Liquid metal batteries are discussed today as an economic grid-scale energy storage, as required for the deployment of fluctuating renewable energies. These batteries consist of three stably stratified liquid layers: two liquid metal electrodes are separated by a thin molten salt electrolyte, this way forming an electrochemical concentration cell. The completely liquid interior, which is on the one hand very beneficial for the energy efficiency, also poses some major challenges on the other hand. Strong cell currents in combination with electromagnetic fields make liquid metal batteries highly susceptible to various kinds of magnetohydrodynamic instabilities. In particular, the so-called metal pad roll instability, which can drive uncontrollable wave motions in both interfaces, was identified as a key limiting factor for the operational safety. The metal pad roll instability is well known from conceptually similar aluminum reduction cells, but still poorly understood in the framework of liquid metal batteries. Mainly by developing analytical wave models, but also by employing numerical simulations and by setting up a newly designed wave experiment, the present thesis pursues the goal of providing a better understanding of interfacial wave dynamics and the manifestation of the metal pad roll instability in liquid metal batteries. As a main result, a three-layer formulation of standing gravity-capillary waves reveals that the pressure coupling between the two interfaces plays a crucial role in the cell stability. Three different coupling regimes, which partially involve novel types of interfacial wave instabilities, are identified and classified by two dimensionless parameters. Building on this theoretical work, the wave experiment is exploited to further investigate different metal pad roll-related wave properties. The crucial importance of the contact line dynamics is emphasized and viscous damping, which is important for the estimation of instability onsets, is discussed as a function of the layer heights. Finally, a hybrid interfacial sloshing model is formulated and equipped with recently derived two-layer damping rates to account for viscous dissipation. The model allows to study and interpret the forced wave mechanics in the wave experiment as a function of eight dimensionless parameters and can, as an additional application, be exploited to optimize mixing in orbitally shaken bioreactors. As a further key result, the sloshing model reveals the formation of novel spiral wave patterns under the effect of strong damping.

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The present research develops a numerical fluid-structure interaction (FSI) code based on CFDShip-Iowa version 4, a general-purpose URANS/DES overset fluid solver. Linear and nonlinear FSI methods are developed to compute structural responses on surface ships or marine structures. The modal superposition transient analysis and the nonlinear FEM structure solver are used for small and large deformation FSI problems, respectively. The gluing method is applied to transfer the forces and displacements on non-matching grids for fluid and structure domains. The linear FEM solver is applied to deform the boundary layer grid with large deformation in the fluid domain, while the deformation is ignored in small deformation problems. Deformation of an interior point in the boundary layer grid is obtained using linear interpolation in both linear and nonlinear deformation problems. The S175 containership is studied in regular waves as an application example for the linear problem. Heave and pitch responses are compared with the experiments, showing good agreement. Time histories of vertical bending moment (VBM) are calculated using rigid model, one-way coupling, and two-way coupling approaches. The elastic models are able to capture the ringing of the VBM induced by slamming, while the rigid model shows a peak at the moment of slamming without further fluctuations. The two-way coupling method shows the effects of hull deformation on the amplitude and phase of VBM as well as the accelerations of heave and pitch. For the nonlinear deformation problem three sloshing tanks with an elastic bar clamped to its bottom or top are simulated and compared with the experiments and other numerical simulation results. The present simulation results show reasonable agreement with the experiments for bar deformation and free surface elevation. A secondary wave on the free surface is creadted by the vorticity generated from the free surface. The effect of the bar on the sloshing impact is studied comparing dynamic pressure acting on the tank wall without bar, with an elatic bar, and with a rigid bar.

