Application of Dirichlet's Principle in A New Panel Method for Surface and Tip Flows of Lifting Bodies

Abstract

At present time the computational models based on solution of perturbation potential flow are widely used to solve the Neumann's problem on the surface of a lifting body. Employing surface paneling discretization of the potential according to the curvature of body and wake surfaces, Fredholm's second kind integral equation is solved numerically, regarding the dipole strength of potential. In the present variational surface panel method a decomposition of the boundary surface is carried out for analytical integration on body and wake panels by polyhedral subpaneling. Using Taylor's series expansion of the dipole strength in the vicinity of each analysed point and employing least squares minimization of its derivatives, the relevant minimal perturbation velocity field on the body surface is obtained. By means of the corresponding streamlines an optimisation of the body boundary surface discretization is done through new asymmetrical streamlines adapted repaneling (SAR). Numerical calculations with wings and propellers are performed in order to prove the agreement of the estimated circulation and pressure distribution, as well as induced downstream flow characteristics with their experimental data. Special attention is paid to obtain a reliable estimation of the tip flow characteristics of wings and propellers.