Interaction of expansion fan with conical shock at Mach 2

Abstract: This paper numerically investigates the effects of an expansion fan originating from the base of a finite cone on the conical shock wave impinging on a plane surface. In this study, inviscid numerical simulations of compressible flow over a cone (at different cone angles) positioned above a flat plate at a Mach 2. The study showed that the interaction of an expansion fan with an incident conical shock decreases the maximum post-shock pressure (P2,max) and maximum wall pressure (P3,max) compared to an infinite cone. The maximum wall pressure to free stream pressure (P3,max/P1) at the symmetric plane in inviscid simulations is found to have a linear relationship with experimental data obtained from Gai & Teh (2000). Further analysis of separation length (Ls) from their wind tunnel experiments revealed a power-law behaviour with (P3,max/P1)inv for all cone angles and cone heights when normalised by the boundary layer thickness at the impingement location. Keywords: Conical shock wave boundary layer interaction, Separation length, Expansion fan