Theoretical and Numerical Modeling of Acoustic Metamaterials for Aeroacoustic Applications

The advent, during the first decade of the 21st century, of the concept of acoustic metamaterial has disclosed an incredible potential of development for breakthrough technologies. Unfortunately, the extension of the same concepts to aeroacoustics has turned out to be not a trivial task, because of the different structure of the governing equations, characterized by the presence of the background aerodynamic convection. Some of the approaches recently introduced to circumvent the problem are biased by a fundamental assumption that makes the actual realization of devices extremely unlikely: the metamaterial should guarantee an adapted background aerodynamic convection in order to modify suitably the acoustic field and obtain the desired effect, thus implying the porosity of the cloaking device. In the present paper, we propose an interpretation of the metamaterial design that removes this unlikely assumption, focusing on the identification of an aerodynamically-impermeable metamaterial capable of reproducing the surface impedance profile required to achieve the desired scattering abatement. The attention is focused on a moving obstacle impinged by an acoustic perturbation induced by a co-moving source. The problem is written in a frame of reference rigidly connected to the moving object to couple the convective wave equation in the hosting medium with the inertially-anisotropic wave operator within the cloak. The problem is recast in an integral form and numerically solved through a boundary-field element method. The matching of the local wave vector is used to derive a convective design of the metamaterial applicable to the specific problem analyzed. Preliminary numerical results obtained under the simplifying assumption of a uniform aerodynamic flow reveal a considerable enhancement of the masking capability of the convected design. The numerical method developed shows a remarkable computational efficiency, completing a simulation of the entire field in a few minutes on mid-end workstations. The results are re-interpreted in term of boundary impedance, assuming a locally-reacting behavior of the outer boundary of the cloaking layer. The formulation is currently being extended to the analysis of arbitrarily complex external flows in order to remove the limitation of the background uniform stream in the host