Numerical study of plume-induced flow separation

Abstract

Laminar, Mach 26 flow past a blunt-nosed cone with a spherical after-body experiencing axial mass injection from its base was numerically studied in two calculations. Mass injection rate for both calculations was 0·15 lb/sec and Reynolds numbers relative to base diameter were 735 and 4150. Numerical computations were performed with a code (AFTON 2A) which solves the time-dependent Navier-Stokes equations for systems with axial symmetry and mass injection. Steady flow in both cases was approached asymptotically with time from initial flow fields derived from simple inviscid theory. At the lower Reynolds number, the cone and after-body boundary layers remained attached, and the interaction between the incident airstream and the injected plume gases is similar to that of two impinging supersonic streams. By contrast, at the higher Reynolds number the cone and after-body boundary layers both separate, giving rise to a double-vortex pattern and a complex system of shock waves. AFTON 2A results were compared with a theoretical inviscid model of a mass source in a uniform hypersonic stream. In the AFTON 2A calculations, the plume radius is predicted to be much larger, with an increased plume volume caused by heat transfer across the dividing streamline. Although absolute magnitudes of plume-shock and dividing-streamline radii differ from inviscid prediction, ratios of these radii are consistent with the inviscid scaling law; i.e. radii are inversely proportional to the fourth root of the plume drag coefficient. The two calculations also demonstrated a structural difference in the plume inner core. At the lower Reynolds number the inner core was nearly isentropic. By contrast, an amount of heat sufficient to destroy isentropy penetrates the inner core of the plume at the higher Reynolds number.