The Three Weak Solution Regimes of Supersonic Conical Flow and Their Impact on Engine Inlets

Abstract

The ideal supersonic ow eld around unyawed right circular cones is unique amongst the various analytical uid dynamic solutions about simple bodies. In two-dimensional ow, two distinct solution regimes exist behind the attached weak shock wave: the subsonic and the supersonic, the former being a small locus in the attached shock solution region. For conical ow however, three distinct regimes occur behind the weak attached shock solution: entirely supersonic, entirely subsonic, and a regime in which a sonic line must be crossed at some point between the cone shock and body. These regimes, their limits and boundaries, and the conditions which de ne them are presented in detail. Based on robust, accurate, and e ciently-computed numerical solutions, conical ow properties are provided in standard formats with each regime clearly indicated. Due to the widespread consideration of conical bodies for compression in supersonic airbreathing propulsion systems, both historically and for contemporary and future concepts, the impact and potential uses of these three regimes for supersonic inlet di users are examined. For mixed-compression and fully external compression applications, only the fully supersonic regime is recommended for any initial conical shock-generating body. Mixed-compression axisymmetric inlet designs may be transiently subjected to mixed supersonic-subsonic regime captured ow from their conical forebodies, and the e ect of such an entrance ow on their internal di users should be considered by their designers. The subsonic shockedow regime merits some consideration in the context of an internal conical body generating the terminal shock in a mixed-compression inlet feeding a gas turbine or subsonic combustion ramjet.