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CSME 2024/02
Volume 45 No.1
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67-76
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Modified Von Karman Treftz Transformation with Computation of Aerodynamic Coefficients
Toufik Yahiaoui a and Toufik Zebbiche a
aInstitute of Aeronautics and Space Studies, University of Blida 1, BP 270 Blida 09000, Algeria.
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Abstract:
The aim of this work is to develop a numerical calculation program to generate new airfoils geometries using a modified conformal transformation of the Von Karman Treftz type from an ellipse, and by the consideration of the nonzero trailing edge angle, as a generalization of the classical transformations using a circle. The numerical calculation is defined by a new method based on the consideration of the transformation of a triangle connecting the two critical points with the point on the ellipse boundary, giving a single image in the airfoil plane. This is for each selected boundary point of the ellipse. Nodes condensation is used to refine the points in the neighbourhood of the leading edge region, in order to ensure its curvature. The determination of the maximum thickness value is presented. In this case, the interpolation of the coordinates of the airfoil points is made by the cubic spline interpolation. Normalization of the airfoil geometry is performed to reduce its size to the standard shape having a chord equal to unity. Infinity of shape of the airfoils is obtained by the variation of the trailing edge angle, the abscissa and the ordinate of the ellipse center, and the ratio of the ellipse radii’s. The second part of the developed program consists in determining the aerodynamic pressure drag, lift and pitching moment coefficients of a subsonic flow around the generated airfoils by the panel method, with a comparison to the classic Von Karman airfoils.
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Keywords: Critical Points, Von Karman Treftz Transformation, Joukowski Transformation, Circle, Ellipse, Airfoils, Trailing Edge angle, Cubic spline interpolation, Stretching function, Aerodynamics coefficients, Subsonic flow, Panels method
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*Corresponding author; e-mail: z_toufik270169@yahoo.fr
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©
2024
CSME , ISSN 0257-9731
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