VALIDATION OF ANALYTIC CONVECTIVE CORRECTIONS FOR METACONTINUA IN THE AEROACOUSTIC SPACETIME

This article deals with the validation of two analytical spacetime corrections for the extension of the acoustic metafluid model to aeroacoustics. The need for convective metafluid corrections is due to the performance decay of a statically-designed acoustic metafluid device in presence of a mean flow in the hosting fluid. Aeronautical applications cannot disregard the presence of a Mach number which causes the distortion of acoustic propagation pattern due to the coupling between acoustic propagation and fluid dynamics phenomena. Hence, analytical corrections represent one of the possible strategies to overcome such performance decay. For a more comfortable manipulation and the introduction of the analytical corrections, a spacetime reinterpretation of the characteristic equations is needed. Two analytical corrections, derived from Taylor’s and Prantdl-Glauert’s transformations, and several Mach numbers up to 0.3 are considered during the validation process. The test case considers a rectangular domain occupied by a metafluid embedded in a conventional medium domain, characterized by a uniform background flow and where a monopole source emits acoustic perturbations. The numerical setup is chosen to eliminate any spurious effects introduced by the analytical approximations and to limit, as much as possible, those related to the numerical implementation. Moreover, it legitimates the comparison between the corrections used. To ensure the continuity of the acoustic propagation between the two media, a crucial role is covered by the correct imposition of the boundary conditions. The importance of using primitive variables in doing so is underlined. Numerical simulations are implemented in the frequency domain using the commercial FEM solver COMSOL Multiphysics.