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  • 學位論文

利用渦旋法探討線性水波通過潛沒平板之研究

Study of Linear Water Waves With a Submerged Flat Plate Using Vortex Method

指導教授 : 黃良雄
共同指導教授 : 林孟郁

摘要


針對水平潛沒零厚度薄板和波浪之交互作用,過去已有諸多相關研究,但大多建立在勢流理論之下進行探討,忽略流體的黏性效應,然而結構物附近,卻因為黏性效應會產生不同程度的渦流。因此,使得勢流理論之分析與真實情形有著相當大的誤差,本研究將針對此點進行改善,以呈現出水平潛沒零厚度薄板產生之渦流現象及其效應。 本研究旨在應用Lin and Huang(2009)發展數值模式GVM(Generalized Vortex Method),進行線性水波通過一水平潛沒零厚度薄板之數值模擬研究。此方法以邊界積分法(boundary integral method)求解非旋性流場與自由水面之運動,並利用渦旋法(vortex method)來求解渦度場,其特色在於同時擁有邊界積分法與渦旋法的優點。另一方面,不同於傳統以使用網格的數值方法,此方法毋須對整個計算域進行黏性流求解,只針對流場中具有黏滯作用之範圍集中計算。因此,減少耗費計算的資源和時間,在數值計算中具有相對的優勢。 為了能充分比較勢流與黏流分析之差異,本文先將渦流忽略,並與Yip and Chwang (1997)之解析分析成果進行比較。而後,經由本研究之數值模擬成果發現,對於線性水波通過零厚度薄板之問題,渦流效應不可忽略,且由於零厚度固體邊界的影響,使得薄板兩端點產生較有厚度之薄板更為明顯的渦流;而水平零厚度薄板之不同潛沒水深對於水波變形和渦流尺度的大小,具有極重要的影響。此外,透過水動力分析,了解在勢流理論下被忽略的渦流效應,對零厚度薄板存在不可忽略的作用力和力矩,是造成前人在比較模擬結果和實驗成果時,發現兩者之間存在差異的主要原因之一。

並列摘要


There are many previous studies investigating the interaction between thin plate and water wave, and most of them are analyzed by potential flow theory. But in real fluid flows, there are vortices which are produced by viscous effect around structures. This research improves the analysis to show the effect of vorticity around submerged flat plate under linear surface . In this research, a numerical scheme that employs GVM(Generalized Vortex Method) is used to investigate the interaction of periodic water waves with a submerged flat plate. The irrotational flow field and the motion of the free surface are solved by using a boundary integral technique, and the vortical flow field is solved via a vortex method. This method contains the advantages of boundary integral technique and vortex method. On the other hand, this method doesn’t have to solve whole flow field, and it needs less resources to focus on compactly confined regions. In order to compare the results obtained from a potential-flow approach and the viscous-flow model, at first we present the numerical results in which the vortical part is neglected, and compare them with the analytic solution of Yip and Chwang (1997). According to the numerical results, vortex effects are not negligible for the flow near the flat plate in this search. Although the vortical regions are mainly confined near the two sharp edges of the plate, their scales are relatively larger than the thickness of the thin plate; and the position of the thin flat plate significantly affects the deformation of the water wave and the scale of vortices. According to the dynamic analysis, the effect of vortex which is neglected in potential flow theory has great influence to the thin plate, and it’s the the analytic error in previous studies.

參考文獻


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