京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第22756号 / 工博第4755号 / 新制||工||1744(附属図書館) / 京都大学大学院工学研究科都市社会工学専攻 / (主査)教授 細田 尚, 教授 戸田 圭一, 准教授 音田 慎一郎 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

Liquid wastes discharged from industrial outfalls have been researched for many years in the past. Majority of past studies, initiated in 1960s, were experimental studies mainly focused on basics of discharges such as key geometrical properties. Eventually, more robust experimental studies were performed to measure the mixing properties of effluent discharges with various jet configurations and ambient water conditions. Discharges could be as a means of submerged diffusers or surface channels and receiving water could vary from a homogenous calm ambient to a very complex stratified turbulent cross flow ambient. Depending on the bathymetric and economic situation around an outfall project, submerged discharges are preferred designs for most of ocean outfalls. It is the reason that majority of past studies have evaluated the mixing characteristics of submerged jets. Since early 1990s, the numerical modelling has emerged to support complex fluid mechanic problems. Later in 1990s and early in 2000s, the use of computational fluid dynamic (CFD) tools emerged in predicting the jet properties for the effluent discharges. Since then different numerical models have been developed for different applications. Similar to experimental studies, most of numerical studies have been focused on the submerged dense jet discharges. The current study intends to stay focused on the numerical modelling of such jets too; however, to cover the gaps in the literature. To achieve this, a thorough literature review was performed on the past CFD studies of over past 20 years to better understand what was done and what the gaps are. The results of this thorough review revealed that although there has been a great progress in the CFD studies in the field of effluent discharges, there are some applications that have not been investigated before, yet. It was found that there are some discharge inclinations that were not studied numerically before. Four discharge angles of 60°,75°, 80° and 85° were selected in this study, as previous studies mostly focused on 30° and 45°. The higher inclinations are more suitable for deep water outfalls where terminal rise height of the jet does not attach to the ambient water surface. The numerical model OpenFOAM was used in this study which is based on the Finite Volume Method (FVM) applying LRR turbulence model closure. LRR turbulence models was proved to be a capable choice for effluent discharge modelling. The second gap identified in the comprehensive literature review completed was the submerged dense effluent discharge into shallow water with surface attachment (for both inclined and vertical discharges). There was no previous numerical study of such jets identified. Three different regimes were identified: full submergence, plume contact and centerline impingement regimes (i.e. FSR, PCR and CIR). Key geometrical and dilution properties of these jets at surface contact (Xs, Ss) and return point (Xr, Sr) were extracted numerically and compared to those available from experiments. Two discharge angles (30° and 45°) were investigated based on the available experimental data. Five Reynolds-averaged Navier-Stokes (RANS) turbulence models were examined in this study: realizable k-ε and k-ω SST models (known as two-equation turbulence models), v2f (four equations to model anisotropic behavior) and LRR and SSG turbulence models (known as Reynolds stress models - six equations to model anisotropic behavior). Vertical dense effluent discharges are popular in the design of outfall systems. Vertical jets provide the opportunity to be efficient for a range of ambient currents, where the jet will be pushed away not to fall on itself. This research work investigates worst case scenario in terms of mixing and dilution of such jets: vertical dense effluent discharges with no ambient current and in shallow water where jet impacts the surface. This scenario provides a conservative design criteria for such outfall systems. The numerical modelling of such jets has not been studied before and this research work provides novel, though preliminary, insights in simulations of vertical dense effluent discharges in shallow waters. Turbulent vertical discharges with Froude numbers ranging from 9 to 24 were simulated using a Reynolds stress model (RSM), based on the results from inclined dense discharges to characterize the geometrical (i.e., maximum discharge rise Zm and lateral spread Rsp) and dilution μmin properties of such jets. Three flow regimes were reproduced numerically, based on the experimental data: deep, intermediate and impinging flow regimes.

Tato diplomová práce se zabývá matematickým modelováním vodních vln v blízkosti pobřeží pomocí parciálních diferenciálních rovnic. Cílem této práce je formulace pohybových rovnic a jejich následné numerické řešení s grafickou interpretací dosažených výsledků.

Shallow water equations are widely used to model water flows in the field of hydrodynamics and civil engineering. They are complex, and except for some simplified cases, no analytical solution exists for them. Therefore, the partial differential equations of the shallow water system have been the subject of various numerical analyses and studies in past decades. In this study, we construct a stable and robust finite volume scheme for the shallow water equations over quadtree grids. Quadtree grids are two-dimensional semi-structured Cartesian grids that have different applications in several fields of engineering, such as computational fluid dynamics. Quadtree grids refine or coarsen where it is required in the computational domain, which gives the advantage of reducing the computational cost in some problems. Numerical schemes on quadtree grids have different properties. An accurate and robust numerical scheme is able to provide a balance between the flux and source terms, preserve the positivity of the water height and water surface, and is capable of regenerating the grid with respect to different conditions of the problem and computed solution. The proposed scheme uses a piecewise constant approximation and employs a high-order Runge-Kutta method to be able to make the solution high-order in space and time. Hence, in this thesis, we develop an adaptive well-balanced positivity preserving scheme for the shallow water system over quadtree grids utilizing different techniques. We demonstrate the formulations of the proposed scheme over one of the different configurations of quadtree cells. Six numerical benchmark tests confirm the ability of the scheme to accurately solve the problems and to capture small perturbations. Furthermore, we extend the proposed scheme to the coupled variable density shallow water flows and establish an extended method where we focus on eliminating nonphysical oscillations, as well as well-balanced, positivity preserving, and adaptivity properties of the scheme. Four different numerical benchmark tests show that the proposed extension of the scheme is accurate, stable, and robust.