<div><br></div><div> Today, autoinjectors are developed for more viscous drug solutions, which require larger forces for actuating the syringe and impose larger stresses on the drug solution during the administration of autoinjectors. We developed experimentally validated high-fidelity simulations to investigate the liquid jet formation, liquid slosh and cavitation during the insertion process of an autoinjector. </div><div> </div><div> The jet formed due to an acceleration-deceleration motion of syringe is found to be governed by the interplay between inertial, viscous, surface tension and gravitational forces. A scaling for the jet velocity and a criterion for the jet breakup in a simplified geometry are proposed.</div><div> </div><div> When the syringe accelerates and decelerates during the insertion, liquid slosh occurs and there is a vehement motion of the air-liquid interface. Here, we quantified the area of air-liquid interface and hydrodynamic strain rate, which increase with the air gap size, syringe velocity, tilt angle and inner wall hydrophobicity, and decrease with the solution viscosity and hardly change with the liquid column height and surface tension. The strain rate is not sufficient to unfold the protein and the air-liquid interface is more likely to cause protein aggregation.</div><div> </div><div> In a spring-driven autoinjector, the plunger is actuated by the impact of a driving rod, which generates a strong pressure wave and can cause cavitation inception. The cavtiation bubbles can be impeded by the syringe walls and form a re-entrant jet shooting toward the syringe wall. During the process, the protein molecules are focused in the jet, pushed toward the syringe wall and spread across the wall, which can be the reason for the protein aggregation and adsorption on the syringe walls. The impedance effects of the wall decreases with the wall distance and increases with the maximum bubble size. The maximum bubble radius also increases with the liquid column size and nucleus size and decreases with the air gap pressure. Since inertia effects dominate in the cavitation process, the liquid viscosity and surface tension hardly changes the cavitation bubble dynamics. Small bubbles can also form in the bulk, which may generate aggregates in the bulk solution. Bubbles in the cavitation bubble cloud may coalesce with nearby bubbles and induce a higher pressure at the collapse (up to 1000 bar). This high pressure can potentially generate hydroxyl radicals that oxidize the protein molecules.</div><div> </div><div> The current study presents a detailed picture of fluid flows in autoinjectors and provide recommendations for mitigating the liquid slosh and cavitation generated in syringes. The results can be combined with future experiments to understand the implications of fluid flows on protein drugs and the performance of autoinjectors.</div>

Fuel leakage through a fill limit vent valve (FLVV) inside a fuel tank is an important factor to consider during the design of a new tank. The performance of the carbon canister which absorbs the hydrocarbon can be compromised if fuel manages to escape through the valve, so called Liquid Carry Over (LCO) and thus not fulfilling the fuel emission requirements. As of today this is not thoroughly investigated using experiments nor Computational Fluid Dynamics. The main focus of this study was to develop a method to simulate the behaviour of the FLVV during various driving conditions at an early design stage and if this gives rise to fuel escaping through the FLVV. This method was later to be validated with an experimental set-up and later used to perform some simulations to investigate LCO by varying different parameters such as fuel level and different types of driving. What happens when the canister is purging was also investigated to see if it has a pronounced effect on LCO. Purging is when hydrocarbons, absorbed by the canister, are sent to the engine and giving rise to an under pressure in the tank.The method was developed to run on a cluster utilizing 200 Central Processing Unit Cores where each simulated physical second required an average of 3 hours of simulation time.The flow inside the tank was simulated using a Volume Of Fluid (VOF) multiphase model and the dynamic behaviour of the floater inside the FLVV was simulated using an overset mesh with a Dynamic Fluid Body Interaction.The movement of the simulated dynamic floater was validated with an experimental set-up specifically developed for the overset mesh validation and the motion of the floater was captured at a fairly accurate level.A prototype for an experimental tank was also developed and produced to validate the VOF set-up used for sloshing inside the tank which was utilized on the real tank but due to time limitation the experiments were not performed. The results from the parameter investigation showed that LCO was present in cases with high fuel level inside the tank 95 % and that an aggressive driving gives rise to a higher level of LCO compared to normal driving. Simulations with a fuel level of 85 % and lower showed no evidence of LCO for this particular tank model. The purging of the tank induced a pumping effect giving rise to a higher level of LCO pumped through by the floater.

