卡艾瑋臺灣大學：土木工程學研究所盧志偉Lu, Chi-WeiChi-WeiLu2007-11-252018-07-092007-11-252018-07-092006http://ntur.lib.ntu.edu.tw//handle/246246/50496本論文目的在於研究當淺水波通過一變動多孔介質層的發展。一個有特色的例子為潰壩問題所造成的波將分別在兩方向形成反射以及透射。論文其中包含理論的推導、實驗的方法、影像分析過程以及數值模擬。再推導統馭方程式過程中我們將會引進如何用漢米頓最小作用量原理說明附加質量的影響。影像分析過程中我們將會提供一個解決鏡像扭曲的簡單2D處理方式，除此之外我們將會呈現如何使用活塞完成無壩堤之潰壩實驗。最後將會使用實驗結果以及數值模擬結果去將慣量以及附加質量特性化在於波的發展過程。The goal of the present thesis is to investigate shallow water flows propagating through a medium of variable porosity. One particular case considered is a dam-break wave partially reflected and transmitted at a vertical porous boundary. The contents of this thesis include the derivation of governing equations, experimental methods, image analysis and the numerical modeling. In the derivation of the governing equations we will introduce how to use the Hamilton’s principle of least action to account for added mass effects. Image processing will offer some sample way to solve the radial distortion problem in 2D. Besides, we will show how to use piston to do dam-break experiment without using a sluice gate. Finally, we use experimental and numerical results to characterize the influence of inertia and added mass on the wave propagation.誌謝 ii 摘要 iii Abstract iv Table of contents v Figure List viii Table List xii CHAPTER 1 1 INTRODUCTION 1 CHAPTER 2 4 THEORY – GOVERNING EQUATION DERIVATION 4 Hamilton’s principle of least action 4 2.1.1. Variational principle derivation of the equation of motion 4 Continuity equation inside porous media 6 2.1.2. Conservation of mass 7 2.1.3. Porosity 7 Momentum equation inside porous media 8 2.1.4. Added mass 8 2.1.5. Porous media of motion 10 2.1.6. Permeability influence 13 2.1.7. Full equation 14 2.1.8. Discussion 15 2.1.8.1 Reduction to Guinot and Soares equation 15 2.1.8.2 Reduction to classical shallow water equation 16 2.1.8.3 Reduction to Dupuit equation 16 CHAPTER 3 17 NUMERICAL SCHEME AND COMPARISON WITH ANALYTICAL SOLUTIONS 17 Computational processing 17 3.1.1. Eigenvalues evaluating 17 3.1.2. Conserved variable form of governing equations 18 3.1.3. Finite volume method 19 3.1.3.1 Numerical scheme of approaching 20 Validation against analytical solution 23 3.1.4. The Riemann dam-break problem 23 3.1.5. The dam-break problem across a porosity discontinuity 24 3.1.5.1 The effect of added mass 25 CHAPTER 4 27 EXPERIMENTAL SET-UP AND METHOD 27 Experimental set-up 27 Experimental method 30 4.1.1. UV lights supply 30 4.1.2. Porosity’s variation in geometric 31 4.1.3. The materials of porous media 33 4.1.4. The raw image catching 35 Image processing 36 4.1.5. Radial distortion. And calibration 36 CHAPTER 5 40 EXPERIMENTAL RESULTS 40 The classical dam-break wave with dye 40 5.1.1. The raw image result 41 5.1.2. Calibration of time 47 5.1.3. Inverse problem of upstream depth 47 The dam-break wave inside porous media 50 5.1.4. The raw image result 51 5.1.5. Calibration of time 53 5.1.6. Inverse problem of upstream depth 53 The dam-break wave in channel of variable porosity 56 5.1.7. The raw image result 57 5.1.8. Calibration of time 62 5.1.9. Inversing upstream depth 62 CHAPTER 6 66 COMPARISON OF NUMERICAL AND EXPERIMENTAL RESULTS 66 The classical dam-break wave with dye 66 The dam-break wave inside porous media 69 6.1.1. Test the influence of added mass 69 6.1.2. Influence of Forchheimer coefficient 70 6.1.3. Comparison between numerical and experimental results 73 The dam-break wave in channel of variable porosity 75 6.1.4. Test the influence of added mass 75 6.1.5. Influence of Forchheimer coefficient 76 6.1.6. Comparison between numerical and experimental results 77 CHAPTER 7 81 CONCLUSIONS AND FURTHER WORK 81 Conclusions 81 Further work 8320147654 bytesapplication/pdfen-US可變性多孔介質層附加質量淺水波variable porous mediaadded massshallow flowthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/50496/1/ntu-95-R93521315-1.pdf