邊界元素法對二維翼型之流場分析

Analysis of Two-Dimensional Airfoil Problems Using Boundary Element Methods

廖健凱(Chien-Kai Liao)

指導教授 ： 黃維信

國立臺灣大學/工學院/工程科學及海洋工程學研究所/碩士(2011年)

https://doi.org/10.6342/NTU.2011.00549

摘要

本文以二維翼型為主要研究之對象，尋找均勻流流經此翼型之尾流位置。本文假設流場內之流體滿足勢流，以邊界元素法描繪物體邊界之幾何及在邊界元素上的物理量分布狀況，使用高斯積分法對離散後的積分方程式進行積分並組成核函數矩陣，求解此翼型表面上之速度勢。最後，將所求的速度勢強度帶入解析公式，以求解流場中各位置點的速度分量，再藉由所算出的法線方向速度尋找出尾流軌跡位置。本文將以賈可斯基翼、及NACA系列之NACA0012、NACA4412翼型為例，尋找出均勻流流經翼型之尾流位置。

關鍵字

翼型 ； 邊界元素法 ； 速度勢 ； 賈可斯基翼 ； 尾流

並列摘要

This study focuses on two-dimensional flows of airfoils, looking for the wake position for a uniform flow over an airfoil. The flow is assumed to satisfy the potential theory. First of all, the Boundary Integral Equation is applied to solve the velocity potential on the boundary of the airfoil. Once the strength of the velocity potential is solved, it is substituted into the analytical formula to find the flow field velocity components at the collocation points. The constraint of normal velocity components to be zero are then used to determine the location of the wake. The Joukowski airfoil and NACA airfoils are used as test cases.

並列關鍵字

airfoil ； boundary element method ； velocity potential ； Joukowski ； wake

參考文獻

[1] Mikhlin, S. G., Integral Equations. London: Press, 1957.

[2] Jaswon, M. A., “Integral Equation Methods in Potential Theory─I” Proc. Roy. Soc. Lond., vol. A273, pp. 23-32, 1963.

[3] Symm, G. T., “Integral Equation Methods in Potential Theory─II” Proc. Roy. Soc. Lond., vol. A275, pp. 33-46, 1963.

[4] Rizzo, F. J. “An integral equation approach to boundary value problems of

classical elastostatics” Quart. Appl. Math., vol. 25, pp. 83-95, 1967.