三維剛性與可變形多面體之流固耦合運動分析

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鄧兆廷(Chao-Ting Deng) 查詢紙本館藏

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土木工程學系

論文名稱

三維剛性與可變形多面體之流固耦合運動分析
(Motion Analysis of 3D Rigid and Deformable Polyhedrons Interacted with Fluid)

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至系統瀏覽論文 (2027-12-31以後開放)

摘要(中)

三維流固耦合行為是生活中處處可見的現象，小如浮球於水中的載浮載沉、風扇運轉推動空氣而造成的風場變化，大則受風力影響的摩天大樓搖擺或者橋梁振動、河川於急流下的沖刷行為，甚至如浮台式風力發電機同時受風和水作用，造成扇葉轉動與浮台浮動的多相流體與固體耦合現象，隨著市面上各式相關的分析軟體，與計算力學在此領域日漸成熟的發展，提供了工程師們許多工具可以處理流固耦合的複雜物理問題。
本研究以柔性體的流固耦合分析模式為基礎，開發另一剛性多面體的流固耦合程序，可依照使用者需求選擇剛體或可變形體的模組做模擬與分析，流體程式使用的是美國Los Alamos National Laborary所開發的軟體Truchas，求解三維不可壓縮流體之Navier-Stokes方程，以流體體積法(Volume of Fluid, VOF)追蹤各相流體運動行為，再利用移動固體法(Moving Solid Algorithm, MSA)計算固體移動後與各流體之互制行為。
固體部分將結構物離散成四面體元素組成，可使用向量式有限元素法(Vector Form Intrinsic Finite Element, VFIFE)進行柔性體的運動求解，以節點為參考計算受力的位移，並以逆向運動扣除元素的剛體運動求解變形及運動，剛性體程序則是以離散元素法(Discrete Element Method, DEM)來進行運動求解，以各離散四面體的慣性矩、慣性積，使用平行軸定理組合成整個結構體的慣性張量，找出主軸、主慣性矩後以塊體的質心做為參考點，分析受流體作用的合力與合力矩下之剛體運動分析。此一雙向的流固耦合分析程序，可模擬分析多相流體與固體的耦合行為，且程式碼為開放式的特性，完全可以依照需求來增加其分析模組，並可廣泛應用於工程上的流固耦合問題。

摘要(英)

The three-dimensional fluid-solid coupling behavior is a very common phenomenon in our life. It is as small as the floating and sinking of a floating ball in the water, and the wind field changes caused by the fan running to push the air, or as big as the swaying of skyscrapers or the vibration of bridges that are affected by wind, and the scouring behavior of rivers under the rapids, even if the floating wind turbine is affected by wind and water at the same time, the multiphase fluid and solid coupling phenomenon caused by the rotation of the fan blade and the floating of the floating platform, with various related analysis software on the market, and the maturing development of computational mechanics in this field, provides engineers with many tools to deal with the complex physics problem of fluid-structure interaction.
Based on the original fluid-structure coupling program of the flexible body, this paper develops another fluid-structure coupling program for a rigid body. According to the user′s needs, a rigid or a deformable body module can be selected for simulation and analysis. The fluid program uses Truchas which developed by Los Alamos National Laborary, solves the Navier-Stokes equations of three-dimensional incompressible fluids, uses the Volume of Fluid (VOF) method to track the fluid motion behavior of each phase, and then uses the Moving Solid Algorithm (MSA) method to calculate the interaction between the solid and each fluid after moving.
The solid is composed of discrete structures into tetrahedral elements, and the motion of the flexible body is solved using the Vector Form Intrinsic Finite Element (VFIFE) method. Deduct the rigid body motion of the elements to solves the deformation, and the rigid body program uses the Discrete Element Method (DEM) to solve the motion, using the inertia moment and inertia product of each discrete tetrahedron, the parallel axis theorem is used to accumulate and combine the inertia tensor of the entire structure, after find out the main axis and the main moment of inertia, then taken as the reference point of the mass center of the block to analyze the rigid body motion, which under the resultant force and resultant moment acted by the fluid. This two-way fluid-solid coupling analysis program can simulate and analyze the coupling behavior of multiphase fluids and solids, because the code is open-ended, so its analysis modules can be added according to requirements, and it can be widely used in engineering fluids-solid coupling problem.

關鍵字(中)

★ 流固耦合
★ 多相流體
★ 多面體
★ 向量式有限元素法
★ 離散元素法

關鍵字(英)

★ fluid-structure interaction
★ multiphase fluid
★ polyhedron
★ vector form intrinsic finite element method
★ discrete element method

論文目次

摘要 i
Abstract ii
致謝 iv
目錄 v
圖目錄 viii
表目錄 xii
第一章、緒論 1
1-1 研究動機與目的 1
1-2 研究方法的特色 2
1-3 論文架構 3
第二章、文獻回顧 4
2-1 流固耦合 4
2-2 向量式有限元素法 7
2-3 時間積分法 8
2-4 離散元素法 9
2-5 浮台式離岸風機 10
第三章、流固耦合介面程序 12
3-1 流體計算力學理論 12
3-1-1 控制方程式 12
3-1-2 流體體積法(Volume of Fluid) 14
3-1-3 有限體積法(Finite Volume Method) 16
3-1-4 改良投影法(分步法) 18
3-1-5 大渦流LES模式 20
3-1-6 有效沉浸邊界法(Effective Immersed Boundary Method, EIBM) 21
3-2 諧和流固時間步長 22
3-3 固體表面之合力計算 24
3-4 固體體積分率計算 29
3-5 固體速度影響流場 31
3-6 流固耦合架構 32
3-7 固體表面壓力驗證 35
第四章、三維固體向量式有限元素法理論 38
4-1 四節點四面體元 38
4-2 四面體元的位移和變形 39
4-2-1 逆向運動 42
4-3 四面體元之內力計算 43
4-3-1 變形座標 44
4-3-2 節點內力計算 49
4-4 四面體元之外力計算 54
4-5 時間積分法 59
4-5-1 中央差分法(Central Difference Method, CDM) 59
4-5-2 完全顯式時間積分法(Completely Explicit Method, CEM) 62
4-6 使用CEM的結果探討 65
4-6-1 精確度比較 66
4-6-2 放大時間步長大小 68
4-6-3 小結 70
第五章、離散元素法 72
5-1 控制方程式 72
5-2 時間積分法 74
5-3 剛性塊體運動分析 75
5-3-1 求解主軸方向和主慣性矩 75
5-3-2 剛體平移和旋轉 80
5-4 剛性固體程序驗證 86
5-4-1 塊體基本性質計算驗證 86
5-4-2 剛體運動計算驗證 91
第六章、流固耦合數值算例 99
6-1 剛性體流固耦合算例 99
6-1-1 圓柱體上下浮動 99
6-1-2 圓柱體左右擺動 106
6-1-3 扇葉與流場的互制行為 109
6-2 柔性體流固耦合算例 121
6-2-1 柔性浮塊變形模擬 121
第七章、結論與建議 126
7-1 結論 126
7-2 建議 128
參考文獻 129
附錄一初始勁度k0推導 134
附錄二空心圓柱質量慣性矩計算 139
附錄三圓柱體上下低速浮動行為解析公式 144
附錄四體積模數(Bulk modulus)推導 147
附錄五水流與鋼纜的互制動力行為分析 149

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指導教授

王仲宇

審核日期

2022-8-23

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