Bandgap characteristics of phononic crystals in steady and unsteady flows

Over the past 30 years, most phononic crystal research has been done for a stationary medium. As reported in a recent experimental study, phononic crystals cannot preserve their bandgaps in the presence of flow. In this study, the bandgap characteristics of a two-dimensional phononic crystal in steady and unsteady flows are investigated theoretically. To identify the effect of the flow on sound insulation in the bandgap frequency ranges, the acoustic reflectance spectra of phononic crystals for different types of background flows, including a uniform flow, a compressible potential flow, and a turbulent flow were calculated. For the steady flows, which include uniform and compressible potential flows, the reflectance spectra are shifted to a lower frequency by the factor 1-M² due to convection when the flow is in the same direction as the incident wave. Moreover, the reflectance spectra of a phononic crystal in a turbulent flow were evaluated for various combinations of inflow speeds and geometric parameters, such as the filling ratio and the number of layers. Due to the aerodynamic noise and fluid convection, a phononic crystal cannot work as an acoustic barrier, rather it becomes an aeroacoustic source in a turbulent flow.