Numerical simulation of characteristics of wave propagation and reflection coefficient in a helix-acoustic black hole

A new type of the acoustic black hole beam-a helix-acoustic black hole-is proposed to overcome the spatial restriction on modular acoustic black hole structures. The modular acoustic black hole structure, consisted of a base and several number of acoustic black hole beams, has potential to apply into real engineering world. There are two main sections in an acoustic black hole beam: (1) a uniform thickness part and (2) an acoustic black hole region of which the thickness decreases according to the power-law profile. Conventional acoustic black hole beams can be ultimately assembled as 8-10 acoustic black hole beams on a modular acoustic black hole structure. In this article, a different shape of an acoustic black hole beam is newly designed to allow the assembly of more acoustic black hole beams on the modular acoustic black hole structure. The shape of the helix-acoustic black hole is such that the thickness of the acoustic black hole region smoothly decreases, just like a conventional acoustic black hole beam, as well as twisting along the longitudinal direction. The normal direction of the bottom surface in the uniform thickness is the same along the longitudinal axis in the conventional acoustic black hole beam. However, the normal direction of the helix-acoustic black hole of the bottom surface in the acoustic black hole region is different along the longitudinal direction. It is necessary to use numerical simulations to explore the performance of the helix-acoustic black hole beam because the shape of acoustic black hole region is different from the conventional one. Two types of numerical simulations were conducted: transient analysis and modal frequency analysis. From the transient analysis, the acoustic black hole effect was investigated by comparing the travel time which is dependent on the variation of the thickness. Using modal frequency analysis, the reflection coefficients between the conventional acoustic black hole beam and helix-acoustic black hole beam are also compared. It is noted that reflection coefficients were additionally compared depending on how "sharply" or "smoothly" they were twisted in the acoustic black hole region of the helix-acoustic black hole. Those results demonstrate that the helix-acoustic black hole has a dynamic characteristic similar to that of conventional acoustic black hole beams, which means that more helix-acoustic black holes can be assembled on the modular acoustic black hole structure by resolving the spatial restriction and leading to expectations of better performance.