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.

Thesis (Ph. D.)--University of Washington, 2005. / Vita. Includes bibliographical references (leaves 162-177).

The purpose of this thesis is to investigate the crossflow and off-the-surface velocity traces on a moderately swept wing at transonic Mach numbers. Computational Fluid Dynamics (CFD) was used to generate the data used to visualize the flow field. This was done for angles of attack of 6, 7, 8 and 10 degrees at a Mach number of 0.8. An overview of flow topology and singular point theory is given as a means to describe the flow field and describe the differences between it at various angles of attack. After performing an investigation of the crossflow velocity traces it was verified that the use of a line of separation in the flow topology as an indication for flow separation is a necessary condition. It was also found that the crossflow topology is more sensitive to shock location than to angle of attack. It has been verified that a line of separation, as defined by Tobak and Peake [ref 1], in the crossflow is an indication that separation may be present on the surface of the wing. Furthermore, shocks complicate the crossflow. In all of the cases the crossflow just aft of a shock becomes much more complex than it was before the shock. New singular points appear and interactions between singular points arise. As angle of attack is increased the flow topology changes critically only in the change from 6 to 7 degrees. This is the range in angle of attack in which a sudden shift in the location of the shock occurs, so it may be postulated that for this wing the flow topology is more sensitive to shock location as opposed to angle of attack. Comparing the topology between the 7, 8 and 10 degree cases, supports this hypothesis as the topology is similar before and after the shock for each case. The flow topology for each case before the shock is much different then the topology just aft of the shock. The investigation of off-the surface traces has shown that as angle of attack is increased the area of separated flow not only grows but also becomes more complex. For the 6 degree angle of attack case, the region of separated flow was concentrated near the surface and as one moved off the surface the flow quickly returned to the attached flow direction with no singular points. This was the case for the 7 degree angle of attack case only the flow did not reattach until after one moved approximately 0.25 feet off the surface. As the angle of attack was increased the distance off the surface in which the flow returned to moving in the downstream direction increased. Furthermore, as angle of attacked was increased the number of singular points and their intensity grew. It was also verified that in all of the cases investigated the presence of a line of separation was an indication of separated flow. Moreover, in all but two cases there were two lines of separation. One located along the furthest outboard and inboard area of the separated region. No lines of separation were observed in or around attached flow, thus the lines of separation may not only indicate that separation is present but in fact give a location for the separated region. / Master of Science

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

Successive Alkalinity-Producing Systems (SAPS) have proven to be a viable alternative to chemical treatment for renovating acidic mine drainage (AMD). The lack of water quality based design guidelines, however, is believed to be a cause of the variability of SAPS performance in the field. This study monitored eight SAPS systems for the purpose of determining the effect of influent water quality and system design on system performance. Monthly water quality data were obtained for each system over periods ranging from 3 to 5 years. All systems demonstrated an ability to generate alkalinity and/or neutralize acidity. These systems revealed significant correlations between net alkalinity production and log residence time (r = 0.7414), influent total iron (r = 0.7357), and influent non-manganese acidity (r = 0.6919). From these relationships, a calibrated model was developed for predicting SAPS net alkalinity generation. As a compliment to the field study, a series of laboratory-scale SAPS columns were studied for a period of 12 months to examine the effect of residence time on system performance and to monitor the internal changes in water quality. The columns were operated at residence times of 17, 30, 60 hours with three replicates each and were subject to ambient temperature fluctuations. Data revealed that systems with residence times below 25 hours in the organic layer were unable to adequately reduce dissolved oxygen concentrations in the organic layer to prevent limestone armoring. The results of this study suggest water quality based guidelines for designing SAPS systems. / Master of Science