This thesis presents an axisymmetric numerical model to simulate interfacial flows near a sharp corner, where contact line pinning occurs. The method has been used to analyze drop imbibition into a capillary. To evaluate the performance of the numerical method, for a liquid drop initially placed partially within a capillary, a thermodynamic model has also been developed, to predict equilibrium states. The first part of this thesis presents an axisymmetric VoF algorithm to simulate interfacial flows near a sharp corner. (1) A new method to exactly calculate the normals and curvatures of any circle with a radius as small as the grid size is presented. This method is a hybrid least squares height function technique which fits a discretized osculating circle to a curve, from which interface normals and curvature can be evaluated. (2) A novel technique for applying the contact angle boundary condition has been devised, based on the definition of an osculating circle near a solid phase. (3) A new flux volume construction technique is presented, which can be applied to any split advection scheme. Unlike the traditional approach where the flux volumes are assumed rectangular, the new flux volumes can be either trapezoidal or triangular. The new technique improves the accuracy and consistency of the advection scheme. (4) Explicit PLIC reconstruction expressions for axisymmetric coordinates have been derived. (5) Finally, a numerical treatment of VoF for contact line motion near a sharp corner is presented, base on the idea of contact line pinning and an edge contact angle. The second part of the thesis is on the imbibition of a drop into an open capillary. A thermodynamic analysis based on minimization of an interfacial surface energy function is presented to predict equilibrium configurations of drops. Based on the drop size compared to the hole size, the equilibrium contact angle, and the geometry of the capillary, the drop can be totally imbibed by the capillary, or may not wet the capillary at all. The thesis concludes with application of the numerical scheme to the same problem, to examine the dynamics of wetting or dewetting of a capillary. All of the simulations yield results that correspond to the equilibrium states predicted by the thermodynamic analysis, but offer additional insight on contact line motion and interface deformation near the capillary edge.

This thesis presents an axisymmetric numerical model to simulate interfacial flows near a sharp corner, where contact line pinning occurs. The method has been used to analyze drop imbibition into a capillary. To evaluate the performance of the numerical method, for a liquid drop initially placed partially within a capillary, a thermodynamic model has also been developed, to predict equilibrium states. The first part of this thesis presents an axisymmetric VoF algorithm to simulate interfacial flows near a sharp corner. (1) A new method to exactly calculate the normals and curvatures of any circle with a radius as small as the grid size is presented. This method is a hybrid least squares height function technique which fits a discretized osculating circle to a curve, from which interface normals and curvature can be evaluated. (2) A novel technique for applying the contact angle boundary condition has been devised, based on the definition of an osculating circle near a solid phase. (3) A new flux volume construction technique is presented, which can be applied to any split advection scheme. Unlike the traditional approach where the flux volumes are assumed rectangular, the new flux volumes can be either trapezoidal or triangular. The new technique improves the accuracy and consistency of the advection scheme. (4) Explicit PLIC reconstruction expressions for axisymmetric coordinates have been derived. (5) Finally, a numerical treatment of VoF for contact line motion near a sharp corner is presented, base on the idea of contact line pinning and an edge contact angle. The second part of the thesis is on the imbibition of a drop into an open capillary. A thermodynamic analysis based on minimization of an interfacial surface energy function is presented to predict equilibrium configurations of drops. Based on the drop size compared to the hole size, the equilibrium contact angle, and the geometry of the capillary, the drop can be totally imbibed by the capillary, or may not wet the capillary at all. The thesis concludes with application of the numerical scheme to the same problem, to examine the dynamics of wetting or dewetting of a capillary. All of the simulations yield results that correspond to the equilibrium states predicted by the thermodynamic analysis, but offer additional insight on contact line motion and interface deformation near the capillary edge.

No description available.

