This thesis describes a new method for simulating high Reynolds number turbulence which requires much less computing power. This involved both theoretical work - to understand and model the important processes - and computational work, to implement the model efficiently. There are 'many different techniques for modelling particle dispersion in turbulent flow (e.g. K-theory and Random Flight) but they make assumptions about the fluid-particle interaction and require empirical coefficients. Theoretical work on the motion of bubbles and varticles in idealised flows has shown that the instantaneous structure of the velocity field is important in determining particle trajectories, and that particle motion cannot currently be modelled reliably in terms of time- or ensemble-averaged fluid velocities. Therefore the solution of many practical problems requires the simulation of the instantaneous structure of a turbulent velocity field. This can now be provided with the very large computers and large amounts of computer time; even then, only low Reynolds number turbulence can be simulated. In the method developed here, the velocity field of homogeneous isotropic turbulence is simulated by a large number of random Fourier modes varying in space and time. They are chosen so that the flow field has certain properties, namely (i) it satisfies continuity, (ii) the two point Eulerian spatial spectra have known form (e.g. the Kolmogorov inertial subrange), (iii) the time dependence is modelled by dividing the turbulence into large- and small-scales eddies, and by assuming that the large eddies advect the small eddies which also decorrelate as they are advected, (iv) the large- and small-scale Fourier modes are each statistically independent and Gaussian. Computations of the streamlines in a sequence of realisations of the flow show that they have a similar structure to that obtained from direct numerical simulations. New results for the statistics of high Reynolds number turbulent flows are obtained, for the velocity and pressure fields . Particle statistics are obtained by computing the trajectories of many particles and taking the ensemble average. Particle dispersion has been computed for a range of particle parameters and the results agree well with experimental measurements such as those of Snyder and Lumley; this enables us to compute empirical coefficients (e.g. Lagrangian timescales) for use in simpler models such as Random Flight, and for modelling other processes such as combustion and mixing. Rapid Distortion Theory is used to investigate the effects of high shear rate on the structure of homogeneous turbulence in chapter 4. The results show that an important effect of the shear acting on initially isotropic turbulence is the selective amplification of structures having large length scale in the mean flow direction.

We present a mathematical study of two conservative systems in fluid mechanics. First, we study a fragmentation model for sprays. The model takes into account the break-up of spray droplets due to drag forces. In particular, we establish the existence of global weak solutions to a system of incompressible Navier-Stokes equations coupled with a Boltzmann-like kinetic equation. We assume the particles initially have bounded radii and bounded velocities relative to the gas, and we show that those bounds remain as the system evolves. One interesting feature of the model is the apparent accumulation of particles with arbitrarily small radii. As a result, there can be no nontrivial hydrodynamical equilibrium for this system. Next, with an interest in understanding hydrodynamical limits in discontinuous regimes, we study a classical model for shock waves. Specifically, we consider scalar nonviscous conservation laws with strictly convex flux in one spatial dimension, and we investigate the behavior of bounded L² perturbations of shock wave solutions to the Riemann problem using the relative entropy method. We show that up to a time-dependent translation of the shock, the L² norm of a perturbed solution relative to the shock wave is bounded above by the L² norm of the initial perturbation. Finally, we include some preliminary relative entropy estimates which are suitable for a study of shock wave solutions to n x n systems of conservation laws having a convex entropy. / text

