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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 楊德良(Der-Liang Young) | |
dc.contributor.author | Ching-Sen Wu | en |
dc.contributor.author | 吳清森 | zh_TW |
dc.date.accessioned | 2021-06-17T00:01:36Z | - |
dc.date.available | 2015-07-18 | |
dc.date.copyright | 2012-07-18 | |
dc.date.issued | 2012 | |
dc.date.submitted | 2012-07-16 | |
dc.identifier.citation | Bibliography
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dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/65723 | - |
dc.description.abstract | 本論文的主旨在於建立一套系統性的數值模式來模擬自由液面流中含碎波現象之問題。欲處理此複雜的流體動力問題,數值的運算通常包括二個要件: 一、可靠而有效率的運算核心 。二、精確的自由液面捕捉方式。首先,在運算核心部份,我們分別嘗試運算子拆解法與SOLA數值技術求解原始變數型態的奈維爾-史托克斯方程式。再者,數值上常見的自由液面的捕捉方式分別為表面追蹤法以及表面捕捉法,二者皆於文中個別做探討。本文主要提出二種處理方式來模擬自由液面的變化,分別使用修正型的高度函數法以及改良型的流體體積法計算之,其主要區別在於描述液面含有碎波現象與否。上述二方法的共通點皆基於滿足質量或體積守恆的條件下做流體動力的分析。此外,於數值驗證中若物理條件包含水中結構物,則採用結合卡氏沈浸邊界法的結構性網格描述其運動行為。最後,擬將以上所提出的要件做結合即可處理自由液面流中含有碎波現象的問題。文中所有數值計算的結果和文獻資料比較都相當吻合,以證明此數值模式開發的可行性。 | zh_TW |
dc.description.abstract | The thesis is concerned with developing a numerical model to study the breaking free-surface flow problem. However, such a robust numerical model in computational fluid dynamics must be composed of the reliable flow solver and the accurate prediction of variations of free surface. At first, the mathematical model is based on solving the Navier-Stokes equations with the operator splitting procedure by a two-step projection method or a solution algorithm with successive over relaxation scheme. Second, to capture the configurations of free surface, the interface tracking and the interface capturing treatments are both concerned in this thesis. Two accurate methods, including the modified height function method and the advanced volume of fluid method, are respectively proposed. The difference between the two proposed methods depends on the access of describing the breaking effects or not. The common mission of the two methods is to benefit the rule of mass/volume conservation in computations. However, to describe the motions of obstacle embedded in the fluid, capability of handling the complex geometry is relied on the hybrid Cartesian immersed boundary method. Finally, the links of flow-field solutions and proposed schemes are used to study the free-surface flow problem with liquid-breaking effects. All the numerical results in this thesis are compared favorably with the reference data. Reasonably good agreements can be observed through the developed numerical model. | en |
dc.description.provenance | Made available in DSpace on 2021-06-17T00:01:36Z (GMT). No. of bitstreams: 1 ntu-101-D96521007-1.pdf: 10571806 bytes, checksum: c708626e4602743db013ef68120d2e22 (MD5) Previous issue date: 2012 | en |
dc.description.tableofcontents | 摘要 I
Abstract II Table of Contents III List of Figures VII List of Tables XIII Abbreviation XIV Symbol List XVI Chapter 1 Introduction 1 1.1 Background of the free-surface flow problem 2 1.2 Review of the kinematical description of fluid motion 4 1.3 Review of free-surface kinematics 6 1.4 Descriptions of motions of complex solid object in the fluid 9 1.5 Organization of the dissertation 10 Chapter 2 Mathematical Formulations 15 2.1 Navier-Stokes equations 16 2.2 Boundary and initial conditions 17 2.2.1 Wall boundary conditions 17 2.2.2 Free-surface boundary conditions 19 2.2.3 Initial conditions 22 2.3 Computational algorithm 22 2.3.1 Projection method 22 2.3.2 Solution algorithm (SOLA) and successive over relaxation (SOR) method 25 2.3.3 Model testing 27 2.4 Treatments of free-surface flow 29 2.4.1 Height function (HF) method 30 2.4.2 Arbitrary Lagrangian-Eulerian (ALE) method 31 2.4.3 Volume-of-fluid (VOF) method 33 2.5 Stability analysis 35 2.6 Computational Cycle 36 Chapter 3 Simulation of Free-Surface Flows with an Immersed Obstacle by the Finite Element Method 43 3.1 Introduction 44 3.2 Mathematical formulations 48 3.2.1 Governing equations and boundary conditions 48 3.2.2 Combination of ALE scheme and projection methods 49 3.2.3 Discretization of equations by FEM 51 3.2.4 Determination of forcing function 52 3.2.5 Interpolation for boundary conditions of immersed body 53 3.3 Numerical simulations and discussions 55 3.3.1 Vortex shedding behind a circular cylinder 55 3.3.2 Free oscillation in a sloshing tank 57 3.3.3 Free-surface flow problem with a stationary circular cylinder 59 3.3.4 Elevations of free surface induced by an oscillating cylinder 62 3.4 Conclusion 64 Chapter 4 Simulations