臺灣博碩士論文加值系統

本研究旨在探討波浪作用下，箱網養殖浮式平台的動力特性。基於計算效率以及應用性的考量下，本研究的問題簡化如下：(1) 假設流場為非黏性、不可壓縮且為非旋性。(2)網袋部分，考慮材質及尺寸條件，以modified Morison equation (或稱Morison type equation of relative motion)計算拖曳力和慣性力。(3)錨碇系統為對稱的線性彈簧系統，忽略流體作用力對其產生的影響。(4)因為網袋質點質量相對於浮式平台而言太輕，必須採用較小的時間步階，才能使數值計算收斂，但所須耗費的計算時間太過冗長，易造成數值誤差的累積(如捨位誤差)，因此假設網袋不會變形。

本研究採用邊界元素法發展二維非線性數值水槽，邊界積分公式由線性元素進行離散，非線性自由液面則採用Mixed Eulerian and Lagrangian method (MEL法)搭配the 4th-order Runge-Kutta method (RK4)和cubic spline scheme處理，造波邊界上的速度採用Stokes二階解給定，水槽前後兩端設置數值消波區，消除波浪與結構物交互作用後產生的反射波和透射波。為準確求解非線性波與浮式結構物交互作用的動力特性，數值模式須同時求解速度場的Φ以及加速度場中的Φt，因此本研究採用加速勢法和模態分解法求解加速度場，進而得到作用在浮式平台上的波浪外力，而網袋受力則透過Modified Morison equation計算，將外力累加到浮式平台上，透動牛頓第二定律，得到浮式平台的運動方程式，最後再由RK4計算下一時刻浮式平台重心的位移和速度，以及自由液面質點的位置和流速勢。

首先，由非線性數值水槽計算結果與Stoke二階解析解的比較可知，波形以及內部的速度和加速度均有良好的準確性，而且採用的數值消波區可適用在廣泛的水深範圍下進行長時間模擬。而數值模式在波浪與固定及錨碇的浮式結構物交互作用的計算結果，與前人研究結果比較也有良好的一致性。

其次，在波浪與浮式平台交互作用的案例中，結果顯示，除了平台運動的roll和heave共振頻率附近以外，計算結果與實驗值相當吻合，這是受到黏性效應影響。為降低黏性效應的影響，並且在不影響計算效率的考量下，本研究在振動系統加入非耦合的阻尼係數矩陣，此阻尼係數由阻尼比來表示( ξ=0.1)，結果發現，結構物各自由度的共振頻率附近的運動反應會明顯的降低，而其餘頻率範圍則無明顯改變，此結果使得數值計算更接近實驗值。而且，在不同波高、錨碇角度、水深以及網袋等條件下的計算結果均與實驗值吻合，因此浮式平台適合的阻尼比為ξ=0.1。

最後，以數值模式來探討浮式平台浸水深、寬度、跨距、彈性係數、錨碇角度以及網袋深度等，對浮式平台動力特性的影響。結果顯示，改變上述的條件都可能會造成結構物運動、錨碇張力、反射率、透射率以及波能反應的頻率偏移以及改變反應值的的大小。就共振反應而言，平台浸水深較小、寬度較大、跨距較小、彈簧係數較小、錨碇角度較小以及網袋深度較大情況下，浮式平台運動的穩定性較好，錨碇張力也較小。而數值模式應用於不規則波的研究結果顯示，規則波與不規則波案例下結構物的動力特性之趨勢相近，但是不規則波作用下，受波譜能量分布的影響，結構物運動的共振頻率稍微移向高頻，且共振值變小，但影響的範圍變廣。

This paper is to investigate the wave-induced dynamic properties of the floating platform for cage aquaculture. Considering the calculation efficiency and its applicability, this problem is simplified by: (1) assuming the flow field is inviscid, incompressible and irrotational; (2) the form drag and inertia drag on the fish net is calculated by the modified Morison equation (or Morison type equation of relative motion), including the material and geometric properties; (3) the moorings is treated as a symmetric linear spring system and the influence of hydrodynamic forces on the mooring lines is neglected; and (4) the net-volume is assumed as un-deformable to avoid the inversely prolonging computing time because the mass of fish net with is too light comparing with the mass of floating platform and cause the marching time step tremendously small to reach the steady-state condition which may lead to larger numerical errors (e.g. truncation errors) in computation.

The BIEM with linear element scheme is applied to establish a 2D fully nonlinear numerical wave tank (NWT). The nonlinear free surface condition is treated by combining the Mixed Eulerian and Lagrangian method (MEL), the fourth-order Runge-Kutta method (RK4) and the cubic spline scheme. The second-order Stokes wave theory is adopted to give the velocity on the input boundary. Numerical damping zones are deployed at both ends of the NWT to dissipate or absorb the transmitted and reflected wave energy. The velocity and acceleration fields should be solved simultaneously in order to obtain the wave-induced dynamic property of the floating platform. Thus, both the acceleration potential method and modal decomposition method are adopted to solve the wave forces on the floating body, while the wave forces on the fish net are calculated by the modified Morison equation. According to Newton’s second law, the total forces on the gravity center of the floating platform form the equation of motion. Finally, the RK4 is applied to predict the displacement and velocity of the platform.

