The research developed by Joukowski to determine the force exerted by a flow on a body around which it is flowing eventually led to the theoretical foundation for practical aircraft construction, and the methods of conformal mapping played an important role in modern aviation. During the 1930s Theodorsen’s iterative method became a pioneer in transforming the exterior of the unit circle onto the exterior of an almost circular contour. But in the potential flow analysis of airfoils, James’s method developed in 1971 turns out to be more successful for all types of contours which do not have corner singularity. We shall develop Joukowski mapping functions, compare numerical solutions of single-element airfoils by both Theodorsen’s and James’s iterative methods, unfold the mechanism of divergence of Theodorsen’s method in the cases where the image boundary is not almost circular, and finally analyze multiple-element airfoils by using von Karman-Trefftz transformations and FFT with Garrick’s method of conjugate functions.
KeywordsUnit Circle Corner Singularity Circular Contour Conjugate Harmonic Function Mobius Transformation
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