Identification of Jet Instability Waves and Design of a Microphone Array

We propose a diagnostic technique to detect instability waves in a round jet using a conical microphone array. The detection algorithm is analogous to the beam-forming technique, which is used with a far-field microphone array to localize noise sources. By replacing the reference solutions used in the conventional beam-forming with eigenfunctions from a linear stability analysis, the amplitude of the low-frequency azimuthal instability waves can be inferred. We use a DNS database and experimental measurements of the mean flow to design a phased microphone array which is placed just outside the shear layer near the nozzle exit. We validate the technique in experiments by checking for consistency of the radial decay, phase correlation, and streamwise evolution of the hydrodynamic pressure. The comparison between the experiment and linear stability analysis shows good agreement, particularly near the most amplified frequency of each azimuthal mode.