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Monday, July 8 • 15:50 - 16:10

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We consider acoustic wave propagation in periodic scaffolds saturated by Newtonian slightly compressible fluids. The wave-induced fluctuations are superimposed to the steady incompressible flow. To analyze the wave dispersion, two approaches are examined: the periodic homogenization (PH) and the Floquet-Bloch wave decomposition (FB). Pursuing the first approach, the homogenization of the Navier-Stokes equations in the rigid skeleton provides the dynamic permeability of the effective porous medium which captures the wave propagation for wave lengths significantly larger than the characteristic porosity size corresponding to the one period of the lattice. The dispersion phenomenon is remarkable for low frequencies, whereas constant phase velocity characterizes the asymptotic behaviour for larger wave numbers. Using the second approach, the FB decomposition enables to capture the wave response for wave numbers within the whole first Brillouin zone. We derive the equations of the cell problems describing the local fluctuations of the wave polarization. Several models are considered. For the inviscid static fluid, the pressure, or velocity formulations are derived. The computational analysis for scaffolds of different types and with variable porosity was performed, showing the band gap between the two lowest frequency modes. Further, using the FB wave decomposition ansatz, we derived a model of viscous fluids in the scaffolds, respecting effect of the fluid convection flow at a steady state upon which perturbations induced by the wave propagation are superimposed. Differences in the wave dispersion between the inviscid and viscous fluid are reported. Dispersion effects influenced by the fluid advection are illustrated for different fluids. Numerical illustration are given.


Pierre Belanger

Professor, Pierre Belanger


Monday July 8, 2019 15:50 - 16:10 EDT
Westmount 1