Effect of non-uniform mean flow to the scattering pattern of acoustic cloak

Abstract

During the last decade, most of acoustic cloak researches have been done within a theoretical framework in which the medium is at rest. However, such acoustic cloaks cannot preserve its unique properties or functions in the presence of flow. In this study, we propose a theoretical framework to consider the effect of non-uniform mean flow to acoustic cloak for the purpose of understanding the physics of acoustic cloak within flow and designing a new concept of metamaterial so called aeroacoustic cloak. We formulate a convective wave equation in which the differential operator contains the non-uniform velocity vector coupled with gradient operator and the equivalent source terms due to the mean flow are divided into two terms with their own physical meanings. The performance of existing convective cloak is investigated by using the present formulation in the presence of non-uniform flow. By comparing the existing and present formulations, the polarity and magnitude of equivalent source are compared: the present source shows hexapole pattern whereas the existing source shows quadrupole pattern. The non-uniformity effect was dominant in hexapole pattern. Finally, we found that although the compressibility effect is much smaller than non-uniformity effect in low Mach number range, it is not negligible in high Mach number flow, especially for small Helmholtz number. Understanding the nature of equivalent source is expected to provide a physical insight to design a new acoustic cloak within fluid convection.