<p>The behavior of fibers suspended in a flow between two counter-rotating discs has been studied experimentally. This is inspired by the refining process in the papermaking process where cellulose fibers are ground between discs in order to change performance in the papermaking process and/or qualities of the final paper product.</p><p>To study the fiber behavior in a counter-rotating flow, an experimental set-up with two glass discs was built. A CCD-camera was used to capture images of the fibers in the flow. Image analysis based on the concept of steerable filters extracted the position and orientation of the fibers in the plane of the discs. Experiments were performed for gaps of 0.1-0.9 fiber lengths, and for equal absolute values of the angular velocities for the upper and lower disc. The aspect ratios of the fibers were 7, 14 and 28.</p><p>Depending on the angular velocity of the discs and the gap between them, the fibers were found to organize themselves in fiber trains. A fiber train is a set of fibers positioned one after another in the tangential direction with a close to constant fiber-to-fiber distance. In the fiber trains, each individual fiber is aligned in the radial direction (i.e. normal to the main direction of the train).</p><p>The experiments show that the number of fibers in a train increases as the gap between the discs decreases. Also, the distance between the fibers in a train decreases as the length of the train increases, and the results for short trains are in accordance with previous numerical results in two dimensions.Furthermore, the results of different aspect ratios imply that there are three-dimensional fiber end-effects that are important for the forming of fiber trains.</p>

Thermal properties of complex suspension flows are investigated using numerical computations. The objective is to develop an efficient and accurate computational method to investigate heat transport in suspension flows. The method presented here is based on solving the lattice Boltzmann equation for the fluid phase, as it is coupled to the Newtonian dynamics equations to model the movement of particles and the energy equation to find the thermal properties. This is a direct numerical simulation that models the free movement of the solid particles suspended in the flow and its effect on the temperature distribution. Parallel implementations are done using MPI (message passing interface) method. Convective heat transfer in internal suspension flow (low solid volume fraction, φ<10%), heat transfer in hot pressing of fiber suspensions and thermal performance of particle filled thermal interface materials (high solid volume fraction, φ>40%) are investigated. The effects of flow disturbance due to movement of suspended particles, thermo-physical properties of suspensions and the particle micro structures are discussed.

The introduction of phase change material fluid and nanofluid in micro-channel heat sink design can significantly increase the cooling capacity of the heat sink because of the unique features of these two kinds of fluids. To better assist the design of a high performance micro-channel heat sink using phase change fluid and nanofluid, the heat transfer enhancement mechanism behind the flow with such fluids must be completely understood. A detailed parametric study is conducted to further investigate the heat transfer enhancement of the phase change material particle suspension flow, by using the two-phase non-thermal-equilibrium model developed by Hao and Tao (2004). The parametric study is conducted under normal conditions with Reynolds numbers of Re=600-900 and phase change material particle concentrations ¡Ü0.25 , as well as extreme conditions of very low Reynolds numbers (Re < 50) and high phase change material particle concentration (0.5-0.7) slurry flow. By using the two newly-defined parameters, named effectiveness factor and performance index, respectively, it is found that there exists an optimal relation between the channel design parameters, particle volume fraction, Reynolds number, and the wall heat flux. The influence of the particle volume fraction, particle size, and the particle viscosity, to the phase change material suspension flow, are investigated and discussed. The model was validated by available experimental data. The conclusions will assist designers in making their decisions that relate to the design or selection of a micro-pump suitable for micro or mini scale heat transfer devices. To understand the heat transfer enhancement mechanism of the nanofluid flow from the particle level, the lattice Boltzmann method is used because of its mesoscopic feature and its many numerical advantages. By using a two-component lattice Boltzmann model, the heat transfer enhancement of the nanofluid is analyzed, through incorporating the different forces acting on the nanoparticles to the two-component lattice Boltzmann model. It is found that the nanofluid has better heat transfer enhancement at low Reynolds numbers, and the Brownian motion effect of the nanoparticles will be weakened by the increase of flow speed.

