Ben Tahar M., Beriot H.

The propagation of linear acoustic waves in non-potential flows (sheared flows, swirling flows) can be written either by the linearized Euler equations or by the non-classical Galbrun’s equation. These two equations represent exactly the same physical problem but the Galbun’s equation is written only in terms of the lagrangian perturbation of the displacement. It is well known that the formulation naturally associated to Galbrun’s equation gives corrupted results because of the presence of spurious modes at low frequency. This problem, called in the literature as the “lockin” phenomenon, is typical of all the displacement based formulations. To avoid it a mixed pressure-displacement formulation combined with a special finite element was proposed for two dimensional and axisymetric problems. This formulation was tested by comparison with semi analytical models for the propagation in constant or varying lined ducts in sheared and swirling flows. In this paper we develop an extension of the method for three dimensional problems. Two different tetrahedrical elements satisfying the inf-sup condition are proposed. The model is compared with the axisymetric model and results in more complex ducts are presented. [1] “A mixed finite element method for acoustic wave propagation in moving fluids based on an Eulerian-Lagrangian description”, Journal of the Acoustical Society of America, 113 (2), pp 705-716, fev 2003 (F. Treyssede, G. Gabard and M. Ben Tahar), [2] «Validation of a finite element method for sound propagation and vibro-acoustic problems with swirling flows», Journal of Acta Acustica, Vol 90, N° 4, July/August 2004, pp 731-745 (F. Treyssede and M. Ben Tahar) [3] «Comparison of a FEM model with a mutliple-scales solution for sound propagation in varying ducts with swirling flows», Journal of the Acoustical Society of America, (F. Treyssede and M. Ben Tahar), 115 (6), june 2004