Slow waves in ducts with external SBH insertion and perforated boundaries

An acoustic duct with external sonic black hole (E-SBH) insertion differs from the widely studied conventional configuration in which SBH components are located inside the duct. The E-SBH has the foreseeable benefit of avoiding flow obstruction inside the conduit while preserving the desired SBH effects. The characterizations of such SBH configurations alongside the wave propagation properties along the duct, however, have been less investigated. In this study, we analyze an E-SBH with perforation-modulated boundaries by means of theoretical, numerical and experimental methods. Wentzel-Kramers-Brillouin (WKB) solutions and their applicable ranges are first developed, allowing for a comprehensive characterization of slow-wave phenomena in both bare E-SBH and perforation-modulated E-SBH (PME-SBH) configurations. These solutions, verified against numerical simulations, provide a complete and analytical description of wave speed variations and define theoretical slow-wave limits for a given set of system parameters. By incorporating perforated boundaries and optimizing the perforation parameters, PME-SBH is shown to entail enhanced wave retarding effect, maintaining slow-sound with fewer inner rings. Finally, time-domain experiments confirm the predicted slow-wave effects in both external SBH configurations.