The behavior of fibers suspended in a flow between two counter-rotating discs has been studied experimentally. This is inspired by the refining process in the papermaking process where cellulose fibers are ground between discs in order to change performance in the papermaking process and/or qualities of the final paper product. To study the fiber behavior in a counter-rotating flow, an experimental set-up with two glass discs was built. A CCD-camera was used to capture images of the fibers in the flow. Image analysis based on the concept of steerable filters extracted the position and orientation of the fibers in the plane of the discs. Experiments were performed for gaps of 0.1-0.9 fiber lengths, and for equal absolute values of the angular velocities for the upper and lower disc. The aspect ratios of the fibers were 7, 14 and 28. Depending on the angular velocity of the discs and the gap between them, the fibers were found to organize themselves in fiber trains. A fiber train is a set of fibers positioned one after another in the tangential direction with a close to constant fiber-to-fiber distance. In the fiber trains, each individual fiber is aligned in the radial direction (i.e. normal to the main direction of the train). The experiments show that the number of fibers in a train increases as the gap between the discs decreases. Also, the distance between the fibers in a train decreases as the length of the train increases, and the results for short trains are in accordance with previous numerical results in two dimensions.Furthermore, the results of different aspect ratios imply that there are three-dimensional fiber end-effects that are important for the forming of fiber trains.

A suspension flow model based on the "suspension balance" approach has been developed. This work modifies the model to allow the solution of suspension flows under general flow conditions. This requires the development of a frame-invariant constitutive model for the particle stress which can take into account the spatially-varying local kinematic conditions. The mass and momentum balances for the bulk suspension and particle phase are solved numerically using a finite volume method. The particle stress is based upon the computed rate of strain and the local kinematic conditions. A nonlocal stress contribution corrects the continuum approximation of the particle phase for finite particle size effects. Local kinematic conditions are accounted through the local ratio of rotation to extension in the flow field. The coordinates for the stress definition are the local principal axes of the rate of strain field. The developed model is applied to a range of problems. (i) Axially-developing conduit flows are computed using both the full two-dimensional solution and the more computationally efficient "marching" method. The model predictions are compared to experimental results for cross-stream particle concentration profiles and axial development lengths. (ii) Model predictions are compared to experiments for wide-gap circular Couette flow of a concentrated suspension in a shear-thinning liquid. With minor modification, the suspension flow model predicts the major trends and results observed in this flow. (iii) Comparisons are made to experiments for an axisymmetric contraction-expansion. Model predictions for a two-dimensional planar contraction flow test the influence of model formulation. The variation of the magnitude of an isotropic particle normal stress with local kinematic conditions and anisotropy in the in-plane normal stresses are both explored. The formulation of the particle phase stress is found to have significant effects on the solid fraction and velocity. (iv) Finally, for a rectangular piston-driven flow and an obstructed channel flow, a "computational suspension dynamics" study explores the effect of particle migration on the bulk flow field, system pressure drop and particle phase composition.

L’effet des inclusions sur la turbulence de l’écoulement est un élément clé à comprendre afin de maîtriser le transport de milieux dispersés, dans le domaine du génie pétrolier, environnemental, agroalimentaire, génie de la réaction chimique ou transformation du solide. Les expériences de Matas et al. (PRL, 2003) ont mis en évidence un effet non monotone des particules isodenses (de densité égale à celle du fluide) sur la transition laminaire-turbulent, cet effet dépendant de la taille des particules et de leur concentration dans la suspension. Une petite quantité de particules de taille finie s’est avérée suffisante pour diminuer considérablement le seuil de transition laminaire turbulent. Nous avons utilisé des simulations numériques, basées sur une approche de type “Force Coupling Method” afin de comprendre cet effet. Les domaines de simulations étaient choisis pour accommoder le minimum de structures cohérentes suffisantes pour entretenir la turbulence. Nous avons particulièrement étudié la corrélation entre le comportement instationnaire de l’écoulement et la distribution instantanée de particules, en fonction de la configuration de l’écoulement (Couette plan ou écoulement en canal), de la forme des particules ainsi que leur inertie et concentration. Dans un écoulement de Couette plan turbulent, la contrainte pariétale est augmentée en présence des particules. Les profiles (dans la direction normale aux parois) de vitesse moyenne et des contraintes de