of Free-Surface Flows with an Embedded Obstacle by the Finite-Difference Method and Modified Height Function Scheme 89 4.1. Introduction 90 4.2 Mathematical formulations of fluid motion with free-surface effects 92 4.2.1 Governing equations 92 4.2.2 Boundary conditions 92 4.2.3 Interpolation for the desired boundary condition 94 4.2.4 Determination of forcing function 95 4.3 Numerical experiments and discussions 95 4.3.1 Validation of the HCIB for vortex shedding behind a circular cylinder 96 4.3.2 In-line oscillating circular cylinder in a fluid 97 4.3.3 Free oscillation in a sloshing tank 100 4.3.4 Sloshing tank on a shaking table 101 4.3.5 Free-surface flow with a stationary obstacle 102 4.3.6 Free-surface elevation deformed by an oscillating moving obstacle 104 4.4 Conclusion 105 Chapter 5 Two-Dimensional Interface Tracking Algorithms of the Free-Surface Problems 117 5.1 Introduction of volume tracking method 118 5.2 Methodology of 2D interface tracking 125 5.2.1 Two-dimensional interface reconstruction algorithm 125 5.2.2 Two-dimensional Lagrangian split advection method 132 5.2.3 Two-dimensional redistribution of volume of fraction 135 5.3 Numerical tests for two-dimensional volume tracking algorithm 137 5.3.1 Translation test of a box 137 5.3.2 Translation tests for hollow geometry 139 5.3.3 Rotation test of Zalesak slotted disk 140 5.3.4 Reversed single vortex tests 142 5.3.5 Reversed deformation field test 145 5.4 Conclusions 146 Chapter 6 Three-Dimensional Interface Tracking Algorithm for the Free Surface Problems 163 6.1 Introduction of 3D interface tracking 164 6.2 Methodology of 3D interface tracking 165 6.2.1 Three-dimensional interface reconstruction algorithm 166 6.2.2 Three-dimensional Lagrangian split advection method 172 6.2.3 Three-dimensional redistribution of volume of fraction 173 6.3. Numerical tests 174 6.3.1 Three-dimensional translation and rotation of a sphere 174 6.3.2 Three-dimensional single vortex test 176 6.3.3 Three-dimensional single vortex with laminar pipe flow and its extreme deformation 177 6.3.4 Three-dimensional deformation field test 179 6.4 Conclusions 181 Chapter 7 Simulations of Free-Surface Flows with Liquid- Breaking Effects 191 7.1 Introduction 192 7.2 Mathematical descriptions and numerical implementations 194 7.2.1 Mathematical formation of the model 194 7.2.2 Numerical implementation 195 7.3 Numerical experiments 197 7.3.1 Plunging breaking test 197 7.3.2 Gravity waves test 199 7.3.3 Collapse of a liquid column 201 7.4 Conclusions 204 Chapter 8 Conclusions and Scope of further research 219 8.1 Conclusions 219 8.2 Scope of further research 221 Appendix A Frequency Response Analyses in Vibroacoustics Using the Method of Fundamental Solutions 223 A.1. Introduction 224 A.2. Problem statements and mathematical formulations 227 A.2.1 Acoustic problem 227 A.2.2 Motion of the beam on elastic foundation 228 A.2.3 Bending vibration analysis of elastic plate 228 A.3 The method of fundamental solutions 230 A.3.1 Fundamental solutions of Helmholtz equation 230 A.3.2 Fundamental solutions to bi-Helmholtz equation for the beam problem 232 A.3.3 Fundamental solutions to bi-Helmholtz equation for the plate problem 232 A.4 Analysis of vibroacoustic systems 233 A.5 Numerical examples and discussions 235 A.5.1 Acoustic-wave propagation over two-dimensional regular topography 235 A.5.2 Acoustic-wave propagation over the two-dimensional irregular topography 237 A.5.3 Two-dimensional vibroacoustic problem 238 A.5.4 Three-dimensional vibroacoustic problem and its application 239 A.6 Conclusions 241 Appendix B 254 Bibliography 255 | |
dc.language.iso | en | |
dc.title | 自由液面流場中含碎波現象之數值模擬 | zh_TW |
dc.title | Numerical Simulations of Breaking Free-Surface Flows | en |
dc.type | Thesis | |
dc.date.schoolyear | 100-2 | |
dc.description.degree | 博士 | |
dc.contributor.oralexamcommittee | 洪宏基,蔡丁貴,陳正宗,許泰文,陳陽益 | |
dc.subject.keyword | 自由液面流,碎波現象,修正型的高度函數法,改良型的流體體積法,卡氏沈浸邊界法, | zh_TW |
dc.subject.keyword | free-surface flow,liquid-breaking effect,modified height function method,advanced volume of fluid method,hybrid Cartesian immersed boundary method, | en |
dc.relation.page | 266 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2012-07-16 | |
dc.contributor.author-college | 工學院 | zh_TW |
dc.contributor.author-dept | 土木工程學研究所 | zh_TW |
顯示於系所單位: | 土木工程學系 |
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ntu-101-1.pdf 目前未授權公開取用 | 10.32 MB | Adobe PDF |
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