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

Abstract

This paper details the statistical and time-resolved analysis of the relationship between the near-field pressure fluctuations of unforced, subsonic free jets (0.4 M 0.6) and their far-field sound emissions. Near-field and far-field microphone measurements were taken on a conical array close to the jets and an azimuthal ring at 20• to the jet axis, respectively. Recent velocity and pressure measurements indicate the presence of linear wave packets in the near field by closely matching predictions from the linear homogenous parabolized stability equations, but the agreement breaks down both beyond the end of the potential core and when considering higher order statistical moments, such as the two-point coherence. Proper orthogonal decomposition (POD), interpreted in terms of inhomogeneous linear models using the resolvent framework allows us to understand these discrepancies. A new technique is developed for projecting time-domain pressure measurements onto a statistically obtained POD basis, yielding the time-resolved activity of each POD mode and its correlation with the far field. A single POD mode, interpreted as an optimal high-gain structure that arises due to turbulent forcing, captures the salient near-field-far-field correlation signature; further, the signatures of the next two modes, understood as suboptimally forced structures, suggest that these POD modes represent higher order, acoustically important near-field behavior. An existing Green's-function-based technique is used to make far-field predictions, and results are interpreted in terms of POD/resolvent modes, indicating the acoustic importance of this higher order behavior. The technique is extended to provide time-domain far-field predictions.

Wave-Packet Models for Jet Dynamics and Sound Radiation

“…But careful observation reveals that the hydrodynamic region of the jet comprises an organised structure: there exist coherent, high-amplitude oscillations, saturated in black and white in Figure 1, and that have the form of a wavepacket. This coherent-structure signature has been observed and studied experimentally for over 50 years [9,10,11,12,13,14]; a recent observation by Breakey et al [14] is shown in section 3 ( Figure 6).…”

“…3.3.4 Spectral Proper Orthogonal Decomposition (ex-ample7.m, example8.m) We now further evaluate the statistics of the stochastic source by taking spectral POD of the CSD in eq 46, using the approach described in section 2.4.2. Figure 14 [14,17], shows that rank reduction is possible with a small number of modes. The first four modes for this case are shown in figures 15 and 16 14 .…”

“…Figure 14 [14,17], shows that rank reduction is possible with a small number of modes. The first four modes for this case are shown in figures 15 and 16 14 .…”

“…Early sound-source models, such as proposed by Lighthill for instance, were based on an assumption of com- Fig. 6: Axisymmetric hydrodynamic pressure signature of a turbulent jet [14] pact sources. This was motivated by the 1950s view that turbulence was comprised of disorganised eddies characterised by the integral turbulence scales.…”

“…In both subsonic and supersonic cases, the L c L limit, synonymous with the stochastic-eddy view of 11 The figures can be generated using matlab script example5.m, which performs the acoustic computation numerically, using the free-space Green's function. The source domain, y 1 = z 1 ∈ [−10, 10], was discretised with N=401 points and the sound field computed on a polar arc of radius, SPL (arbitrary dB) [14,17], subsonic and supersonic cases differ. In the former case, superdirective radiation is again observed (albeit less marked than in the time-periodic model), but with SPL levels boosted by almost 30dB (three orders of magnitude).…”