Receptivity analysis in under-expanded supersonic impinging jets

This paper presents the receptivity process at the nozzle-lip to an external forcing in the configuration of under-expanded supersonic impinging jets. The nozzle-lip is considered as a linear transformer. Therefore, the linearised three-dimensional Navier Stokes equations in cylindrical coordinate are considered. The mean flow fields are obtained from large-eddy simulations. An impulse response analysis of the linearised system is performed which allows a wide range of frequencies to be excited. The transfer function at the nozzle-lip is used to characterise the receptivity process. The sensitivity of the transfer function to the pulse location and the azimuthal wave number is performed. It is found that external forces at the vicinity of the infinite lip and with Strouhal numbers in the ranges of 0.7 to 6.5 have the highest amplification. This is consistent for all the azimuthal wave numbers in the nozzle-to-wall distance of 2d but not for the azimuthal wave number two for the nozzle-to-wall distance of 5d. For this case, external forces located at angles between 15° and 50° from the jet centreline also have high amplification in contrast to the nozzle-to-wall distance of 2d. Based on these results, the region close to the infinite lip is found to be a prominent candidate to control instabilities in this configuration.