Reynolds ne sont pas significativement modifiés en présence des particules, si la viscosité du fluide est remplacée par la viscosité effective de la suspension dans le calcul du nombre de Reynolds de l’écoulement. Par contre l’analyse temporelle et modale des fluctuations de l’écoulement suggère que les particules modifient légèrement le cycle de régénération de la turbulence, à travers l’augmentation d’énergie à petites échelles. En effet, la forme des streaks et le caractère intermittent de l’écoulement sont impactés par la présence des particules, surtout quand elles sont inertielles (de densité supérieure à celle du fluide). Ces résultats ont été publiés dans le journal Physical Review F (Wang et al., 2017). En outre, nous avons montré qu’à fraction volumique égale, les propriétés d’écoulement turbulent des suspensions de particules sphéroïdales de rapport de taille compris entre 0.5 et 2, sont similaires à celles des suspensions de particules sphériques. Le transfert de particules entre les différentes structures cohérentes de l’écoulement est analysé à la fin de la thèse. Néanmoins dans un écoulement en canal, les particules iso denses augmentent l’intensité des contraintes de Reynolds dans le plan transverse. Nous montrons que par leur concentration préférentielle dans les structures cohérentes à côté des parois (les éjections), elles influencent significativement le cycle de régénération en agissant sur tous les processus à la fois linéaires et non linéaires du cycle: la formation des streaks, puis leur rupture et la régénération des vortex alignés avec l’écoulement. La diminution du seuil de transition est la conséquence directe de cette modulation du cycle. / The effect of particles on turbulence is a key phenomenon in many practical industrial applications encountered in petroleum engineering, chemical reactors and food or solid processing (transport of slurries in pipes, reactive fluidized beds, and pneumatic transport of particles), environmental engineering (such as sand storm and Particulate Matter (PM) Pollution), and biological fluid mechanics (e.g. drug delivery in blood flow and inhaled particles through the respiratory system). The experiments of Matas et al. (PRL, 2003) have highlighted the non-monotonous effect of neutrally buoyant particles on the laminar-turbulent flow transition, depending on the particle-to-pipe size ratio and on the suspension volumetric concentration. A small amount of finite size particles allowed sustaining the turbulent state and decreasing the transition threshold significantly. The complex mechanisms related to particle flow interactions are often difficult to elucidate experimentally. During the last 4 decades, direct numerical simulations have proven to be a powerful tool for understanding the features of single-phase turbulent flows. Currently, it starts to play an important role in the investigation of suspension flows as well. Almost a decade after the experiments of Matas et al. (PRL, 2003), particle-resolved numerical simulations are able to evidence that at moderate concentration, particles have a significant impact on the unsteady nature of the flow, enhancing the transverse turbulent stress components and modifying the flow vortical structures (Loisel et al. Phys. Fluids, 2013; Yu et al. Phys. Fluids, 2013; Lashgari et al. PRL, 2015). In this work, we use particleresolved numerical simulations to understand the effect of finite sized particles on wall-bounded (pressure-driven or plane Couette) turbulent flows, slightly above the laminar-turbulent transition limit. We find that in turbulent Couette flow, wall-normal profiles of the flow velocity and Reynolds stress components reveal that there is no significant difference between single phase and two-phase flows at equivalent effective Reynolds number, except that the wall shear stress is higher for the two-phase flow. At concentration up to 10%, neutrally buoyant spherical particles have a negligible effect on both the intensity and intermittency of the Reynolds stress. However temporal and modal analysis of flow fluctuations, suggest that besides increasing small scale perturbation due to their rigidity, particles have an effect on the regeneration cycle of turbulence (streak formation, streak breakdown and streamwise vortex regeneration). Indeed, the shape of the streaks and the intermittent character of the flow (amplitude and period of oscillation of the modal fluctuation energy) are all altered by the particle presence, and especially by the inertial particles (Wang et al. Phys. Rev. Fluid, 2017). When the particle shape deviates from sphericity (spheroids with aspect ratios ranging between 0.5 and 2), the features of turbulent suspension flow are not significantly impacted. The transfer of particles between different coherent structures (along the regeneration cycle period) is analyzed at the end of the thesis. Nevertheless in channel flow, neutrally-buoyant spherical particles have a drastic impact on the regeneration cycle of turbulence, decreasing thereby the transition threshold. Particles enhance the intensity of the Reynolds stress although the frequency of burst events is decreased. Particles enhance the lift-up effect and act continuously within the buffer layer. Moreover, they increase the vorticity stretching, leading to smaller and more numerous wavy streaks for suspension flows compared to the single-phase configuration.

