The global stability or instability of supersonic ramp flow and of a jet in supersonic cross-flow is investigated. The three-dimensional Navier-Stokes equations are solved directly with no model applied. Ramp flow is studied at Mach number 4.8 and Reynolds numbers 6,843 and 3,422, based on inflow boundary layer displacement thickness and freestream velocity. The laminar base flows are stable in two-dimensions. Simulations in three-dimensions show that the high Reynolds number case is globally unstable, while the flow is stable at the lower Reynolds number, suggesting that a critical Reynolds number for instability exists between these two Reynolds numbers. A spanwise wavelength of 12 times the incoming boundary layer displacement thickness is found to be the most unstable for the ramp flow with Reynolds number of 6,843. Similar conclusions are found for a sonic jet injected into a Mach 6.7 crossflow, which is stable at low jet momentum flux ratios (J_p), but becomes globally unstable as J_p increases. Streamwise vortices are observed in the unstable jet cases and a spanwise wavelength of 8 times the incoming boundary layer displacement thickness is found to be the preferred mode of global instability.
展开▼
