A doublet panel method for generalized supersonic lifting surfaces

Abstract

An improved doublet panel method for calculating the aerodynamic properties of lifting surfaces in supersonic flows is derived and implemented. The lifting surfaces are discretized into an arbitrary number of doublet panels with unknown singularity strength, whose perturbation velocity potentials satisfy the supersonic Prandtl-Glauert equation. To prevent field singularities in the potential and velocity, the doublet strength of each panel is piecewise linear and continuous in the streamwise direction. In addition, the panels can be swept at different angles at their leading and trailing edges, allowing for generalized lifting surfaces to be analyzed. The component of the perturbation velocity that is normal to the lifting surface at each specified control point induced by each doublet panel is calculated. Applying the flow tangency boundary condition at the control points forms a linear system that is solved for the difference in doublet strength between the trailing and leading edges of each panel. The perturbation velocity components of this method are compared to those of the Woodward method. The numerical solutions of this method are compared to the analytical solutions of some test cases. Convergence is obtained for both the lift coefficient and the perturbation velocity component distribution.