Wavepacket models for supersonic jet noise

Abstract

Gudmundsson and Colonius (J. Fluid Mech., vol. 689, 2011, pp. 97-128) have recently shown that the average evolution of low-frequency, low-azimuthal modal large-scale structures in the near field of subsonic jets are remarkably well predicted as linear instability waves of the turbulent mean flow using parabolized stability equations. In this work, we extend this modelling technique to an isothermal and a moderately heated Mach 1.5 jet for which the mean flow fields are obtained from a high-fidelity large-eddy simulation database. The latter affords a rigourous and extensive validation of the model, which had only been pursued earlier with more limited experimental data. A filter based on proper orthogonal decomposition is applied to the data to extract the most energetic coherent components. These components display a distinct wavepacket character, and agree fairly well with the parabolized stability equations model predictions in terms of near-field pressure and flow velocity. We next apply a Kirchhoff surface acoustic propagation technique to the near-field pressure model and obtain an encouraging match for far-field noise levels in the peak aft direction. The results suggest that linear wavepackets in the turbulence are responsible for the loudest portion of the supersonic jet acoustic field.

Experimental study of turbulent-jet wave packets and their acoustic efficiency

“…The details are provided in Appendix A, where it is shown that the discrepancy between the inferred amplitudes is significantly reduced, again consistent with the hypothesis. Finally, we note that in applications to sufficiently supersonic jets, where there is no mismatch between the acoustic and wave-packet wavelengths at the Mach angle, PSE predictions can be extended directly into the acoustic field with reasonable agreement with the directly measured field from LES [39]. This effect, though not as pronounced at higher Mach number, clearly occurs in that dataset as well.…”

Parabolized stability analysis of jets from serrated nozzles

“…These, and other details of the PSE implementation (e.g. radial discretization and iterative axial marching scheme), have been described by Gudmundsson & Colonius (2011) and Sinha et al (2014).…”

“…Gudmundsson & Colonius (2011) reported similar deficiencies of the PSE model for the round jet instabilities, and Baqui et al (2013) observed the same behavior for instability waves derived from linearized Euler equations. The discrepancy is likely due to nonlinear effects on these modes, as well as a possible inadmissibility of the mildly non-parallel assumption for these long-wavelength wavepackets (Gudmundsson & Colonius 2011;Baqui et al 2013;Sinha et al 2014).…”

“…Suitable numerical considerations (Li & Malik 1997) then allow the solution to be marched downstream. Linear PSE has been applied successfully to predict the coherent wavepackets extracted from data of round jets, both subsonic and supersonic (Gudmundsson & Colonius 2011;Cavalieri et al 2013;Sinha et al 2014).…”

Instability waves and low-frequency noise radiation in the subsonic chevron jet

“…Through parabolized stability equations (PSE) [4][5][6] or linearized Euler equation (LEE) [7], the connections among the linear instability waves inside the potential core, near-field hydrodynamic fluctuations, and far-field noise can be constructed in the linear regime. Although the far-field noise calculated with the linear instability wavepackets is not as accurate as LES in subsonic jets, this approach can still capture some noise emission properties.…”