Dans le but d’améliorer le comportement thermo-mécanique des aubes de turbine présentes dans les moteurs d’avion développés par SAFRAN, il est nécessaire de mettre au point un nouveau matériau composite. Le procédé de fabrication de ce matériau est complexe et requiert une densification par voie liquide divisée en deux étapes. Cette thèse s’intéresse à la modélisation numérique de la première étape appelée Slurry Cast/APS.Celle-ci consiste en l’injection et le confinement, dans la préforme fibreuse, de particules préalablement mises en suspension. Pour cela, nous avons développé à l’échelle des fibres,un modèle qui utilise les équations de Navier-Stokes incompressibles et monophasiques ,l’équation de Phillips [Phillips et al., 1992] et une loi rhéologique [Krieger, 1972]. Après validation des résultats numériques par comparaison avec des résultats expérimentaux [Hampton et al., 1997] et théoriques [Belfort et al., 1994], le modèle est utilisé pour simuler l’écoulement autour de géométries de tissage proches du matériau étudié. / In order to improve thermo-mechanical behavior of tubine blades in SAFRAN engines plane, a new composite material is necessary. The manufacturing process to obtain this composite is intricate and requires a two steps fluid densification process. This thesis focuses on numerical simulation of the first one called Slurry Cats/APS. In this step, suspended particles are introducted and captured in the reinforcement. For that purpose,we carry out a model at fiber scale, using Navier-Stokes equations in incompressible and monophasic formulation, Phillips equations [Phillips et al., 1992] and a rheological law [Krieger, 1972]. After validation step consisting in a comparison of computational results with experiments [Hampton et al., 1997] and theorical law [Belfort et al., 1994], this model has been used to simulate flow around geometries similar to those encountered in our composite material.

Dans cette thèse, nous nous intéressons à la modélisation et l'analyse mathématique de certains problèmes liés aux écoulements en suspension.Le premier chapitre concerne la justification du modèle de type transport-Stokes pour la sédimentation de particules sphériques dans un fluide de Stokes où l'inertie des particules est négligée et leur rotation est prise en compte. Ce travail est une extension des résultats antérieurs pour un ensemble plus général de configurations de particules.Le deuxième chapitre concerne la sédimentation d'une distribution d'amas de paires de particules dans un fluide de Stokes. Le modèle dérivé est une équation de transport-Stokes décrivant l'évolution de la position et l'orientation des amas. Nous nous intéressons par la suite au cas où l'orientation des amas est initialement corrélée aux positions. Un résultat d'existence locale et d'unicité pour le modèle dérivé est présenté.Dans le troisième chapitre, nous nous intéressons à la dérivation d'un modèle de type fluide-cinétique pour l'évolution d'un aérosol dans les voies respiratoires. Ce modèle prend en compte la variation du rayon des particules et leur température due à l'échange d'humidité entre l'aérosol et l'air ambiant. Les équations décrivant le mouvement de l'aérosol est une équation de type Vlasov-Navier Stokes couplée avec des équations d'advection diffusion pour l'évolution de la température et la vapeur d'eau dans l'air ambiant.Le dernier chapitre traite de l'analyse mathématique de l'équation de transport-Stokes dérivée au premier chapitre. Nous présentons un résultat d'existence et d'unicité globale pour des densités initiales de type $L^1 cap L^infty$ ayant un moment d'ordre un fini. Nous nous intéressons ensuite à des densités initiales de type fonction caractéristique d'une gouttelette et montrons un résultat d'existence locale et d'unicité d'une paramétrisation régulière de la surface de la gouttelette. Enfin nous présentons des simulations numériques montrant l'aspect instable de la gouttelette. / This thesis is devoted to the modelling and mathematical analysis of some aspects of suspension flows.The first chapter concerns the justification of the transport-Stokes equation describing the sedimentation of spherical rigid particles in a Stokes flow where particles rotation is taken into account and inertia is neglected. This work is an extension of former results for a more general set of particles configurations.The second chapter is dedicated to the sedimentation of clusters of particle pairs in a Stokes flow. The derived model is a transport-Stokes equation describing the time evolution of the position and orientation of the cluster. We also investigate the case where the orientation of the cluster is initially correlated to its position. A local existence and uniqueness result for the limit model is provided.In the third chapter, we propose a coupled fluid-kinetic model taking into accountthe radius growth of aerosol particles due to humidity in the respiratorysystem. We aim to numerically investigate the impact of hygroscopic effects onthe particle behaviour. The air flow is described by the incompressibleNavier-Stokes equations, and the aerosol by a Vlasov-type equation involving the air humidity and temperature, both quantities satisfying a convection-diffusion equation with a source term.The last chapter is dedicated to the analysis of the transport-Stokes equation derived in the first chapter. First we present a global existence and uniqueness result for $L^1cap L^infty$ initial densities with finite first moment. Secondly, we consider the case where the initial data is the characteristic function of a droplet. We present a local existence and uniqueness result for a regular parametrization of the droplet surface. Finally, we provide some numerical computations that show the regularity breakup of the droplet.

