Soft and deformable silicone rubber spheres ricochet from a water surface when rigid spheres and disks (or skipping stones) cannot. This dissertation investigates why these objects are able to skip so successfully. High speed cameras allow us to see that these unique spheres deform significantly as they impact the water surface, flattening into pancake-like shapes with greater area. Though the water entry behavior of deformable spheres deviates from that of rigid spheres, our research shows that if this deformation is accounted for, their behavior can be predicted from previously established methods. Soft spheres skip more easily because they deform significantly when impacting the water surface. We present a diagram which enables the prediction of a ricochet from sphere impact conditions such as speed and angle. Experiments and mathematical representations of the sphere skipping both show that these deformable spheres skip more readily because deformation momentarily increases sphere area and produces an attack angle with the water which is favorable to skipping. Predictions from our mathematical representation of sphere skipping agree strongly with observations from experiments. Even when a sphere was allowed to skip multiple times in the laboratory, the mathematical predictions show good agreement with measured impact conditions through subsequent skipping events. While studying multiple impact events in an outdoor setting, we discovered a previously unidentified means of skipping, which is unique to deformable spheres. This new skipping occurs when a relatively soft sphere first hits the water at a high speed and low impact angle and the sphere begins to rotate very quickly. This quick rotation causes the sphere to stretch into a shape similar to an American football and maintain this shape while it spins. The sphere is observed to move nearly parallel with the water surface with the tips of this “football” dipping into the water as it rotates and the sides passing just over the surface. This sequence of rapid impact events give the impression that the sphere is walking across the water surface.

A parallel numerical method has been implemented for solving the Navier Stokes equations on Cartesian and non-orthogonal meshes. To ensure the accuracy of the code first, second and third order differencing schemes, with and without flux-limiters, have been implemented and tested. The most computationally expensive task in the code is the solution of linear equations, and a number of linear solvers have been tested to determine the most efficient. Krylov space, incomplete factorisation, and other iterative and direct solvers from the literature have been implemented, and have been compared with a novel black-box multigrid linear solver that has been developed both as a solver and as a preconditioner for the Krylov space methods. To further reduce execution time the code was parallelised, after a series of experiments comparing the suitability of different parallelisation techniques and computer architectures for the Navier Stokes solver. The code has been applied to the solution of two classes of problem. Two natural convection flows were studied, with an initial study of two dimensional Rayleigh Benard convection being followed by a study of a transient three dimensional flow, in both cases the results being compared with experiment. The second class of problems modelled were free surface flows. A two dimensional free surface driven cavity, and a two dimensional flume flow were modelled, the latter being compared with analytic theory. Finally a three dimensional ship flow was modelled, with the flow about a Wigley hull being simulated for a range of Reynolds and Froude numbers.

This article aims to design an innovative polishing method that can do polishing job to a complicated axial symmetric free surface. The main task of the system is to increase the precision of a middle size (diameter range from 50mm to 150mm) free surface with low precision (form error is larger than 10£gm, even reach few hundred £gm. By using the developed polishing system, the precision is expected to reach and order of sub-micron. It is a machining method which able to outcome a precise free surface, and also a high efficient free surface machining method compared to machining technique nowadays. At the beginning of this article, a logical thinking method will be used to set up a number of sub-targets from the task of the article. From those sub-targets, the keys of the polishing method would come out to accomplish the task. They are: 1.The machining tool is deformable and able to match up the shape of the surface of the tool to enlarge the polishing area. This will increase the efficiency of the machining method; 2.The pressure distribution between the tool and work piece is controllable to let the surface area with larger error form has larger machining rate. By accomplish the sub-targets above, a set of form error compensate strategy can be use to remove the error profile of the free surface with high efficiency. To increase the efficiency of the polishing system, the analysis of the force guide by ANSYS (a finite element analysis software) will be done to create a relation between the force applied and the pressure distribution. This will make the pressure distribution construction task easy and the efficiency of polishing will be increased. According to the machining method designed above, a prototype polishing machine will be designed, and a series of experiments will be done on the designed prototype polishing machine to test the workability of the polishing method. The outcome of the experiments shows that the machine not only has good repeatability, but also has a very high machining efficiency. Besides, the machining distribution experiment shows that the machining method has ability to remove the error distribution from the free surface. It means that is able to do precision machining job to the free surface.

