中文摘要

本文研究重點在建立一流固耦合數值模型，此問題可以流固耦合通式： 表示，式中M為結構體之慣性矩陣(Inertia Matrix)，K為剛性矩陣(Stiffness Matrix)，F為流場作用於結構體之載荷，q為結構體之廣義座標(Generalized Coordinate)。本研究結合計算流體力學(Computational Fluid Dynamics)及有限元素法(Finite Element Method)，以前者計算流場作用於結構體之載荷，後者提供結構體之慣性與剛性矩陣來進行交互作用之數值模擬。由於結構體在每一瞬間均會因流場作用之載荷變動而產生變形，必須以動態格點法(Dynamic Grid)與幾何守恆律(Geometric Conservation Law)來處理此一介面網格變形。本文利用狀態過渡矩陣(State Transition Matrix)時間積分方法處理流體與結構交互作用的問題，以不可壓縮那威爾-史托克(Navier-Stokes)流體與一維線性繩索結構模型來進行流固交互作用之研究。本研究發展的流固耦合方法，可做為將來發展非線性大變形結構模型之參考。本研究驗證了流力、結構及交互作用模型之正確性，並應用於一彈性壁面(Flexible Wall)腔室開孔流場之數值模擬，分析了入流位置與開孔比例對於繩索變形與腔室壓力變化的影響。

Abstract

The objective of this work is to develop a numerical procedure that can solve a fluid/structure interaction problem, expressed by a general formula, . In this equation system, M and K are the inertia and stiffness matrices of the structure, respectively, F is the load vector exerted by the flow field on the structure, q is the general coordinate vector of the structure. In the present work, Computational Fluid Dynamic (CFD) and Finite Element Method (FEM) are integrated, foe which the former computes the loads acting on the structure and the latter provides the inertia and stiffness matrices in the modeling of the structure. To evaluate fluid-induced loads on the structure, the grid movement must be carefully treated for CFD computation during each time step. Dynamic grid technique that can strictly enforce the geometric conservation law has been employed to cope with the grid deformation of the interface. State transition matrix time integration method was used to march the fluid/structure system represented by an incompressible Navier-Stokes fluid and an one dimensional linear string model. The presently developed fluid/structure interaction scheme can serve as a basis for developing non-linear, large-deformation structure model in the future. The accuracy the proposed fluid/structure interaction scheme has been verified. A simulation of a cavity problem with a flexible wall and inlet, the relationship of inflow position, size of inlet, deformation of string and pressure variation of the cavity were analyzed.

目 錄

中文摘 要………………………………………………………………….I
英文摘要………………………………………………………………...II
誌謝……………………………………………………………………..III
目錄……………………………………………………………………..IV
圖目錄………………………………………………………………...VIII
符號說明…………………………………………………………….…..X


第一章 緒論……………………………………………………………..1
1-1 前言………………………………………………………...1
1-2 流力與結構交互作用……………………………………...3
1-3 研究目的及內容…………………………………………...3


第二章 流場解子………………………………………………………..6
2-1 不可壓縮流體方程式……………………………………...6
2-1-1 統御方程式………………………………………...6
2-1-2 源項………………………………………………...9
2-2 有限體積法………………………………………………..9
2-3 數值通量之計算………………………………………….10
2-3-1 非黏性通量之計算……………………………….10
2-3-2 黏性通量之計算………………………………….12
2-4 時間積分………………………………………………….13
2-5 LU分解法……………………………………………….14
2-6 動態格點………………………………………………….15
2-6-1 幾何守恆律及格點速度………………………….15
2-7 邊界條件之處理………………………………………….17
2-7-1 壁面速度邊界條件……………………………….17
2-7-2 壁面壓力邊界條件……………………………….17
2-7-3 入口與出口之邊界條件………………………….18


第三章 FEM模型……………………………………………………...19
3-1前言………………………………………………………..19
3-2 結構動力方程式………………………………………….19
3-3 有限元素法……………………………………………….21
3-4 邊界條件………………………………………………….23


第四章 流固耦合………………………………………………………24
4-1 物理模型………………………………………………….24
4-2 固流耦合時間積分……………………………………….24
4-3 格點更新系統…………………………………………….26
4-4 交互作用流程…………………………………………….29


第五章 結果與討論……………………………………………………31
5-1 流場解子驗證測試………………………………………31
5-1-1 均勻流場測試…………………………………….31
5-1-2 二維非黏性圓柱流場測試……………………….32
5-1-3 層流平板邊界層流場測試……………………….33
5-1-4 振盪平板流場測試……………………………….34
5-2 有限元素法程式驗證…………………………………….35
5-2-1 自由振動(Free-vibration)測試..…...……………...35
5-2-2 時間積分方法比較……………………………….36
5-2-3 常數分布力負載測試…………………………….37
5-3 交互作用介面力驗證…………………………………….38
5-4 單區塊流場分析……………...…………………………..39
5-4-1 開孔大小變化之影響…………………………….40
5-4-2開孔位置變化之影響……………………………..40
5-5三區塊流場分析………………..…………………………..41
5-5-1 開孔位置變化之影響…..…………………………..42
第六章 結論與未來工作………………………………………………44
6-1 結論……………………………………………………….44
6-2 未來工作………………………………………………….44


參考文獻………………………………………………………………..46
附錄……………………………………………………………………..49
圖…..……………………………………………………………………51

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