Finite element modelling of acoustic field inside small components: application to an annular slit terminated by an aperture in an infinite screen

Abstract

Investigating accurately the acoustic behaviour of small fluid-filled cavities and ducts and their association is a problem of persistent importance, because nowadays both experimental investigations and theoretical modelling must provide results of increasingly higher precision. The motivation here is provided mainly by the acoustic measurement tools used for both the calibration of microphones and the artificial ear (IEC 60318-1). Both improved analytical models of small acoustic components (small tubes and slits), which account for the effects of the viscous and thermal boundary layers accurately in the frequency range of interest (20 Hz to 20 kHz), and experimental characterization of their input impedances (with a relative uncertainty of the order of magnitude of 10−2) have been proposed recently (Rodrigues et al 2008 J. Sound Vib. 315 890–910). Existing analytical procedures for coupled components suffer from strong approximations at the interfaces between narrow tubes and slits or other elements as well as the open space. A dedicated numerical model can be used in order to investigate accurately the acoustic field at these interfaces. The numerical model presented in the paper relies on a suitable linear exact formulation, based upon two coupled equations involving particle velocity and temperature variation (Joly 2010 Acta Acust. United Acust. 96 102–14) and utilizes an adaptive anisotropic meshing technique to model correctly the strong variations which occur around the geometrical discontinuities and inside the boundary layers. Application to a 2D axisymmetrical device (annular slit ending in an aperture in an infinite screen) is considered to present the ability of the method. Acoustic pressure, temperature variation and particle velocity distributions inside and around the end of the slit are depicted, and the input acoustic admittance of the slit obtained numerically is compared with both experimental and analytical results available.

Transfer function of small convergent–divergent (C–D) nozzles and opposite (D–C) devices filled with thermo-viscous fluid at rest

“…These two variables are subject to Dirichlet conditions on the rigid isothermal boundaries (v ¼ 0; s ¼ 0). A time-periodic source set at the entrance is a virtual adiabatic (@ n s ¼ 0) source described by its normal velocity [11,13,15]. This velocity is non-uniformly distributed over the section of the component: it has the same profile as the analytically calculated particle velocity (which accounts for the viscous boundary layers) over the diameter of the tube (which is the same as the one of the component entrance).…”

“…This velocity is non-uniformly distributed over the section of the component: it has the same profile as the analytically calculated particle velocity (which accounts for the viscous boundary layers) over the diameter of the tube (which is the same as the one of the component entrance). Note that such profile of the input particle velocity vanishes at the wall of the component in order to avoid discontinuities of the particle velocity on the rigid boundaries that must satisfy the non-slip condition [11,15]. The results for the pressure transfer function and input impedance obtained from the numerical model have been calculated using mean quantities over cross-section at the input or output of the component.…”