Comparison of a finite element model with a mutliple-scales solution for sound propagation in varying ducts with swirling flows

Fabien Treyssède (1) , Mabrouk Ben Tahar (1)

1 Roberval - Roberval

A multiple-scales (MS) solution is proposed to study sound propagation in slowly varying ducts with mean swirling flows. Instead of the standard linearized Euler equations, the MS method is applied to the so-called Galbrun's equation. This equation is based on an Eulerian-Lagrangian description and corresponds to a wave equation written only in terms of the Lagrangian perturbation of the displacement. This yields simpler differential equations to solve for the MS model as well as simpler boundary conditions. In this paper, Galbrun's equation is also solved by a mixed pressuredisplacement finite element method (FEM). The proposed FEM model has already been tested in authors' previous papers. This model is quite general and is extended here to arbitrary mean flows, including compressibility and swirling flow effects. Some MS and FEM solutions are then compared in order to validate both models.

Mots clés: Acoustic signal processing; Acoustic wave propagation; Finite-element analysis; Partial differential equations; Fluid dynamics; Vortex dynamics

Domaines: Sciences de l'ingénieur [physics]; Acoustique [physics.class-ph]; Acoustique [physics.class-ph]

Fabien Treyssède, Mabrouk Ben Tahar. Comparison of a finite element model with a mutliple-scales solution for sound propagation in varying ducts with swirling flows. Journal of the Acoustical Society of America, 2004, 115, pp.2716-2730. ⟨10.1121/1.1707084⟩. ⟨hal-01067467⟩