Der zunehmende Einsatz regenerativer Energiequellen erfordert die Nutzung von Energiezwischenspeichern, die umweltfreundlich, günstig und skalierbar sein sollten. Die Zink-Luft-Flussbatterie (ZLFB) kann perspektivisch diese Anforderungen erfüllen, wobei zur Bereitstellung der gespeicherten Energie eine Suspension aus Zinkpartikeln in einem gelierten Elektrolyt durch eine elektrochemische Zelle gepumpt wird. Um die Strömungsstruktur der ZLFB auszulegen und Fehlfunktionen zu vermeiden, ist ein grundlegendes Verständnis der Rheologie der Zinksuspension notwendig. Außerdem kann über die Einstellung einer geeigneten Strömung die bei der Entladung erreichte elektrische Leistungsdichte gesteigert werden. Bereits die Flüssigphase der Zinksuspension weist eine komplexe nicht-Newtonsche Rheologie auf, welche durch die Zugabe der Partikel komplexer wird. Für das grundlegende Verständnis der Rheologie werden daher Modellexperimente durchgeführt, wobei in dieser Arbeit ein L-förmiger Kanal mit Strömungsaufweitung untersucht wurde, um die komplexen strömungsmechanischen Eigenschaften der Zinksuspension abzubilden. Zur Erfassung des Strömungsfeldes ist eine Ortsauflösung von 1 … 2 mm in einem Messbereich von 20 × 15 mm2 erforderlich. Ultraschall ist prinzipiell geeignet, um das Strömungsfeld in der opaken Suspension zu erfassen, wobei die wesentliche Herausforderung in den starken Wellenfrontverzerrungen besteht, welche durch die Zinkpartikel eingebracht werden. Es konnte gezeigt werden, dass die Ultrasound Imaging Velocimetry (UIV) robuster gegenüber diesen Störungen ist, als die Ultraschall-Doppler-Velozimetrie (UDV). Die UIV wurde daher mittels Geschwindigkeitsnormal an die messtechnischen Randbedingungen der Zinksuspension angepasst und charakterisiert. Bei einer Ortsauflösung von 1,6 mm wurde eine Gesamtmessunsicherheit von 2,5 % axial und 4,1 % lateral zur Schallausbreitungsrichtung erreicht. Das im Modellexperiment gemessene Strömungsfeld weist eine Totzone an der Strömungsumlenkung auf, deren Auftreten durch eine von der Scherhistorie abhängige Viskosität erklärt werden kann. Dieser Effekt wird als Thixotropie bezeichnet. Durch die In-situ-Messung der Strömung in einer aktiven ZLFB kann eine Korrelation von Strömung und elektrischer Leistung erfolgen und die erzielte Leistungsdichte perspektivisch durch eine Anpassung der Strömung gesteigert werden. Bei der Messung im 2,6 mm hohen Anodenspalt muss aufgrund der komplexen Rheologie der Suspension und der daraus resultierenden hohen Geschwindigkeitsgradienten eine Ortsauflösung von unter 100 µm bei gleichzeitig kleiner Ultraschallfrequenz realisiert werden, da der Ultraschall für hohe Frequenzen nicht in die Zinksuspension eindringt. Um dieses Ziel zu erreichen, wurde die Super Resolution Ultrasound Particle Tracking Velocimetry (SRPTV) genutzt, welche Ortsauflösungen unterhalb des Beugungslimits ermöglicht. Einzelne nichtlineare Streupartikel werden mittels Harmonic Imaging isoliert abgebildet und verfolgt, wobei die durch die Zinkpartikel eingebrachten Wellenfrontstörungen durch einen kohärenzgewichteten Strahlformer kompensiert werden. Es wurde eine Ortsauflösung von 67 µm axial und 30 µm lateral zur Schallausbreitungsrichtung bei einer