Inverse Schwartz–Christoffel Panel Method
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A two-dimensional panel method is proposed based on the Schwartz–Christoffel transformation from a unit circle to a polygonal aerofoil. Although numerical integration of the panel length is necessary, this method gives analytical solution for an aerofoil approximated as a polygon. It is also found that this method solves an extremely thin aerofoil problem properly. This is because the solution is simply an analytical transformation of the potential flow around a circular cylinder. In this paper, an inverse design method of a two-dimensional aerofoil is proposed based on the Schwartz–Christoffel transformation. The velocity distribution in the physical plane is given. Calculations are conducted backward from the solutions of symmetric Joukowski and NACA0012 aerofoils together with non-symmetric NACA4412 where simultaneous equations are solved to get the aerofoil. A non-linear inverse method is finally proposed. Triangular and NACA aerofoils are tested to show the concept.
aerofoil, inverse design, conformal mapping