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Inverse method with geometric constraints for transonic aerofoil design
Author(s) -
Fray J. M. J.,
Slooff J. W.,
Boerstoel J. W.,
Kassies A.
Publication year - 1986
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620220204
Subject(s) - transonic , airfoil , mathematics , supersonic speed , residual , finite volume method , inverse problem , mathematical optimization , flow (mathematics) , inverse , aerodynamics , geometry , mathematical analysis , algorithm , mechanics , physics
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.