底板傾斜式造波水槽造波的數值模擬

Numerical simulation of wave generation by a bottom-tilting flume wavemaker

王昕兒(Hsin-Erh Wang)

指導教授 ： 詹益齊

國立臺灣大學/工學院/土木工程學研究所/碩士(2019年)

https://doi.org/10.6342/NTU201902759

摘要

本文採用 OpenFOAM 軟體以及專門處理邊界條件及孔隙介質流之求解器
olaFlow,以流體體積法(VOF)和有限體積法,計算體積平均的雷諾平均方程式(VARANS),模擬底板傾斜式造波水槽(bottom-tilting flume wavemaker)。而本研究之邊界條件皆為不透水,因此並不考慮孔隙率的問題。
本文所建立之數值模式的驗證分成兩個部分,第一部分為與 Madsen et al. (2008)對於矩形波自由液面變化的分析進行比較;第二部分為設計與 Lu (2017)相同的底板傾斜式造波水槽,將其實驗資料與本模式之數值模擬結果進行驗證。兩項驗證結果皆十分擬合,藉以證明本研究數值水槽模擬結果的可信度。
本文重點為以數值模擬底板傾斜式造波水槽,並以移動底床長度、底床移動位移、底床移動歷時以及水深四種造波參數,探討造波條件對於流體自由液面、波長、振幅、波速的相關性。研究結果也與相同振幅之孤立波(solitary wave)有效波長作比較,證明底床傾斜式造波水槽能更有效的產生長波。

關鍵字

OpenFAOM ； olaFlow ； 體積平均之雷諾平均方程式 ； 流體體積法 ； 有限體積法 ； 底板傾斜式造波水槽

並列摘要

In this thesis, the OpenFOAM software and the solver olaFlow, which specialize in boundary conditions and porous media flow, are used to calculate the volume-averaged Reynolds average equation VARANS by the volume of fluid method and the finite volume method, and simulate the bottom-tilting wave maker. The boundary conditions of this model are impermeable, so the porosity is not considered.
The validation is divided into two parts. The first part is the analysis of the change of the free surface elevation of rectangular-shape wave by Madsen et al. (2008). The first part is the comparison between the analysis of the free surface elevation of the rectangular-shaped wave by Madsen et al. (2008) and the model in this paper only to find out the result is well fitted. The second part is to design the same wave maker as Lu’s (2017).Then the numerical results are carried out to compare with the experiments data of Lu (2017) and show high degree of accuracy to prove that the numerical wave maker of this study is correct.
At the end of the paper, we simulated the bottom-tilting wave maker and changed the four wave maker parameters : moving bottom length, bottom motion displacement, bottom
motion duration and initial water depth, to observe the free surface elevation, wave length, amplitude and phase velocity. The results of the study are also compared with the effective wavelengths of solitary waves of the same amplitude, which proves that the bottom-tilting wave wave can generate long waves more effectively.

並列關鍵字

OpenFOAM ； olaFlow ； VARANS ； VOF ； finite volume method ； bottom-tilting flume wavemaker

參考文獻

1. Benjamin, T. B., & Lighthill, M. J. (1954). On cnoidal waves and bores. The Royal Society, 224(1159), 448-460.

2. 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 Mathematiques Pures et Appliquees, 55-108.

3. Byatt-Smith, J. G. B. (1970). An exact integral equation for steady surface waves.The Royal Society, 315(1522), 405-418.

4. Dean, R. G., & Dalrymple, R. A. (1991). Water wave mechanics for engineers and scientists (Vol. 2): World Scientific Publishing Company.

5. del Jesus, M., Lara, J. L., & Losada, I. J. (2012). Three-dimensional interaction of waves and porous coastal structures: Part I: Numerical model formulation. Coastal Engineering, 64, 57-72.