利用勢流-渦流分解法探討水波與潛沒平板交互作用之研究

Study of Water Waves with a Submerged Flat Plate Using Potential-Vorticity Decomposition

溫嘉琪(Chia-Chi Wen)

指導教授 ： 黃良雄

國立臺灣大學/工學院/土木工程學研究所/碩士(2008年)

https://doi.org/10.6342/NTU.2008.00762

摘要

中文摘要

關鍵詞：水平潛沒平板，勢流-渦流分解法，渦旋法，邊界積分法，反射率，高階諧和波

本研究旨在應用Lin and Huang(2008)利用勢流-渦流分解法所發展之數值方法，進行週期水波通過一水平潛沒平板之數值模擬研究。此方法的特色在於同時應用了邊界積分法(boundary integral method)與渦旋法(vortex method)的優點。此數值方法應用Helmholtz分解法，將流場分為具有渦度之旋性流場與不具渦度之非旋性流場；其中，利用渦旋法(vortex method)來求解渦度場，另外，以邊界積分法求解非旋性流場與自由水面之運動。此方法保留勢流架構下的優點，能以邊界積分法處理自由水面；另一方面，此方法不同於傳統以使用網格的數值方法，毋須對整個計算域進行黏性流求解，而可只針對流場中具有黏滯作用之範圍集中計算。

為了瞭解水波通過潛沒平板的表現行為，本研究進行一系列水波通過一潛沒薄平板之數值模擬研究。對一薄平板而言，其產生的渦流僅侷限於二端點附近，對於整個流場，此渦流現象不甚明顯；而相較於薄平板本身，二端點之渦度表現範圍則較平板厚度大了許多，顯示出渦流現象並不可被忽略。為能充分比較勢流與黏流分析之差異，本文先將渦流忽略，採用勢流的理論進行分析，並探討反射率與高階諧和波的生成。而後，本文將探討在黏滯效應的作用之下，水波通過平板之渦流生成現象。此外，本文並將針對線性水波之旋性流場與非旋性流場，探討線性水波條件下，以勢流理論分析之適用性。

經由本研究之數值模擬成果發現，分別於勢流與渦流之假設條件之下，潛沒平板之置放深度對於水波變形之影響極有重要性；且對於薄平板而言，渦流效應不可忽略，其對於反射率值與主頻波振幅的變化皆有一定之影響。而對於水波通過薄平板之問題，即使於線性水波的條件下，薄平板之兩端點仍會產生明顯的小尺度渦流，雖然此渦流散逸現象並不明顯，但其對於平板端點處之有效邊界的影響，將使得勢流理論的分析容易產生較大的誤差。

關鍵字

水平潛沒平板 ； 勢流-渦流分解法 ； 渦旋法 ； 邊界積分法 ； 反射率高階諧和波

並列摘要

Abstract

Keywords：Submerged flat plate, Potential-Vorticity decomposition, Boundary integral method, Vortex method, Reflection coefficients, Higher harmonics.

In this research, a numerical scheme that employs a potential-vorticity decomposition is used to investigate the interaction of periodic water waves with a submerged flat plate. This method uses Helmholtz decomposition to decompose the flow field into its rotational and irrotational parts. The vortical flow field is solved via a vortex method; the irrotational flow field and the motion of the free surface are solved using a boundary integral technique. The major advantage of this method is the efficiency of the boundary integral method for solving the free surface motion, and the essentially grid-free nature of the vortex method for the vorticity field, which is predominantly confined in compact regions.

A series of simulations were conducted to study the free surface deformation and the flow pattern. Although the vortical regions are mainly confined near the two sharp edges of the plate, their scales are relatively larger then the thickness of the thin plate. 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 then the generation and evolution of vortices as well as their effects are reported.

According to the numerical results, the position of the thin flat plate affects the deformation of the free surface significantly. Furthermore, vortex effects are not negligible for the flow near the flat plate, and may affect the reflection of surface waves and the generation of higher harmonics. Even if linear waves cases, vortices around the tips of the thin plate affected the effective boundary. This may lead significant error in the analysis using a potential flow theory.

並列關鍵字

Submerged flat plate ； Potential-Vorticity decomposition ； Boundary integral method ； Vortex method ； Reflection coefficients ； Higher harmonics

參考文獻

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