Recently, a new kind of turbulence has been discovered in the flow of concentrated polymer melts and solutions. These flows, known as purely elastic flows, become unstable when the elastic forces are stronger than the viscous forces. This contrasts with Newtonian turbulence, a more familiar regime where the fluid inertia dominates. While there is little understanding of purely elastic turbulence, there is a well-established dynamical systems approach to the transition from laminar flow to Newtonian turbulence. In this project, I apply this approach to purely elastic flows. Laminar flows are characterised by ordered, locally-parallel streamlines of fluid, with only diffusive mixing perpendicular to the flow direction. In contrast, turbulent flows are in a state of continuous instability: tiny differences in the location of fluid elements upstream make a large difference to their later locations downstream. The emerging understanding of the transition from a laminar to turbulent flow is in terms of exact coherent structures (ECS) — patterns of the flow that occur near to the transition to turbulence. The problem I address in this thesis is how to predict when a purely elastic flow will become unstable and when it will transition to turbulence. I consider a variety of flows and examine the purely elastic instabilities that arise. This prepares the ground for the identification of a three-dimensional steady state solution to the equations, corresponding to an exact coherent structure. I have organised my research primarily around obtaining a purely elastic exact coherent structure, however, solving this problem requires a very accurate prediction of the exact solution to the equations of motion. In Chapter 2 I start from a Newtonian ECS (travelling wave solutions in two-dimensional flow) and attempt to connect it to the purely elastic regime. Although I found no such connection, the results corroborate other evidence on the effect of elasticity on travelling waves in Poiseuille flow. The Newtonian plane Couette ECS is sustained by the Kelvin-Helmholtz instability. I discover a purely elastic counterpart of this mechanism in Chapter 3, and explore the non-linear evolution of this instability in Chapter 4. In Chapter 5 I turn to a slightly different problem, a (previously unexplained) instability in a purely elastic oscillatory shear flow. My numerical analysis supports the experimental evidence for instability of this flow, and relates it to the instability described in Chapter 3. In Chapter 6 I discover a self-sustaining flow, and discuss how it may lead to a purely elastic 3D exact coherent structure.

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Zur Verminderung der Kosten und zur Erhöhung der Zuverlässigkeit ist es zukünftig erforderlich, den Verkabelungsaufwand bei Sensoren im Kraftfahrzeug zu senken. Ein Ansatz ist der so genannte autarke Sensor, der seine Hilfsenergie drahtlos aus dem Umfeld gewinnt und seine gewonnen Messdaten ebenfalls drahtlos an einen Kommunikationspunkt überträgt. In der vorliegenden Dissertation wurde die autarke Energiegewinnung für Sensoren anhand mechanisch / elektrischer Energiewandlersysteme untersucht, die eine von Kabelverbindungen unabhängige Energieversorgung des Sensors ermöglichen sollen. Für ein System, welches aus einem translatorischen Schwinger mit magnetischer Federung und einer Anordnung von Induktionsspulen ohne Eisenkreis besteht, wurden theoretische und praktische Untersuchungen durchgeführt. Ausgehend von der, die Bewegung des Systems beschreibenden Differentialgleichung wurden die Einflüsse verschiedener Federungs- und Dämpfungskräfte untersucht. Daraus wurde eine effektive Schwingungsgleichung abgeleitet und hinsichtlich der Amplitude und der Phase gelöst. Die umgesetzte elektrische Leistung des Wandlers wurde aus dem Realteil des Stromflusses abgeleitet. Mit einem realen Fahrzeug wurden Testfahrten durchgeführt, um verschiedene signifikante Fahrbahndaten zu erhalten. Mit diesen Prozessparametern erfolgten später Messungen im Labor. Dafür wurde ein Schwingprüfstand aufgebaut und mehrere Funktionsmuster von Energiewandlersystemen untersucht. / In the future a decrease in sensor cabling inside vehicles becomes of greater importance to reduce cost and increase reliability. One approach is the so called autarkic sensor that generates energy wireless from the sensor's environment and transmits the derived measuring data also wireless to a communication node. Purpose of this dissertation is to discuss the autarkic energy recovery sensors based on a mechanical to electrical conversion which should allow a cable less energy supply. Theoretical and practical tests where made for a system which consists out of a translatory vibration with magnetic suspension and coreless coils. Starting from the differential equations describing the movement of the system, the influence of different ways of suspension and damping forces where investigated. As a result, the actual equation of oscillation was derived and solved with respect to amplitude and phase. The gained electrical power was derived from the real part of the current. Multiple test runs inside a car where performed to obtain some realistic measurement values. Based on those measurements, a test stand was set up inside the laboratory which should simulate normal road conditions. Using this test stand, multiple functional models of energy converting systems were investigated.