翼理論方程式に関する自己随伴型変分原理について

概要

論文の詳細を見る
Self-adjoint variational principle on the integral equation of wing theory was found without distinction of 2D wing, 3D wing and propeller. It was based on the fact that the solution of the adjoint integral equation is related directory to the solution of the original integral equation expressed by the strength density of bound vortex, if the adjoint camber line is chosen symmetric of the original in flow direction. The self-adjoint functional described by quadratic form has symmetric kernel. The accompanying homogeneous integral equation of 2D wing theory becomes an eigenvalue problem of a polar type of which weight function is the solution for a flat plate. The eigenfunctions were utilized for obtaining canonical form of the functional so that the solution was expanded by the eigenfunctions . Symmetry of 3D wing contour which cancels the irreversibility that the vortex flows out rear is required for existence of the exact self-adjoint variational principle. However, in the case of high-aspect-ratio airfoil or propeller, the self-adjoint variational principle exists without asking the symmetry of wing contour.
社団法人日本船舶海洋工学会の論文
2003-09-25