Summary
It is known from Lighthill's exact solution of the incompressible inverse problem that in the inverse design problem the surface pressure distribution and the free stream speed cannot both be prescribed independently. This implies the existence of a constraint (regularity condition) on the prescribed pressure distribution. The same constraint exists at compressible speeds. In this paper, an inverse design method for transonic airfoil is presented. In the method, the target pressure distribution contains a free parameter that is adjusted during the computation to satisfy the regularity condition derived in this paper. A few design results are presented here in order to demonstrate the capability of the method.
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References
Slooff, J. W.: A survey of computational methods for subsonic and transonic aerodynamic design. Paper at ICIDES-I, Austin, Tex., U.S.A., 1984.
Volpe, G., Melnik, R. E.: The role of constraints in the inverse design problem for transonic airfoils. AIAA Paper 81-1233, 1981.
Carlon, L. A.: Transonic airfoil design using cartesian coordinates. NASA CR-2578, 1976.
Tranen, T. L.: A rapid computer aided transonic airfoil design method. AIAA Paper 74-501, 1974.
Henne, P. A.: An inverse transonic wing design method. AIAA Paper 80-0330, 1980.
Shankar, V.: A full potential inverse method based on a density linearization scheme for wing design. AIAA Paper 81-1234, 1981.
Davis Jr., W. H.: Technique for developing design tools from the analysis methods of computational aerodynamics. AIAA Paper 79-1259, 1979.
McFadden, G. B.: An artificial viscosity method for the design of supercritical airfoils. Ph. D. Thesis, N. Y. University, 1979.
Fray, J. M. J., Slooff J. W., Boerstoel, J. W., Kassies, A.: Inverse method with geometric constraints for transonic airfoil design. Int. J. Num. Meth. Eng.22, 327–339 (1986).
Greff, E., Mantel, J.: An engineering approach to the inverse transonic wing design problem. Comm. Appl. Num. Meth.2, 47–56 (1986).
Takanashi, S.: Iterative three-dimensional transonic wing design using integral equations. J. Aircraft22, No. 8 (1985).
Lighthill, M. J.: A new method of two-dimensional aerodynamic design. ARC RM 2112, April 1945.
Nørstrud, H.: High speed flow past wings. NASA CR-2246, 1973.
Zhu Z. Q., Bai, X. S.: The computation of transonic analysis and design. Acta Mech.78, 81–94 (1989).
Strand, T.: Exact method of designing airfoils with given velocity distribution in incompressible flow. J. Aircraft10, No. 11 (1973).
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Zhu, Z.Q., Xia, Z.X. & Wu, L.Y. An inverse method with regularity condition for transonic airfoil design. Acta Mechanica 95, 59–68 (1992). https://doi.org/10.1007/BF01170804
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DOI: https://doi.org/10.1007/BF01170804