Influence of nozzle external geometry on wavepackets in under-expanded supersonic impinging jets

Abstract

In this study, large-eddy simulations are utilised to unravel the influence of the nozzle's external geometry on upstream-travelling waves in under-expanded supersonic impinging jets. Three configurations, a thin-lipped, a thin-lipped with a sponge and an infinite-lipped nozzle are considered with the other non-dimensionalised geometrical and flow variables identical for the three cases. Spectral proper orthogonal decomposition is applied to the Mack norm, i.e. the energy norm based on the stagnation energy, to obtain the spatial modes at their corresponding frequency. The spectral decomposition of the spatial modes at optimal and suboptimal frequencies is used to isolate the wavepackets into upstream- and downstream-propagating waves based on their phase velocity. It is found that the external geometry of the nozzle has a significant influence on the first-order statistics even though the governing non-dimensional parameters are the same for all three cases. Multiple peaks emerge in the energy spectra at distinct frequencies corresponding to axisymmetric azimuthal modes for each case. The downstream-propagating wavepackets have a high amplitude at the shear layer of the three jets with the mode shapes resembling Kelvin–Helmholtz instability waves, while the upstream-travelling wavepackets exist in the three regions of the near field, shear layer and inside of the jet. The barrel shock at the nozzle exit appears as a flexible shield, which prevents upstream-travelling waves from reaching the internal region of the nozzle, where the upstream-travelling waves travel obliquely with one side of the wavefront is crawling on the reflected shock while the other side is guided by the shear layer. These latter waves can reach the nozzle lip via inside of the jet. The spectral decomposition of the spatial modes at optimal and suboptimal frequencies show that all three forms of the near field, shear layer and inside jet upstream-travelling wavepackets contribute to the receptivity process while their contributions and strength are altered by the change of the external geometry of the nozzle.

Effects of nozzle-lip thickness on the tones in the near-field pressure spectra and on the initial instability waves of jets

“…It was shown to depend on several flow parameters, such as the angle of incidence, the azimuthal mode number and the frequency of the waves hitting the nozzle, but also on geometric parameters. Thus, for impinging jets, the strengths of the feedback loops are sensitive to the external geometry of the nozzle and to the presence of reflective surfaces upstream of the jets, as illustrated in Weightman et al [5] and Karami and Soria [6]. For screeching jets, they have been known to be sensitive to the thickness of the nozzle lip, on which upstream-propagating waves are reflected back and force the near-nozzle shear layer, at least since the work of Powell [7].…”