Receptivity at the nozzle lip of under-expanded supersonic impinging jets*

The receptivity of an under-expanded supersonic impinging jet flow at the sharp nozzle lip to acoustic impulse disturbances is investigated as a function of geometric and flow parameters. Receptivity is defined as the internalisation of an external disturbance into the initial condition that either initiates or sustains a vortical instability. In the case of under-expanded impinging jet flow subjected to an acoustic disturbance receptivity is located at the nozzle lip and amenable to an impulse response analysis using the linearised compressible three-dimensional Navier-Stokes equations. Under-expanded supersonic jets emanate from an infinite-lipped nozzle with a nozzle pressure ratio of 3.4 for two nozzle-to-wall distances (h) of 2 and 5 jet diameters have been studied. It is found that for both cases, acoustic disturbances located at angles greater than 80$^o$ from the jet centreline have the highest receptivity for all azimuthal mode-numbers, except the azimuthal mode-number 2 for h=5d. For h=5d there is also high receptivity to acoustic disturbances located at angles 15$^o$ - 50$^o$ from the jet centreline for all azimuthal mode-numbers.