Acoustically informed statistics for wavepacket models

Resumo

© 2018 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.The dominant acoustic radiation from turbulent jets has been associated with coherent wavepacket structures in the core. Predictive models for jet noise are therefore often designed using the statistics of decomposed coherent fluctuations, which display wavepacket attributes. In the absence of a universal definition for the wavepacket component of fluctuations, there exist various approaches to educe wavepackets using different techniques, such as azimuthal and/or proper orthogonal decompositions, on variables including pressure and velocity. This yields distinct models that differ from each other. In this work, we suggest a candidate field, comprised of the irrotational and isentropic component of momentum fluctuations, termed the acoustic component/mode, to obtain wavepacket statistics. We test the statistical properties of this mode to show that it reproduces wavepacket statistics known to be crucial for acoustic field modeling, and smoothly degenerates to the pressure field (scaled by the ambient speed of sound) outside of the turbulent core. A Large-Eddy Simulation of a turbulent Mach 0.9 jet is considered. The acoustic component extracts the wavepacket form of turbulent momentum density in the turbulent jet by effectively filtering out the high-energy hydrodynamic fluctuations. Wavepacket properties, including local spatio-temporal coherence and radiative efficiency, are demonstrated through several statistical analyses. Cross-spectral-density maps and amplitude envelopes of the acoustic mode show higher spatio-temporal coherence than axisymmetric components of raw fluctuations, which are typically used to define traditional wavepacket structures. The fluctuation amplitude of the acoustic mode scales directly according to a homogeneous wave propagator. Furthermore, compared to the raw pressure fluctuations, it optimally reconstructs the near and farfield acoustic radiation. The inherent difference between the acoustic mode and the pressure field is related to the distribution of phase speeds: at all jet Mach numbers, the former successfully filters out the convective hydrodynamic component, thus correctly isolating those components that are efficient at radiating sound.