利用最小方差法對二維翼型之跡流定位

Abstract

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跡流位置。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。最後將邊界上所求的速度位勢帶入邊界積分式以求解流場中各點位置的速度位勢，再藉由三次曲線(Cubic Spline)法線方向速度會有最小值的關係式找出跡流軌跡位置。本文將以賈可斯基翼為例，尋找出均勻流流經翼型之跡流位置。

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 Boundary Integral Equation to find the flow field velocity potential at the collocation points. Use cubic curve (Cubic Spline) 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.