In this study, commercially available Computational Fluid Dynamics (CFD) software, CFX-4.4 has been used for the simulations of aerosol transport through various aerosol-sampling devices. Aerosol transport was modeled as a classical dilute and dispersed two-phase flow problem. Eulerian-Lagrangian framework was adopted wherein the fluid was treated as the continuous phase and aerosol as the dispersed phase, with a one-way coupling between the phases. Initially, performance of the particle transport algorithm implemented in the code was validated against available experimental and numerical data in the literature. Code predictions were found to be in good agreement against experimental data and previous numerical predictions. As a next step, the code was used as a tool to optimize the performance of a virtual impactor prototype. Suggestions on critical geometrical details available in the literature, for a virtual impactor, were numerically investigated on the prototype and the optimum set of parameters was determined. Performance curves were generated for the optimized design at various operating conditions. A computational model of the Linear Slot Virtual Impactor (LSVI) fabricated based on the optimization study, was constructed using the worst-case values of the measured geometrical parameters, with offsets in the horizontal and vertical planes. Simulations were performed on this model for the LSVI operating conditions. Behavior of various sized particles inside the impactor was illustrated with the corresponding particle tracks. Fair agreement was obtained between code predictions and experimental results. Important information on the virtual impactor performance, not known earlier, or, not reported in the literature in the past, obtained from this study, is presented. In the final part of this study, simulations on aerosol deposition in turbulent pipe flow were performed. Code predictions were found to be completely uncorrelated to experimental data. The discrepancy was traced to the performance of the code's turbulent dispersion model. A detailed literature survey revealed the inherent technical deficiencies in the model, even for particle dispersion. Based on the results of this study, it was determined that while the code can be used for simulating aerosol transport under laminar flow conditions, it is not capable of simulating aerosol transport under turbulent flow conditions.

In this study, commercially available Computational Fluid Dynamics (CFD) software, CFX-4.4 has been used for the simulations of aerosol transport through various aerosol-sampling devices. Aerosol transport was modeled as a classical dilute and dispersed two-phase flow problem. Eulerian-Lagrangian framework was adopted wherein the fluid was treated as the continuous phase and aerosol as the dispersed phase, with a one-way coupling between the phases. Initially, performance of the particle transport algorithm implemented in the code was validated against available experimental and numerical data in the literature. Code predictions were found to be in good agreement against experimental data and previous numerical predictions. As a next step, the code was used as a tool to optimize the performance of a virtual impactor prototype. Suggestions on critical geometrical details available in the literature, for a virtual impactor, were numerically investigated on the prototype and the optimum set of parameters was determined. Performance curves were generated for the optimized design at various operating conditions. A computational model of the Linear Slot Virtual Impactor (LSVI) fabricated based on the optimization study, was constructed using the worst-case values of the measured geometrical parameters, with offsets in the horizontal and vertical planes. Simulations were performed on this model for the LSVI operating conditions. Behavior of various sized particles inside the impactor was illustrated with the corresponding particle tracks. Fair agreement was obtained between code predictions and experimental results. Important information on the virtual impactor performance, not known earlier, or, not reported in the literature in the past, obtained from this study, is presented. In the final part of this study, simulations on aerosol deposition in turbulent pipe flow were performed. Code predictions were found to be completely uncorrelated to experimental data. The discrepancy was traced to the performance of the code's turbulent dispersion model. A detailed literature survey revealed the inherent technical deficiencies in the model, even for particle dispersion. Based on the results of this study, it was determined that while the code can be used for simulating aerosol transport under laminar flow conditions, it is not capable of simulating aerosol transport under turbulent flow conditions.

Porous media affect hydrate stability by forcing hydrate-liquid interfaces to form high curvature geometries and by forcing the molecules of the hydrate, liquid, and sedimentary particles that compose the medium to interact where they are in close proximity. To evaluate these effects we first create synthetic spherical packings to approximate pore space geometry. We use the synthetic pore space to calculate the perturbation to the chemical potential caused by the geometrical constraints. Our model predictions agree with published data for ice-water and water-vapor systems. When particles are well-approximated as spheres, our model fits the data with R-squared values that range between about 80% to over 99%. However, our model needs to be improved for porous media that contain a significant fraction of non-equant particles such as clay. Lastly, we demonstrate how our model can be used in predictions for the evolution of hydrate saturation. This thesis includes unpublished co-authored material.

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.

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.

