A visco-thermal acoustic model and its equivalent properties for narrow slit by considering viscosity of air and thermal dissipation to surrounding structure

Abstract

Acoustic damping in narrow slit becomes significant issues when the slit width is comparable to viscous and thermal skin depth. Acoustic transfer functions between two cavities connected through a narrow slit cannot be predicted precisely by the conventional Helmholtz equation. In this study, air is considered as compressible viscous fluid and linearized Navier-Stokes equation is applied assuming that amplitude of particle velocity is very small. Fourier's law is also applied to account for thermal conductivity between air and surrounding structure. Then, two acoustic damping mechanism can be considered; viscous dissipation in the vicinity of boundaries between air and surrounding structure and thermal dissipation from medium to surrounding structures. Finite element discretization of narrow slit is studied to express gradient of velocity and temperature profile in the vicinity of the boundary between slit and surrounding structure. Velocity obtained numerically is compared to analytical solution and error on the velocity averaged in a cross-section is considered. A simple test rig that has two acoustic cavities connected through a narrow slit is created. Numerical predictions agree well with measured results although computational cost is considerably high. Equivalent density and bulk modulus to be applied in Helmholtz equation are calculated by averaging velocity, pressure, temperature variation. The properties can be applied to other systems as long as the dimension of the slit remains unchanged.