臺灣博碩士論文加值系統

　　本論文研究目的為利用三維數值模式模擬孤立波與一透水潛堤之交互作用，其中透水潛堤以兩種不同概念進行模擬，一是空間平均（spatial average）孔隙結構物、另一則與實驗相同配置由玻璃圓球所構成之三維真實透水結構物。數值模式使用基於黏性流體運動方程式（Navier-Stokes equation） 推導出巨觀型態（macroscopic）的運動方程式，同時搭配大渦流模擬（large eddy simulation）之紊流模式(Hu et al., 2012)。另外，空間平均部分則是使用Sollitt and Cross (1972)孔隙結構物阻力項來進行模擬Sollitt and Cross (1972)。
　　
　　驗證部分與Hsu et al. (2012)的質點軌跡追蹤實驗，並以本模式進行比較，模擬結果良好；在實體結構物部分則與Yasuda et al. (1997)的孤立波通過半無限長潛提實驗進行比較，從模擬結果發現，本模式在模擬具有非常優越的模擬能力。而在空間平均阻力項之透水結構物部分，則是與Lara et al. (2012)的實驗及數值做驗證，驗證結果與Lara et al. (2012)數值近乎相同，與實驗結果十分相近，也證明空間平均阻力項之透水結構物應用是可信的。

　　本文最後也是最主要目的以Wu et al. (2012a)的實驗配置為主，利用三維模式模擬，在空間平均結構物上探討不同阻力參數的影響並與實驗比較其自由液面、流場、速度剖面。在三維真實圓球透水結構物與實驗比較自由液面、流場、速度剖面。最後比較空間平均結構物與三維真實圓球透水結構物在自由液面、流場、速度剖面、壓力、質點軌跡等差異加以討論。

This study investigates a solitary wave interaction with a submerged permeable structure using three-dimensional numerical solver. The porous structure considered in this paper is twofold. One is considered as an idealized rectangular permeable dike using spatial-averaged concept to derive the macroscopic Navier-Stokes equation for porous media flow coupled with large-eddy-simulation (Hu et al., 2012). The other is to use a series of uniform glass spheres to consist a three-dimensional porous structure.

To validate the present numerical model, the comparisons between simulated results and available experimental data/ analytical solutions in literatures are necessary. We first test solitary wave propagating in a constant water depth, in which the calculated initial wave form and particle trajectories of solitary wave are performed against with Boussiesq theory of solitary wave and measurements by Hsu et al. (2012), respectively. Then numerical tests are carried out to compare with experiments of Yasuda et al. (1997) for solitary wave propatation over semi-infinite breaker step. Finally, numerical experiments are done to compare with results by Lara et al. (2012) for solitary wave over an emerged three-dimensional permeable prism. Generally, the present numerical results show high degree of accuracy, compared to the existing experiments.

Based on the experimental setup for submerged permeable breakwater under solitary wave forcing by Wu et al. (2012a), we conduct two types of porous object, i.e., two-dimensional (2D) spatial-averaged porous media and three-dimensional (3D) real permeable obstacle consisted by uniform glass spheres. The comparisons of the free surface elevation, overall velocity fields as well as cross-section of velocity components are performed between measurements, 2D and 3D numerical simulations. Discussions for the discrepancies between experiments and calculations were given. Moreover, numerical results for the pressure fields and trajectories of marked fluid particles were also discussed.

