Aeroacoustics of Supersonic Jet Issued from Corrugated Nozzle: New Approach and Prospects

Abstract

It is generally accepted that one of the main sources of acoustic radiation from a supersonic jet is due to spatial instability wave packets propagating downstream within the jet. This approach has enabled us to explain and predict the principal features of sound radiated by a supersonic jet with a circular nozzle. The aim of this present work is to generalize such an approach to jets with a circular nozzle deformed into a weakly corrugated (s-lobed) shape. This leads to the presence of two additional parameters, the lobe number (an integer) characterizing the corrugation wavelength and the corrugation amplitude. Their presence can be shown to lead to a resonant coupling between different instability waves which, in turn, can both intensify and suppress the aerodynamic noise. The assumption of a small corrugation amplitude allows us to consider the problem analytically using disturbance theory methods. The structure of the eigen-oscillations is determined at leading orders, where it is shown that differing azimuthal harmonics are coupled over a wide range of frequencies. The result of such couplings on the radiated sound is significant, even for a small corrugation amplitude. The above suggests that the effect of mode coupling, due to nozzle corrugation, could be used as a tool for noise control in supersonic jets.

Spatial stability analysis of subsonic corrugated jets

“…This observation is consistent with previous works (Kopiev et al. 2004; Gudmundsson 2010; Sinha & Colonius 2015; Sinha et al. 2016 a ).…”

“…Such behaviour was observed analytically by Kopiev et al. (2004), and we expect it to be a common feature in both corrugated jets considered here. Since eigenfunctions for can no longer be associated with a single azimuthal wavenumber , we identify these solutions according to the azimuthal mode from which they emerge (now labelled as ) and whether the (pressure) eigenfunction has peaks aligned with the lobes (referred to with superscript ‘ ’) or flats (superscript ‘ ’), making reference to their cosinusoidal and sinusoidal character (Morris & Miller 1984; Koshigoe & Tubis 1986).…”

“…We expect the conclusions reached in this work to extend to other cases (Kopiev et al. 2004; Sinha et al. 2016 a ).…”

Temporal stability analysis of jets of lobed geometry

“…The temporal growth rate, on the other hand, starts to drop at low frequencies (αa < 0.5), but gradually changes to increase at high frequencies, although both are on a small scale. The different eigenvalues of modes ±1, hence distinctive characteristics of instability waves of modes ±1, are consistent with the analytical results obtained by Crighton (1973) for elliptic vortex sheets and also agree with the findings in the spatial stability analysis carried out by Kopiev et al (2004) (because the mode number 1 is a half of the number of lobes N = 2). Figure 9(c,d) shows the results for N = 3 and N = 5, respectively.…”

“…The open literature on the stability of lobed jets Temporal stability analysis of jets of lobed geometry 3 is however very sparse (Morris 2010). In a study carried out by Kopiev et al (2004) on supersonic jet noise, a spatial stability analysis was undertaken to examine the effects of weak corrugation on the instability characteristics of a parallel vortex sheet with supersonic flow speed. A leading-order asymptotic correction to the complex wavenumber α for the round jet when ǫ → 0 was obtained.…”