Time-reversal in phononic crystal-based water filled pipe

Abstract

Time-reversal based source localization in a conventional water-filled pipe using acoustic waves is hamstrung by the diffraction limit (λ/2). In this paper, time reversal in a novel metamaterial-based water pipeline is studied where a conventional rigid pipe is modified to have periodic square corrugations. Based on the choice of periodicity, such a novel waveguide can support subwavelength resonance in the low frequency regime while exhibiting Bragg resonance, avoided crossing of modes and forbidden bands in diffraction regime. This paper focuses on the latter such that a band structure is obtained. Full wave simulation performed on COMSOL verifies the phononic crystal-like properties in the diffraction regime. Time reversal refocusing is performed by placing a point source in the middle of the corrugated section while a receiver outside the said section records the response of the system. The receiver acts as a Time Reversal Mirror (TRM) such that it flips and reinjects the recorded signal into the system which retraces its path and focuses on its source. Time-reversal refocusing is found to be sensitive to the recorded frequency grains in addition to the energy propagated from the source such that if the source encompasses a band gap, the time reversal quality deteriorates.