Field panel method with grid stretching technique for solving transonic potential flow around arbitrary airfoils

Abstract

The Field Panel Method (FPM) with grid stretching technique, presented in this paper, was developed for solving transonic full potential flow around arbitrary airfoils at incidence. In this method, the total potential values are represented by boundary integrals together with a volume integral. The volume integral domain includes both inside and finite outside of the configuration and can be discretisized in a Cartesian grid which may penetrate into the configuration surface. Thus, we avoid the very difficult task of generating body-fitted grids around complex configurations. The boundary potential values are obtained by implementing a standard panel method (symmetrical singularity model), whereas the field potential values are estimated by solving the full potential equation (using AF3 scheme in a Cartesian grid) with approximate inner and proper outer boundary conditions. Furthermore, the grid stretching technique has been utilized that allows to capture the shock waves in a much better quality. It is also shown that both field grid and panel distribution have to be stretched at the same time. Results for transonic potential flows about NACA0012 and RAE2822 airfoils at different Mach numbers and incidences are obtained and compared with other numerical solutions. Great improvement in shock wave quality was achieved by using the present method.