Effect of steady and unsteady flows on the bandgap characteristics of phononic crystal

In this study, we investigate the bandgap characteristics of a two-dimensional phononic crystal consisting of a square lattice array of circular cylinders with consideration of fluid convection. As reported in a recent study, it was experimentally shown that the sound insulation capability of phononic crystal decreased within air flow. To identify the flow effect on the sound insulation in bandgap freqeuncy range, we calculate the acoustic reflectance spectra for the different types of background flows such as uniform flow, compressible potential flow, and turbulent flow. In steady flow, the reflectance spectrum is shifted to lower frequency due to the convection effect in the case that the direction of flow is same with the one of incident wave. In unsteady flow, the aerodynamic noise generated by turbulent flow passing through the phononic crystal is calculated by using Lighthill's analogy. The reflectance at bandgap region decreases when the aerodynamic noise increases in the bandgap frequency range. We investigate the reflectance spectra of the phononic crystals in turbulent flow as inflow speeds or filling ratio increase.