Le ballottement dans les réservoirs d'ergols est une des perturbations les plus importantes de la stabilité d'un satellite en orbite. En considérant des manœuvres faiblement inertielles, il n'existe pas de modèle analytique et l'expérimentation nécessite de longues périodes de temps en micro-gravité. Nous nous proposons donc, dans cette thèse, de réaliser des simulations numériques de ce phénomène. L'étude est basée sur le solveur DIVA résolvant les équations de Navier-Stokes diphasiques avec les méthodes level-set et Ghost Fluid. Deux technologies de réservoirs sont à l'étude : les réservoirs classiques, ne contenant que l'ergol liquide et le gaz pressurisant, et les réservoirs à membrane, pour lesquels une membrane hyperélastique sépare les deux fluides. Dans le premier cas, une étude paramétrique complète sur les effets du ballottement lors d'une manœuvre de rotation est menée et les différents régimes d'écoulement obtenus sont décrits par rapport aux paramètres d'études. Par la suite, les données de l'expérience FLUIDICS, envoyée à bord de la Station Spatiale Internationale, sont comparées aux résultats numériques et montrent un très bon accord. Par rapport au second cas, un modèle d'interaction fluides-membrane est développé en s'inspirant de travaux sur la déformation de cellules biologiques. Les déformations et contraintes propres à la membrane sont suivies de façon Eulérienne, les efforts exercés par la membrane sur les fluides environnants en sont déduits et intégrés au solveur diphasique. Les résultats obtenus sont validés par comparaison à des cas-tests de la littérature. / Propellant sloshing in tanks is one of the most important disturbances of satellite stability in orbit. Considering low-inertial manoeuvres, there is no analytical model and experimental facilities require long time period of microgravity conditions. Thus, this PhD thesis aims to predict this phenomenon by numerical simulations. The study is based on the DIVA code which solves the Navier-Stokes equations for two-phase flows with the level-set method and the Ghost Fluid method. Two tank technologies are studied: simple tanks, which only contain the liquid propellant and the gas maintaining the pressure, and diaphragm tanks, for which a hyperelastic membrane separates both fluids. In the first case, a parametric study on the sloshing effects is done considering rotational manoeuvres and the different behaviours observed are described in relation to the study parameters. Thereafter, the data from the FLUIDICS experiment, sent to the International Space Station, are compared to the numerical results and exhibit good agreement. In the second case, a fluids-membrane interaction model inspired from works on the deformation of biological cells is developed. The membrane strains and stresses are computed in an Eulerian way, from which the force exerted by the membrane on the surrounding fluids is deduced and integrated in the two-phase flows solver. The numerical results are validated by comparison with benchmarks from the literature.

Command shaping creates reference commands that reduce residual vibrations in a flexible system. This thesis examines the use of command shaping for flexible system control in three industrial applications: cam-follower systems, sloshing liquids, and cherrypickers. One common type of command shaping is command smoothing which creates a smooth transition between setpoints. A specific type of command smoothing used in cam-follower systems is the polynomial profile. An alternative technique to reduce vibration in flexible systems is input shaping. In this thesis, input-shaped commands are compared to polynomial profiles for applications requiring both vibration suppression and fast motion. Simulation and experimental results show that input shaping is faster than polynomial profiles and provides a simple approach to suppressing residual vibration. Secondly, significant experimental contributions have been made in the area of slosh control. The oscillation of liquids in a container can cause liquid spillage or can cause stability issues, especially in space vehicles. In the past, a number of control techniques have been proposed, but only a few recommend the use of input shaping. This thesis describes the use of command shaping to limit slosh. Results are supported by numerical and experimental testing. Input-shaped commands reduce residual slosh amplitude compared to unshaped commands and polynomial profiles. Input-shaped commands can also accommodate uncertainties and changes in the sloshing frequencies. Lastly, a small-scale cherrypicker was constructed to study the use of input-shaping control on these types of aerial lifts. Cherrypickers have flexible dynamic effects that can cause dangerous and life-threatening situations. To study this class of machines and to provide future students an experimental testbed, several design criteria were established before construction began. The resulting machine achieved most design objectives, including a simple-to-use graphical user interface and accurate state measurements. Robust input-shaping controllers were implemented to limit endpoint vibration. The design of the cherrypicker is discussed and experimental results are reported.

