Kinematic wavepacket model for broadband shock associated noise in underexpanded supersonic jets

Motivated by the success of wavepackets in modelling the noise from subsonic and perfectly-expanded supersonic jets, we apply the wavepacket model to imperfectly expanded supersonic jets. Previous work by Savarese et al. [1] adopted a kinematic single-point wavepacket model first formulated by Lele [2]. Recent studies with subsonic jets, however, have demonstrated the importance of capturing the ‘jittering’ of wavepackets in order to correctly predict the intensity of far-field sound. Following the analysis of Cavalieri and Agarwal [3], we extend their methodology to model the acoustic sources of broadband shock-associated noise in imperfectlyexpanded supersonic jets using cross-spectral densities of the turbulent and shock-cell velocity quantities. We model the downstream propagating vortices as wavepackets, with the aim of determining the relationship between coherence decay, the statistical representation of jitter, and broadband shock-associated noise. Unlike the subsonic case where inclusion of coherence decay amplifies sound pressure level over the whole acoustic spectrum, we find that it does not play a critical role in increasing sound amplitude for shock-cell noise. When higher-order shock-cell modes are used to capture high frequency noise, however, the inclusion of a jittering wavepacket is necessary.