<p>We investigate the dielectrophoretic separation of microparticles. Two different models are formulated in two characteristic time scales. The first model mainly accounts for the orientation behavior and rotational motion of non-spheric microparticles. The concept of effective charge is suggested to calculate the finite size non-spheric particles. It is combined with the fluid particle dynamics method to calculate hydrodynamic as well as dielectrophoretic forces and torques. The translational motion and the particle-particle interaction are calculated also, but they take much longer time to be observed due to the different time scales of the rotational and translational motions By viewing the particle as spheres, the second model focus on the translational motion of spheres. The hydrodynamic force between particles and particle-particle electrostatic interactions are also taken into account. We check the relative magnitude ratio between these forces in order to determine the importance of these forces. To predict and guide the design of experimental dielectrophoretic separation, two numerical applications are carried out. The first calculation suggests optimum patterns to improve the trapping efficiency of<em> E.coli.</em> cells by applying superimposed AC electric fields. The second calculation finds out the mobility and separation rate of particles which differs in size and electric properties by a multi-step trapping-releasing strategy.</p>

Context: Fluid-particle systems are seldom used in games, the apparent performance costs of simulating a fluid-particle system discourages the developer to implement a system of such. The processing power delivered by a modern GPU enables the developer to implement complex particle systems such as fluid-particle systems. Writing efficient fluid-particle systems is the key when striving for real-time fluid-particle simulations with good scalability. Objectives: This thesis ultimately tries to provide the reader with a well-performing and scalable fluid-particle system simulated in real-time using a great number of particles. The fluid-particle system implements two different fluid physics models for diversity and comparison purposes. The fluid-particle system will then be measured for each fluid physics model and provide results to educate the reader on how well the performance of a fluid-particle system might scale with the increase of active particles in the simulation. Finally, a performance comparison of the particle scalability is made by completely excluding the fluid physics calculations and simulate the particles using only gravity as an affecting force to be able to demonstrate how taxing the fluid physics calculations are on the GPU. Methods: The fluid-particle system has been run using different simulation scenarios, where each scenario is defined by the amount of particles being active and the dimensions of our fluid-particle simulation space. The performance results from each scenario has then been saved and put into a collection of results for a given simulation space. Results: The results presented demonstrate how well the fluid-particle system actually scales being run on a modern GPU. The system reached over a million particles while still running at an acceptable frame rate, for both of the fluid physics models. The results also shows that the performance is greatly reduced by simulating the particle system as a fluid-particle one, instead of only running it with gravity applied. Conclusions: With the results presented, we are able to conclude that fluid-particle systems scale well with the number of particles being active, while being run on a modern GPU. There are many optimizations to be done to be able to achieve a well-performing fluid-particle system, when developing fluid-particle system you should be wary of the many performance pitfalls that comes with it. / Vätskebaserade partikelsystem används sällan inom realtidsspel. Dessa system är väldigt prestandakrävande, till den grad att de avskräcker utvecklare från att implementera dem i sina realtidsspel. GPGPU ger utvecklare möjligheten att implementera komplexa partikelsystem, såsom vätskepartikelsystem, och simulera dessa system i realtid. Den här uppsatsen utforskar två olika fysikmodeller som kan användas för vätskesimulering, och sedan utförs det prestandamätningar under varierande omständigheter. Baserat på dessa prestandamätningar så kan slutsatser dras om hur skalbart ett vätskepartikelsystem är, alltså hur prestandan sjunker i förhållande till antalet partiklar i systemet. Slutsatser som dras efter att samtliga mätningar har utförts är att dessa system har en god skalbarhet, men att det finns många prestandafallgropar man måste se upp för när man utvecklar ett vätskepartikelsystem.

We investigate the dielectrophoretic separation of microparticles. Two different models are formulated in two characteristic time scales. The first model mainly accounts for the orientation behavior and rotational motion of non-spheric microparticles. The concept of effective charge is suggested to calculate the finite size non-spheric particles. It is combined with the fluid particle dynamics method to calculate hydrodynamic as well as dielectrophoretic forces and torques. The translational motion and the particle-particle interaction are calculated also, but they take much longer time to be observed due to the different time scales of the rotational and translational motions By viewing the particle as spheres, the second model focus on the translational motion of spheres. The hydrodynamic force between particles and particle-particle electrostatic interactions are also taken into account. We check the relative magnitude ratio between these forces in order to determine the importance of these forces. To predict and guide the design of experimental dielectrophoretic separation, two numerical applications are carried out. The first calculation suggests optimum patterns to improve the trapping efficiency of E.coli. cells by applying superimposed AC electric fields. The second calculation finds out the mobility and separation rate of particles which differs in size and electric properties by a multi-step trapping-releasing strategy. / QC 20101118