Die in dieser Arbeit vorgestellten Simulationen aufsteigender fluider Partikel wurden mit dem CFD-Programm FS3D durchgeführt, welches auf der Volume-of-Fluid (VoF) Methode basiert. Die Validierung des Codes erfolgt durch Vergleich der numerischen Lösungen für schleichende Strömungen mit analytischen Lösungen, wobei eine gute Übereinstimmung festgestellt wird. Im ersten Teil der Dissertation werden Simulationen für den freien Aufstieg von Öltropfen in Wasser mit experimentellen Beobachtungen hinsichtlich der Aufstiegsgeschwindigkeit, der Tropfenform und der Bewegungsbahn verglichen. Die Aufstiegsgeschwindigkeiten und Widerstandsbeiwerte sind vergleichbar, die simulierten Tropfen sind jedoch deutlich flacher. Dieser Unterschied kann durch Verunreinigungen der Grenzfläche im Experiment verursacht sein. Der Übergang von einem gradlinigen Aufstieg zu zickzack-förmigen Aufstiegsbahnen kann mit Hilfe der Simulationen auf Instabilitäten im Nachlauf der Blasen zurückgeführt werden, die zu einer periodischen Wirbelablösung führen. Im zweiten Teil der Dissertation wird der Aufstieg von Blasen in linearen Scherströmungen untersucht. Steigen die Blasen in einer vertikalen Scherströmung auf, so beobachtet man eine seitliche Migration. Diese seitliche Migration der Blasen wird durch die sogenannte Liftkraft verursacht, deren Vorzeichen und Betrag von der Blasengröße und den Stoffeigenschaften der Flüssigkeit abhängt. Die Simulationen zeigen, daß das Vorzeichen der Liftkraft für eher sphärische Blasen durch den Bernoulli-Effekt erklärt werden kann. An stark deformierten Blasen hingegen wirkt die Liftkraft in umgekehrter Richtung. Dieses Phänomen tritt auch in den Simulationen auf. Verschiedene Hypothesen für die Ursache dieses Phänomens werden überprüft. Die bekannteste experimentelle Korrelation für die Liftkraft von Tomiyama u.a. (2002) wird durch Simulation von realen Flüssigkeiten mit bekannten Stoffeigenschaften wie auch von Modellfluiden mit willkürlichen Stoffeigenschaften validiert und weitgehend bestätigt. Die Lift-Korrelation hat demnach hinsichtlich der Stoffeigenschaften der Flüssigkeit einen größeren Geltungsbereich, als bisher experimentell überprüft wurde. The simulations presented in this thesis were performed with the CFD code FS3D which is based on the Volume of Fluid method. The code is validated using analytical solutions for creeping flows and a good agreement is observed between simulation and analytical solution. In the first part of the thesis, the free rise of oil drops in water is simulated and compared with experimental observations. The results show that the rising velocities and the drag coefficients are similar in both cases, but the simulated drops are flatter (more oblate). This difference may be caused by impurities of the particle surface (surfactants) in the experiments. The simulations show that the transition from rectilinear to periodic trajectories is caused by instabilities in the wake, which lead to a periodic vortex shedding. In the second part of the thesis, the rise of bubbles in linear shear flows is investigated. If bubbles rise in a vertical shear flow, a lateral migration can be observed. This migration is caused by the so called lift force. Sign and magnitude of the lift force depend on the size of the bubble and the material properties of the liquid. The simulation results show that the sign of the lift force on spherical bubbles can be explained by the Bernoulli effect. However, the lift force on more distorted bubbles acts in the opposite direction. This phenomenon can also be observed in the simulation. In this work several hypotheses for the reason of this phenomenon are checked. Furthermore, most common correlation for the lift force (developed by Tomiyama et al. in 2002) is validated for fluids of known material and model fluids with arbitrary material data. The correlation is valid in a wider range of fluid material properties than proved experimentally up to now.

