A sponge-layer damping technique for aeroacoustic Time-Reversal

Abstract

This paper presents the underlying theory, associated mathematical modelling and analysis of a sponge-layer damping technique, termed the Time-Reversal-Sponge-Layer (TRSL), that significantly improves the performance of aeroacoustic Time-Reversal (TR). The TR technique requires the use of multiple Line Arrays (LAs) in a Time-Reversal Mirror (TRM) to accurately predict the source location and its characteristics. However, it is shown that when using multiple LAs, the interference between the opposite propagating fluxes near the LA boundaries results in the formation of spurious local maxima regions throughout the computational domain, thereby reducing the capacity of TR to resolve acoustic sources. The novel TRSL technique proposed in this work minimises this unwanted interference by damping the flux normally incident on a LA boundary and is implemented using the Pseudo-Characteristic Formulation (PCF) of the two-dimensional Linearised Euler Equations (LEE). The performance of TRSL is assessed by simulating a number of test cases such as an idealised time-harmonic monopole, dipole and lateral quadrupole sources as well as multiple (two) dipole sources of different strengths located in a nonuniform mean shear flow. The use of TRSL suppresses the formation of spurious maxima and significantly improves the source map, thereby demonstrating the effectiveness of this damping technique. The performance of TRSL is compared with two other methods: a TR superposition technique and Conventional Beamforming (CB). The TR superposition technique prevents the flux interference problem near the LA boundaries by superposing the instantaneous time-reversed acoustic pressure fields computed from individual LAs. The source map obtained using the superposition technique was found to be identical to that obtained using the TRSL damping technique, however, the computational cost was much higher. A comparison with CB indicated that although CB accurately predicts the aeroacoustic source location, the relative magnitudes of the side-lobes in the CB source map(s) are substantially higher in comparison to the corresponding TR source map(s). It was also shown that TR with use of the TRSL is better suited for resolving multiple coherent sources in a domain than the CB method, especially when one source is much weaker than other sources in the domain.