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.

Significant quantities of hydrocarbons are found in complex salt environments. One of the modern challenges of exploration and production activities is to image below salt. This challenge arises from the complexities of salt structures, weak primaries from the subsalt, and the interference of free-surface multiples with the weak primaries of the subsalt. To effectively process subsalt data, we need to develop a method of attenuating free-surface multiples that preserves the amplitude and phase of primaries and does not introduce artifacts at either near and far offsets. In this thesis, we will demonstrate that the weak primaries of the subsalt can be preserved while attenuating free-surface multiples. The method used for the demonstration is the bottom-multiple generator (BMG) reflector approximation. This technique requires that a portion of the data containing only primaries be defined. A multidimensional convolution of the data containing only primaries with the actual data will predict free-surface multiples and hence is used to attenuate free-surface multiples from the actual data. This method is one of the most effective methods for attenuating free-surface multiples; however, the method requires muting data at the BMG location. One of the issues investigated in this thesis, is to establish the sensitivity of the BMG demultiple technique when the mute at the BMG location end up cutting some seismic reflections, which can be the case in complex environments such as the Gulf of Mexico and Gulf of Guinea, where freesurface multiples interfere with primaries. For this investigation, we generated synthetic data through the 2D elastic finite-difference modeling technique. The synthetic seismic data contain primaries; free-surface multiples, and internal multiples, and direct waves acquired over a 2D geological model that depicts a shallow-water geology. In this thesis, we also investigate if the first step of the BMG demultiple technique can sufficiently attenuate free-surface multiples. For this investigation, we designed a 2D geological model, which depicts the deep offshore environment, and we generated synthetic data through the 2D elastic finite-difference modeling technique. After performing the various investigations mentioned above, the following conclusions were made, that the demultiple result is not affected when the mute at the BMG location end up cutting some primaries, that the first step of the BMG demultiple technique is not sufficient for the demultiple, and that the weak subsalt primaries are preserved during demultiple processes. We compared shot gathers and zero offset data before and after the demultiple.

The goal of this thesis is to develop a novel polishing tool system. This system can be attached to a CNC machine and execute a precision polishing job mainly for an axially symmetric free surface. The precision polishing job is to remove the error surface profile on the work to improve its form precision, which was left by the previous machining process. An inferential rule, which was based on a top-down planning strategy, was utilized to gradually decompose the design goals of the tool system to facilitate the process for generating all of the possible design proposals. The major design goal is to render all the rotational axes of the tool system to exactly intersect at the tool center. To analyze the effects of the structure and interface stiffness of tool system on the major goal, the finite element method was adopted. Further, the homogeneous transformation scheme is applied to establish the forward kinematic error of the designed system and to analyze the effect of different manufacturing and assembly errors on the major goal.Accordingly, two novel polishing tool systems were developed. The simulation study indicated that the total errors after assembly at the tool center and the two rotation axes were dominated by the stiffness at the interfaces of the tool system, in addition to the influence of structure stiffness. An assembly strategy was then proposed in the study to reduce the total error.

A parallel numerical method has been implemented for solving the Navier Stokes equations on Cartesian and non-orthogonal meshes. To ensure the accuracy of the code first, second and third order differencing schemes, with and without flux-limiters, have been implemented and tested. The most computationally expensive task in the code is the solution of linear equations, and a number of linear solvers have been tested to determine the most efficient. Krylov space, incomplete factorisation, and other iterative and direct solvers from the literature have been implemented, and have been compared with a novel black-box multigrid linear solver that has been developed both as a solver and as a preconditioner for the Krylov space methods. To further reduce execution time the code was parallelised, after a series of experiments comparing the suitability of different parallelisation techniques and computer architectures for the Navier Stokes solver. The code has been applied to the solution of two classes of problem. Two natural convection flows were studied, with an initial study of two dimensional Rayleigh Benard convection being followed by a study of a transient three dimensional flow, in both cases the results being compared with experiment. The second class of problems modelled were free surface flows. A two dimensional free surface driven cavity, and a two dimensional flume flow were modelled, the latter being compared with analytic theory. Finally a three dimensional ship flow was modelled, with the flow about a Wigley hull being simulated for a range of Reynolds and Froude numbers.

Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第14147号 / 工博第2981号 / 新制||工||1442(附属図書館) / 26453 / UT51-2008-N464 / 京都大学大学院工学研究科都市環境工学専攻 / (主査)教授 後藤 仁志, 教授 細田 尚, 准教授 牛島 省 / 学位規則第4条第1項該当

L'objectif principal de cette étude consiste à réduire les temps de calcul des simulations de procédés de mise en forme continus sous le logiciel Forge3®. Ces procédés, tel que le laminage et le tréfilage, sont caractérisés par des pièces dont la longueur est très importante en comparaison des dimensions de la section ainsi que de la zone de contact. Une approche incrémentale générale implique des temps de calcul conséquents allant de quelques heures à plusieurs jours. En se concentrant sur le régime quasi permanant de ces procédés, une formulation stationnaire est développée pour accélérer leur simulation. Le domaine de calcul correspond initialement à une estimation de la forme de l'écoulement solution au voisinage des outils. Une étape de correction du domaine est ajoutée en plus du calcul stationnaire de l'écoulement. Comme les conditions aux limites sont modifiées, ces deux étapes sont répétées jusqu'à convergence.L'étude s'est concentrée principalement sur l'étape de correction du domaine correspondant à la résolution d'un problème de surface libre par la méthode des éléments finis. Le caractère purement convectif du problème ainsi que la prise en compte du contact nécessite l'utilisation de formulations faibles faisant apparaître un décalage amont (SUPG). Deux nouvelles formulations basées sur la méthode des moindres carrés sont développées avec succès (MC_supg et MC_lc). Pour appliquer la méthode à des géométries complexes, différentes méthodes de généralisations sont développées où un 2ème degré de liberté est ajouté aux nœuds de surface. La méthode la plus performante (CSL_dif) consiste à utiliser ce 2ème degré de liberté pour le calcul de surface libre uniquement sur les nœuds appartenant à une arête géométrique, pour les autres une régularisation du maillage dans la direction tangente y est effectuée. Des résultats excellents ont été observés sur un grand nombre de cas tests analytiques. Le contact est appliqué par une méthode de pénalisation aux nœuds. Afin de renforcer le couplage entre cette étape et celle du calcul de l'écoulement, un contact bilatéral glissant est attribué aux nœuds en compression alors que pour les autres nœuds un contact unilatéral est employé. Un algorithme spécifique est développé pour déterminer avec précision la zone de contact.Cette formulation itérative pour la recherche de l'état stationnaire a été appliquée avec succès sur un grand nombre de cas tests de mise en forme. Des accélérations comprises entre 10 et 60 ont été obtenues par rapport à Forge3®. / The aim of this study is to reduce the computational time for the simulation of continuous material forming processes with Forge3® software. These processes, like rolling and wire drawing, are characterized by an important length of the pieces in comparison to their sectional's dimensions and to the local contact area. A general and incremental approach requires important computational times ranging from a few hours to several days. By focusing on the quasi permanent regime of these processes, a stationary approach is developed to speed up their simulation. The computational domain consists of an initial guess of the steady flow near the tools. A domain correction stage is added after the computation of the steady flow. As boundary conditions are changed, these two stages are repeated until the convergence is reached.Most of the works is concentrated on the domain correction which is a free surface problem solved by the finite elements method. As it is a case of a pure convection problem where the treatment of contact is necessary, weak formulations have to show up an upwind shift (SUPG). Two new formulations based on the least squares method have been successfully developed (MC_supg, MC_lc). To take into account complex geometries, severals new methods have been developed by adding a second degree of freedom for surface nodes. The most efficient method (CSL_dif) uses this second degree of freedom for free surface computation only for nodes belonging to geometric edges, whereas the other nodes have a mesh regularization in tangent direction of the surface. Excellent results are obtained for many analytical test cases. A penalization method is used to apply contact equations on nodes. In order to enforce the coupling between this stage and the one for the computation of the flow, a bilateral sliding contact is assigned to the nodes in compression, whereas for the others a unilateral contact is used. A specific algorithm has been developed to efficiently compute the contact area.This iterative formulation for the search of the steady state is successfully used on a large number of material forming test cases. Important accelerations are gained compared to Forge3®, ranging from 10 to 60.