Student Number : 9804064R - MSc research report - School of Mechanical, Industrial and Aeronautical Engineering - Faculty of Engineering and the Built Environment / A qualitative and quantitative study of the hydraulic analogy; that is the analogy between flow with a free surface and two dimensional compressible gas flow, is described. The experimentation was done using a water table, and results are compared with Computational Fluid Dynamic (CFD) results for actual free surface flow models, and a fictitious gas model. Different test cases are considered (i) a wedge moving at steady supersonic/supercritical speeds of Froude or Mach number equal to 2.38, 3.12 and 4.31 (ii)unsteady motion of a wedge accelerating to supersonic speeds and then decelerating. Quantitative results for the experimental case are achieved by using a colour encoding slope detection technique. Qualitatively, with respect to wave angles, the fictitious gas case shows the best agreement to the experimental case, but at higher Froude/Mach numbers the free surface models also show good agreement. Quantitatively, with respect to wave location and depth profile, the free surface models show better agreement to the experimental case. For the unsteady case the resulting flow patterns are quite similar for the two cases considered, namely the experimental and free surface CFD cases.

Turbulence is a familiar phenomenon which gives rise to complicated problems in many branches of engineering. Hinze has set forth the following definition for turbulence: "Turbulent fluid motion is an irregular condition of flow in which the various quantities show a random variation in time pnd space coordinates, so that statistically distinct average values can be discerned." Osborne Reynolds (1894) was the first to introduce the notion of statistical mean values into the study of turbulence. He visualized turbulent flow as the sum of mean and eddying motion. By introducing this sum of mean velocity and fluctuating velocity into the Navier-Stokes equations and with the aid of the continuity equation, he derived equations giving relationships between the various components of the fluctuating velocity. It was soon realized that before any further results could be obtained from a theoretical analysis of Reynold;s equations of motion, a mechanism had to be postulated for the ihteraction of fluctuating v~locity components at different points in the turbulent field. Consequently, three decades after Reynold's: work, phenomenological theories of turbulence, such as the momentum-transfer theory of Prandtl (1926), the vorticity transport theory of Taylor (1932) and the similarity theory of Karman (1930) were introduced. Not only are they based on unrealistic physical models, but they do not furnish any information beyond temporal-mean velocity distribution. A complete theory of turbulence should describe the mechanism of production of turbulence, its convection, diffusion, distribution, and eventual dissipation for any given boundary conditions.

No / Free surface flows of practical relevance in many engineering problems are almost always turbulent. In this paper, a numerical model to compute the free surface flow with turbulent effects is presented. The shallow water equations together with a k-ε turbulent model are discretized and simulated using a MUSCL-HANCOCK finite volume scheme. The proposed 2D k-ε shallow water model calculates the depth-averaged quantities such as water depth and velocity profile. The depth-averaged turbulent viscous stresses are determined from the depthaveraged version of a traditional 3D k-ε turbulent model. The numerical model is applied to a flow within channels that contain full depth obstructions. The k-ε turbulent model results are compared with existing Direct Numerical Simulations (DNS) predictions and show a high level of accuracy.

