Acoustic fields in thermo-viscous binary gas mixtures: finite element modelling on adapted meshes

International audienceĂThe acoustic behaviour of thermo-viscous gas mixtures, both in proximity of walls and far from them, differs significantly from those of gases that are assumed to have homogeneous combination of constituents. Indeed, an acoustic field propagating in a gas mixture composed of multiple molecular species having different physical properties, involves several diffusive fields, namely momentum by shear, entropic and concentration variation fields. Unified analytical solutions to the fundamental equations of acoustics in thermo-viscous binary gas mixtures, subjected to non-slip, isothermal and vanishing concentration flux boundary conditions, have already been proposed in an infinite, semi-infinite and finite medium, throughout and beyond the boundary layers. These solutions highlight the strong coupling between the acoustic propagation and the heat and concentration diffusive fields in the boundary layers, while their effects appear to be simple additive processes in the bulk of the medium. However, relevant experimental validations for these analytical solutions are still missing. A finite element solution for the acoustic behaviour of the gas mixture is computed in using a coupled formulation based on particle velocity, temperature and concentration variations. Because of the strong variations of all of these variables inside the boundary layers, anisotropic meshing technique with an adaptive process is required to interpolate the solution. This numerical modelling procedure is applied here to describe a 1D acoustic propagation and the acoustic field in a 2D axisymmetrical enclosure, both considering a helium-argon gas mixture. The results then obtained are compared to analytical solutions in order to check their validity