In nature, many of the flapping wings and fins in swimming and flying animals have various degrees of flexibility with strong and coupled solid-fluid interactions between the structure and the fluid. In most cases, the wing structure, the flow and their interactions are complex. This thesis experimentally investigates a ‘simple’ fluid-flexible foil interaction problem: flow generated by a pitching foil with chordwise flexibility. To explore the effect of flexibility on the flow, we study the flow generated in quiescent water (the limiting case of infinite Strouhal number) by a sinusoidally pitching rigid symmetrical NACA0015 foil to which is attached a 0.05 mm thick chordwise flexible polythene flap at the trailing edge. The chordwise length of flap is 0.79 c, where c = 38 mm is the chord length of the rigid foil; span of the foil and flap is 100 mm. Detailed particle image velocimetry (PIV) and flow visualization measurements have been made for twelve cases, corresponding to three pitching amplitudes, ±10◦,± 15◦, ±20◦, and four frequencies, 1, 2, 3 and 4 Hz for each amplitude. For most of these cases, a narrow coherent jet aligned along the center-line, containing a reverse B’enard–K´arm´an vortex street, and a corresponding unidirectional thrust are generated. This thrust is similar to the upward force generated during hovering, but motion of our foil is much simpler than the complex wing kinematics found in birds and insects; also the thrust generation mechanism seems to be different. In our case, the thrust is from a coordinated pushing action of the rigid foil and the flexible flap. Control volume analysis reveals the unsteady nature of thrust generation. In this intricately coupled flow generation problem, chordwise flexibility is found to be crucial in producing the coherent jet. In this thesis, we explore in detail the physics of jet flow produced by the foil with a flexible flap, and identify the importance of flexibility in flow generation. Flap motion ensures appropriate spatial and temporal release of vortices, and also imparts them convective motion, to obtain the staggered pattern that produces the jet. To describe the fluid-flap interaction, we conveniently characterize the flap through a non-dimensional stiffness, ‘effective stiffness’ (EI)∗ of the flap, that captures the effects of both the flap properties as well as the external forcing. With the same flap by changing the pitching parameters, we cover a fairly large (EI)∗ range varying over nearly two orders of magnitude. However, we observed that only moderate (EI)∗ (~0.1 - 1) generates sustained narrow, orderly jet. We provide thrust estimates useful for the design of flapping foil thrusters/propulsors. Although this study has only indirect connections with the hovering in nature, it may be useful in understanding the role of flexibility of bird and insect wings during hovering. In contrast, a foil with a rigid trailing edge produces a weak jet whose inclination changes continually with time. This meandering is observed to be random and independent of the initial conditions over a wide range of pitching parameters.

The present thesis involves the study of introducing passive exit flexibility in a two dimensional starting jet. This is relevant to various biological flows like propulsion of aquatic creatures (jellyfish, squid etc.) and flow in the human heart. In the present study we introduce exit flexibility in two ways. The first method was by hinging rigid plates at the channel exit and the second was by attaching deformable flaps at the exit. In the hinged flaps cases, the experimental arrangement closely approximates the limiting case of a free-to-rotate rigid flap with negligible structural stiffness, damping and flap inertia; these limiting structural properties permitting the largest flap openings. In the deformable flaps cases, the flap’s stiffness (or its flexural rigidity EI) becomes an important parameter. In both cases, the initial condition was such that the flaps were parallel to the channel walls. With this, a piston was pushed in a controlled manner to form the starting jet. Using this arrangement, we start the flow and visualize the flap kinematics and make flow field measurements. A number of parameters were varied which include the piston speed, the flap length and the flap stiffness (in case of the deformable flaps). In the hinged rigid flaps cases, the typical motion of the flaps involves a rapid opening with flow initiation and a subsequent more gradual return to its initial position, which occurs while the piston is still moving. The initial opening of the flaps can be attributed to an excess pressure that develops in the channel when the flow starts, due to the acceleration that has to be imparted to the fluid slug between the flaps. In the case with flaps, additional pairs of vortices are formed because of the motion of the flaps and a complete redistribution of vorticity is observed. The length of the flaps is found to significantly affect flap kinematics when plotted using the conventional time scale L/d. However, with a newly defined time-scale based on the flap length (L/Lf ), we find a good collapse of all the measured flap motions irrespective of flap length and piston velocity for an impulsively started piston motion. The maximum opening angle in all these impulsive velocity program cases, irrespective of the flap length, is found to be close to 15 degrees. Even though the flap kinematics collapses well with L/Lf , there are differences in the distribution of the ejected vorticity even for the same L/Lf . In the deformable flap cases, the initial excess pressure in the flap region causes the flaps to bulge outwards. The size of the bulge grows in size, as well as moves outwards as the flow develops and the flaps open out to reach their maximum opening. Thereafter, the flaps start returning to their initial straight position and remain there as long as the piston is in motion. Once the piston stops, the flaps collapse inwards and the two flap tips touch each other. It was found that the flap’s flexural rigidity played an important role in the kinematics. We define a new time scale (t ) based on the flexural rigidity of the flaps (EI) and the flap length (Lf ). Using this new time scale, we find that the time taken to reach the maximum bulge (t* 0.03) and the time taken to reach the maximum opening (t* 0.1) were approximately similar across various flap stiffness and flap length cases. The motion of the flaps results in the formation of additional pairs of vortices. Interestingly, the total final circulation remains almost the same as that of a rigid exit case, for all the flap stiffness and flap lengths studied. However, the final fluid impulse (after all the fluid had come out of the flap region) was always higher in the flap cases as compared to the rigid exit case because of vorticity redistribution. The rate at which the impulse increases was also higher in most flap cases. The final impulse values were as large as 1.8 times the rigid exit case. Since the time rate of change of impulse is linked with force, the measurements suggest that introduction of flexible flaps at the exit could result in better propulsion performances for a system using starting jets. The work carried out in this thesis has shown that by attaching flexible flaps at the exit of an unsteady starting jet, dramatic changes can be made to the flow field. The coupled kinematics of the flaps with the flow dynamics led to desirable changes in the flow. Although the flaps introduced in this work are idealized and may not represent the kind of flexibility we encounter in biological systems, it gives us a better understanding of the importance of exit flexibility in these kinds of flows.