Cette thèse est motivée par un problème aéronautique: le ballottement du carburantdans des réservoirs d’ailes d’avion très flexibles. Les vibrations induites par le couplagedu fluide avec la structure peuvent conduire à des problèmes tels que l’inconfort des passagers,une manoeuvrabilité réduite, voire même provoquer un comportement instable. Cette thèse apour objectif de développer de nouveaux modèles d’interaction fluide-structure, en mettant enoeuvre la théorie des systèmes Hamiltoniens à ports d’interaction (pHs). Le formalisme pHsfournit d’une part un cadre unifié pour la description des systèmes multi-physiques complexeset d’autre part une approche modulaire pour l’interconnexion des sous-systèmes grâce auxports d’interaction. Cette thèse s’intéresse aussi à la conception de contrôleurs à partir desmodèles pHs. Des modèles pHs sont proposés pour les équations de ballottement du liquide en partantdes équations de Saint Venant en 1D et 2D. L’originalité du travail est de donner des modèlespHs pour le ballottement dans des réservoirs en mouvement. Les ports d’interaction sont utiliséspour coupler la dynamique du ballottement à la dynamique d’une poutre contrôlée par desactionneurs piézo-électriques, celle-ci étant préalablement modélisée sous forme pHs. Aprèsl’écriture des équations aux dérivées partielles dans le formalisme pHs, une approximation endimension finie est obtenue en utilisant une méthode pseudo-spectrale géométrique qui conservela structure pHs du modèle continu au niveau discret. La thèse propose plusieurs extensionsde la méthode pseudo-spectrale géométrique, permettant la discrétisation des systèmesavec des opérateurs différentiels du second ordre d’une part et avec un opérateur d’entrée nonborné d’autre part. Des essais expérimentaux ont été effectués sur une structure constituéed’une poutre liée à un réservoir afin d’assurer la validité du modèle pHs du ballottementdu liquide couplé à la poutre flexible, et de valider la méthode pseudo-spectrale de semi-discrétisation.Le modèle pHs a finalement été utilisé pour concevoir un contrôleur basé surla passivité pour réduire les vibrations du système couplé. / This thesis is motivated by an aeronautical issue: the fuel sloshing in tanksof very flexible wings. The vibrations due to these coupled phenomena can lead to problemslike reduced passenger comfort and maneuverability, and even unstable behavior. Thisthesis aims at developing new models of fluid-structure interaction based on the theory ofport-Hamiltonian systems (pHs). The pHs formalism provides a unified framework for thedescription of complex multi-physics systems and a modular approach for the coupling ofsubsystems thanks to interconnection ports. Furthermore, the design of controllers using pHsmodels is also addressed. PHs models are proposed for the equations of liquid sloshing based on 1D and 2D SaintVenant equations and for the equations of structural dynamics. The originality of the workis to give pHs models of sloshing in moving containers. The interconnection ports are used tocouple the sloshing dynamics to the structural dynamics of a beam controlled by piezoelectricactuators. After writing the partial differential equations of the coupled system using thepHs formalism, a finite-dimensional approximation is obtained by using a geometric pseudospectralmethod that preserves the pHs structure of the infinite-dimensional model at thediscrete level. The thesis proposes several extensions of the geometric pseudo-spectral method,allowing the discretization of systems with second-order differential operators and with anunbounded input operator. Experimental tests on a structure made of a beam connected to atank were carried out to validate both the pHs model of liquid sloshing in moving containersand the pseudo-spectral semi-discretization method. The pHs model was finally used to designa passivity-based controller for reducing the vibrations of the coupled system.

