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.

An axisymmetric perfectly expanded Mach 1.3 jet, with a Reynolds number based on the nozzle exit diameter (ReD) of 1.1 × 106 and turbulent boundary layer at the nozzle exit, was excited using localized arc filament plasma actuators over a wide range of forcing Strouhal numbers (StDF). Eight actuators distributed azimuthally were used to excite azimuthal modes m = 0–3. Far-field acoustic, flow velocity and irrotational near-field pressure were probed with a three-fold objective: (i) to investigate the broadband far-field noise amplification reported in the literature at lower speeds and ReD using excitation of m = 0 at low StDF; (ii) to explore broadband far-field noise suppression using excitation of m = 3 at higher StDF; and (iii) to shed some light on the connection between the flow field and the far-field noise. The broadband far-field noise amplification observed is not as extensive in amplitude or frequency range, but still sufficiently large to be of concern in practical applications. Broadband far-field noise suppression of 4–5 dB at 30° polar angle peak frequency, resulting in approximately 2 dB attenuation in the overall sound pressure level, is achieved with excitation of m = 3 at StDF ~ 0.9. Some of the noteworthy observations and inferences are (a) there is a strong correlation between the far-field broadband noise amplification and the turbulence amplification; (b) far-field noise suppression is achieved when the jet is forced with the maximum jet initial growth rate frequency thus limiting significant dynamics of structures to a shorter region close to the nozzle exit; (c) structure breakdown and dynamic interaction seem to be the dominant source of noise; and (d) coherent structures dominate the forced jet over a wide range of StDF (up to ~ 1.31) with the largest and most organized structures observed around the jet preferred mode StDF.

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This paper makes contributions towards reduced-order models of wave packets in supersonic, turbulent jets. Wave packets are large-scale turbulent structures that are correlated and advected over distances that are large compared to the integral scales of turbulence, i.e., many jet diameters at the lowest frequencies. They are thought to be responsible for the peak noise radiated at shallow angles to the jet axis. Linear wave packet models based on the Parabolized Stability Equations (PSE) have been shown in the past to be in excellent agreement with statistical structures educed from experimental pressure and velocity data in subsonic jets. Here, we extend these models to supersonic jets and validate them using a Large Eddy Simulation (LES) database for an isothermal and a moderately heated Mach 1.5 turbulent jets. For supersonic jets, inlet conditions for PSE models are ambiguous, as a parallel flow stability analysis shows several unstable modes at the inlet cross section. We develop a bi-orthogonal decomposition and project the LES data onto the relevant families of instability waves. These serve as inlet conditions, including the amplitude and shape functions, for PSE solutions which are then favorably compared to the near-field pressure fields educed from LES. C 2013 AIP Publishing LLC. [http://dx

We study the viscous spatial linear stability characteristics of the time-averaged flow in turbulent subsonic jets issuing from serrated (chevroned) nozzles, and compare them to analogous round jet results. Linear parabolized stability equations (PSE) are used in the calculations to account for the non-parallel base flow. By exploiting the symmetries of the mean flow due to the regular arrangement of serrations, we obtain a series of coupled two-dimensional PSE problems from the original three-dimensional problem. This reduces the solution cost and manifests the symmetries of the stability modes. In the parallel-flow linear stability theory (LST) calculations that are performed near the nozzle to initiate the PSE, we find that the serrated nozzle reduces the growth rates of the most unstable eigenmodes of the jet, but their phase speeds are approximately similar. We obtain encouraging validation of our linear PSE instability wave results vis-à-vis near-field hydrodynamic pressure data acquired on a phased microphone array in experiments, after filtering the latter with proper orthogonal decomposition (POD) to extract the energetically dominant coherent part. Additionally, a large-eddy simulation database of the same serrated jet is investigated, and its POD-filtered pressure field is found to compare favourably with the corresponding PSE solution within the jet plume. We conclude that the coherent hydrodynamic pressure fluctuations of jets from both round and serrated nozzles are reasonably consistent with the linear instability modes of the turbulent mean flow.