Anregungswellenlänge von 330 µm erreicht. Trotz der stark streuenden Zinksuspension, konnte so eine Messung in der aktiven ZLFB mit einer maximalen Messunsicherheit von 12,5 % durchgeführt werden. Dabei wurde eine Wandgleitgeschwindigkeit von 3 mm s−1 bei einer maximalen Geschwindigkeit von etwa 8 mm s−1 festgestellt. Die SRPTV kann darüber hinaus in anderen technischen Prozessen eingesetzt werden, in denen Suspensionsströmungen in kleinen Geometrien auftreten.:Symbolverzeichnis xiii Abkürzungsverzeichnis xv 1 Einleitung 1 1.1 Motivation und Zielstellung 1 1.2 Stand der Technik 4 1.3 Lösungsansatz und Struktur der Arbeit 8 2 Theoretische Grundlagen 11 2.1 Grundlagen der Schallausbreitung 11 2.1.1 Schallausbreitung in homogenen Medien 11 2.1.2 Schallausbreitung in inhomogenen Medien 13 2.2 Ultraschall Bildgebung 14 2.2.1 Phased-Array-Prinzip 15 2.2.2 Plane wave imaging 16 2.2.3 Grenzen der Schallfeldfokussierung 16 2.3 Messung von Strömungsfeldern 17 2.3.1 Ultraschall-Doppler-Velozimetrie 18 2.3.2 Ultrasound Imaging Velocimetry 19 2.3.3 Ultrasound Particle Tracking Velocimetry 19 2.4 Nichtlineare akustische Effekte 20 2.4.1 Beschreibung von Linearität 20 2.4.2 Interaktion von nichtlinearen Streupartikeln und Schallwelle 20 2.4.3 Harmonic Imaging 21 3 Experimentelle Grundlagen 25 3.1 Charakterisierung der Zinksuspension 25 3.1.1 Zusammensetzung der Zinksuspension 25 3.1.2 Bestimmung von Dämpfung und Schallgeschwindigkeit 26 3.1.3 Bestimmung der spezifischen akustischen Impedanz 29 3.2 Messtechnik 30 3.2.1 Ultraschallforschungsplattform: Phased Array Ultrasound Dopp- ler Velocimeter 30 3.2.2 Ultraschallwandler 32 4 Verfahren zur Strömungsmessung im Modellexperiment 37 4.1 Experimenteller Aufbau 37 4.2 Untersuchung geeigneter Verfahren zur Messung von Strömungsfel- dern in der Zinksuspension 38 4.3 Optimierung der Signalverarbeitung und Charakterisierung der Messei- genschaften 44 4.3.1 Geschwindigkeitsnormal 44 4.3.2 Optimierung der Messsystemparameter 45 4.3.3 Charakterisierung der Messeigenschaften 48 4.3.4 Validierung 49 4.4 Messung der Suspensionsströmung im Modellexperiment 55 4.4.1 Messergebnisse 55 4.4.2 Vergleich von Simulation und Messung 58 4.5 Fazit 61 5 Verfahren zur In-situ-Strömungsmessung in einer Zink-Luft-Flussbatterie 63 5.1 Experimenteller Aufbau 63 5.2 Strömungsmessung unterhalb des Beugungslimits - Super Resolution Ultrasound Particle Tracking Velocimetry (SRPTV) 65 5.2.1 Nutzung nichtlinearer Streupartikel 68 5.2.2 Trennung von linearem und nichtlinearem Signalanteil 72 5.2.3 Strahlformung mit Kompensation der Streuung 76 5.2.4 Particle Tracking 80 5.3 Charakterisierung der Messeigenschaften 81 5.3.1 Vorgehen zur Charakterisierung der Messeigenschaften 82 5.3.2 Untersuchung der Positionsunsicherheit 83 5.3.3 Untersuchung der Geschwindigkeitsunsicherheit 92 5.4 Messung an einer aktiven Zink-Luft-Flussbatterie 95 5.4.1 Aufbau und Durchführung 95 5.4.2 Messergebnisse 97 5.4.3 Vergleich von Simulation und Messung 97 5.5 Fazit 102 6 Zusammenfassung und Ausblick 103 6.1 Erkenntnisse und Fortschritt 103 6.1.1 Ultrasound Imaging Velocimetry 103 6.1.2 Super Resolution Ultrasound Particle Tracking Velocimetry 104 6.1.3 Fazit 106 6.2 Ausblick und weiterführende Arbeiten 106 6.2.1 Messtechnik 