An improved 2.75D method relating pressure distributions of 2D airfoils and 3D wings

Since the 2.75D method takes both wing sweep and taper into consideration, it can build a transformation relation for pressure distributions between a 2D airfoil and a 3D wing under the assumption of conical flow. However, it is observed that the classical 2.75D method proposed by Lock has insufficient transformation accuracy in subsonic flow regions on transonic and subsonic wings. This article proposes an improved 2.75D method to address this problem. For subsonic flow region(s), a method based on Kaman-Tsien compressibility correction is proposed; for supersonic flow region(s), the original method of enforcing an equal normal Mach number between an airfoil and the corresponding wing section is used. Lock's and the improved methods are demonstrated by test cases of transonic and subsonic wings. Results show the transformation accuracy of pressure distributions between 2D airfoils and 3D wings is dramatically improved using the proposed method. The application of these methods to the pressure distribution design for a tapered swept wing section is also demonstrated. The design optimization using the improved 2.75D method leads to a design result being more approximate to a 3D tapered swept wing with a computation effort similar to a 2D airfoil design.