A computer program is developed to implement a numerical solution of the incompressible, steady flow around two dimensional multi-element aerofoils having a rough or smooth surface.
The potential flow over the aerofoil is solved by replacing the aerofoil contour with a polygon of plane panels and using linear distributed vorticity on the panels to represent the aerofoil. Boundary layer effects are included in the calculation by utilizing linear distributions of sources on the panels to model the displacement effects due to the boundary layer. Boundary layer development is calculated using Thwaites' method for the laminar portion of the boundary layer and Head's entrainment method for the turbulent portion of the boundary layer. Empirical correlations are used to predict transition. A modified skin friction law accounts for the effects of roughness on the wall shear stress. The boundary layer development calculation must make use of static pressure distributions calculated by the potential flow analysis. An iterative solution procedure is thus required with the source distribution in the potential flow analysis being determined from the preceding pass through the boundary layer development calculation