En zone littorale, la houle subit de fortes transformations par effets bathymétriques. Une meilleure compréhension de ses modifications et des transferts d'énergie associés permet de mieux appréhender les problèmes de dimensionnement de structures côtières et d'aménagement du littoral (protection du littoral, influence des ouvrages sur la côte).<br />L'objectif de ce travail est d'étudier expérimentalement et numériquement la propagation et le déferlement<br />d'ondes de gravité.<br />La première partie, expérimentale, propose des méthodes de calcul, basées sur les houles de Stokes, pour la mesure d'ondes partiellement stationnaires à partir d'instruments de type électromagnétique (S4) ou<br />acoustique (ADV) donnant des mesures synchrones de vitesses et/ou de pression. Les influences du courant,<br />de la direction de propagation, de la profondeur d'immersion des appareils ainsi que des effets non<br />linéaires sont alors étudiés à partir de données en bassin et in situ.<br />La deuxième partie, numérique, consiste en la validation d'une méthode de suivi de surface libre de type<br />SL-VOF (Semi-Lagrangian Volume Of Fluid), insérée dans un code de calcul industriel (code EOLE de la<br />société Principia R&D). L'onde de gravité est modélisée par un soliton. L'étude de la propagation et du<br />déferlement du soliton est effectuée pour deux applications : sur une marche (discontinuité du fond) puis sur un fond de pente constante 1/15. L'évolution de la surface libre, son élévation et le champ de vitesses<br />sont alors comparés aux résultats expérimentaux.

Liquid droplet breakup and dynamics is a phenomena of immense practical importance in a wide variety of applications in science and engineering. Albeit, researchers have been studying this problem for over six decades, the fundamental physics governing droplet deformation and fragmentation is still unknown, not to mention the formulation and development of generalized correlations to predict droplet dynamics. The presence of disparate length and time scales, along with the complex unsteady physics, makes this a formidable problem, theoretically, experimentally and computationally. One of the important applications of interest and the motivation for the current research is a liquid fueled propulsion device, such as diesel, gas turbine or rocket engine. Droplet vaporization and ensuing combustion is accelerated if the droplet size is smaller, which makes any process leading to a reduction in drop size of prime importance in the combustion system design. This thesis is an attempt to address several unanswered questions currently confronting the spray community. Unanswered questions include identification and prediction of breakup modes at varying operating conditions, quantitative description of fundamental processes underlying droplet breakup and generalized correlations for child droplet size distributions and drag coefficient associated with the deformation and fragmentation of Newtonian and non-Newtonian fluids. The present work is aimed at answering the above questions by investigating the detailed flowfield and structure dynamics of liquid droplet breakup process and extracting essential physics governing this complex multiphase phenomena. High-fidelity direct numerical simulations are conducted using a volume-of-fluid (VOF) interface capturing methodology. To isolate the hydrodynamic mechanisms dictating droplet breakup phenomena, evaporation and compressibility are neglected, and numerical studies are performed for incompressible fluids at isothermal conditions. For Newtonian fluids, four different mechanisms are identified- oscillatory, bag, multimode and shear breakup modes. Various events during the deformation and fragmentation process are quantitatively identified and correlations are developed to predict the breakup mechanisms and droplet size distributions for a broad range of operating conditions. It was found that for We > 300 and Oh < 0.1 for rho_l/rho_g = 8.29, the child droplet size distributions can be modeled by a log-normal distribution. A correlation to predict the sauter mean diameter, d32, is also developed, given by d32 / D = 8We^-0.72 / Cd. Temporal evolution of momentum balance and droplet structure are also used to calculate the drag coefficient at each time step from first principles. Results show that the drag coefficient first increases to a maximum as the droplet frontal area increases and then decreases at the initiation of breakup. The drag coefficient reaches a steady value at the end of droplet lifetime, corresponding to the momentum retained by the droplet. A correlation to predict the time-mean drag coefficient given by, Cd / Cd,0 = 2We-^0.175, is developed, which indicates that the time averaged drag coefficient decreases with Weber number. The motivation to study non-Newtonian liquid droplet breakup stems from the various advantages gelled propellants offer as compared to traditional liquid or solid propellants in combustion systems, particularly in rocket engines. It was found that the breakup behavior of pseudoplastic, non-Newtonian liquids is drastically different as compared to Newtonian droplets. Several flow features commonly exhibited by non-Newtonian fluids are observed during the breakup process. The breakup initiates with the formation of beads-in-a-string due to the non-Newtonian nature of the fluid under consideration. This is followed by rapid rotation of the droplet with the appearance of helical instability and liquid budges, which forms the sites for primary and satellite droplet shedding. Child droplet size distribution are also examined and it is found that a Gaussian curve universally characterizes the droplets produced during non-Newtonian droplet breakup process. To put all things in perspective, the objectives of the thesis were two folds: (1) elucidate breakup physics for Newtonian and non-Newtonian liquid droplet deformation and breakup, and (2) develop correlations which can be used in an Eulerian-Lagrangian framework to study large-scale engineering problems. It is hoped that this research contributed to droplet breakup and dynamics literature by providing a more thorough and quantitative understanding of the breakup phenomena of liquid droplets and furnished models which can be used in future research endeavors.

