撓性樑於方柱尾流中之渦漩誘發振動分析

Vortex-Induced Vibrations of a Flexible Cantilever Beam in the Wake of a Square Cylinder

仁飄零(Binyet, Emmanuel Mbondo)

指導教授 ： 張禎元

國立清華大學/工學院/動力機械工程學系/博士(2020年)

摘要

由於近幾十年壓電材料的普遍性有明顯增加，竟而延伸出許多新壓電獵能器的概念。所謂的壓電獵能器，是利用壓電效應，將動能轉換成電能。舉例來說，可以利用環境中的振動能，透過壓電效應將機械動能轉換成電能。本論文基於此概念，研析流致振動系統，透過流固耦合的理論與實驗參數分析，提出結構振動所產生之應變能最佳化的設計。此流致振動系統包含一端固定於方柱之懸臂式撓性樑以及流速可變之流場系統。該方柱的尾流由於雷諾數的變化，將會發生渦漩洩離。這個現象導致撓性樑兩側行進波性的壓力差，使撓性樑產生振動。也就是說，撓性樑在方柱的尾流中，會因為動壓的不穩定性因振動而產生應變能。另一方面，撓性樑的變形也會反饋到尾流而改變動壓場。也就是說，此撓性樑變形狀，將類似鰻魚或水蛇的鰻行式擺尾方式。此撓性樑的動態反應和應變能因上流速度、集合參數和彎曲剛度來控制。面對這類高強度、多物理量的流固耦合問題，本論文提出兩個分析方法：水洞實驗分析以及數值模擬計算。水洞實驗的部分包括動態反應分析與質點影像測速(PIV) ；模擬計算部分結合計算流體力學與計算固體力學來求取結構振動與流場變化之間的作動響應。從本研究所得到之實驗與計算的結果，經驗證後可將撓性樑的擺動方式可分為分隔板式振動以及行進波式振動。因樑剛度、動壓場、渦流脫落頻率等參數的變化也會引起擺動方式極大改變。雖然波動式變形所造成的應變能可轉換成較高的電能，然而本研究發現，由於擺動頻率相當低且曲率變化可能造成正負電荷互相抵消，故轉換率較低。透過參數分析與實驗驗證，本研究提出撓性樑最大的應變能量，將發生在撓性樑與尾流呈現最佳耦合時。

關鍵字

流固耦合 ； 流致振動 ； 渦漩誘發振動 ； 撓性懸臂樑 ； 壓電獵能器 ； 質點影像測速 ； 計算流體力學 ； 計算固體力學 ； 可再生能源

並列摘要

Owing to the increased availability of piezoelectric materials, there has been a growing interest towards piezoelectric energy harvesters in the last decades as they can use ambient vibrations for powering low-consumption electronic devices. Periodic vortex shedding occurs in the wake of square cylinders placed in fluid flow. This results in a travelling pressure wave in the wake which can cause structural vibrations. When placing a flexible polymeric plate in the wake of a square cylinder, the oscillatory dynamic pressure impinging on the plate will trigger its vibrations. The plate response simultaneously modifies the wake structures and thus the dynamic pressure. If the plate is flexible enough, it starts to undulate in a manner similar to anguilliform swimming motion. Optimum anguilliform swimming motion is almost two-dimensional and therefore, the plate response can be considered as a cantilever beam response. Electricity can be generated from the strain energy resulting from acute bending by using piezoelectric cells attached at the plate surface. The geometric parameters of the bluff body and the beam, the stiffness and the incoming fluid velocity: determine its response and strain energy output. Such a strongly coupled fluid-structure interaction problem was investigated by carrying out experiments in water tunnel involving shape capture and particle image velocimetry studies as well as fluid-structure interaction modelling where computational structural mechanics and computational fluid dynamics solvers are coupled. Results showed that the beam can jump into radically different flapping patterns. From splitter plate oscillations to travelling waves; depending on: the dynamic pressure distribution, the vortex shedding frequency and the beam stiffness. The undulating pattern showing optimum plate-wake interaction leads to greater power output. Piezoelectric energy harvesting from the undulating plate is more challenging as there is a greater risk of charge cancellations resulting from the frequent curvature changes. Moreover, the low flapping frequency also limits the power output.

並列關鍵字

Vortex induced vibrations ； Flow induced vibrations ； Fluid-structure interaction ； Cantilever flexible beam ； Particle image velocimetry ； Computational fluid dynamics ； Computational structural dynamics ； Piezoelectric energy harvester ； Renewable energy

參考文獻

Publications

Binyet, E.; Huang, C. Y.; Chang, J. Y. Polymeric flexible plate in the wake of a bluff body for energy harvesting, Procedia Engineering, 2017, 199, 1296-1301

Binyet, E.; Huang, C. Y.; Chang, J. Y. Characterization of a vortex-induced vibrating thin plate energy harvester with particle image velocimetry. Microsystem Technologies, 2018, 24, 4569-4576.

Binyet, E.; Huang, C. Y.; Chang, J. Y. Water tunnel study of a cantilever flexible plate in the wake of a square cylinder. Microsystem Technologies, in press.

Binyet, E.; Chang, J.; Huang, C. Flexible Plate in the Wake of a Square Cylinder for Piezoelectric Energy Harvesting—Parametric Study Using Fluid–Structure Interaction Modeling. Energies, 2020, 13(10), 2645