The effect of vegetation on the dissipation of waves is important in understanding the vegetation's role in protecting coastal communities during extreme events such as hurricanes and tsunamis. Numerical modeling makes it possible to study the flow through vegetation fields, but it is important to understand the flow dynamics around one piece of vegetation and validate the numerical model used, before the dynamics of an entire vegetated patch can be modeled and understood. This project validated GPUSPH, a Lagrangian mesh-free numerical model, by determining the optimal characteristics to obtain accurate simulations for flow through a flume with and without an obstruction. The validation of GPUSPH and determination of optimal characteristics was accomplished by varying model particle spacing, sub-particle scale (SPS) turbulence inclusion in the conservation of momentum equation, and kernel weighting function for two test cases. The model particle spacing sets the initial distance between the moving grid points, known as particles, in the system. The SPS turbulence term is intended to account for turbulence generated at the sub-particle scale between the particles. The kernel weighting functions used are the quadratic kernel and the cubic spline kernel. These kernels determine how much influence surrounding particles have on the flow characteristics of an individual particle. The numerical results of these tests were compared with experimental results to obtain conclusions about the accuracy of these simulations. Based on comparisons with experimental velocities and forces, the optimal particle spacing was found to occur when the number of particles was in the high 100,000s for single precision calculations, or mid-range capabilities, for the hardware used in this project. The sub-particle scale turbulence term was only necessary when there was large-scale turbulence in the system and created less accurate results when there was no large-scale turbulence present. There was no definitive conclusion regarding the best kernel weighting function because neither kernel had overall more accurate results than the other. Based on these conclusions, GPUSPH was shown to be a viable option for modeling free-surface flows for certain conditions concerning the particle spacing and the inclusion of the subparticle scale turbulence term.

This research presents an experimental study of the formation of drops of suspensions consisting of a viscous liquid and spherical, neutrally buoyant, noncolloidal particles. Pendant drop formation and low Reynolds number jetting of suspensions are investigated, as is the transition between the two. Throughout, the particles utilized are on the order of 100 μm and the orifice from which the drops are formed is on the order of 1 mm. The presence of the particulate phase causes the structure at pinch-off in the pendant drop regime to change noticeably from that of pure liquids. Thick cone-like structures, termed "spindles" here, form at either end of the slender thread and are the result of particle motions during necking. These spindles become more pronounced with increasing particle concentration. Depending on particle concentration, the particles can have either a destabilizing effect (low concentration) on drop formation or a stabilizing one (high concentration). At low concentrations, the particles lead to earlier rupture of the thread and much shorter jet lengths, while at elevated concentrations the particles stabilize the thread after rupture and lead to fewer satellite drops as well as induce jetting at lower flower rates. A two-stage model has been proposed to describe the necking process for particle-laden suspensions in the pendant drop regime. The first stage occurs when the thread is thick relative to the particles and the effect of the particles can be attributed solely to a change in the effective viscosity of the mixture. The second stage occurs nearer pinch-off when the thread has thinned to only a few particle diameters. In this stage the individual particle motions within the thread determine the behavior and the thread ultimately ruptures over a region of the thread devoid of particles.

Free-surface modelling (FSM) is a highly relevant and computationally intensive area of study in modern computational fluid dynamics. The Elemental software suite currently under development offers FSMcapability, and employs a preconditioned GMRES solver in an attempt to effect fast solution times. In terms of potential solver performance however, multigrid methods can be considered state-of-the-art. This work details the investigation into the use of AlgebraicMultigrid (AMG) as a high performance solver tool for use as black box plug-in for Elemental FSM. Special attention was given to the development of novel and robust methods of addressing AMG setup costs in addition to transcribing the solver to efficient C++ object-oriented code. This led to the development of the so-called Freeze extension of the basic algebraic multigrid method in an object-oriented C++ programming environment. The newly developed Freeze method reduces setup costs by periodically performing the setup procedure in an automatic and robust manner. The developed technology was evaluated in terms of robustness, stability and speed by applying it to benchmark FSM problems on structured and unstructured meshes of various sizes. This evaluation yielded a number of conclusive findings. First, the developed Freeze method reduced setup times by an order of magnitude. Second, the developed AMG solver offered substantial performance increases over the preconditioned GMRES method. In this way, it is proposed that this work has furthered the state-of-the-art of algebraic multigrid methods applied in the context of free-surface modelling. / Dissertation (MEng)--University of Pretoria, 2011. / Mechanical and Aeronautical Engineering / unrestricted

