Localisation of a stationary time-harmonic dipole sound source in flows using time-reversal simulation

Abstract

This work analyses the accuracy of numerical Time-Reversal (TR) simulations implemented using two different Time-Reversal Mirror (TRM) configurations for localising and characterising a stationary acoustic dipole source in a mean flow. The forward time evolution of the acoustic fields is simulated by means of the numerical solution of the inhomogeneous 2-D Linearised Euler Equations (LEE) with uniform subsonic mean flow. Only the acoustic pressure is recorded with two line arrays (LAs) of boundary nodes in a TRM corresponding to the top and bottom boundaries. The time-reversed acoustic pressure history is used as input data for simulating two numerical TR experiments; (a) one line array (LA) in a TRM corresponding to the top boundary and (b) two LAs in a TRM corresponding to the top and bottom boundaries. The Root-Mean-Square (RMS) of the time-reversed acoustic pressure field obtained by the first experiment indicates only one spatial maxima region (focal spot), therefore incorrectly suggests that the source is a monopole, whereas the second experiment correctly reveals the source to be a dipole. The local acoustic pressure history at two source locations is shown to be coherent with relative phase exactly equal to  radian, thereby confirming the dipole source nature. This demonstrates that two LAs in a TRM located on either sides of the mean flow are required to take into consideration, the complete phase information and thereby accurately characterise a dipole.