Title: Barotropic ocean tide model Author: David Einšpigel Department: Department of Geophysics Supervisor: prof. RNDr. Zdeněk Martinec, DrSc., Department of Geophysics Abstract: The main aim of this thesis is developing of a numerical model of an oceanic circulation forced by the lunisolar tidal potential. The circulation is described by the shallow water equations which are derived from the fundamental balance laws assuming that the ratio of the vertical and horizontal dimension of the investigated problem is small, which leads to the formulation of the 2- D task. Furthermore, programs for solving the shallow water equations were written. Their functionality is demonstrated on several examples. The programs include an ephemeridal tidal modul which computes the complete lunisolar tidal potential. Keywords: oceanic flow, shallow water equations, lunisolar tidal potential

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No / Nazarbayev University Seed Grant, entitled “Environmental assessment of sediment pollution impact on hydropower plants”.

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Mathematical modeling of ocean waves is based on the formulation and solution of the appropriate equations of continuity, momentum and the choice of proper initial and boundary conditions. Under the influence of gravity, many free surface water waves can be modeled by the shallow water equations (SWE) with the assumption that the horizontal length scale of the wave is much greater than the depth scale and the wave height is much less than the fluid's mean depth. Furthermore, to describe three dimensional flows in the hydrostatic and Boussinesq limits, the multilayer SWE model is used, where the fluid is discretized horizontally into a set of vertical layers, each having its own height, density, horizontal velocity and geopotential. In this study, we used an explicit staggered finite volume method to solve single and multilayer SWE, with and without density stratification and bathymetry, to understand the dynamic of surface waves and internal waves. We implemented a two-dimensional version of the incompressible DYNAMICO method and compare it with a one-dimensional SWE. For multilayer SWE, we considered both two layer and a linear stratification of density, with very small density gradient, consistent with Boussinesq approximation. We used Lagrangian vertical coordinate which doesn't allow mass to flow across vertical layers. Numerical examples are presented to verify multilayer SWE model against single layer SWE, in terms of the phase speed and the steepness criteria of wave profile. In addition, the phase speed of the barotropic and baroclinic mode of two-layer SWE also verified our multilayer SWE model. We found that, for multilayer SWE, waves move slower than single layer SWE and get steeper than normal when they flow across bathymetry. A series of numerical experiment were carried out to compare 1-D shallow water solutions to 2-D solutions with and without density as well as to explain the dynamics of surface wave and internal wave. We found that, a positive fluctuations on free surface causes water to rise above surface level, gravity pulls it back and the forces that acquired during the falling movement causes the water to penetrate beneath it's equilibrium level, influences the generation of internal waves. Internal waves travel considerably more slowly than surface waves. On the other hand, a bumpy or a slicky formation of surface waves is associated with the propagation of internal waves. The interaction between these two waves is therefore demonstrated and discussed. / Thesis / Master of Science (MSc) / In the modelling of ocean wave, the formulation and solution of appropriate equations and proper initial and boundary conditions are required. The shallow water equations (SWE) are derived from the conservation of mass and momentum equations, in the case where the horizontal length scale of the wave is much greater than the depth scale and the wave height is much less than the fluid's mean depth. In multilayer SWE, the fluid is discretized horizontally into a set of vertical layers, each having its own height, density, horizontal velocity and geopotential. In this study, we used an explicit staggered finite volume method to solve single and multilayer SWE, with and without density stratification and bathymetry, to understand the dynamic of surface waves and internal waves. A series of numerical experiments were carried out to validate our multilayer model. It is found that, in the presence of density differences, surface waves for the multilayer SWE move slowly and get more steep than normal when they flow across bathymetry. Also, a positive fluctuations on free surface generates internal waves at the interior of ocean which propagate along the line of density gradient.

Yes / A two-dimensional model based on OpenTidalFarm is applied to simulate tidal stream flow around turbines. The model is governed by shallow water equations and is able to optimize the layout of the deployed turbine array in terms of maximizing the energy outputs. Three turbine array layouts including two structured layouts (regular and staggered) and one unstructured layout (optimized) are simulated to investigate the effect of turbine layouts on energy extraction. The present study shows that more energy could be extracted when lateral spacing decreases and longitudinal spacing increases within the same domain, namely the effective turbine layout is to deploy more turbines in the first row to extract energy from undisturbed tidal stream, while larger longitudinal spacing will make it possible for tidal stream to recover more before reaching the next turbines row. Taking the tidal stream turbines array around Zhoushan Islands as a case study, results show that the optimized layout can extract 106.8% energy of that extracted by the regular and staggered layout for a full tide in the same marine area. Additionally, the turbine array has a great influence on tidal stream velocities immediately behind the array and has little effect on far-field wake flow. / National Natural Science Foundation Council of China (51879098), and the Marine Renewable Energy Research Project of State Oceanic Administration (GHME2015GC01).