[pt] O processo de revestimento por extrusão é usado na manufatura de diversos produtos. A espessura da camada de líquido depositada é determinada pela vazão de líquido e pela velocidade do substrato, e independe das outras variáveis de operação do processo. Um importante limite de operação deste processo é a espessura mínima que pode ser depositada sobre um substrato a uma determinada velocidade, geralmente chamado de limite de vazão mínima. Para líquidos Newtonianos, o mecanismo que define este limite é o balanço de forças viscosas, de capilaridade e inerciais no escoamento. A pesar da maioria dos líquidos usados em processos de revestimento industriais serem soluções poliméricas ou dispersões que possuem comportamento não Newtoniano, a maioria das análises de limites de operação do processo de revestimento por extrusão são restritas à líquidos Newtonianos. No caso particular de soluções poliméricas as tensões elásticas podem alterar o balanço de forças em diversas regiões do escoamento e consequentemente os limites de operação do processo. Neste trabalho o limite de vazão mínima no caso de líquidos não Newtonianos é analisado teoricamente e experimentalmente. Os modelos constitutivos de Oldroyd-B e Giesekus, que descrevem o comportamento de soluções poliméricas diluídas, em conjunto com as equações de conservação de massa e quantidade de movimento são usados para descrever o escoamento bidimensional que ocorre no processo de revestimento por extrusão. O sistema de equações diferenciais foi resolvido usando o método de elementos finitos. Os resultados mostram como as propriedades viscoelásticas influenciam a distribuição de tensão no escoamento e o balanço de forças nas proximidades da superfície livre à jusante da região de deposição. / [en] Slot coating is a common method in the manufacture of a wide variety of products. The thickness of the coated liquid layer is set by the flow rate fed to the coating die and the speed of the substrate, and is independent of other process variables. An important operating limit of slot coating is the minimum thickness that can be coated at a given substrate speed,generally referred to as the low- flow limit. For Newtonian liquids, the mechanism that defines this limit balances the viscous, capillary and inertial forces in the flow. Although most of the liquids coated industrially are polymeric solutions and dispersions that are not Newtonian, most of the previous analyses of operability limits in slot coating dealt only with Newtonian liquids. In the case of liquids made non- Newtonian by polymer viscoelasticity, stresses can alter the force balance in various parts of the coating bead and consequently the onset of instability. In this work, the low-flow limit in cases of non-Newtonian liquids is examined by both theory and experiment. The Oldroyd-B and Giesekus constitutive equations that approximate viscoelastic behavior of polymer solutions were used, together with momentum and continuity equations, to model two-dimensional flow in the downstream part of a slot coating bead. The equation system was solved with the Finite Element Method. The results show how the viscoelastic properties can affect the stress field in the liquid and the force balance near and at the downstream meniscus, thereby illustrating how non-Newtonian behavior can alter the flow instabilities that determine the coating window of slot coating. The flows themselves were visualized by video microscopy and the low-flow limit was found by observing, at given substrate speed, the feed rate at which the flow becomes unstable. Different solutions of low molecular weight polyethylene glycol and high molecular weight polyethylene oxide in water were used in order to evaluate the effect of mildly viscoelastic behavior on the process.

O tema deste trabalho é o estudo de métodos numéricos para a simulação de escoamentos incompressíveis com superfície livre a baixos Reynolds, por meio da metodologia GENSMAC e suas formulações explícita e implícita. Neste contexto, temos especial interesse na formulação implícita, objetivando o enfraquecimento da restrição de estabilidade parabólica no passo temporal em escoamentos com superfície livre. O trabalho pode ser dividido em duas partes: na primeira, algumas modificações são discutidas, propostas e testadas com o objetivo de tornar a formulação implícita mais eficiente e precisa; em seguida, aproveitamos os resultados obtidos e generalizamos o método numérico existente para simular escoamentos viscoelásticos modelados pela equação constitutiva SXPP. Em ambos os casos, a formulação explícita também é usada para comparação e teste. Resultados que demonstram a eficiência e robustez das técnicas desenvolvidas são apresentados por meio da simulação numérica de complexos problemas envolvendo superfície livre.O tema deste trabalho é o estudo de métodos numéricos para a simulação de escoamentos incom- pressíveis com superfície livre a baixos Reynolds, por meio da metodologia GENSMAC e suas formulações explícita e implícita. Neste contexto, temos especial interesse na formulação implícita, objetivando o en- fraquecimento da restrição de estabilidade parabólica no passo temporal em escoamentos com superfície livre. O trabalho pode ser dividido em duas partes: na primeira, algumas modificações são discutidas, propostas e testadas com o objetivo de tornar a formulação implícita mais eficiente e precisa; em seguida, aproveitamos os resultados obtidos e generalizamos o método numérico existente para simular escoamentos viscoelásticos modelados pela equação constitutiva SXPP. Em ambos os casos, a formulação explícita também é usada para comparação e teste. Resultados que demonstram a eficiência e robustez das técnicas desenvolvidas são apresentados por meio da simulação numérica de complexos problemas envolvendo superfície livre / The purpose of this work is the study of numerical methods for low Reynolds number incompressible free surface flows, including the GENSMAC methodology and its explicit and implicit formulations. In this context, we have special interest in the implicit formulation, in order to circumvent the parabolic stability restriction in the time step for free surface flows. The work can be divided into two parts: firstly, some modifications are proposed, discussed, and tested with the purpose of making the implicit formulation more e¢ cient and accurate; secondly, we take advantage of the results derived in the first part to generalize the numerical method for simulating viscoelastic free surface flows modeled by the constitutive equation SXPP. In both cases, the explicit formulation is also used for comparison and tests. Results that demonstrate the e¢ ciency and robustness of the developed techniques are presented and illustrated by the numerical simulation of complex problems involving free surface flows