Liquid sloshing with unrestrained free surface in a moving container is associated with various engineering problems, such as tankers on highways, liquid oscillations in large storage tanks caused by earthquakes, sloshing of liquid cargo in ocean-going vessels, and the motion of liquid fuel in aircraft and spacecraft. The purpose of this study is to develop a three-dimensional (3D) numerical wave tank with or without internal structures to investigate the mechanism of liquid sloshing and the interaction between the fluid and internal structures. The developed 3D time-independent finite difference method is applied on solving liquid sloshing in tanks with or without the influence of baffles under the ground motion of six-degrees of freedom. The 3D Navier-Stokes equations were solved and transformed to a tank-fixed coordinate system, and the fully nonlinear kinematic and dynamic free surface boundary conditions for fluid sloshing in a rectangular tank with a square base were considered. The fluid is assumed incompressible in this study. The complicated interaction in the vicinity of the fluid-structure interface was solved by implementing one dimensional ghost cell approach and the stretching grid technique near the fluid-structure boundaries were used to catch the detailed evolution of local flow field. A PC-cluster was established by linking several single computers to reduce the computational times due to the implementation of the 3D numerical model. The Message Passing Interface (MPI) parallel language and MPICH2 software were utilized to code the computer codes and to carry out the circumstance of parallel computation, respectively. The developed numerical scheme was verified by rigorous benchmark tests. Not only the reported analytical, numerical and experimental studies were compared with the present numerical results, the experimental investigation was also involved in the present work to further validate the accuracy of the numerical scheme. All the benchmark tests of this study showed excellent accuracy of the developed numerical scheme. For a tank without internal structures, the coupled motions of surge and sway are simulated with various excitation angles, excitation frequencies and water depths. The characteristics of sloshing waves are dissected in terms of the classification of sloshing wave types, sloshing amplitude, beating phenomenon, sloshing-induced forces and energy transfer of sloshing waves. Six types of sloshing waves, named single-directional, diagonal, square-like, swirling-like, swirling and irregular waves, were found and classified in the present study and the occurrence of these waves are tightly in connection with the excitation frequency of the tank. The effect of excitation angle on the characteristics of sloshing waves is explored and discussed, especially for swirling waves. The spectral analyses of sloshing displacement of various sloshing waves are examined and a clear evidence of the correlation between sloshing wave patterns and resonant modes of sloshing waves are demonstrated. The mechanism of switching direction of swirling waves is discussed by investigating the situation of circulatory flow, the instantaneous free surface, the gravitational effect and the instantaneous direction of external forcing. The coupling effects of heave, surge and sway motions were also included in this study and the result showed an unstable influence of heave motion on the kinematic and dynamic characteristics of sloshing waves when the vertical excitation frequency of the tank is twice as large as the fundamental natural frequency. Except irregular waves, the other types of sloshing waves are converted into swirling waves due to the effect of heave motion. The study related to tuned liquid damper (TLD) in 2D and 3D tanks were considered. A comprehensive investigation for a 2D tank with vertically tank bottom-mounted baffles (baffled tank) are demonstrated and discussed with respect to the influence of baffle height on the natural mode of the tank, the evolution of vortices and vortex shedding phenomenon, the relationship between the vortex shedding frequency and the excitation frequency of the tank, the vortex size generated in the vicinity of the baffle tip, the interaction of vortices inside the tank. The baffle height shows a significant influence on the shift of the first natural frequency of the baffled tank and the liquid depth also plays an important part in determining this influence. In other words, the shift of the first natural mode due to various baffle height is varied with water depths. The design of two baffles separated by 0.2 times the tank breadth is an efficient tool to not only reduce the sloshing amplitude but switch the first natural frequency of the tank. The sloshing displacement is affected distinctly by different numbers of baffles mounted vertically on the tank bottom. The more baffles mounted onto the tank bottom, the smaller the sloshing displacement is presented in both the transient and steady-state periods. The processes of the evolution of vortices near the baffle tip are categorized into four phases: the formation of separated shear layer and generation of vortices, the formation of a vertical jet and shedding of vortices, the interaction between shedding vortices and sloshing flow (the generation of snaky flow) and the interaction between snaky flow and sloshing waves. Vortex shedding phenomenon due to stronger vertical jets occurs when the excitation frequency is close to the first natural mode of the baffled tank. The size of the vortex generated near the baffle tip is discussed and the vortex size is closely correlated with the baffle height. Two types of 3D tuned liquid dampers, a vertically tank bottom-mounted baffle and a vertical plate, are discussed for a tank under coupled surge-sway motions. The wave types of diagonal and single-directional waves switch to the swirling type due to the influence of the baffle. The phenomenon of square-like waves or irregular waves coexisting with swirling waves is found in the baffled tank under diagonal excitation. The baffle and the vertical plate mounted parallel to the east (west) wall of the tank can effectively reduce the sloshing amplitude when the excitation angle is between 0 degree and 10 degree and the corresponding sloshing displacement in the sway (z) direction becomes more dominant with the increase of the excitation angle. The shift of the first natural mode of the baffled tank due to various baffle heights in the x direction is dominated in this design of baffled tank. The length of the plate can cause a significant influence on not only the variation of the natural frequencies but the type of the sloshing waves. The influence of the vertical plate on the irregular waves is insignificant and several peaks appear in the spectral analysis of the sloshing displacement for the irregular waves and the numbers of peaks are more than that of the baffled tank.

