Hybrid Inverse Airfoil Design Method for Complex Three-Dimensional Lifting Surfaces

Abstract

A method is presented for inverse design of airfoils for complex three-dimensional wings in incompressible e ow. The method allows for prescription of inviscid velocity distributions over different cross sections of the wing in a multipoint fashion. A hybrid approach is used to determine the shapes of the wing cross sections that satisfy the design specie cations. The airfoils forming the cross sections of the wing are generated using an inverse code for isolated airfoil design. A three-dimensional panel method is then used to obtain the velocity distributions over the resulting wing. The isolated airfoil velocity distributions are then used as design variables in a multidimensional Newton iteration method to achieve the design specie cations on the wing. The method is particularly useful for complex geometries such as junctures, where three-dimensional and interference effects have to be accounted for in the design process. Akey feature ofthedesign method is a schemeto avoid using thepanel method for sensitivity computations for the Newton iterations. This scheme not only results in signie cant reductions in computation time but also enables the integration of any readily available three-dimensional analysis code in executable form. Examples are shown to demonstrate the usefulness of the method. Nomenclature Cl = airfoil lift coefe cient, chord D1 c = airfoil/section chord F = vector containing the residuals J = Jacobian matrix n = number of design variables V = airfoil/section velocity nondimensionalized by the freestream velocity v = desired value for the velocity difference over a segment ® = angle of attack, deg 1V = velocity difference over a segment normalized by the freestream velocity ±x = vector containing the corrections to the design variables Subscripts i = index of design variable for the Newton iteration r = property associated with the wing root t = property associated with the wing tip w = property associated with the wing 2D = property associated with an airfoil in isolation 3D = property associated with a cross section of a three-dimensional lifting surface