삼각형 패널 상에 선형적으로 분포된 다이폴 강도를 갖는 패널법의 정식화

Abstract

A high-order potential-based panel method based on Green's theorem, with piecewise-linear dipole strength on triangular panels, is formulated for the analysis of potential flow around a three-dimensional wing. Previous low-order panel methods adopt square panels with piecewise-constant dipole strength, which results in inherent errors. Square panels can not represent a high curvature lifting body, such as propellers, since the four vertices of the square panel do not locate at the same flat plane. Moreover the piecewise-constant dipole strength induces inevitable errors due to the steps in dipole strength between adjacent panels. In this paper a high-order panel method is formulated to improve accuracy by adopting a piecewise linear dipole strength on triangular panels. Firstly, the square panels are replaced by triangular panels in order to increase the geometric accuracy in representing the shape of the object with large curvature. Next, the step difference of the dipole strength between adjacent panels is removed by adopting piecewise-linear dipole strength on the triangular panels. The calculated results by the present method is compared with analytical ones for simple non-lifting geometries, such as ellipsoid. The results for an elliptic wing with zero thickness at finite angle of attack are compared with Jordan's results. The comparison shows reasonable agrements for the both lifting and non-lifting bodies.