Near-field wavepackets and the far-field sound of a subsonic jet

Abstract

This paper details the analysis of the relationship between the near-field pressure fluctuations of an unforced, subsonic free jet (0.4 ≤ M ≤ 0.6) and its low-angle, far-field sound emissions. Azimuthal rings of six microphones recorded pressure fluctuations on a conical surface in the jet near field while an azimuthal ring of three microphones recorded fluctuations in the far field at θ = 20° and R/D = 47.1. Recent measurements have shown close agreement between the velocity fluctuations up to the end of the potential core of the currently studied jet and predictions from the linear Parabolised Stability Equations (PSE), indicating the presence of linear wavepackets in the jet velocity field. Solutions of the Linearised Euler Equations (LEE) reported in the present paper also show good agreement with measurements, and provide a first step toward a time-domain description of the said wavepackets. Though the agreement for PSE in the velocity field breaks down downstream of the potential core, Proper Orthogonal Decomposition (POD) of the current results shows that the wavepackets do persist in this region and are clearly apparent in the near pressure field. Attention is then turned to establishing a relationship between these wavepackets and the radiated sound by comparing simultaneously-obtained measurements of the far-field pressure both directly to the near-field signature as well as to numerical predictions of the far-field emissions available from a recent technique using a tailored Green’s function. The direct comparisons are made by correlations between the POD modes and the far-field sound. The first POD mode captures most of the flow energy for the frequency range studied, and the correlation between this mode and the far field is nearly identical to the correlation using the full near-field signal. Higher POD modes also show significant correlation to the far field with a different space–time structure than the first mode. The Green’s function predictions are performed both statistically and in the time domain, and though they are shown to be valid for a near-field array with a long axial extent, the experimental limitation of a shorter array (0.5 ≤ x/D ≤ 8.9), which truncates the wavepacket source in the calculations, causes inaccurate predictions for the experimental data. This error is thought to be the result of a spurious source introduced by the truncation that interferes both constructively and destructively with the wavepacket source. A validation problem shows that this error would be smaller for a higher-M jet.