Direct Correlation of Noise and Flow of a Jet

A direct correlation between the flow and noise of a jet—between the “cause” and the “effect”—has been measured. Two kinds of correlations were explored, namely (1) the broad-band turbulence signal (hot-film) with the broad-band acoustic signal (microphone), and (2) the narrow-band filtered turbulence signal with the narrow-band filtered acoustic signal; the latter approach was ultimately adopted. The correlations were analyzed in terms of an extension of Proudman's form of Lighthill's integral for aerodynamic noise; this yielded the relative intensity and spectrum of the noise originating from unit volume of a jet (35 locations) and received at a farfield point (r = 96D, φ = 40°); this in turn led to the relative emission of successive “slices” of a jet versus axial distance X over the measurement range (1D ⩽ × ⩽ 7D). Qualitative agreement was found with Ribner's X° law, and the spectral peaks for each slice were located in frequency essentially as predicted by Powell. The maximum normalized broad-band correlation of 1%–2% implies roughly that a turbulence “eddy” centered at the hot-film contributes only 1%–2% of the rms sound pressure at the microphone. The total effective number of uncorrelated noise-producing eddies is thus of order (1/0.02)2, or some 2500 on an equal strength basis.