The development of a fuel filler pipe is based solely on experience and physical experiment. The challenge lies in designing the pipe to fulfill the customer needs. In other words designing the pipe such as the fuel flow does not splash back on the fuel dispenser causing a premature shut off. To improve this “trial-and-error” based development a computational fluid dynamics (CFD) model of the refueling process is investigated. In this thesis a CFD model has been developed that can predict the fuel flow in the filler pipe. Worst case scenario of the refueling process is during the first second when the tank is partially filled. The most critical fluid is diesel due to the commercially high volume flow of 55 l/min. Due to limitations of computational resources the simulations are focused on the first second of the refueling process. The challenge in this project is creating a CFD model that is time efficient, thus require the least amount of computational resources necessary to provide useful information. A multiphase model is required to simulate the refueling process. In this project the implicit volume of fluid (VOF) has been used which has previously proven to be a suitable choice for refueling simulations. The project is divided into two parts. Part one starts with experiments and simulations of a simplified fuel system with water as acting liquid with a Reynolds number of 90 000. A short comparison between three different turbulence models has been investigated (LES, DES and URANS) where the most promising turbulence model is URANS, specifically the SST k-ω model. A sensitivity analysis was performed on the chosen turbulence model. Between the chosen mesh and the densest mesh the difference of streamwise velocity in the boundary layer was 2.6 %. The chosen mesh with 1.9 M cells and a time step of 1e-4 s was found to be the best correlating model with respect to the experiments. In part two a real fuel filling system was investigated both with experiments and simulations with the same computational model as the chosen one from part one. The change of fluid and geometry resulted in a lower Reynolds number of 12 000. Two different versions of the fuel system was investigated; with a bypass pipe and without a bypass pipe. Because of a larger volumetric region the resulting mesh had 3.7 M cells. The finished model takes about 230 h on a local workstation with 11 cores. On a cluster with 200 cores the same simulation takes 30 h. The resulting model suffered from interpolation errors at the inlet which resulted in a volume flow of 50 l/min as opposed to 55 l/min in the experiments. Despite the difference the model could capture the key flow characteristics. With the developed model a new filler pipe can be easily implemented and provide results in shorter time than a prototype filler pipe can be ordered. This will increase the chances of ordering one single prototype that fulfills all requirements. While the simulation model cannot completely replace verification by experiments it provides information that transforms the development of the filler pipe to knowledge based development.

