Noise propagation mechanisms in presence of a rotational flow are currently receiving some attention from the aircraft industry. Different methods are used in order to compute the acoustic wave propagation in sheared flows in terms of pressure perturbations (e.g. Linearized Euler Equations (LEE), Lilley’s and Galbrun’s equations). Nevertheless, they have drawbacks in terms of computational performance (high number of DOFs per node, inadequacies of classical numerical schemes like standard FE). In contrast with other studies, in this work, the fluctuating total enthalpy is selected as the main variable in order to describe the acoustic field, which obeys to a convected wave equation obtained by linearization of momentum (Crocco’s form), energy and continuity equations and with coefficients depending on flow variables. The resulting 3D convected wave operator is an extension of the Möhring acoustic analogy which is able to predict the sound propagation through rotational flows in the subsonic regime and is well adapted to FE discretization. A 2D convected wave equation is generated from the previous operator. This is followed by a numerical solution based on FEM with two types of boundary conditions: non reflecting BC and incident plane wave excitation. The numerical results are used to estimate the reflection coefficient generated by the shear flow. The new acoustic wave operator is compared to well-known theories of flow acoustics (Pridmore-Brown wave operator) and shows promising results. Finally additional development steps are presented so further improvements on the new operator can be carried out.

Inside micro cavities, specific dissipative mechanisms influencing acoustic wave propagation occur due to viscous and heat-conducting nature of the fluid. This work focuses on a possible extension of the so called “Low Reduced Frequency” model for acoustic wave propagation in a thermoviscous fluid. This extension is built starting from geometrical and physical assumptions (boundary layer theory, straight waveguides) and consists in the incorporation of a stationary laminar and subsonic mean flow. The resulting equivalent fluid model provides a new damping coefficient which depends on the Mach number, the shear and thermal wave numbers and the cross-sectional profiles of axial velocity and temperature. The main application area is the study of acoustic attenuation within automotive catalytic converters or also thin fluid layers like cooling systems in small electronic devices. This formulation has been implemented for a simple one dimensional thin tube. Convergence to the original model in the absence of mean flow has been reached and comparisons with variational solutions given by Peat show good agreements.