Leading-Edge Cone Method for Waverider Design

Abstract

Leading edge is a primary element that forms waverider configurations. To design waveriders from given leading edges directly and accurately, a new method named the “leading-edge cone method” has been proposed. The leading-edge cone is a conical surface whose tip lies on the leading edge. The shock surface related to the leading edge is the enveloping surface of multiple leading-edge cones. The geometric relationship between leading-edge cones and the shock surface is a particular case of the Apollonius problem in mathematics. Six conditions of leading-edge cones have been discussed, and mathematical expressions of the shock surface are presented. The leading-edge cone method is then established based on these mathematical expressions. Three test cases and three application cases are employed to validate the effectiveness and accuracy of the leading-edge cone method. Results show that all the cases designed by the leading-edge cone method meet the design requirements, and shocks derived from given leading edges coincide well with the shocks generated in numerical simulations.