結合沉浸式邊界法與晶格波茲曼法進行雙向流固耦合分析於壓電能量擷取系統

Abstract

本論文利用晶格波茲曼法結合沉浸式邊界法以及平板疊加法，應用於壓電能量擷取系統單邊固定壓電陶瓷雙晶片之數值分析，分析由金屬圓柱於風洞中產生之卡門渦街激振壓電陶瓷雙晶片之振動特性，並以實驗量測進行驗證。 平板疊加法計算先以平板理論將壓電陶瓷雙晶片的三層結構等效成單層平板，再利用疊加法將單邊固定的矩形平板拆成四個結構進行疊加，其特性可滿足其中四個邊界條件，剩下的四個邊界條件透過正交函數展開得到壓電平板在單邊固定邊界下之共振頻率與模態振形，並將結果與實驗及有限元素法模擬結果進行驗證。 以晶格波茲曼法結合沉浸式邊界法建立單向流固耦合之二維圓柱繞流數值分析模型，針對圓柱所受之阻力、升力、卡門渦街之頻率進行模型之收斂性分析，並與文獻、商用模擬軟體之收斂後的模型進行驗證，並分析不同流速下的結果，以三維圓柱繞流數值模型進行收斂性分析，找出足夠準確且計算時間合理的模型設定，分析不同流速下的結果並與文獻做比較，在模型中加入壓電平板的幾何邊界，並加以平板疊加法之動態響應分析，建構雙向流固耦合模型以計算可變形壓電平板在流場中與流場的交互作用，求解壓電能量擷取系統之位移與輸出電壓，並從結果可看出當流場中的卡門渦街頻率接近壓電平板之第一振動模態頻率時，壓電能量擷取系統有最大的變形與最高的輸出電壓。 使用晶格波茲曼法進行數值計算透過搭配圖形處理器，相比使用中央處理器進行多核心運算，計算速度提高14倍，考慮到使用晶格波茲曼法結合沉浸式邊界法在高網格數模型會有計算速度大幅下降的現象，提出映射層演算法演算法並加入後，在二維高網格數模型中速度提升為原先6倍以上，且計算時間不受固體邊界增加而大幅降低，使模型更適用於複雜幾何結構之流固耦合分析。在雙向流固耦合模型中透過修正固體位移計算之更新週期，在不影響結果的精度下將速度提升為原先2.5倍，並搭配平板受力簡化模型進一步提高單邊固定壓電平板之第一振動模態響應計算速度。 實驗部分先以雷射都卜勒振動儀量測壓電平板第一振動模態，其頻率與疊加法理論、有限元素法模擬等結果均相符。壓電能量擷取系統之風洞實驗，先以皮托管校正熱線測速儀後，在無障礙物之風洞進行之均勻度及紊流強度量測，在確保風洞流場品質下加入障礙物金屬圓柱及壓電片，建構完整的壓電能量擷取系統，並分別以雷射都卜勒振動儀及示波器，量測在不同流速下壓電平板之位移與電壓，並與雙向流固耦合數值方法結果做比較，兩者有高度的對應性。

This research uses lattice Boltzmann method(LBM) combined with immersed boundary method(IBM) and the superposition method to apply the analytical solution to the energy harvesting system with piezoelectric ceramic bimorphs in the cantilevered boundary condition. Analyze the Karman vortex produced by the metal circular cylinder vibrating piezoelectric ceramic bimorphs, and verified it by experimental measurements. In the calculation of the superposition method, the three-layer structure of the piezoelectric ceramic bimorph is equivalent to a sigle-layer plate based on the plate theory, and the superposition method is used to split the rectangular plate into four structures to satisfy the plate's boundary conditions. The resonant frequency and mode shape of the piezoelectric plate with one side fixed are obtained by theoretical analysis and verified with the finite element method (FEM) results. The lattice Boltzmann method combined with the immersed boundary method was used to establish a numerical analysis model of one-way fluid-structure interaction simulation for flow pass a cylinder in two and three dimension. The convergence analysis of the model was performed on the drag force, lift force, and the frequency of the Karman vortex, and verify the results with literature and commercial simulation software, and analyze the results under different flow rates. A two-way fluid-structure interaction simulation model is constructed by adding the boundary of the piezoelectric plate and the dynamic response of the superposition method to calculate the interaction between the deformable piezoelectric plate and the flow field, and solve the displacement and voltage of the piezoelectric energy harvester system. From the results, it can be seen that the piezoelectric energy harvester system has the largest deformation and the highest voltage when the Karman vortex frequency is close to the first vibration mode frequency of the piezoelectric plate. Using a graphics processor unit to perform LBM analysis, the calculation speed can be up to 14 times that of multi-core computing using a central processor. Since the calculation speed of using IB-LBM model will decrease significantly in high grid number models, the Flash Translation Layer(FTL) algorithm was proposed and added, and the speed was increased to the original more than 6 times, and the calculation time is not highly affected by solid boundary, making the model more suitable for fluid-structure interaction simulation with complex geometric structures. By correcting the update cycle of the solid displacement calculation in the two-way fluid-structure interaction simulation, the speed is increased to 2.5 times, and the accuracy of the results is not affected. The model is combined with a simplified forced plate model to further improve the calculation speed. In the experiment part, the Laser Dopple Vibrometer(LDV) was used to measure the first vibration mode of the piezoelectric plate, and the result was consistent with the results of superposition method and finite element method simulation. For the wind tunnel experiment of the piezoelectric energy harvesting system, a hot-wire anemometer was calibrated by pitot turb, and used to measure the uniformity and turbulence intensity in the wind tunnel without obstacle to ensure the quality of the flow field in the wind tunnel. A complete piezoelectric energy harvest system was constructed by adding onstacle and piezoelectric in the wind tunnel. An oscilloscope and LDV were used to measure the displacement and voltage of the piezoelectric plate at different flow rates. There is a high degree of correspondence between the results of experiments and the two-way fluid-structure interaction simulation model.