摘要 I
Abstract II
致謝 IV
目錄 V
表目錄 VIII
圖目錄 IX
符號表 XII
第一章　緒論 1
1-1　研究目的與動機 1
1-2　文獻回顧 2
1-2-1　孤立波理論 2
1-2-2　孤立波通過不透水潛沒結構物 4
1-2-3　孤立波通過透水結構物 5
1-3　本文架構 6
第二章　數值方法 7
2-1　模式簡介 7
2-2　控制方程式 8
2-2-1　流體之連續方程式及動量方程式 8
2-2-2　流體經孔隙結構物之控制方程式 9
2-3　大渦模擬 11
2-4　有限體積法 14
2-5　流體體積法 15
2-5-1　流體體積法 16
2-5-2　自由液面之建立 18
2-5-3　部分網格法 20
2-6　投影法 22
2-7　程式計算流程 23
2-8　邊界條件 24
2-8-1　不可滑動邊界 24
2-8-2　自由滑動邊界 25
2-8-3　波浪入射邊界 25
2-8-4　壓力狄利克雷邊界 26
2-8-5　數值海綿層設定 26
2-9　數值穩定度 26
第三章　模式驗證 28
3-1　孤立波解析與驗證 28
3-1-1　Boussinesq解析解 28
3-1-2　Grimshaw三階解 29
3-1-3　試驗配置及條件 31
3-1-4　驗證結果 31
3-2　質點軌跡追蹤 38
3-2-1　原理及步驟 38
3-2-2　試驗配置及條件 38
3-2-3　驗證結果 40
3-3　孤立波通過不透水結構物 42
3-3-1　試驗配置及條件 42
3-3-2　驗證結果 43
3-4　孤立波通過空間平均孔隙結構物 45
3-4-1　試驗配置及條件 45
3-4-2　驗證結果 47
第四章　結果與討論 54
4-1　孤立波通過空間平均孔隙結構物 54
4-1-1　試驗配置及條件 54
4-1-2　試驗結果 56
4-1-3　小結 69
4-2　孤立波通過真實孔隙結構物 70
4-2-1　試驗配置及條件 70
4-2-2　試驗結果 72
4-2-3　小結 89
4-3　平均與真實三維之比較 90
4-3-1　波形、流場及速度剖面 90
4-3-2　壓力分佈 96
4-4　質點軌跡追蹤 104
4-4-1　配置條件 104
4-4-2　驗證結果 105
第五章 結論與建議 112
5-1　結論 112
5-1-1　空間平均阻力項參數的差異 112
5-1-2　真實三維透水潛堤 112
5-1-3　空間平均與真實三維之差異 113
5-1-4　質點軌跡追蹤 113
5-2　未來發展與建議 114
參考文獻 115
附錄A　x-y平面之流場 120

