Non-stationary shock motion unsteadiness in an axisymmetric geometry with pressure gradient

Shock wave/boundary layer interaction (SWBLI) is studied in a large area-ratio axisymmetric nozzle comprising a design exit Mach number of 5.58. Shock motion unsteadiness is captured by way of the dynamic wall pressure and is evaluated during overexpanded operations up to a nozzle pressure ratio of 65. Stationary SWBLI is first considered at a nozzle pressure ratio of 28.7 such that the internal flow structure is in a restricted shock separated state; the mean position of the annular separation shock resides at a fixed position. Conditional averages of the wall pressure fluctuations show how the motion of the incipient separation shock is out of phase with pressure fluctuations measured in the separated region downstream of the shock; pressure decreases when the shock moves downstream and vice versa. This is indicative of a long intermittent region, in terms of the boundary layer thickness, as the observed phenomena can be explained by translating the static wall pressure profile along with the shock motion. Non-stationary SWBLI is then considered by increasing the nozzle pressure ratio over time (transient start-up). Under these conditions, the shock pattern varies in strength and structure as it sweeps through the nozzle. A time-frequency analyses of the fluctuating wall pressure during the non-stationary operations, and at the same location that the stationary unsteadiness is analyzed, reveals a similar spectral footprint. However, for relatively slower start-ups, the amplitude of the unsteadiness is reduced by a factor of about seven. The findings demonstrate how the rate at which the nozzle pressure ratio increases can have a significant influence on the amplitude of the unsteady shock foot motion.