Validation of acoustic-analogy predictions for sound radiated by turbulence

Abstract

Predicting sound radiated by turbulence is of interest in aeroacoustics, hydroacoustics, and combustion noise. Significant improvements in computer technology have renewed interest in applying numerical techniques to predict sound from turbulent flows. One such technique is a hybrid approach in which the turbulence is computed using a method such as direct numerical simulation (DNS) or large eddy simulation (LES), and the sound is calculated using an acoustic analogy. In this study, sound from a turbulent flow is computed using DNS, and the DNS results are compared with acoustic-analogy predictions for mutual validation. The source considered is a three-dimensional region of forced turbulence which has limited extent in one coordinate direction and is periodic in the other two directions. Sound propagates statistically as a plane wave from the turbulence to the far field. The cases considered here have a small turbulent Mach number so that the source is spatially compact; that is, the turbulence integral scale is much smaller than the acoustic wavelength. The scaling of the amplitude and frequency of the far-field sound for the problem considered are derived in an analysis based on Lighthill’s acoustic analogy. The analytical results predict that the far-field sound should exhibit “dipole-type” behavior; the root-mean-square pressure in the acoustic far field should increase as the cube of the turbulent Mach number. The acoustic power normalized by the turbulent dissipation rate is also predicted to scale as turbulent Mach number cubed. Agreement between the DNS results and the acoustic-analogy predictions is good. This study verifies the ability of the Lighthill acoustic analogy to predict sound generated by a three-dimensional, turbulent source containing many length and time scales.