Fray, J. M. J.; Slooff, J. W.; Boerstoel, J. W.; Kassies, A. Inverse method with geometric constraints for transonic aerofoil design. (English) Zbl 0591.76098 Int. J. Numer. Methods Eng. 22, 327-339 (1986). Summary: An engineering method for the design of aerofoils having a prescribed pressure distribution in subsonic or transonic flow is described. The method is based on an iterative procedure of ’residual-correction’ type. In each iteration step, the difference between a current and a target pressure distribution (residual) is determined by a fast (multi-grid) finite-volume full-potential code. Corrections to the geometry driving the pressure residual to zero are determined by a global, inverse, thin- aerofoil theory based method for the subsonic part of the flow field, and by means of a local, inverse, wavy-wall theory based formula for the supersonic part of the flow field. The determination of the geometry correction has been formulated as a minimization problem in the sense that pressure distribution and geometry requirements may be balanced in a weighted least squares sense. The method is described briefly, including the basic mathematical/physical formulation and the main computational aspects. The capabilities of the method are illustrated by means of examples of aerofoil designs. Cited in 1 Document MSC: 76H05 Transonic flows 76G25 General aerodynamics and subsonic flows 76M99 Basic methods in fluid mechanics Keywords:Dirichlet boundary condition; Neumann boundary condition; design of aerofoils; pressure distribution; iterative procedure of ’residual- correction’ type; finite-volume full-potential code; Corrections to the geometry; pressure residual; global, inverse, thin-aerofoil theory; local, inverse, wavy-wall theory; minimization problem PDFBibTeX XMLCite \textit{J. M. J. Fray} et al., Int. J. Numer. Methods Eng. 22, 327--339 (1986; Zbl 0591.76098) Full Text: DOI References: [1] ’Survey of computational methods for subsonic and transonic aerodynamic design’, paper presented at ICIDES Conf. (Oct. 1984). [2] and , ’The role of constraints in the inverse design problem for transonic airfoils’ A.I.A.A. Paper 81-1233 (1981). [3] and , ’A constrained inverse method for the aerodynamic design of thick wings with given pressure distribution in subsonic flow’, AGARD CP-No. 285, Paper 16 (1980). [4] and , ’Integrating multi-grid relaxation into a robust fast-solver for transonic potential flow around lifting airfoils’, A.I.A.A. Paper 83-1885 (1983), NLR MP 83021 U (1983). [5] ’Technique for developing design tools from the analysis methods of computational aerodynamics’, A.I.A.A. Paper 79-1529 (1979). [6] and , Aerodynamics of Wings and Bodies, Addison-Wesley, Reading, Mass., 1965. · Zbl 0161.22502 [7] Perturbation Methods in Fluid Mechanics, Academic Press, N.Y., 1964. · Zbl 0136.45001 [8] and , ’Thin aerofoil theory based on approximate solution of the transonic flow equation’, NACA Report 1359 (1958). [9] The Dynamics and Thermodynamics of Compressible Fluid Flow, The Ronald Press Company, N.Y., 1953. [10] Pearcey, Adv. Aeron. Sci. 3 pp 277– (1962) · doi:10.1016/B978-0-08-006550-2.50021-1 [11] , and , ’Design of transonic aerofoils with given pressure, subject to geometric constraints’, NLR Report TR 84 (to be published). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.