On the use of the analogue transformation acoustics in aeroacoustics

Abstract

The objective of the paper is the assessment of the Analogue Transformation Acoustics (ATA) in the design of acoustic metamaterial for aeronautical applications. The work focuses on the consistency of the background flow resulting from the application of the ATA with the equations governing the potential aerodynamics. Indeed, in case of acoustic perturbations propagating within moving media, the convective terms in the governing equations are responsible for the failure of formal invariance under the action of conformal mappings. The ATA approach overcomes this limitation, introducing the possibility of handling the convective form of the wave equation in a straightforward and elegant way. It is based on the concept of analogue space-time and fully relies on the analytical tools of Lorentzian differential geometry. The present paper analyses the relationship between the analogue velocity field with a realistic potential flow. The method is validated through numerical simulations using two widely assessed acoustic cloaking problems. The preliminary results obtained show that the use of numerical, quasi-conformal mappings can lead to transformed streamlines negligibly deviating from those of the potential velocity field satisfying the fluid-dynamic conservation laws, but with incompatible intensity of the local velocity.