oscillating wall. By comparing the results between the response of the LNSE considered here to this type of flow control against a drag-reduction map obtained by DNS in other studies, it is possible to assess the correlation between streak evolution and disruption of the skin-friction drag. A good agreement between these two responses is found for the parameter space of the streamwise-travelling spanwise oscillation waves

Study of the most Amplified Wavelength Gortler Vortices

Ph.DDOCTOR OF PHILOSOPH

Optimal streaks amplification in wakes and vortex shedding control

Les amplifications optimales d'énergie de structures quasiment alignées dans le sens de l'écoulement sont calculées dans le cas d'un sillage parallèle, d'un sillage synthétique faiblement non-parallèle et du sillage d'un cylindre. Il a été observé que de très grandes amplifications d'énergie peuvent être supportés par ces sillages. L'amplification d' énergie s'accroît avec la longueur d'onde des perturbations en envergure à l'exception du sillage du cylindre pour lequel l'accroissement d'énergie est maximal pour λz ≈ 5 − 7 D. Les structures amplifiées de manière optimale sont les streaks fluctuant dans le sens de l’écoulement. Il est montré que ces streaks sont capables de supprimer complètement l'instabilité absolue d'un sillage parallèle lorsqu'ils sont déclenchés avec une amplitude finie. L'instabilité globale d'un sillage faiblement non-parallèle et celle du sillage d'un cylindre peuvent être complètement supprimées par des streaks d'amplitude modeste. L'énergie de contrôle requise pour stabiliser le sillage est très faible lorsque les perturbations optimales sont utilisées, et il est montré qu'elle est toujours plus faible que celle qui devrait être utilisée pour un contrôle uniforme en envergure (2D). Il est aussi montré que la dépendance du taux de croissance est quadratique et que, par conséquent, les classiques analyses de sensibilité au premier ordre ne permettent pas de prédire la grande efficacité de la technique de contrôle par streaks. La dernière partie de ce travail livre des résultats préliminaires sur l'étude expérimentale du contrôle par streaks dans le cas du sillage turbulent d'un corps 3D. Il est montré que les streaks forcés artificiellement dans la zone d'instabilité absolue de l'écoulement sont capables de modifier la dynamique du sillage. ABSTRACT : We compute optimal energy growths leading to streamwise streaks in parallel, weakly non-parallel and the circular cylinder wakes. We find that very large energy amplifications can be sustained by these wakes. The energy amplifications increase with the spanwise wavelength of the perturbations except in the circular cylinder wake where maximum energy growths are reached for λz ≈ 5 − 7 D. The optimally amplified structures are streamwise streaks. When forced with finite amplitudes these streaks are shown, in parallel wakes, to be able to completely suppress the absolute instability. The global instability of the weakly non-parallel and the circular cylinder wakes can be completely suppressed with moderate streaks amplitudes. The energy required to stabilize the wake is much reduced when optimal perturbations are used, and it is shown to be always smaller than the one that would be required if a 2D control was used. It is also shown that the sensitivity of the global mode growth rate is quadratic and that therefore usual first order sensitivity analyses are unable to predict the high efficiency of the control-by-streaks strategy

О нелинейных механизмах неустойчивости в пограничном слое

Представлены результаты исследований синусоидальной и варикозной неустойчивости полосчатых структур на нелинейной стадии ламинарно-турбулентного процесса в сдвиговых течениях. Обсуждается поведение течения в процессе пространственной эволюции полосчатых структур с генерированным на них вторичным высокочастотным возмущением. Рассмотрены различные сценарии возникновения и развития когерентных вихревых структур, исследованных как в физическом, так и в численном экспериментах. Показаны особенности развития синусоидального и варикозного случаев разрушения продольной стационарной полосчатой структуры, такие как модуляция структуры в трансверсальном и продольном направлениях частотой вторичного возмущения, появление новых полосчатых структур вниз по потоку и возникновение и развитие локализованных по пространству нестационарных образований типа L-структур в обоих случаях.Представлено результати дослiджень синусоїдальної та варикозної нестiйкостi смужчатих структур на нелiнiйнiй стадiї ламiнарно-турбулентного процесу в зсувних течiях. Обговорюється поведiнка потоку в процесi просторової еволюцiї смужчатих структур з генерованим на них вторинним високочастотним збуренням. Розглянуто рiзнi сценарiї виникнення та розвитку когерентних вихрових структур, дослiджених як у фiзичному, так i у чисельному експериментi. Показано особливостi розвитку синусоїдального та варикозного випадкiв руйнування поздовжньої стацiонарної смужчатої структури, такi як модуляцiя структури у трансверсальному та поздовжньому напрямках частотою вторинного збурення, виникнення нових смужчатих структур вниз за течiєю, виникнення та розвиток локалiзованих у просторi нестацiонарних утворень типу L-структур в обох випадках.There are presents the results of analysis of sinusoidal and varicose instability of streaky structures on the nonlinear stage of laminar-turbulent process in shear flows. Discussed is the behavior of the flow during the process of spatial evolution of streaky structures with generated on them secondary high-frequency perturbation. Considered are various scenarios of appearance and development of coherent vortical structures investigated in both physical and numerical experiments. Shown are details of sinusoidal and varicose cases of destruction of steady longitudinal streaky structure, such as modulations of the structure in transversal and longitudinal directions by the secondary perturbation frequency, appearance of new streaky structures downstream, and appearance and spatial development of unsteady formations of the kind of L-structure in both cases

Experimental Study on Influences of Riblets on Laminar-Turbulent Transition and Dependence of Wall Turbulence Generation on Disturbance Nature