106 6.2.2 Anwendung 107 Literaturverzeichnis 109 Publikationsverzeichnis 117 Artikel in Zeitschriften mit peer-review 117 Tagungsbeiträge 117 Patente 119 / For the efficient use of renewable energies, energy storage systems are required that are environmentally friendly, low priced and scalable. The zinc-air flow battery (ZAB), which is operated by pumping an opaque suspension of zinc particles in an gelled electrolyte through an electrochemical cell, is a promising candidate as energy storage system for these requirements. To design the fluidic structures and avoid malfunction, a fundamental understanding of the rheology of the zinc suspension is required. Additionally, the electrical performance of the cell can be imporved by optimizing the flow in the electrochemical cell. The liquid phase of the suspension itself has complex non-Newtonian properties, which are even more complex when the particles are considered. For the fundamental understanding of the suspension rheology, model experiments are conducted. In this work an L-shaped channel with a widening is used to represent relevant effects from the complex rheology of the suspension. To measure the flow field, a spatial resolution of 1 … 2 mm and a measurement area of 20 × 15 mm2 are required. Ultrasound can be used to measure the flow in opaque liquids, but wavefront distortions are introduced by the zinc particles. Established measurement methods for homogeneous opaque fluids, the Ultrasound Imaging Velocimetry (UIV) and the Ultrasound Doppler Velocimetry (UDV), were compared for the application at the suspension. The UIV has a 50 % lower random deviation, which makes it more suitable for the flow measurement in the suspension and it was adapted to the measurement conditions in the suspension. At a spatial resolution of 1.66 mm, a velocity uncertainty of 2.5 % axial and 4.1 % lateral to the ultrasound propagation were achieved. The application of the UIV to the suspension flow in the model experiment revealed a thixotropic behavior of the fluid, which resulted in a dead flow zone opposite to the inlet of the channel. The in situ measurement of the flow in an active ZAB, allows to correlate electrical performance and flow and thereby an improvement of the cell performance by adapting the flow. For the measurement in the anodic channel with a width of 2.6 mm, a spatial resolution of 100 µm is required because of the high velocity gradients due to the non-Newtonian rheology of the suspension. The high spatial resolution has to be achieved at low ultrasound frequencies, since the ultrasound does not penetrate into the suspension for high frequencies. To achieve this, the Super Resolution Ultrasound Particle Tracking Velocimetry (SRPTV) was used, which allows a spatial resolution beyond the diffraction limit. Harmonic Imaging is used to image isolated non-linear tracer particles, which are tracked for velocity estimation. The speckle and image distortion due to the induced wavefront distortions are compensated with a coherence weighting beamformer. A spatial resolution of 67 µm axial and 30 µm lateral to the ultrasound propagation were achieved. Despite the strong scattering of the ultrasound at the zinc particles, a maximum velocity