The performance of PEM fuel cells (PEMFC) relies on the proper control and management of the liquid water that forms as a result of the electrochemical process, especially at high current densities. The liquid water transport and removal process in the gas flow channel is highly dynamic and many of its fundamental features are not well understood. This thesis presents an experimental and theoretical investigation of the emergence of water droplets from a single pore into a microchannel. The experiments are performed in a 250 µm × 250 µm air channel geometry with a single 50 µm pore that replicates a PEMFC cathode gas channel. A droplet manipulation platform is constructed using a microfluidics soft lithographic process to allow observation of the dynamic nature of the water droplets. Flow conditions that correspond to typical operating conditions in a PEMFC are selected. A test matrix of experiments comprised of different water injection velocities and air velocities in the gas microchannel is studied. Emergence, detachment and subsequent dynamic evolution of water droplets are analyzed, both qualitatively and quantitatively. Quantitative image analysis tools are implemented and applied to the time-resolved images to document the time evolution of the shape and location of the droplets, characteristic frequencies, dynamic contact angles, flow regime and stability maps. Three different flow regimes are identified, slug, droplet, and film flow. The effects of the air flow rate and droplet size on the critical detachment conditions are also investigated. Numerical simulations using Volume-of-Fluid method are presented to investigate the water dynamics in the droplet flow. The focus of the modeling is on methods that account for the dynamic nature of the contact line evolution. Results of different approaches of dynamic contact angle formulations derived empirically and by using the theoretically based Hoffmann function are compared with the static contact angle models used to date. The importance of the dynamic formulation as well as the necessity for high numerical resolution is highlighted. The Hoffmann function implementation is found to better capture the salient droplet motion dynamics in terms of advancing and receding contact angle and periodicity of the emergence process. To explore the possibility of using the pressure drop signal as a diagnostic tool in operational fuel cells that are not optically accessible, a flow diagnostic tool was developed based on pressure drop measurements in a custom designed two-phase flow fixture with commercial flow channel designs. Water accumulation at the channel outlet was found to be the primary cause of a low-frequency periodic oscillation of pressure drop signal. It is shown that the flow regimes can be characterized using the power spectrum density of the normalized pressure drop signal. This is used to construct a flow map correlating pressure drop signals to the flow regimes, and opens the possibility for practical flow diagnostics in operating fuel cells. / Graduate

This thesis discusses the development of a Numerical Wave Tank (NWT) capable of describing the coupled behaviour of Wave Energy Converters (WECs) and their moorings under extreme wave loading. The NWT utilises the open-source Computational Fluid Dynamics (CFD) software OpenFOAM(R) to solve the fully nonlinear, incompressible, Reynolds-Averaged Navier-Stokes (RANS) equations for air and water using the Finite Volume Method (FVM) and a Volume of Fluid (VOF) treatment of the interface. A method for numerically generating extreme waves is devised, based on the dispersively-focused NewWave theory and using the additional toolbox waves2Foam. A parametric study of the required mesh resolution shows that steeper waves require finer grids for mesh independence. Surface elevation results for wave-only cases closely match those from experiments, although an improved definition of the flow properties is required to generate very steep focused waves. Predictions of extreme wave run-up and pressure on the front of a fixed truncated cylinder compare well with physical measurements; the numerical solution successfully predicts the secondary loading cycle associated with the nonlinear ringing effect and shows a nonlinear relationship between incident crest height and horizontal load. With near perfect agreement during an extreme wave event, the reproduction of the six degree of freedom (6DOF) motion and load in the linearly-elastic mooring of a hemispherical-bottomed buoy significantly improves on similar studies from the literature. Uniquely, this study compares simulations of two existing WEC designs with scale-model tank tests. For the Wavestar machine, a point-absorber constrained to pitch motion only, results show good agreement with physical measurements of pressure, force and float motion in regular waves, although the solution in the wake region requires improvement. Adding bespoke functionality, a point-absorber designed by Seabased AB, consisting of a moored float and Power Take-Off (PTO) with limited stroke length, translator and endstop, is modelled in large regular waves. This represents a level of complexity not previously attempted in CFD and the 6DOF float motion and load in the mooring compare well with experiments. In conclusion, the computational tool developed here is capable of reliably predicting the behaviour of WEC systems during extreme wave events and, with some additional parameterisation, could be used to assess the survivability of WEC systems at full-scale before going to the expense of deployment at sea.

