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博碩士論文 etd-0117107-160731 詳細資訊
Title page for etd-0117107-160731
論文名稱
Title
應用非線性數值水槽研究波流與潛式結構物之交互作用
Study on the interactions between submerged bodies and wave-current by a nonlinear numerical wave tank approach
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
98
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2006-12-28
繳交日期
Date of Submission
2007-01-17
關鍵字
Keywords
邊界元素法、總流速勢
total potential, BEM
統計
Statistics
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The thesis/dissertation has been browsed 5692 times, has been downloaded 1482 times.
中文摘要
本文主旨為應用邊界元素法(BEM)求解二維非線性波流與潛式結構物之交互作用,與往昔不同的是本文採用總流速勢(波+流)新觀念來進行研究。造波邊界採用feeding function的方式造波,水槽前後皆設置消波區進行消波,非線性自由液面的邊界條件則採用MEL法(mixed Eulerian-Lagrangian method)進行修正,最後搭配RK4 (Runge-Kutta 4th order method)即可在時間領域中計算自由液面波形與場內全域之流速勢。為能準確計算結構物外力,速度場求解後,立即求解加速度場(acceleration field)之邊界積分法(BIEM),以求得結構物邊界上的加速勢,再透過Bernoulli equation求得結構物承受的外力。
為證明本研究方法之可靠性,首先進行非線性波流數值水槽的檢驗,並與其他學者所作之研究相互比較,結果皆非常接近。接續研究單一圓柱、雙圓柱與矩形結構物的受力在非線性效應不明顯時,發現結果與線性波的模擬也幾近一致,因此可確定本文採用總流速勢來求解是可行的。同時,本文也可提供未來在波流與動態海洋結構物交互作用研究之基礎。
Abstract
The objective of this study is to investigate the fully nonlinear interactions of wave-current and submerged bodies by a BEM-based numerical wave tank (NWT). In this paper, a new concept, a total velocity potential function (a combining form of a regular wave and a uniform current potential function), is adopted to solve the wave-current- body interaction problems. Two sets of the boundary integral equation (BIE) included velocity and local acceleration fields are adopted in order to find the surface wave forms and to calculate the hydrodynamic forces on the body. Applying the linear wave-current solution as a feeding function to the input boundary, it can generate waves similar to a wave maker. A numerical damping zone performed by Cointe(1990) is modified and deployed to dissipate the wave energy of the wave-current field near the end-wall and input boundary. Finally, both Mixed Eulerian-Lagrangian method (MEL) and Runge-Kutta 4th order scheme (RK4) are used to update the water elevation and velocity potential.
To prove the reliability of this study, a fully nonlinear NWT is established and examined by comparing the simulated results with other researches'. It shows well agreement with analytic solutions published by others. On the other hand, three different types of structures which are submerged circular cylinder, rectangular and dual-cylinder are adopted to investigate the effects of nonlinear interactions of wave-current-body. The simulated results in weak nonlinear effect show excellent agreement with the linear solutions. Therefore, we conclude that the current method adopting the total velocity potential in the wave-current-body interaction problems is very robust and stable, and lay a good foundation for the advanced ydrodynamic problems.
目次 Table of Contents
第1 章緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 前言. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 文獻回顧. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 研究目的. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 本文組織. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
第2 章研究方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 二維波流數值水槽. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 波流共存之控制方程與邊界條件. . . . . . . . . . . . . . . . . . 5
2.1.2 邊界積分描寫. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.3 非奇點積分運算. . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.4 奇點積分運算. . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 二維波流與結構物之交互作用. . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 控制方程. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.2 速度場之邊界條件. . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.3 加速度場之邊界條件. . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 三維數值水槽. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.1 控制方程與邊界條件. . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.2 邊界積分描寫. . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.3 非奇點積分運算. . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.4 奇點積分運算. . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4 孤立波造波方式. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.5 最合適的時間步階(time stepping) . . . . . . . . . . . . . . . . . . . . . 22
2.6 水面高程與流速勢的更新(time marching and regridding) . . . . . . . . 22
2.7 控制領域內之速度的求法. . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.7.1 二維內部點微分公式推導. . . . . . . . . . . . . . . . . . . . . . 25
2.7.2 三維內部點微分公式推導. . . . . . . . . . . . . . . . . . . . . . 26
第3 章研究結果與討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1 二維數值模擬結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.1 二維數值模擬結果. . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.2 波流與結構物交互作用結果. . . . . . . . . . . . . . . . . . . . . 40
3.2 三維週期波模擬結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.3 三維潛堤模擬結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.4 三維孤立波碎波結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
第4 章結論與建議. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
附錄A 三維MII 運算範例. . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
附錄B 三維G矩陣的奇點積分運算. . . . . . . . . . . . . . . . . . . . . . . . 79
附錄C 孤立波造波公式. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
附錄D sliding element 說明. . . . . . . . . . . . . . . . . . . . . . . . . . . 84
附錄E 單值函數說明. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
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