1.Barth, T.J., (1994) Aspects of unstructured grids and finite-volume solvers for the euler and navier-stokes equations, 5. Van Kareman Institute, Rhode-Saint-Gen＆se, Belgiqueb.
2.Bear, J., (1972) Dynamics of fluids in porous media, Elsevier, New York.
3.Boussinesq, J., (1872) Théorie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond. Journal de Mathematique Pures et Appliquees, Deuxieme Serie 17:pp. 55-108.
4.Cabot, W. and Moin, P., (2000) Approximate wall boundary conditions in the large-eddy simulation of high reynolds number flow. Flow, Turbulence and Combustion, 63(1):pp. 269-291.
5.Chang, K.-A., (1999) Experimental study of wave breaking and wave-structure interaction, Cornell University.
6.Chang, K.-A., Hsu, T.-J. and Liu, P.L.F., (2001) Vortex generation and evolution in water waves propagating over a submerged rectangular obstacle: Part i. Solitary waves. Coastal Engineering, 44(1):pp. 13-36.
7.Chang, K.-A. and Liu, P.L.F., (1999) Experimental investigation of turbulence generated by breaking waves in water of intermediate depth. Physics of Fluids, 11(11):pp. 3390.
8.Chorin, A.J., (1968) Numerical solution of the navier-stokes equations. Mathematics of Computation, 22(104):pp. 745-762.
9.Chorin, A.J., (1969) On the convergence of discrete approximations to the navier-stokes equations. Mathematics of Computation, 23(106):pp. 341-353.
10.Darcy, H., (1856) Les fontaines publiques de la ville de dijon., Dalmont, Paris.
11.Deardorff, J.W., (1970) A numerical study of three-dimensional turbulent channel flow at large reynolds numbers. Journal of Fluid Mechanics, 41:pp. 453-480.
12.del Jesus, M., Lara, J.L. and Losada, I.J., (2012) Three-dimensional interaction of waves and porous coastal structures. Coastal Engineering, 64:pp. 57-72.
13.Fenton, J., (1972) A ninth-order solution for the solitary wave. Journal of Fluid Mechanics, 53:pp. 257-271.
14.Forchheimer, P., (1901) Wasserbewegung durch boden. Z. Ver. Deutsch. Ing, 45:pp. 1782-1788.
15.Goring, D.G., (1978) Tsunamis -- the propagation of long waves onto a shelf, California Institute of Technology.
16.Goring, D.G. and Raichlen, F., (1992) Propagation of long waves onto shelf, 118. American Society of Civil Engineers, Reston, VA, ETATS-UNIS.
17.Grimshaw, R., (1970) The solitary wave in water of variable depth. Journal of Fluid Mechanics, 42:pp. 639-656.
18.Gu, Z. and Wang, H., (1991) Gravity waves over porous bottoms. Coastal Engineering, 15(5–6):pp. 497-524.
19.Hirt, C.W. and Nichols, B.D., (1981) Volume of fluid (vof) method for the dynamics of free boundaries. Journal of Computational Physics, 39(1):pp. 201-225.
20.Hsu, H.C., Chen, Y.Y. and Hwung, H.H., (2012) Experimental study of the particle paths in solitary water waves. Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, 370(1964):pp. 1629-37.
21.Hu, K.C., Hsiao, S.C., Hwung, H.H. and Wu, T.R., (2012) Three-dimensional numerical modeling of the interaction of dam-break waves and porous media. Advances in Water Resources, 47(0):pp. 14-30.
22.Huang, C.-J., Chang, H.-H. and Hwung, H.-H., (2003) Structural permeability effects on the interaction of a solitary wave and a submerged breakwater. Coastal Engineering, 49(1–2):pp. 1-24.
23.Huang, C.-J. and Dong, C.-M., (2001) On the interaction of a solitary wave and a submerged dike. Coastal Engineering, 43(3–4):pp. 265-286.
24.Irmay, S., (1958) On the theoretical derivation of darcy and forchheimer formulas. Transactions of the American Geophysical Union, 39(4):pp. 702-707.
25.Jaluria, Y. and Torrance, K.E., (1986) Computational heat transfer, Washington, D. C., Hemisphere.
26.Korteweg, D.J. and Vries, G.d., (1895 ) On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. Philosophical Magazine Series 5 Volume 39( Issue 240):pp. 422-443.
27.Kozeny, J., (1927) ber kapillare leitung des wassers im boden. Sitzungsber. Akad. Wiss. Wien, 136:pp. 271-306.
28.Lai, J.-W., (2009) Experimental and numerical studies on wave propagation over carse grained sloping beach, National Cheng Kung University.
29.Lara, J.L., del Jesus, M. and Losada, I.J., (2012) Three-dimensional interaction of waves and porous coastal structures. Coastal Engineering, 64:pp. 26-46.
