A coherence-matched linear source mechanism for subsonic jet noise

Abstract

We investigate source mechanisms for subsonic jet noise using experimentally obtained datasets of high-Reynolds-number Mach 0.4 and 0.6 turbulent jets. The focus is on the axisymmetric mode which dominates downstream sound radiation for low polar angles and the frequency range at which peak noise occurs. A linearized Euler equation (LEE) solver with an inflow boundary condition is used to generate single-frequency hydrodynamic instability waves, and the resulting near-field fluctuations and far-field acoustics are compared with those from experiments and linear parabolized stability equation (LPSE) computations. It is found that the near-field velocity fluctuations closely agree with experiments and LPSE computations up to the end of the potential core, downstream of which deviations occur, but the LEE results match experiments better than the LPSE results. Both the near-field wavepackets and the sound field are observed directly from LEE computations, but the far-field sound pressure levels (SPLs) obtained are more than an order of magnitude lower than experimental values despite close statistical agreement of the near hydrodynamic field up to the potential core region. We explore the possibility that this discrepancy is due to the mismatch between the decay of two-point coherence with increasing distance in experimental flow fluctuations and the perfect coherence in linear models. To match the near-field coherence, experimentally obtained coherence profiles are imposed on the two-point cross-spectral density (CSD) at cylindrical and conical surfaces that enclose near-field structures generated with LEEs. The surface pressure is propagated to the far field using boundary value formulations based on the linear wave equation. Coherence matching yields far-field SPLs which show improved agreement with experimental results, indicating that coherence decay is the main missing component in linear models. The CSD on the enclosing surfaces reveals that the application of a decaying coherence profile spreads the hydrodynamic component of the linear wavepacket source on to acoustic wavenumbers, resulting in a more efficient acoustic source.

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

“…Using just the PSE or first POD mode reduces the prediction by as much as 20 dB over all angles, which indicates that the source of the large discrepancy is likely associated with mechanics missing from the PSE model as opposed to simple truncation errors. Similar discrepancies, noted by Baqui et al [26] while using homogeneous linear models to compute hydrodynamic wave packets, have been attributed to the inability of these models to capture coherence decay. Baqui et al [26] show how, using the two-point coherence measured in the present work, those linear models can be corrected such that they recover the correct acoustic efficiency.…”

“…Similar discrepancies, noted by Baqui et al [26] while using homogeneous linear models to compute hydrodynamic wave packets, have been attributed to the inability of these models to capture coherence decay. Baqui et al [26] show how, using the two-point coherence measured in the present work, those linear models can be corrected such that they recover the correct acoustic efficiency. In light of these results, the large differences in level observed, between the acoustic extrapolation of the full data on one hand, and that of the linear models and the first POD mode on the other, underline once again the importance of the two-point coherence for the acoustic efficiency of wave packets.…”

“…The agreement was found to break down downstream, and from their measurements, the mechanism responsible was unclear. Baqui et al [26] also noted disagreement in the two-point coherence.…”

“…A subsonic wave packet of given spatial amplitude envelope, but no spatial coherence envelope (L c = ∞), generates several orders of magnitude less sound energy than a wave packet of similar amplitude envelope but with a realistic spatial coherence envelope (L c and L with comparable magnitudes). In order for a subsonic wave packet to emit sound at all, it must have a finite spatial envelope, which causes part of the k−f spectrum to "leak" into the radiating zone, resulting in escaping sound emissions [1]; the coherence envelope further enhances this effect [11,26].…”

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.…”