Im Rahmen dieser Arbeit wurde der Einfluss von passiven und elastischen Rückstromklappen, die auch als Flaps bezeichnet werden, auf einen Tragflügel mit NACA0020 Profil untersucht. Mithilfe einer Kraftwaage erfolgte zunächst die Erfassung der Auswirkungen auf das aerodynamische Verhalten des Tragflügels vor und nach der Strömungsablösung. Für ein detailliertes Verständnis wurde zusätzlich die Umströmung mit der Rauchdrahttechnik visualisiert und die Flapkinematik mit der Stereo Vision Technik aufgenommen. Es konnte festgestellt werden, dass die Vorderkantenflaps mit der geringsten Biegesteifigkeit die Gleitzahl des Tragflügels vor allem in abgelöster Strömung erhöhen. Die festgestellte Auftriebssteigerung resultiert aus der langsamen Aufstellbewegung und beschleunigten Anlegebewegung der Flaps, die eine einhergehende Reduzierung der turbulenten Ablösung verursachen. Die Ergebnisse der Arbeit liefern zahlreiche Erkenntnisse, die eine Übertragung des festgestellten Effekts auf andere technische Anwendungen erleichtern.:Abbildungsverzeichnis....................................................................... VII Tabellenverzeichnis............................................................................ XII Symbol- & Abkürzungsverzeichnis..................................................XVI 1 Einleitung......................................................................................... 1 2 Stand der Forschung........................................................................ 4 2.1 Wesentliche Aspekte von Profilumströmungen ................................. 4 2.2 Zusammenfassung essenzieller Aspekte von Tragflügeln mit Flaps ......7 3 Numerische Untersuchung der Profilumströmung....................... 13 3.1 Numerische Modell ......................................................................13 3.1.1 Grundgleichungen und Turbulenzmodell ..............................13 3.1.2 Randbedingungen und Diskretisierungsschema .....................16 3.2 Ergebnisse für das NACA0018 Profil .............................................18 3.3 Ergebnisse für das NACA0020 Profil .............................................19 3.4 Schlussfolgerung aus den Simulationen ..........................................22 4 Kraftmessungen an einem NACA0020 Tragflügel ....................... 23 4.1 Versuchsvorbereitung ...................................................................23 4.1.1 Windkanal ........................................................................23 4.1.2 Tragflügel und Funktionsweise der Kraftwaage .....................25 4.2 Messunsicherheit und Validierung .................................................27 4.3 Position der Flaps auf dem Tragflügel............................................ 31 4.3.1 Flapgeometrie und Flappositionen....................................... 31 4.3.2 Polardiagramme für variierende Flapposition........................34 4.4 Faserverstärkte Silikonflaps...........................................................36 4.4.1 Verwendeten Materialien ....................................................36 4.4.2 Polardiagramm für faserverstärkte Silikonflaps .....................38 4.5 Flapgeometrie .............................................................................40 4.5.1 Untersuchte Flapformen .....................................................40 4.5.2 Polardiagramm der untersuchten Flapformen ....................... 41 4.6 Wirkung der Flaps bei instationären Anströmung...........................43 4.6.1 Versuchsdurchführung ........................................................43 4.6.2 Ergebnisse der instationären Untersuchung...........................45 4.7 Schlussfolgerung der Auftriebs- und Widerstandsuntersuchungen .....47 5 Strömungsvisualisierung mithilfe der Rauchdrahttechnik........... 49 5.1 Experimenteller Aufbau ...............................................................49 5.2 Vorgehensweise bei der Auswertung...............................................50 5.3 Ergebnisse der Visualisierung........................................................ 51 6 Flapkantenkinematik..................................................................... 58 6.1 Versuchsaufbau und Versuchsdurchführung ....................................58 6.2 Bildauswertung ........................................................................... 61 6.3 Ergebnisse ..................................................................................62 6.3.1 VK Konfiguration - ohne Faserverstärkung...........................62 6.3.2 Bewegungsausführung des Vorderkantenflaps der VK-HK Konfiguration - ohne Faserverstärkung.......................................69 6.3.3 Bewegungsausführung des Vorderkantenflaps der VK-HK Konfiguration - mit Faserverstärkung ........................................75 6.3.4 Auswertung und Interpretation ...........................................82 7 Zusammenfassung.......................................................................... 87 8 Ausblick.......................................................................................... 89 Anhang ................................................................................................ 