Control of laminar-turbulent transition in boundary layers is one of key technologies to reduce aerodynamic drag of aircraft. Lots of theoretical, experimental and computational studies have been conducted and our knowledge on the mechanism of boundary-layer transition has been much improved for the last few decades. However, some fundamental problems have still remained open to control the transition process. The present thesis deals with some problems related to drag reduction and the underlying mechanisms. The main objective of this thesis is to clarify effects of riblets which are often used for drag reduction of wall turbulence on the instability and transition of boundary layer. Detailed experiments were conducted on the Blasius boundary layer with zero pressure gradient in a low turbulence wind tunnel and a low turbulence channel flow equipment. The thesis consists of five chapters. Chapter 1 describes the background and objective of the present study, the related work on the boundary-layer instability and transition, and recent studies on wall turbulence and drag reduction by riblets. Chapter 2 discusses the experimental work on influence of small-sized riblets on the streamwise growth of Tollmien-Schlichting (T-S) waves, which was conducted in a channel flow. Riblets having triangular ridges and trapezoidal valleys, with a height-to-width ratio of 0.5, were used. The result showed that the streamwise riblets had a strong destabilizing effect and reduced the critical Reynolds number for the linear instability by more than 25%. It was also found that when the riblets were inclined to the streamwise direction, the critical Reynolds number increased as the oblique angle φ of riblets. For φ ≥ 45°, the riblets had no noticeable influence on the structure of T-S wave and the growth rates were the same as those in the smooth-wall case. Chapter 3 describes the experimental work on influences of streamwise riblets on the lateral growth of turbulent region localized in span in a boundary layer. The optimal-geometry riblets with drag-reducing size in wall turbulence were used. The lateral spreading angle of the outer edge of laminar-turbulent interface, which approached about 10° in the downstream over the smooth wall, was reduced only by 0.5° by riblets, despite of the destabilizing effect of riblets mentioned in Chapter 2. Thus, the effect of riblets was weak on the lateral turbulent contamination. Chapter 4 discusses the mechanism of wall turbulence through the experiment on instability and breakdown of a low-speed streak initially forced by disturbances whose frequency-spectrum was similar to that of wall turbulence. Turbulent velocity fluctuations having various spanwise coherencies were used as the forcing signals to excite the streak instability. The results showed that the magnitude of the sinuous instability mode excited was dependent on the initial disturbances, but not very strongly. That is, the magnitude of the sinuous instability mode excited by turbulence components was about 75% of that in the case of anti-symmetric forcing which gave the largest magnitude. Thus the results strongly suggest that fluctuations existing in wall turbulence is rather effective for exciting the streak instability. Chapter 5 summarizes the important findings described in Chapters 2 to 4.首都大学東京, 2018-09-21, 博士（工学）首都大学東

INFLUENCE OF CONVERGENT RIBLET IN BLASIUS BOUNDARY LAYER

Ph.DDOCTOR OF PHILOSOPH

Vortex interaction with a rough wall formed by a hexagonal lattice of posts

An experimental study is reported which investigates the head-on collision of a laminar vortex ring of diameter D (Re{\Gamma}= 3000) on a fakir-like surface composed of circular posts of height h*=0.068 located on a planar bed. Lattices of the posts in hexagonal and random distribution (average porosity of e = 0.94 in the layer) are compared to each other with respect to the plain wall. Prior to impact, the vortex ring develops the early state of natural azimuthal instabilities of different mode numbers N=5-7 competing with each other. While impacting with the rough wall, a secondary ring is observed which is pushed outwards and is not wrapped around the primary ring as in flat wall impact. Between both rings of opposite sign vorticity, a strong fluid rebound is induced. The hexagonal lattice causes the rapid growth of further secondary vortex structures in a regular mode number N=6 arrangement at the outer edge of the primary ring in form of six lobes which are aligned with the orientations of preferential pathways in the layer. At the outer tip of the lobes radial wall-jets are generated. Rotating the fakir geometry around the centre of impact also rotates the jets location and direction accordingly. A surface with random lattice of the posts at the same average number density is not able to repeat this observation and no regular secondary flow pattern is visible until full breakdown of the ring. The results show that a tailored arrangement of such posts can be used for near-wall flow control when patterns of preferred pathways in the posts layer lock-on with existing instability modes such as in impacting jet flows or in turbulent boundary layer flows

The potential of flexible micro pillars to investigate near wall flow

The potential of flexible micro pillars for measuring near wall flow phenom- ena was theoretically and experimentally investigated. The bending of the micro pillars is a measure for the local wall shear stress (WSS) or a visualisa- tion of near wall flow phenomena. Polydimethylsiloxane (PDMS) was chosen as material for the sensor. Within the thesis the experimental work with the shear stress sensor mainly has the focus on the transition to turbulence. Closely connected are improvements of the measurement techniques. The transition is thereby investigated qualitatively and quantitatively. Another huge part of the thesis was the improvement of the reliability of the manu- facturing process of the micro pillars. For this purpose new manufacturing methods for single pillars and pillar arrays have been tested. Further on, dif- ferent detection methods for capturing the bending of the pillar were tested, too. The measurements of the transitional flow were performed at flat plate boundary layer in an oil channel. Ondina 913 was used as test fluid. The physical properties of the PDMS changed dramatically while longer exposed to Ondina 913. Hence, it was unfeasible to receive reproducible quantita- tive results. Better results were achieved if the pillars are used as flexible micro tufts revealing the flow and WSS topology directly at the wall quali- tatively. With the pillar sensor it was possible to detect turbulent spots in the transitional state of the flat plate boundary layer. Furthermore, coherent structures and their typical sign in the viscous sublayer could be identified and the occurrence of critical points and back flow could be experimentally verified