Analogue transformation acoustics in aeronautics

The objective of the paper is a critical review within the context of aeronautical applications of the Analogue Transformation Acoustics (ATA) approach for the modelling of acoustic metamaterials. The ATA approach has been introduced to overcome the limitation of the metamaterials design methods based on the Standard Transformation Acoustics (STA) imposed by the requirement of a strict formal invariance of the governing equations. Indeed, in case of acoustic perturbations propagating within moving media, the convective terms are responsible of the failure of formal invariance under the action of conformal mappings as a consequence of the combination of space and time derivatives. The ATA is based on the concept of analogue spacetimes and fully relies on the analytical tools of Lorentzian differential geometry. The great advantages of the method is the possibility to handle a background flow, conversely to the STA which fails in presence of convection. Despite the undoubted appeal of this feature in the eyes of an aeroacoustician, its potential has not been completely disclosed yet. The class of transformations that yield a physically meaningful aerodynamics in the virtual analogue spacetime has not been explored in details, preventing the application of the method in aeronautics. The present paper analyses the relationship between the the analogue velocity field with a realistic potential flow. The analytical comparison is validated through numerical simulations of two classic benchmarks: the irrotational flow of an inviscid, incompressible fluid around a circular cylinder and the flow through a bumped wall. The target acoustic behaviour is the cancellation of the scattering (cloaking) induced by the cylinder and the bump.