97 A Anhang 1....................................................................................97 B Anhang 2....................................................................................98 C Anhang 3....................................................................................99 / In the following study the effects of elastic and passive flaps were investigated on an airfoil with a NACA0020 profile. At first the aerodynamic performance of different configurations was measured with a force balance. In order to detect its effects before and after stall the angle of attack was varied during the experiments. For the configurations with increased aerodynamic performance additional experiments were carried out. The smoke wire visualization and stereo vision technique allowed a detailled insight in the flow around the NACA0020 profile and the flap movement. The results show that elastic flaps at the leading and trailing edge of the airfoil improve notably the airfoil performance in deep stall. Furthermore, the highest increase of the lift-to-drag ratio was achieved for the configuration with lowest bending stiffness. It was observed that the highest reduction of the turbulent separation region is caused by the flap movement. The increase of lift-to-drag ratio results from a slow upward and a fast downward motion of the elastic flap. The study delivers helpful information for transfer of the observed effect to other technical applications.:Abbildungsverzeichnis....................................................................... VII Tabellenverzeichnis............................................................................ XII Symbol- & Abkürzungsverzeichnis..................................................XVI 1 Einleitung......................................................................................... 1 2 Stand der Forschung........................................................................ 4 2.1 Wesentliche Aspekte von Profilumströmungen ................................. 4 2.2 Zusammenfassung essenzieller Aspekte von Tragflügeln mit Flaps ......7 3 Numerische Untersuchung der Profilumströmung....................... 13 3.1 Numerische Modell ......................................................................13 3.1.1 Grundgleichungen und Turbulenzmodell ..............................13 3.1.2 Randbedingungen und Diskretisierungsschema .....................16 3.2 Ergebnisse für das NACA0018 Profil .............................................18 3.3 Ergebnisse für das NACA0020 Profil .............................................19 3.4 Schlussfolgerung aus den Simulationen ..........................................22 4 Kraftmessungen an einem NACA0020 Tragflügel ....................... 23 4.1 Versuchsvorbereitung ...................................................................23 4.1.1 Windkanal ........................................................................23 4.1.2 Tragflügel und Funktionsweise der Kraftwaage .....................25 4.2 Messunsicherheit und Validierung .................................................27 4.3 Position der Flaps auf dem Tragflügel............................................ 31 4.3.1 Flapgeometrie und Flappositionen....................................... 31 4.3.2 Polardiagramme für variierende Flapposition........................34 4.4 Faserverstärkte Silikonflaps...........................................................36 4.4.1 Verwendeten Materialien ....................................................36 4.4.2 Polardiagramm für faserverstärkte Silikonflaps .....................38 4.5 Flapgeometrie .............................................................................40 4.5.1 Untersuchte Flapformen .....................................................40 4.5.2 Polardiagramm der untersuchten Flapformen ....................... 41 4.6 Wirkung der Flaps bei instationären Anströmung...........................43 4.6.1 Versuchsdurchführung ........................................................43 4.6.2 Ergebnisse der instationären Untersuchung...........................45 4.7 Schlussfolgerung der Auftriebs- und Widerstandsuntersuchungen .....47 5 Strömungsvisualisierung mithilfe der Rauchdrahttechnik........... 49 5.1 Experimenteller Aufbau ...............................................................49 5.2 Vorgehensweise bei der Auswertung...............................................50 5.3 Ergebnisse der Visualisierung........................................................ 51 6 Flapkantenkinematik..................................................................... 58 6.1 Versuchsaufbau und Versuchsdurchführung ....................................58 6.2 Bildauswertung ........................................................................... 61 6.3 Ergebnisse ..................................................................................62 6.3.1 VK Konfiguration - ohne Faserverstärkung...........................62 6.3.2 Bewegungsausführung des Vorderkantenflaps der VK-HK Konfiguration - ohne Faserverstärkung.......................................69 6.3.3 Bewegungsausführung des Vorderkantenflaps der VK-HK Konfiguration - mit Faserverstärkung ........................................75 6.3.4 Auswertung und Interpretation ...........................................82 7 Zusammenfassung.......................................................................... 87 8 Ausblick.......................................................................................... 89 Anhang ................................................................................................ 97 A Anhang 1....................................................................................97 B Anhang 2....................................................................................98 C Anhang 3....................................................................................99