# Acoustic Pressure Amplification through In-Duct Sonic Black Holes
## 1 Introduction
It was able to provide superior acoustic enhancement by a factor of 2.5 over a wide range of incident angles with the inclusion of the coiled structure. Inspired by these results, we explore the use of acoustic metamaterials for pressure sensing, considering a fully opened ducted geometry, in order to assess and monitor defaults in HVAC (heating, ventilation and air-conditioning) systems. A concept denoted Sonic Black Hole (SBH) has appeared in the field of noise control with great potential for acoustic energy trapping [16]. It was initially designed for the control of vibrations propagating along a beam with a thickness decreasing according to a power law [17]. The retarding mechanism progressively reduces to zero the effective velocity of the incoming perturbation until it reaches the structure edge, where a non-reflecting condition takes place. This slow-sound generation phenomenon has also been considered for the design of metamufflers in order to trap and dissipate the energy of acoustic waves propagating in a waveguide [18; 19; 20]. Such metamufflers are composed of a set of ring sections separated by air cavities of variable depths distributed along the whole axial length. The radii of the air cavities progressively increase following an expanding power law from the inlet towards the outlet. Initial studies focused on closed SBH configurations [16] for the development of short anechoic terminations. More recently, opened SBHs have also been addressed for the simultaneous reduction of both reflection and transmission [16; 21]. Excellent broadband performance has been achieved, but the problem was to extend the SBH effect towards the low frequency range to tackle, for instance, HVAC fans and pump noise sources below 800 Hz. One solution was to incorporate micro-perforated linings [22] at the entrance of the SBH outer cavities [23; 24]. In this work, we analyze the ability of opened SBHs, already designed as metamurflers for duct noise control, to also work as sensors to enhance incident signals and ensure acoustic monitoring and fault detection in HVAC systems. A critical point is to determine if such dual-purpose metamaterial can be achieved for a similar or different set of constitutive parameters. To the author's knowledge, the use of opened SBH as acoustic sensors has not been examined up to now. Moreover, it is compulsory to consider an opened configuration to comply with situations when there is an axial flow conveyed along the SBH axis. Section 2 will describe the internal structure of the opened SBHs as well as the analytical and numerical models developed for the prediction of their amplification performance. Section 3 will analyze the simulation results obtained on the slow sound, dissipation, impedance matching, and pressure gain performance of the opened SBHs with respect to those achieved by a closed SBH. The analytical transfer matrix approach will be assessed against the numerical model. Parametric studies will be performed to improve the amplification of a broadband incident pulse signal. It will be completed by an optimization study to find out the opened SBH parameters that maximize its sensing properties. In Section 4, an experimental validation is carried out in a low-speed flow duct wind-tunnel to assess the pressure gain performance of a 3D printed opened SBH subjected to different types of acoustic or aero-acoustic excitations. The main results are discussed in Section 5, followed by conclusions and ideas for future work in Section 6.