Denis Lafarge

Spatial Fourier‐transform method for measuring reflection coefficients at oblique incidence. II. Experimental results

A method using spatial Fourier transforms for measuring the plane‐wave reflection coefficient at oblique angles of incidence has been proposed in an earlier paper [M. Tamura, J. Acoust. Soc. Am. 88, 2259–2264 (1990)]. The present paper gives experimental verification of the method. Experimental results are shown for two types of samples: a perfectly absorbing plane (an imaginary plane in the air) and a layer of a polyurethane foam backed by a hard plywood board. The measured results are generally in good agreement with the theoretical value (for the first sample) or with the results calculated from the acoustical parameters of the material (for the second sample). The agreement shows the usefulness of the method for measuring acoustic properties of absorbent materials.

An improved multimodal method for sound propagation in nonuniform lined ducts

An efficient method is proposed for modeling time harmonic acoustic propagation in a nonuniform lined duct without flow. The lining impedance is axially segmented uniform, but varies circumferentially. The sound pressure is expanded in term of rigid duct modes and an additional function that carries the information about the impedance boundary. The rigid duct modes and the additional function are known a priori so that calculations of the true liner modes, which are difficult, are avoided. By matching the pressure and axial velocity at the interface between different uniform segments, scattering matrices are obtained for each individual segment; these are then combined to construct a global scattering matrix for multiple segments. The present method is an improvement of the multimodal propagation method, developed in a previous paper [Bi et al., J. Sound Vib. 289, 1091-1111 (2006)]. The radial rate of convergence is improved from O(n(-2)), where n is the radial mode indices, to O(n(-4)). It is numerically shown that using the present method, acoustic propagation in the nonuniform lined intake of an aeroengine can be calculated by a personal computer for dimensionless frequency K up to 80, approaching the third blade passing frequency of turbofan noise.

Influence of pore roughness on high-frequency permeability

The high-frequency behavior of the fluid velocity patterns for smooth and corrugated pore channels is studied. The classical approach of Johnson et al. [J. Fluid Mech. 176, 379 (1987)] for smooth geometries is obtained in different manners, thus clarifying differences with Sheng and Zhou [Phys. Rev. Lett. 61, 1591 (1988)] and Avellaneda and Torquato [Phys. Fluids A 3, 2529 (1991)]. For wedge-shaped pore geometries, the classical approach is modified by a nonanalytic extension proposed by Achdou and Avellaneda [Phys. Fluids A 4, 2561 (1992)]. The dependency of the nonanalytic extension on the apex angle of the wedge was derived. Precise numerical computations for various apex angles in two-dimensional channels confirmed this theoretical dependency, which is somewhat different from the original Achdou and Avellaneda predictions. Moreover, it was found that the contribution of the singularities does not alter the parameters of the classical theory by Johnson et al..

Characteristic dimensions and prediction at high frequencies of the surface impedance of porous layers

The surface acoustic impedance of a glass wool and a reticulated foam is measured in a free field up to 20 000 Hz. The characteristic dimensions Λ and Λ’ can be calculated for the glass wool, and the surface impedance can be predicted with no adjustable parameters. The motion of the frame is not taken into account. The agreement between measurement and prediction is good. For the foam, the characteristic dimensions cannot be calculated, because the geometry of the frame is not simple. A correct choice of Λ and Λ’ allows a precise prediction of the surface impedance for a large range of frequencies and different thicknesses.

Measurement and prediction of the reflection coefficient of porous layers at oblique incidence and for inhomogeneous waves

Near‐field acoustical holography (NAH) is used in the present work to measure the reflection coefficient of porous layers from normal to grazing incidence and for inhomogeneous waves. Measurements are compared with predictions obtained from a recent model. A lateral propagating mode inside the porous layer is evident.

