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Inverse method with geometric constraints for transonic aerofoil design. (English) Zbl 0591.76098

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.

MSC:

76H05 Transonic flows
76G25 General aerodynamics and subsonic flows
76M99 Basic methods in fluid mechanics
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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).
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