點吸式波浪發電裝置最佳化形狀之計算流體力學研究

Abstract

本研究以開源計算流體力學軟體 OpenFOAM v8，基於雷諾平均納維-斯托克斯方程式，建立三維數值水槽，將起伏運動的能量擷取系統 (power take off system，PTO) 簡化成線性阻尼，模擬點吸式波浪發電裝置浮體的真實起伏運動， 並限制其他方向運動，以審視 Edwards and Yue (2022, Journal of Fluid Mechanics, 933, A1) 基於線性勢流理論和深水假設的點吸式波浪發電裝置浮體形狀優化框架中，只在起伏運動方向，並限制其他五個運動方向的圓柱和最佳化形狀 (no-kink-2nd-order) 所預測的發電效率及動態響應的差異。線性勢流理論雖廣泛應 用於浮體初步設計，但因未考慮黏滯力與水面上形狀等影響，對阻尼與動態響應的預測準確性有限。由模擬結果顯示，在深水二階斯托克斯波作用下，圓柱和最佳化形狀的發電效率相近，其運動響應約為波浪振幅的 0.7 倍，未達到理論預測的 3 倍，顯示線性勢流理論高估浮體動態響應。此外，本研究深入探討不同的參數改變對於發電效率的影響；第一為固定週期和水深，發現波高越小，無因次化後的發電效率越好；第二為固定波高和週期，發現圓柱在中間水深條件下之發電效率略低於深水條件，係因為其沒水深度較深，使底部所受到的能量相較於深水波還要小，而最佳化形狀由於沒水深度較淺，中間水深和深水所受到的波浪能量相當，所以發電效率表現較不敏感；第三為浮體密度變小，且圓柱和最佳化形狀的水下形狀與 Edwards and Yue (2022) 相同，發現兩浮體密度變小，發電效率會增加，尤其在浮體剛好不會被液體淹沒的時候，會有最好的發電效率，當密度再繼續降低，發電效率趨緩甚至不再增加；第四為 PTO 的線性阻尼變化，發現在未發生共振情況下，發電效率主要受到 PTO 線性阻尼係數的主導。當阻尼設定為自身輻射阻尼的 20 倍時，圓柱與最佳化形狀的發電效率分別提升約 3.7 倍與 4.5 倍，當線性阻尼係數繼續增加，發電效率因浮體起伏運動速度降低顯著而下降；最後本研究設計三種新浮體形狀，其沒水表面積與圓柱或是最佳化形狀相同且線性阻尼係數為自身的輻射阻尼係數，發現未產生共振現象，且新形狀之起伏運動振幅與圓柱和最佳化形狀相近，但新形狀有更大的輻射阻尼係數，因此發電效率較高，顯示在難以達成共振的情境下，選用輻射阻尼係數較高的浮體形狀能提升發電效率。綜合以上結果，顯示線性勢流理論在不考慮黏滯力和水面上形狀下，無法準確預測真實的動態響應，並難以反映浮體密度、波高、沒水深度等關鍵參數改變對發電效率的影響。本研究成果不僅揭示線性勢流理論的侷限性，更提供未來波浪發電裝置設計一具體、可行之數值分析與優化參考依據。

This study utilizes the open-source computational fluid dynamics software OpenFOAM v8, based on the Reynolds-Averaged Navier–Stokes equations, to establish a three-dimensional numerical wave tank. The power take-off system (PTO) in the heave mode of the point-absorber wave energy converter is simplified as a linear damping model to simulate the realistic heaving motion of the floating body, while constraining other degrees of freedom. This simulation aims to examine the differences in predicted power generation efficiency and dynamic response between the cylindrical and optimized (no-kink-2nd-order) shapes from Edwards and Yue (2022, Journal of Fluid Mechanics, 933, A1), which are based on linear potential flow theory and deep-water assumptions, specifically considering motion only in the heave direction and constraining the other five degrees of freedom. Although linear potential flow theory is widely used in preliminary floating body designs, its predictions regarding damping and dynamic response are limited due to neglecting viscous effects and the influence of above-water geometry. Simulation results show that under deep-water second-order Stokes waves, the power generation efficiencies of both the cylindrical and optimized shapes are similar, with their heave motion amplitudes approximately 0.7 times the wave amplitude, which falls short of the theoretically predicted factor of 3, indicating an overestimation of dynamic response by linear potential flow theory. Further parametric studies reveal the following: (1) with fixed wave period and water depth, power generation efficiency improves as wave height decreases; (2) with fixed wave height and period, the power of cylindrical shape generation efficiency in intermediate water depths is slightly lower than in deep water, due to its deeper draft causing less wave energy to reach its bottom compared to deep water; conversely, the optimized shape, with a shallower draft, captures wave energy effectively in both intermediate and deep water depths, making its efficiency less sensitive to water depth changes; (3) reducing the density of floating body while maintaining the underwater geometry consistent with Edwards and Yue (2022), the power generation efficiency increases and reaches its peak when the body is just barely not fully submerged by the liquid. Further reductions in density result in diminishing returns or stagnation in power generation efficiency; (4) variation in the linear damping coefficient of the PTO in the heave mode shows that, absent resonance, power generation efficiency is mainly governed by this coefficient. When the damping is set to twenty times the radiation damping coefficient, the cylindrical and optimized shapes achieve approximately 3.7 and 4.5 times improvements in power generation efficiency, respectively. However, further increases in the linear damping coefficient reduce efficiency due to significant decreases in the heave velocity of the floating body. Finally, three new floating body shapes with identical underwater surface areas to the cylindrical or optimized shapes were designed, and their PTO damping coefficients were set equal to their own radiation damping. These new shapes exhibited no resonance and showed heave motion amplitudes comparable to the cylindrical and optimized shapes. However, due to their larger radiation damping coefficients, the new shapes demonstrated higher power generation efficiencies. This indicates that in scenarios where resonance is difficult to achieve, selecting floating bodies with larger radiation damping coefficient can enhance power conversion performance. In summary, the results indicate that linear potential flow theory, neglecting viscous effects and above-water geometry, cannot accurately predict the real dynamic responses nor reflect the influence of key parameters such as floating body density, wave height, and draft on power generation efficiency. This study not only reveals the limitations of linear potential flow theory but also provides a concrete and feasible numerical analysis and optimization reference for future wave energy converter designs.