A numerical solution algorithm based on finite volume method is developed for unsteady, two-dimensional, depth-averaged shallow water flow equations. The model is verified using test cases from the literature and free surface data obtained from measurements in a laboratory flume. Experiments are carried out in a horizontal, rectangular channel with vertical solid boxes attached on the sidewalls to obtain freesurface data set in flows where three-dimensionality is significant. Experimental data contain both subcritical and supercritical states. The shallow water equations are solved on a structured, rectangular grid system. Godunov type solution procedure evaluates the interface fluxes using an upwind method with an exact Riemann solver. The numerical solution reproduces analytical solutions for the test cases successfully. Comparison of the numerical results with the experimental two-dimensional free surface data is used to illustrate the limitations of the shallow water equations and improvements necessary for better simulation of such cases.

O tema deste trabalho é o estudo de métodos numéricos para a simulação de escoamentos incompressíveis com superfície livre a baixos Reynolds, por meio da metodologia GENSMAC e suas formulações explícita e implícita. Neste contexto, temos especial interesse na formulação implícita, objetivando o enfraquecimento da restrição de estabilidade parabólica no passo temporal em escoamentos com superfície livre. O trabalho pode ser dividido em duas partes: na primeira, algumas modificações são discutidas, propostas e testadas com o objetivo de tornar a formulação implícita mais eficiente e precisa; em seguida, aproveitamos os resultados obtidos e generalizamos o método numérico existente para simular escoamentos viscoelásticos modelados pela equação constitutiva SXPP. Em ambos os casos, a formulação explícita também é usada para comparação e teste. Resultados que demonstram a eficiência e robustez das técnicas desenvolvidas são apresentados por meio da simulação numérica de complexos problemas envolvendo superfície livre.O tema deste trabalho é o estudo de métodos numéricos para a simulação de escoamentos incom- pressíveis com superfície livre a baixos Reynolds, por meio da metodologia GENSMAC e suas formulações explícita e implícita. Neste contexto, temos especial interesse na formulação implícita, objetivando o en- fraquecimento da restrição de estabilidade parabólica no passo temporal em escoamentos com superfície livre. O trabalho pode ser dividido em duas partes: na primeira, algumas modificações são discutidas, propostas e testadas com o objetivo de tornar a formulação implícita mais eficiente e precisa; em seguida, aproveitamos os resultados obtidos e generalizamos o método numérico existente para simular escoamentos viscoelásticos modelados pela equação constitutiva SXPP. Em ambos os casos, a formulação explícita também é usada para comparação e teste. Resultados que demonstram a eficiência e robustez das técnicas desenvolvidas são apresentados por meio da simulação numérica de complexos problemas envolvendo superfície livre / The purpose of this work is the study of numerical methods for low Reynolds number incompressible free surface flows, including the GENSMAC methodology and its explicit and implicit formulations. In this context, we have special interest in the implicit formulation, in order to circumvent the parabolic stability restriction in the time step for free surface flows. The work can be divided into two parts: firstly, some modifications are proposed, discussed, and tested with the purpose of making the implicit formulation more e¢ cient and accurate; secondly, we take advantage of the results derived in the first part to generalize the numerical method for simulating viscoelastic free surface flows modeled by the constitutive equation SXPP. In both cases, the explicit formulation is also used for comparison and tests. Results that demonstrate the e¢ ciency and robustness of the developed techniques are presented and illustrated by the numerical simulation of complex problems involving free surface flows

