在2015年尼泊爾地震中，有一段視頻記錄了飯店游泳池水劇烈飛濺過程。出於對地震引發的劇烈池水晃蕩效應的流場動力學和波浪形態的好奇，我們研究了有結構物在內的方形水池在非線性外加振盪下的強迫池水晃蕩效應。
本篇論文採用計算流體力學模式Splash3D研究池水晃蕩問題。Splash3D直接求解三維納維爾-斯托克斯方程，採用大渦類比模式作為紊流閉合模式。流體體積法(Volume of Fluid)結合PLIC (Piecewise Linear Interface Calculation)技術被用於追蹤複雜的發生碎波的自由液面。以外加加速度晃蕩池水。模式驗證部分，以數值類比結果與三維實驗實測值及前人研究對比，可得到良好的對比結果。
在完成模式驗證後，我們進行了地震力驅動下之方形水槽池水晃蕩效應模擬。水槽12公尺長，8公尺寬，18公尺深，其中水體深度7公尺，水體底部浸沒有被簡化為孔隙介質之結構物。地震晃動以三維地震加速度時序表示，加速度量級為水準方向0.5 g到1.2 g，垂直方向0.3 g到1.2 g。動力學分析集中在從三維角度描述波高、自由液面，流速向量場，壓力場，以及最重要的動能垂向分佈。有關地震力和底部結構物孔隙率的參數敏感性分析實驗結果也展示於文中。從模擬結果可以看到，相較於邊壁中央，在水池角落處可觀察到更大的平均波高。如果池壁足夠高，水池角落處最大波高可達6公尺。如果池壁不夠高，水體將翻越邊壁溢出造成體積損失，最大波高也因而較低。三維波浪形態如對角波和旋轉波可以從水位計耦合分析和自由液面分佈時間序列圖兩方面觀察到。
我們發現，顯著的流體動力學過程（80%的總動能）發生在上層30%的水體中，這被我們成為30-80假說。30-80現象亦可在各參數敏感性分析實驗中觀察到。當比較不同量級地震引發的釋性波高時，我們發現了與地震量級排序相異常的波高排序，並將異常部分歸因於與池水自然頻率發生共振，但仍推測可能是波浪調製及非線性交互作用導致了波高排序異常。文中亦通過自由池水振盪和快速傅裡葉分析討論內部結構物屬性，如圓柱高度，對水體自然頻率之影響。

In the event of 2015 Nepal earthquake, a worldwide broadcasting video clip showed a violent water spilling in a hotel swimming pool. Motivated by the curiosity to investigate the dynamics of fluid field and the wave motion of violent sloshing during an earthquake, we studied forced sloshing in a rectangular tank with internal structure, excited by nonlinear external excitation.
In this thesis, the computational fluid dynamical model, Splash3D, was adopted for studying the sloshing problem accurately. Splash3D solved the 3D Navier-Stokes Equations directly with Large-Eddy Simulation (LES) turbulent closure. The Volume-of-fluid (VOF) method with piecewise linear interface calculation (PLIC) was used to track the complex breaking water surface. The time series of external acceleration was used to excite the water. A series model validations were conducted by comparing numerical results with 3D experimental measurements and previous studies’ results. Good comparisons were observed.
After validations, we performed the simulations for considering a seismic excited sloshing case in a rectangular water tank with a dimension of 12 m long, 8 m wide and 18 m deep, which contained water with 7 m in depth and the bottom structure simplified to porous medium. The seismic movement was imported by considering time-series acceleration in three dimensions, which were about 0.5 g to 1.2 g in the horizontal directions, and 0.3 g to 1 g in the vertical direction, respectively. We focused on describing the kinematics of the wave height, water surface, velocity vector field, pressure field, and most importantly, the vertical kinetic energy distribution in three dimensional view. Sensitivity tests about seismic magnitude, porosity of bottom structure were also conducted. From the simulations, higher averaged wave height can be found at the corner rather than at the middle of each side wall. The maximum wave height can be 6 m occurring at corners in case of water is well prescribed by side walls. If side walls were not high enough, water would jump cross it causing volume-loss, and the maximum wave height would be lower. Three-dimensional wave motion such as diagonal wave and swirling wave can be detected by both coupled wave height analysis and snapshots of free surface distribution.
We found that, the significant fluid dynamics (80% of kinetic energy) occurs at the top 30% of the water body, which can be called a 30-80 hypothesis. 30-80 phenomenon were also found in sensitivity testing cases. When comparing the significant wave heights (SWH) under different magnitude of earthquake events, we found the order anomaly of SWHs and conjectured the reason partly to resonance with natural frequency of the tank of water, furthermore, to wave modulation and nonlinear wave interactions. Discussions about how internal structure properties, rods’ height for example, influence the natural frequency of water body were performed by free sloshing analysis and FFT analysis.

Table of Contents
Abstract i
摘要 iv
Appreciation vi
Table of Contents vii
List of Figures x
List of Tables xiv
Notation Illustration xv
Abbreviation xvi
1. Introduction 1
1.1 Motivation 1
1.2 Statement of problem 2
1.3 Literature Review 3
1.3.1 Analytical and numerical methods to study sloshing 4
1.3.2 Basic solutions of wave motions from theoretical studies 5
1.3.3 Nonlinear sloshing and violent sloshing 5
1.3.4 Sloshing effected by internal structure in the tank 7
1.3.5 Sloshing excited by seismic accelerations 8
1.4 Scope of Present Study 9
2. Computational model 11
2.1 Governing equation and turbulence closure model 11
2.2 Interface reconstruction method and boundary condition 16
2.2.1 VOF with PLIC 16
2.2.2 Partial-Cell Method 16
2.2.3 Boundary Conditions 17
2.3 Two-step projection method and discretization 18
2.4 Porous drag module 19
2.5 Numerical stability criterion 21
2.6 Real-time Acceleration Loading Module 22
3. Model validation 24
3.1 Lab Experiments 24
3.2 Numerical results 26
3.2.1 Convergence analysis 26
3.2.2 Gauge data validation 28
3.3 Validation with the previous studies 32
4. Sloshing excited under seismic excitation 45
4.1 Statement of the problem 45
4.2 Numerical setup 45
4.3 Case study 46
4.3.1 Fluid field analysis 47
4.3.2 Sensitivity test 52
4.3.2.1 Porosity testing 52
4.3.2.2 Seismic magnitude testing 53
4.3.2.3 Water temperature testing 54
5. Discussion 66
5.1 FFT used to calculate natural frequency 66
5.2 Possible reasons for SWH anomaly 71
5.3 Internal structure effect 72
6. Conclusion 84
7. Future work 85
Bibilographies 86
Appendix A 92
Appendix B 149

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