Die in dieser Arbeit vorgestellten Simulationen aufsteigender fluider Partikel wurden mit dem CFD-Programm FS3D durchgeführt, welches auf der Volume-of-Fluid (VoF) Methode basiert. Die Validierung des Codes erfolgt durch Vergleich der numerischen Lösungen für schleichende Strömungen mit analytischen Lösungen, wobei eine gute Übereinstimmung festgestellt wird. Im ersten Teil der Dissertation werden Simulationen für den freien Aufstieg von Öltropfen in Wasser mit experimentellen Beobachtungen hinsichtlich der Aufstiegsgeschwindigkeit, der Tropfenform und der Bewegungsbahn verglichen. Die Aufstiegsgeschwindigkeiten und Widerstandsbeiwerte sind vergleichbar, die simulierten Tropfen sind jedoch deutlich flacher. Dieser Unterschied kann durch Verunreinigungen der Grenzfläche im Experiment verursacht sein. Der Übergang von einem gradlinigen Aufstieg zu zickzack-förmigen Aufstiegsbahnen kann mit Hilfe der Simulationen auf Instabilitäten im Nachlauf der Blasen zurückgeführt werden, die zu einer periodischen Wirbelablösung führen. Im zweiten Teil der Dissertation wird der Aufstieg von Blasen in linearen Scherströmungen untersucht. Steigen die Blasen in einer vertikalen Scherströmung auf, so beobachtet man eine seitliche Migration. Diese seitliche Migration der Blasen wird durch die sogenannte Liftkraft verursacht, deren Vorzeichen und Betrag von der Blasengröße und den Stoffeigenschaften der Flüssigkeit abhängt. Die Simulationen zeigen, daß das Vorzeichen der Liftkraft für eher sphärische Blasen durch den Bernoulli-Effekt erklärt werden kann. An stark deformierten Blasen hingegen wirkt die Liftkraft in umgekehrter Richtung. Dieses Phänomen tritt auch in den Simulationen auf. Verschiedene Hypothesen für die Ursache dieses Phänomens werden überprüft. Die bekannteste experimentelle Korrelation für die Liftkraft von Tomiyama u.a. (2002) wird durch Simulation von realen Flüssigkeiten mit bekannten Stoffeigenschaften wie auch von Modellfluiden mit willkürlichen Stoffeigenschaften validiert und weitgehend bestätigt. Die Lift-Korrelation hat demnach hinsichtlich der Stoffeigenschaften der Flüssigkeit einen größeren Geltungsbereich, als bisher experimentell überprüft wurde. The simulations presented in this thesis were performed with the CFD code FS3D which is based on the Volume of Fluid method. The code is validated using analytical solutions for creeping flows and a good agreement is observed between simulation and analytical solution. In the first part of the thesis, the free rise of oil drops in water is simulated and compared with experimental observations. The results show that the rising velocities and the drag coefficients are similar in both cases, but the simulated drops are flatter (more oblate). This difference may be caused by impurities of the particle surface (surfactants) in the experiments. The simulations show that the transition from rectilinear to periodic trajectories is caused by instabilities in the wake, which lead to a periodic vortex shedding. In the second part of the thesis, the rise of bubbles in linear shear flows is investigated. If bubbles rise in a vertical shear flow, a lateral migration can be observed. This migration is caused by the so called lift force. Sign and magnitude of the lift force depend on the size of the bubble and the material properties of the liquid. The simulation results show that the sign of the lift force on spherical bubbles can be explained by the Bernoulli effect. However, the lift force on more distorted bubbles acts in the opposite direction. This phenomenon can also be observed in the simulation. In this work several hypotheses for the reason of this phenomenon are checked. Furthermore, most common correlation for the lift force (developed by Tomiyama et al. in 2002) is validated for fluids of known material and model fluids with arbitrary material data. The correlation is valid in a wider range of fluid material properties than proved experimentally up to now.