Στην παρούσα εργασία εξετάζεται η επίδραση του κλυδασμού στην απόκριση σφαιρικών δεξαμενών με άκαμπτα τοιχώματα για τυχαίο ποσοστό πλήρωσης, υπό οριζόντια σεισμική διέγερση. Πραγματοποιείται η ιδιομορφική ανάλυση της κίνησης του κλυδασμού χρησιμοποιώντας τη μέθοδο των πεπερασμένων στοιχείων και το πρόγραμμα ANSYS για την διατύπωση και επίλυση των εξισώσεων. Υπολογίζονται τα ιδιοδιανύσματα και εξάγονται νομογραφήματα της ιδιοσυχνότητας σε συνάρτηση με τη διάμετρο της σφαίρας, το ποσοστό πλήρωσης και την επιτάχυνση της βαρύτητας. Για την ερμηνεία της υδροδυναμικής συμπεριφοράς του περιεχόμενου υγρού υιοθετείται η καθιερωμένη θεώρηση της επαλληλίας των επιδράσεων δύο ανεξάρτητων κινήσεων: Της κίνησης της κυκλοφορούσας μάζας και της κίνησης της ωστικής μάζας του υγρού. Προτείνεται και τεκμηριώνεται μια μεθοδολογία για τον προσδιορισμό της κυκλοφορούσας και της ωστικής μάζας για κάθε μορφή δεξαμενής και κάθε ποσοστό πλήρωσης. Για την περίπτωση των σφαιρικών δεξαμενών εξάγονται νομογραφήματα που αναπαριστούν την κυκλοφορούσα και την ωστική μάζα ως συνάρτηση του ύψους πλήρωσης. Παράλληλα, παράγεται ένα ισοδύναμο σύστημα διακριτών μαζών και ελατηρίων που προσομοιώνει την υδροδυναμική συμπεριφορά του περιεχόμενου υγρού σε οριζόντια διέγερση, για κάθε στάθμη της ελεύθερης επιφάνειας. Μεταξύ άλλων, προσδιορίζονται οι κατανομές της κυκλοφορούσας και της ωστικής υδροδυναμικής πιέσης για συγκεκριμένα ποσοστά πλήρωσης και η τιμή της συνολικής πίεσης σε τυχαίο σημείο του σφαιρικού κελύφους. Τέλος, παρουσιάζονται αποτελέσματα εφαρμογών σχετικά με την σεισμική απόκριση σφαιρικών δεξαμενών, χρησιμοποιώντας το προτεινόμενο ισοδύναμο διακριτό σύστημα, και συγκρίνονται με τα αντίστοιχα άλλων εργασιών για την τεκμηρίωση της ορθότητας και της αποτελεσματικότητας του. / The present work considers the sloshing effects on the seismic response of spherical tanks with rigid walls and filled with liquid up to an arbitrary level. The sloshing eigenmode analysis is performed by means of the finite element method utilizing the ANSYS program. The eigenfunctions are computed and nomographs of the corresponding natural frequencies are obtained. Each nomograph is a multivariable function of tank diameter and filling level of the content liquid. The hydrodynamic behaviour of the liquid motion can be considered to be equivalent to the superposition of two independent motions; the motion of an impulsive and all convective masses. The main goal of the present work is the development of a methodology to determine the impulsive and the major convective masses for arbitrary tank diameter and filling level values. The accuracy of the proposed methodology is verified for the case of vertical cylindrical tanks, where the analytical solution is well known. Applying the proposed methodology to the case of spherical tanks, the impulsive and the major convective masses are computed as functions of the non-dimensional liquid filling level. It is found that the convective mass corresponding to the first eigenmode is by far more significant than all the higher order convective masses; therefore, the liquid sloshing motion is dominated by this mode. Then, the hydrodynamic behaviour of the content liquid is simulated by means of an equivalent discrete system of masses and springs. In addition, the wall distributions of convective and impulsive pressures are calculated. Finally, utilizing the obtained equivalent discrete system, numerical results of the seismic response of typical spherical tanks are presented and compared to those obtained by other semi-analytical and numerical methods.