30.Lara, J.L., Losada, I.J., Maza, M. and Guanche, R., (2011) Breaking solitary wave evolution over a porous underwater step. Coastal Engineering, 58(9):pp. 837-850.
31.Larsen, J. and Dancy, H., (1983) Open boundaries in short wave simulations — a new approach. Coastal Engineering, 7(3):pp. 285-297.
32.Lin, M.-Y. and Huang, L.-H., (2010) Vortex shedding from a submerged rectangular obstacle attacked by a solitary wave, 651. Cambridge University Press, Cambridge, ROYAUME-UNI, 16 pp.
33.Lin, P., (1998) Numerical modeling of breaking waves, Cornell University, USA. .
34.Lin, P., (2004) A numerical study of solitary wave interaction with rectangular obstacles, 51. Elsevier, Kidlington, ROYAUME-UNI, 17 pp.
35.Lin, P. and Karunarathna, S.A.S.A., (2007) Numerical study of solitary wave interaction with porous breakwaters. Journal of Waterway, Port, Coastal ＆ Ocean Engineering, 133(5):pp. 352-363.
36.Liu, P.L.-F., Lin, P., Chang, K.-A. and Sakakiyama, T., (1999) Numerical modeling of wave interaction with porous structures. Journal of Waterway, Port, Coastal ＆ Ocean Engineering, 125(6):pp. 322-330.
37.Liu, P.L.F., Davis, M.H. and Downing, S., (1996) Wave-induced boundary layer flows above and in a permeable bed. Journal of Fluid Mechanics, 325:pp. 195-218.
38.Liu, P.L.F., Wu, T.R., Raichlen, F., Synolakis, C.E. and Borrero, J.C., (2005) Runup and rundown generated by three-dimensional sliding masses. Journal of Fluid Mechanics, 536:pp. 107-144.
39.Lynett, P., Liu, P.L.F., Losada, I.J. and Vidal, C., (2000) Solitary wave interaction with porous breakwaters. Journal of Waterway, Port, Coastal ＆ Ocean Engineering, 126(6):pp. 314.
40.M'Cowan, J., (1890) On the solitary wave. Proceedings of the Edinburgh Mathematical Society, 9:pp. 49-49.
41.Madsen, O.S. and Mei, C.C., (1969) The transformation of a solitary wave over an uneven bottom. Journal of Fluid Mechanics, 39:pp. 781-791.
42.Orszag, S.A., (1970) Analytical theories of turbulence. Journal of Fluid Mechanics, 41:pp. 363-386.
43.Philip, J., (1970) Flow in porous media. Annual Review of Fluid Mechanics, 2:pp. 177-204.
44.Polubarinova-Kochina, P., (1962) Theory of ground water movement, Princeton University Press Princeton, NJ.
45.Rayleigh, L., (1876) On waves. Acta Mechanica Sinica, ser. 5, Vol. 1, No. 4:pp. 257-279.
46.Seabra-santos, F.J., Renouard, D.P. and M., T., (1987) Numerical and experimental study of the transformation of a solitary wave over a shelf or isolated obstacle, 176. Cambridge University Press, Cambridge, ROYAUME-UNI.
47.Smagorinsky, J., (1963) General circulation experiments with the primitive equations. Monthly Weather Review, 91(3):pp. 99.
48.Sollitt, C. and Cross, R., (1972) Wave transmission through permeable breakwaters. Proceedings of 13th International Conference on Coastal Engineering, ASCE, Canada:pp. 1827-1846.
49.Tang, C.-J. and Chang, J.-H., (1998) Flow separation during solitary wave passing over. Journal of Hydraulic Engineering, 124(7):pp. 742.
50.van Gent, M.R.A., (1992) Formulae to describe porous flow. TU Delft
51.van Gent, M.R.A., (1995) Wave interaction with permeable coastal structures, Delft University of Technology, The Netherlands. .
52.Wu, N.-J. and Chang, K.-A., (2011) Simulation of free-surface waves in liquid sloshing using a domain-type meshless method. International Journal for Numerical Methods in Fluids, 67(3):pp. 269-288.
53.Wu, T.R., (2004) A numerical study of three-dimensional breaking waves and turbulence effects, Cornell University.
54.Wu, Y.-T., Hsiao, S.-C. and Chen, G.-S., (2012a) Solitary wave interaction with a submerged permeable breakwater: Experiment and numerical modeling. Int. Conf. Coast. Eng., Santander, Spain (Accepted). Int. Conf. Coast. Eng.( ICCE).
55.Wu, Y.-T., Hsiao, S.-C., Huang, Z.-C. and Hwang, K.-S., (2012b) Propagation of solitary waves over a bottom-mounted barrier. Coastal Engineering, 62:pp. 31-47.
56.Yasuda, T., Mutsuda, H. and Mizutani, N., (1997) Kinematics of overturning solitary waves and their relations to breaker types. Coastal Engineering, 29(3–4):pp. 317-346.
57.Zabusky, N.J. and Kruskal, M.D., (1965) Interaction of solitons in a collisionless plasma and the recurrence of initial states. Physical Review Letters, 15(6):pp. 240-243.