On the Use of the Transformation Acoustics Approach in Aeroacoustics

Aim of the paper is to propose a different paradigm in the application of the transformation acoustics to aeroacoustic problems. Indeed, a strategy for the full disclosure of the potential of this groundbreaking concept when an aerodynamic flow plays a key role in the generation and propagation of sound is still missing. The advent of the transformation acoustics has made possible in a simple and elegant way the modeling of devices capable to deeply modify the acoustic response of an object. The application of the approach in presence of convective terms is not straightforward, due to the non- Riemannian structure of the governing equations. Recently, an extension of the approach has been introduced to overcome this difficulty, showing its effectiveness in simulations of simple test cases. Nevertheless, the results are biased by the fundamental assumption that the device should be porous to suitably modify the acoustic field without affecting the background aerodynamics. The approach proposed here removes this unlikely assumption, to focus on the prediction of the surface impedance profile that would modify in the appropriate way the response of the static metamaterial. This is not a trivial task, and the transformation approach would greatly help the designer in the identification of the optimal impedance profiles.