Incompressible free-surface flows involving highly complex and violent phenomena are of great importance to the engineering industry. Applications such as breaking-wave impacts, fluid-structure interaction, and sloshing tanks demand an accurate and noise-free pressure field, and require large-scale simulations involving millions of computation points. This thesis addresses the need with the novel use of a graphics processing unit (GPU) to accelerate the incompressible smoothed particle hydrodynamics (ISPH) method for highly non-linear and violent free-surface flows using millions of particles in three dimensions. Compared to other simulation techniques, ISPH is robust in predicting a highly accurate pressure field, through the solution of a pressure Poisson equation (PPE), whilst capturing the complex behaviour of violent free-surface flows. However, for large-scale engineering applications the solution of extremely large PPE matrix systems on a GPU presents multiple challenges: constructing a PPE matrix every time step on the GPU for moving particles, overcoming the GPU memory limitations, establishing a robust and accurate ISPH solid boundary condition suitable for parallel processing on the GPU, and exploiting fast linear algebra GPU libraries. A new GPU-accelerated ISPH algorithm is presented by converting the highly optimised weakly-compressible SPH (WCSPH) code DualSPHysics and combining it with the open-source ViennaCL linear algebra library for fast solutions of the ISPH PPE. The challenges are addressed with new methodologies: a parallel GPU algorithm for population of the PPE matrix, mixed precision storage and computation, and extension of an existing WCSPH boundary treatment for ISPH. Taking advantage of a GPU-based algebraic multigrid preconditioner for solving the PPE matrix required modification for ISPH's Lagrangian particle system. The new GPU-accelerated ISPH solver, Incompressible-DualSPHysics, is validated through a variety of demanding test cases and shown to achieve speed ups of up to 25.3 times and 8.1 times compared to single and 16-threaded CPU computations respectively. The influence of free-surface fragmentation on the PPE matrix solution time with different preconditioners is also investigated. A profiling study shows the new code to concentrate the GPU's processing power on solving the PPE. Finally, a real-engineering 3-D application of breaking focused-wave impacting a surface-piercing cylindrical column is simulated with ISPH for the first time. Extensions to the numerical model are presented to enhance the accuracy of simulating wave-structure impact. Simulations involving over 5 million particles show agreement with experimental data. The runtimes are similar to volume-of-fluid and particle-in-cell solvers running on 8 and 80 processors respectively. The 3-D model enables post-processing analysis of the wave mechanics around the cylinder. This study provides a substantial step for ISPH. Incompressible-DualSPHysics achieves resolutions previously too impractical for a single device allowing for the simulation of many industrial free-surface hydrodynamic applications.

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.

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

High velocity channels are typically designed to discharge surplus water during severe flood events, and these types of flow are distinguished by high velocity, usually supercritical. A major challenge in high velocity channel design is to predict the free surface flow. Being able to predict the free surface flow profile beforehand can assist in selecting the best design for the channel as a whole. When the flow encounters a bridge pier, the streamline of the flow is separated and pressure may drop to a minimum; in contrast, velocity rises to its maximum value. As a result, cavitation damage may occur. The present study has used the computational fluid dynamics code ANSYS-CFX to investigate a full scale, three-dimensional engineering flow simulation of high velocity channels with different cross sections. The simulations were carried out on a high performance computing HPC cluster with 32 nodes. The code is based on the finite volume method and the Volume of Fluid (VOF) method was used to predict the position of the free surface profile. The impact of variation of the following parameters was investigated in terms of the free surface flow profile, both along the centreline and the wall of the channel: the minimum cavity index, and maximum shear stress on both bed and wall of the channel and on bridge pier; aspect ratio (channel bed width/flow depth), bed and side slopes of the channel, different discharges, which are represented by Froude numbers; the length and thickness of the bridge pier. First, the code sensitivity tools for convergence were examined. For this purpose, cases with different mesh sizes were examined and the best size chosen, depending on computation expense and convergence. Then, different turbulence models, such as the standard k-ε, RNG k-ε, and SST turbulence models were tested. The results show that the standard k-ε gives satisfactory results. Next, efforts were made to establish whether the flow achieved steady state conditions. This involved simulating two cases, one with steady state and the other with a transient state. Comparison of the two results shows that the flow properties do not change after three seconds and stay stable thereafter, so the flow can be considered as attaining a steady state. Finally, symmetry within the model geometry was tested, as this would allow a reduction in computation time, with only one side of the symmetrical model needing to be simulated. Two cases were investigated: firstly a simulation of only half of the channel geometry, and secondly a full geometry simulation. A comparison of the results of each case showed that the flow can be considered symmetrical along the centreline of the channel. Next, the code was validated against both numerical and experimental published results. For the free surface flow profile and velocity distribution the published experimental and numerical work of Stockstill (1996) was used; the ANSYS-CFX code results agree more closely with Stockstill’s experimental data than Stockstill’s numerical data. To test for shear stress distribution on the wall, uniform flow within a trapezoidal cross section channel was investigated and the results compared with those presented in the literature. The comparison shows good agreement between the ANSYS-CFX and published experimental works, for the predicted shear stress distributions on the walls and the bed of the channel. In total, sixty cases were simulated in order to investigate the impact of variations in the aforementioned parameters on maximum flow depth (both along the centreline and the wall of the channel) minimum cavity index, and maximum shear stress on both bed and wall of the channel and on bridge pier. Finally, non-dimensional curves are provided in addition to formulae derived from the data regression, which are intended to provide useful guidelines for designers.