Firstly, the NWT is validated by comparing the wave elevation, internal velocity and acceleration with those from the second-order Stokes wave theory. Moreover, the numerical damping zone is suitable for long time simulation with a wide range of wave depth. The simulated results on wave-body interactions of fixed or freely floating body also indicate good agreement with those of other published results.

Secondly, in the case of the interaction of waves and the floating platform, the simulated results show well agreement with experimental data, except at the vicinity of resonant frequency of roll and heave motions. This discrepancy is due to the fluid viscous effect. To overcome this problem and maintain the calculation efficiency, an uncoupled damping coefficient obtained by a damping ratio (ξ=0.1 ) is incorporated into the vibration system. Results reveal that responses of body motion near the resonant frequencies of each mode have significant reduction and close to the experimental data. Moreover, the results are also consistent well with experiments in different wave height, mooring angle, water depth either with or without fish net. Therefore, the suitable value of the damping ratio for the floating platform is ξ=0.1.

Finally, the present model is applied to investigate the dynamic properties of the floating platform under different draft, width, spacing, spring constant, mooring angle and depth of fish net. Results reveal that the resonant frequency and response of body motion, mooring force, reflection and transmission coefficients and wave energy will be changed. According to the resonant response, the platform with shallower draft, larger width, longer spacing between two pontoons, smaller spring constants, or deeper depth of fish net has more stable body motions and smaller mooring forces. Irregular wave cases are presented to illustrate the relationship with the regular wave cases. Results indicate that the dynamic responses of body motion and the reflection coefficient in irregular waves have similar trend with regular waves. However, in the irregular wave cases, the resonant frequency is moved to the higher frequency. Similarly, resonant response function is smaller but wider, which is due to the energy distribution in the wave spectrum.

目錄
中文摘要 i
英文摘要 iii
目錄 v
圖目錄 ix
表目錄 xvi
第一章 緒論 1
1.1研究動機與目的 1
1.2 文獻回顧 2
1.2.1 非線性數值水槽 3
1.2.2 浮式結構物 3
1.2.3 雙胴浮式結構物 5
1.2.4 箱網養殖結構物 5
1.3 本研究之考慮 6
1.4 本文組織 6
第二章 數值模式 8
2.1 控制方程式及邊界積分方程式 9
2.1.1控制方程式 9
2.1.2邊界積分方程式 9
2.2 邊界條件 9
2.2.1 造波邊界 9
2.2.2 底床及直立壁邊界 10
2.2.3 自由液面邊界 10
2.2.4數值消波區 11
2.2.5 結構物邊界條件 12
2.3 結構物外力計算 13
2.4 加速勢法 14
2.5 模態分解法 15
2.6數值方法 17
2.6.1曲線座標系統 17
2.6.2自由液面與固體交界面速度修正 18
2.6.3 The 4th-order Runge-Kutta method 19
2.6.4網格重置 20
2.6.5自由液面平滑化 20
2.6.6 數值精度檢查 21
2.7 錨碇系統 21
2.8 網袋外力計算 22
2.8.1 Modified Morison equation 23
2.8.2流阻力 24
2.9 含阻尼效應的自由振動系統 24
2.10 流程圖 25
第三章 數值模式驗證 27
3.1 非線性數值水槽的驗證 27
3.2單浮體案例 35
3.2.1 散射問題 37
3.2.2 輻射及散射問題 42
3.3雙胴浮體案例 45
3.3.1 輸入條件 45
3.3.2 精度控制 46
3.3.3 時序列資料 46
3.3.4 模式驗證 49
3.3.5 入射波高的影響 54
3.3.6 阻尼係數的影響 56
第四章 水工模型試驗 60
4.1 水工模型試驗簡述 60
4.1.1 模型尺寸及材質 60
4.1.2 試驗佈置 61
4.1.3 試驗條件 62
4.2 結果與討論 64
4.2.1 不同波高的影響 64
4.2.2 不同錨碇角度的影響 68
4.2.3 不同水深的影響 73
4.2.4 有無網袋的影響 77
第五章 數值模式應用 81
5.1 浮式平台案例之應用 81
5.1.1 平台浸水深的影響 82
5.1.2 平台寬度的影響 84
5.1.3 平台跨距的影響 86
5.1.4 彈性係數的影響 88
5.1.5 錨碇角度的影響 90
5.1.6 網袋深度的影響 92
5.2 不規則波案例之應用 94
5.2.1不規則波造波函數 94
5.2.2不規則波數值消波區 95
5.2.3 資料分析 96
5.2.3.1 飄移力 96
5.2.3.2 頻率反應函數 96
5.2.4 不規則波數值水槽驗證 98
5.2.5單浮體結構物 100
5.2.5.1 散射問題 102
5.2.5.2 輻射及散射問題 104
5.2.6浮式平台 109
第六章 結論與建議 113
6.1 結論 113
6.2 建議 115
參考文獻 114
附錄A 結構物運動及邊界條件 121
附錄B 數值水槽內之速度和加速度 126
附錄C 反射率和透射率之計算 129
附錄D 孤立波案例之應用 132
作者簡歷 137

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