uncertainty of 12.5 % referred to the maximum velocity was achieved for the measurement in the active ZAB. A slip velocity of 3 mm at a maximum velocity of 8 mm was observed. The SRPTV can be applied to other technical processes, where suspension flows in small geometries play an important role.:Symbolverzeichnis xiii Abkürzungsverzeichnis xv 1 Einleitung 1 1.1 Motivation und Zielstellung 1 1.2 Stand der Technik 4 1.3 Lösungsansatz und Struktur der Arbeit 8 2 Theoretische Grundlagen 11 2.1 Grundlagen der Schallausbreitung 11 2.1.1 Schallausbreitung in homogenen Medien 11 2.1.2 Schallausbreitung in inhomogenen Medien 13 2.2 Ultraschall Bildgebung 14 2.2.1 Phased-Array-Prinzip 15 2.2.2 Plane wave imaging 16 2.2.3 Grenzen der Schallfeldfokussierung 16 2.3 Messung von Strömungsfeldern 17 2.3.1 Ultraschall-Doppler-Velozimetrie 18 2.3.2 Ultrasound Imaging Velocimetry 19 2.3.3 Ultrasound Particle Tracking Velocimetry 19 2.4 Nichtlineare akustische Effekte 20 2.4.1 Beschreibung von Linearität 20 2.4.2 Interaktion von nichtlinearen Streupartikeln und Schallwelle 20 2.4.3 Harmonic Imaging 21 3 Experimentelle Grundlagen 25 3.1 Charakterisierung der Zinksuspension 25 3.1.1 Zusammensetzung der Zinksuspension 25 3.1.2 Bestimmung von Dämpfung und Schallgeschwindigkeit 26 3.1.3 Bestimmung der spezifischen akustischen Impedanz 29 3.2 Messtechnik 30 3.2.1 Ultraschallforschungsplattform: Phased Array Ultrasound Dopp- ler Velocimeter 30 3.2.2 Ultraschallwandler 32 4 Verfahren zur Strömungsmessung im Modellexperiment 37 4.1 Experimenteller Aufbau 37 4.2 Untersuchung geeigneter Verfahren zur Messung von Strömungsfel- dern in der Zinksuspension 38 4.3 Optimierung der Signalverarbeitung und Charakterisierung der Messei- genschaften 44 4.3.1 Geschwindigkeitsnormal 44 4.3.2 Optimierung der Messsystemparameter 45 4.3.3 Charakterisierung der Messeigenschaften 48 4.3.4 Validierung 49 4.4 Messung der Suspensionsströmung im Modellexperiment 55 4.4.1 Messergebnisse 55 4.4.2 Vergleich von Simulation und Messung 58 4.5 Fazit 61 5 Verfahren zur In-situ-Strömungsmessung in einer Zink-Luft-Flussbatterie 63 5.1 Experimenteller Aufbau 63 5.2 Strömungsmessung unterhalb des Beugungslimits - Super Resolution Ultrasound Particle Tracking Velocimetry (SRPTV) 65 5.2.1 Nutzung nichtlinearer Streupartikel 68 5.2.2 Trennung von linearem und nichtlinearem Signalanteil 72 5.2.3 Strahlformung mit Kompensation der Streuung 76 5.2.4 Particle Tracking 80 5.3 Charakterisierung der Messeigenschaften 81 5.3.1 Vorgehen zur Charakterisierung der Messeigenschaften 82 5.3.2 Untersuchung der Positionsunsicherheit 83 5.3.3 Untersuchung der Geschwindigkeitsunsicherheit 92 5.4 Messung an einer aktiven Zink-Luft-Flussbatterie 95 5.4.1 Aufbau und Durchführung 95 5.4.2 Messergebnisse 97 5.4.3 Vergleich von Simulation und Messung 97 5.5 Fazit 102 6 Zusammenfassung und Ausblick 103 6.1 Erkenntnisse und Fortschritt 103 6.1.1 Ultrasound Imaging Velocimetry 103 6.1.2 Super Resolution Ultrasound Particle Tracking Velocimetry 104 6.1.3 Fazit 106 6.2 Ausblick und weiterführende Arbeiten 106 6.2.1 Messtechnik 106 6.2.2 Anwendung 107 Literaturverzeichnis 109 Publikationsverzeichnis 117 Artikel in Zeitschriften mit peer-review 117 Tagungsbeiträge 117 Patente 119