A soleira lateral desempenha um papel importante nos reservatórios de detenção/ retenção (off-line), atuando na captação das vazões afluentes e evitando possíveis enchentes, problema em destaque nos períodos chuvosos das principais capitais brasileiras. Um melhor entendimento do seu comportamento hidráulico possibilitará o desenvolvimento de estruturas laterais mais eficientes. O presente trabalho tem como objetivo criar um modelo da soleira lateral através da tecnologia CFD (Dinâmica dos Fluidos Computacional) e validá-lo através de experimentos em modelo reduzido do Laboratório de Hidráulica da Escola Politécnica da USP. A partir disso, explorar as características hidráulicas do modelo de CFD, como o comportamento dos níveis dágua e a distribuição de velocidades. No estudo da validação estudaram-se três tipos de refinamento de malhas e três modelos de turbulência (k-, k- (RNG) e SST k-). O modelo computacional validado é composto pela malha 3, com um refinamento cerca de 342000 elementos (hexaédricos predominante), e o modelo de turbulência k- (RNG), que apresentaram a maior precisão dos resultados. A análise da distribuição de velocidades possibilitou visualizar uma região de mínima velocidade abaixo da soleira lateral, e também quantificar uma região de baixas velocidades no início da soleira, onde é pequena a eficiência das vazões escoadas. Através do comportamento da superfície dágua foi possível visualizar a região de influência do dispositivo lateral no canal principal. A comparação do coeficiente de descarga do modelo de CFD com trabalhos de outros pesquisadores, um nacional e outro internacional, mostrou a representatividade do modelo criado para condições diferentes. A ferramenta CFD é promissora para o estudo de estruturas hidráulicas, contribuindo para o seu desenvolvimento e aperfeiçoamento. / The side weir plays an important role in the detention / retention tanks (off-line), operating in the uptake of water inflow and preventing possible flooding, which is a highlighted problem on rainy periods of the main Brazilian capitals. A better understanding of the hydraulic behavior allows the development of more efficient lateral structures. This work aims at creating a model of the side weir through CFD technology (Computational Fluid Dynamics) and validating it through experiments on a reduced model of the Laboratório de Hidráulica da Escola Politécnica da USP. Thereafter, explore the hydraulic characteristics of the CFD model, like the behavior of water levels and the velocity distribution. In the validation study, three types of mesh refinement and three turbulence models were studied (k-, k- (RNG) and SST k-). The computational model is validated by the composite mesh 3 with a refinement about 342,000 elements (hexahedral predominant), and the turbulence model k- (RNG), which had the highest precision of results. Analysis of the velocities distribution allowed us to visualize a region of minimum velocity below the side weir, and also to quantify a region of low velocities at the beginning of the weir, where the efficiency of overflows is small. Through water surface behavior it was possible to visualize the influence region of the side device in the main channel. A comparison of discharge coefficient of the CFD model between other works (one national and the other one international) showed the representativeness of the model created for different conditions. The CFD is a promising tool for the study of hydraulic structures, contributing to its development and improvement.

Numerical simulation of mold filling in low pressure die casting is considered in this study. The physical model includes modeling of free surface flow, heat transfer with phase change, surface tension, natural convection together with effect of trapped air in the mold. The governing equations are discretized by control volume finite difference method. The pressure field is computed by two-step projection method and the free surface is tracked by PLIC-VOF method. Water analog model is used for the validation purpose. Good agreement between numerical and experimental results is observed which supports the feasibility of the presented method.