Wave-Packet Models for Large-Scale Mixing Noise

Abstract

A wave-packet Ansatz is used to model jet noise generation by large-scale turbulence. In this approach, an equivalent source is defined based on the two-point space-time correlation of hydrodynamic pressure on a conical surface surrounding the jet plume. The surface is sufficiently near the turbulent flow region to be dominated by non-propagating hydrodynamic signatures of large-scale turbulent structures, yet sufficiently far that linear behavior can be assumed in extending the near-field pressure to the acoustic field. In the present study, a 78-microphone array was used to measure hydrodynamic pressure on the conical surface in order to identify parameters for the model and to validate the approach. Six microphones were distributed in the azimuthal direction at each of 13 axial locations spanning the first 8 jet diameters, allowing decomposition of azimuthal modes m = 0 and m = 1. We show that a source model based on a Gaussian correlation function provides a consistently good representation of the noise source attributed to large-scale structures. The results provide evidence that large-scale wave-like structures, known to dominate aft radiation at supersonic phase speeds, are also relevant at subsonic speeds.

Axisymmetric superdirectivity in subsonic jets

“…An envelope function given by a Gaussian, as in ( 3.6), is supported by the near-field measurements of forced jets by Laufer & Yen (1983), and of unforced, heated jets with Mach numbers ranging from 0.9 to 1.58 (Reba, Narayanan & Colonius 2010). Gaussian envelopes were also seen to match envelopes taken from the velocity field of large-eddy simulations of cold M = 0.9 jets (Cavalieri et al 2011b).…”

“…The first is in an average sense: we look for an averaged mutual interference between the different positions of a jet, and particularly for its average effect in the sound field. For this evaluation, correlations and crossspectra are appropriate measures, and, especially in the near field, as shown by Tinney & Jordan (2008) and Reba et al (2010), these prove to be significant over a region extending several jet diameters from the nozzle exit. Furthermore, since for many practical applications determination of the radiated spectra is sufficient, this can be accomplished by coupling such correlation data with an acoustic analogy, as done, for example, by Karabasov et al (2010), among others, or with a Kirchhoff surface, as shown by Reba et al (2010).…”

“…For this evaluation, correlations and crossspectra are appropriate measures, and, especially in the near field, as shown by Tinney & Jordan (2008) and Reba et al (2010), these prove to be significant over a region extending several jet diameters from the nozzle exit. Furthermore, since for many practical applications determination of the radiated spectra is sufficient, this can be accomplished by coupling such correlation data with an acoustic analogy, as done, for example, by Karabasov et al (2010), among others, or with a Kirchhoff surface, as shown by Reba et al (2010). For such an approach, stability calculations may constitute an appropriate dynamic model, and indeed it has been shown that reasonable A. V. G. Cavalieri, P. Jordan, T. Colonius and Y. Gervais predictions can be obtained for the radiated sound at low angles (Colonius, Samanta & Gudmundsson 2010).…”

The impulse response of a high-speed jet forced with localized arc filament plasma actuators

“…By positioning the probes just outside the shear layer, we obtain a non-intrusive measurement of the hydrodynamic pressure field that is linearly driven by large-scale structures. [12][13][14][15][16][17] This avoids the strong nonlinear vorticity and entropy disturbances inside the shear layer, as well as the acoustic waves that dominate further outward. 12,15 Plasma actuation manipulates the LSS, so that the forcing effect can be conveniently assessed by analyzing the NFP.…”

Sensitivity analysis of an equivalent source model for military jet aircraft noise

“…These wavepackets consist of traveling waves with finite extent whose amplitudes grow and decay as a result of turbulence instabilities; they are responsible for correlated noise generation through Mach wave radiation. Source characterization and radiation based on wave packet models have been described by Suzuki and Colonius, 4 Reba et al, 5 etc. The different spectral shapes seen in supersonic jet noise to the sideline (rounded) and downstream (peaked) have been described in terms of wavepacket broadening by Papamoschou.…”