Computation of Two-Dimensional Potential Flow Using Elementary Vortex Distributions

The two-dimensional potential flow problem is formulated using surface-vorticity distribution coupled with the conventional zero-normal-flow boundary condition. More specifically, velocity and pressure distributions are computed on the surface of a circular cylinder and NACA basic thickness form airfoils. A second-order equation defines the profile curve of the cylinder, and the bounding surface of the airfoil is analytically represented by a higher-order expression. The surface-vorticity method coupled with zero-normal-velocity boundary condition gives a Fredholm integral equation of the first kind. An elementary vortex distribution technique which utilizes a linear distribution on each element is employed to approximate the integral equation by a set of linear algebraic equations. The resulting coefficient matrix has diagonal entries larger than other entries, which is a crucial factor in numerical solution. Nonlifting and lifting flows are computed for NACA symmetrical airfoils with very high accuracy.