On the dynamic viscous permeability tensor symmetry

Based on a direct generalization of a proof given by Torquato for symmetry property in static regime, this express letter clarifies the reasons why the dynamic permeability tensor is symmetric for spatially periodic structures having symmetrical axes which do not coincide with orthogonal pairs being perpendicular to the axis of three-, four-, and sixfold symmetry. This somewhat nonintuitive property is illustrated by providing detailed numerical examples for a hexagonal lattice of solid cylinders in the asymptotic and frequency dependent regimes. It may be practically useful for numerical implementation validation and/or convergence assessment.

Characteristics of penalty mode scattering by rigid splices in lined ducts

In lined ducts, incident modes are scattered by axially and circumferentially nonuniform impedance. Experiments and numerical calculations have proved that this mode scattering can reduce the liner performance in some cases. This paper is devoted to the characterization of the penalty mode scattering excited by hard-walled splices which often exist in lined ducts. It is shown that, in the range of small splice angles, the transmission loss may decrease sharply with increasing splice angle when one mode, which is near cut-off or has high azimuthal order, is incident. When the incident sound field is composed of several acoustical modes, the phase interferences of incident modes are important for the penalty mode scattering. The effects of other parameters, e.g., liner length, mode quasiresonance on the penalty mode scattering are also presented.

Reciprocity and antireciprocity in sound transmission through layered materials including elastic and porous media

Abstract Sound transmission through elastic solids and porous media having an elastic frame involves longitudinal and transverse waves. A modelling of sound propagation through layers of these media by transfer matrices, which is equivalent to a representation by analogous multi-port circuits was performed previously. The different ports of the circuits are related to the normal and the tangential strains and velocities on the two faces of the layers. The use of impedance matrices instead of transfer matrices shows that the coupling between the normal and the tangential conjugate variables is antireciprocal, and is reciprocal for conjugate variables having the same nature. Moreover, it can be proven that the transmission loss through strafied materials in contact with the same fluid on the and the rear face is the same in opposite directions of propagation.

Comments on ‘‘Rigorous link between fluid permeability, electrical conductivity, and relaxation times for transport in porous media’’

Recently, Avellaneda and Torquato [Phys. Fluids A 3, 2529 (1991)] derived several expressions for both the static and dynamic permeability for flow through porous media, in terms of the characteristic viscous relaxation times. In this Brief Communication the focus is on the physical interpretation, Darcy’s law is explicitly obtained, and a slightly misleading statement (which has no effect on the mathematics but may induce erroneous interpretations) is corrected.

Sound Propagation in Varying Cross Section Ducts Lined with Non-uniform Impedance by Multimode Propagation Method

A Multimode Propagation Method (MPM) is proposed to study sound propagation in varying cross section lined ducts. The lined impedance may be arbitrary nonuniform in both axial and circumferential directions. It may be local or bulk reaction (in this paper, only local reaction boundary condition is studied). The cross section variation need not to be slow. The dimensionless wavenumber K (K = kR, where k = !=c, R is the typical radius of ducts) may be high enough to suit for the turbofan duct problem. This method models the above wave propagation as a scattering problem. It decomposes the whole duct into three contiguous regions with respect to axial coordinate z: left and right semiinflnite uniform rigid ducts connected by an arbitrary varying cross section transition lined region. The sound pressure and axial particle velocity are decomposed using the local rigid modes, which are known a priori and correspond to the exact, physical decomposition in the uniform rigid regions, while they provide a coupled, mathematical representation of the total wave fleld in the transition region. Evanescent modes are included. Two stable reformulations, of the Helmholtz wave propagation problem, are obtained accounting for exact boundary conditions and initial conditions by introducing modal impedance Z and an additional operator T. The complicated boundary conditions (varying section with axial and circumferential nonuniform impedance) are included in the formulas naturally. The two difierential matrix equations are integrated simultaneously from the free end (or the output end for flnite duct with known radiation modal impedance) to the source plane. Memory requirement is in the order O(N 2 t ), but not O(N 2 t Nz) where Nt is the number of mode truncation, Nz refers to the number of steps of axial discretization. The modal coe‐cients of re∞ection and transmission are then obtained which means that only one calculation is needed for any kind of source conflguration. This method obeys the energy conservation when the liner is not dissipative and could be generalized to account for the presence of ∞ow.