Aeration issued through a ventilation shaft is an important measure to prevent cavitation and large gauge pressure in flood discharge tunnels. In order to dimension the ventilation shaft appropriately, itis necessary to have a good understanding of the air-water flow in the tunnel. In this study, the multiphase flow through a discharge tunnel was simulated in the computational fluid dynamics (CFD) software ANSYS Fluent. Since the flow was separated, the simulation setup used the volume of fluid (VOF) multiphase model, that could track the water surface. Furthermore, the so called RNG k-epsilon turbulence model was used. The CFD model was validated with measured data provided from two open channel experiments carried out on a scaled model at Sichuan University. To ensure mesh independence, grid convergence index (GCI)studies were performed for the two validating cases. After the validation, a top wall and a ventilation shaft was added to the CFD model. The flow was then simulated for four different shaft designs and four different water inlet velocities. The air demand and air supply for the various scenarios could thereby be calculated. The results of this study were also compared with previous research on multiphase flow through tunnels with similar design. It was concluded that the air flow downstream in the tunnel converged for the two larger designs. It was also concluded that the air demand in the tunnel was satisfied for the larger ventilation shafts. A smaller study on cavitation was made and the risk was considered non-existent for all the simulated cases.

No description available.

<p> </p> <p>Interfaces separating two fluids are incredibly complex physical structures and are common throughout science, technology, and nature. Examples from daily life include the air-water interface separating a water drop that is dripping from a leaky faucet from the surrounding air and the interface of a soap bubble (which actually consists of two interfaces) separating the interior of the bubble from its exterior. Other common examples from nature include interfaces between falling rain drops and the surrounding air, and the mist that one encounters at beaches, waterfalls, and fountains where the spray droplets are separated from the surrounding air by an interface. Interfaces and manipulating them are key to technological applications such as thin film coating flows and diverse processes involving drop-by-drop processing such as ink-jet printing, drop-wise manufacturing, spray coating, DNA microarraying, and chemical separations, e.g. extraction. Aside from the coating flows example, the aforementioned situations are all examples of free surface flows that involve abrupt and catastrophic topological changes of interfaces that include physical processes such as breakup (also called pinch-off) as in drop breakup, rupture as in liquid-film or liquid-sheet rupture, and coalescence as in drop or bubble coalescence (similar phenomena also arise in sintering and/or fusion of ceramic, metallic, and polymer particles). These topological changes entail what are referred to as finite-time hydrodynamic singularities. For example, at the location(s) where a drop breaks, the thickness of the drop locally tends to zero while fluid pressure and velocity diverge (hence the reason for the word singularity). In addition to hydrodynamic singularities, the presence of surface-active agents or surfactants at fluid interfaces in free surface flows is another reason scientists have been attracted to the study of such problems.</p> <p>Adsorption onto and lowering of the surface tension of a fluid interface by surfactants are exploited in applications such as enhanced oil recovery, coating flows, lung surfactants, drop/jet breakup, and film/sheet rupture, with the latter two being among the prime motivators for this PhD thesis. However, surfactant concentration can be nonuniform at the interface because surfactant molecules can be transported along it by convection and diffusion and also due to normal dilatation and tangential stretching of the interface. Thus, aside from simply lowering surface tension, nonuniformity in surfactant concentration causes gradients in surface tension and gives rise to tangential interfacial (Marangoni) stresses. The latter brings about rich physics including tears of wine, interfacial turbulence in mass transfer, and droplet bouncing. In addition to lowering surface tension and the Marangoni effect, surfactants may also induce surface rheological or viscous effects as surfactant molecules deform against each other. The primary goal of this thesis is to advance the understanding of surface rheological effects in situations involving the breakup of surfactant-covered liquid threads (which also includes jets and drops) and liquid sheets. The fundamental understanding developed in this thesis is likely to prove indispensable in and/or assist the development of new technologies where surface rheological effects are central to the processes at hand, e.g. in controlling drop size distributions and avoiding undesirable satellite droplets and/or misting. An initially unexpected but highly rewarding outcome of the research has been the development of techniques for the measurement of surface viscosities, a task that has heretofore proven to be a formidable challenge to experimentalists.</p> <p>In this thesis, surface rheological effects in free surface flows are examined through both analytical and numerical solution of the incompressible Navier-Stokes equations subjected to the traction boundary condition augmented by the Boussinesq-Scriven constitutive equation to account for surface viscous effects. Rigorous and robust numerical algorithms based on the Galerkin finite element (GFEM) method are developed for predictions of surfactant transport, surface rheological effects and hydrodynamics in response to the motion of moving boundaries. The accuracy of computational predictions is verified by demonstrating that computed results accord well with scaling theories.</p>