Summary
The present work extends the approximate analytical solution of Niyogi [9] for shock-free transonic flow past thin symmetric airfoils at zero incidence, to the inverse problem for which the velocity distribution is prescribed and the airfoil shape is to be determined. The first step in the solution of the inverse problem leads to a singular integral equation of Betz's type solution of which has been improved iteratively using the transonic integral equation of Oswatitsch and satisfying the tangency boundary condition on the profile contour. Computational results have been presented for Nieuwland airfoils and a NACA 0012 airfoil, all of which indicate very good agreement with exact solutions.
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Basu, S., Niyogi, P. Approximate solution of inverse shock-free transonic airfoil problem at zero incidence. Acta Mechanica 70, 169–176 (1987). https://doi.org/10.1007/BF01174653
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DOI: https://doi.org/10.1007/BF01174653