Luc Kelders

Determination of the viscous characteristic length in air‐filled porous materials by ultrasonic attenuation measurements

The concept of viscous characteristic length is used to describe the acoustical behavior of fluid‐saturated porous media in the high‐frequency regime. A method to determine this parameter consists of measuring the wave attenuation in the high‐frequency limit. This method has already been used for porous materials saturated by superfluid 2He. It is tested in the case of air‐filled absorbent materials in a frequency range of [50–600 kHz]. The thermal characteristic length is assumed to be known or measured independently. Two examples are presented. In the first one the method is usable and the viscous characteristic length Λ is deduced from the high‐frequency behavior of the attenuation per cycle. In the second example, an additional attenuation occurs at high frequencies and only an estimate of Λ can be given. Nevertheless, the estimation appears to be rather accurate. The values obtained by this method are compared to those determined by a nonlinear fit of the dispersion curves.

Sound propagation in air-saturated random packings of beads

In the pore space of packed grain material, transport properties are characterized by macroscopic parameters. Some of them, tortuosity, characteristic dimensions, viscous permeability, and trapping constant, are measured for a random packing of glass beads and compared to evaluations performed in previous studies. These parameters are used to predict the surface impedance at normal incidence of a layer of glass beads. The predictions are compared to measurements performed at normal incidence in a Kundt tube.

Ultrasonic surface waves above rectangular-groove gratings

A modal model, initially developed to modelize diffraction of electromagnetic waves by rectangular-groove gratings, is used to describe ultrasonic surface waves above the same structures in air. A simple analytical formulation which provides results comparable to the modal method is presented. Measurements performed on ultrasonic surface waves are compared to predictions obtained with the simplified formulation and the modal model.

ULTRASONIC WAVE PROPAGATION IN RETICULATED FOAMS SATURATED BY DIFFERENT GASES : HIGH FREQUENCY LIMIT OF THE CLASSICAL MODELS

Transmission experiments are performed on high porosity reticulated polyurethane foams saturated by different gases at ultrasonic frequencies up to 800 kHz. An excess attenuation is observed at high frequencies, when the wavelength is not sufficiently large compared to the lateral dimensions of the fibers. At lower frequencies, these experiments lead by using classical models of equivalent fluids, to a fast and reliable method for determining the characteristic length Λ.

Surface waves and leaky waves above a porous layer

Abstract In porous layers saturated by air, the vibrations of the frame induced by an acoustic field in air can often be neglected, due to the large density of the frame. To a good approximation the frame can be considered motionless. The air inside the layer can be replaced by an equivalent fluid in which acoustic waves propagate more slowly than in free air. Similarly, electromagnetic waves propagate more slowly in dielectrics than in vacuum. The close analogy which exists between TM electromagnetic surface waves above grounded dielectrics and acoustic surface waves above a porous layer on a rigid impervious backing is displayed in this work. The velocity of air inside the layer close to the backing is parallel to this impervious and motionless surface, and the electric field close to the perfectly conducting backing is perpendicular to the plane. The correspondence relates perpendicular components of acoustic velocity and electric field. The losses in the equivalent fluid are neglected in a first approach to adapt the description of electromagnetic surface waves for acoustics. Subsequently the damping is taken into account.

Surface waves above thin porous layers saturated by air at ultrasonic frequencies

Experimental evidence of surface waves above thin porous layers of thickness varying from 1.8 to 6 mm of plastic foams having a porosity close to one is presented. Phase velocity measurements at 40 kHz indicate the presence of waves propagating slower than homogeneous plane waves. The pole of the reflection coefficient related to these waves is detected by near-field holography at 20 kHz. The different experimental results are compared with predictions obtained by replacing the air inside the layers by an equivalent fluid, and using methods developed in the context of electromagnetism to localize the poles of the reflection coefficient.

Surface waves above gratings having a triangular profile

The velocity of ultrasonic waves above gratings having triangular shaped grooves, is measured and compared with predictions obtained from several simple models developed in optics and acoustics. Only a model initially developed for electromagnetic waves provides predictions which are in good agreement with measurements.

Surface waves over bead layers

For thin bead layers saturated by air, a pole of the reflection coefficient related to a trapped mode inside the layer and a surface wave in air is predicted, and detected with the Tamura method [J. Acoust. Soc. Am. 88, 2259 (1990)]. For semi-infinite layers, the Brewster angle is observed with the same method at oblique incidence at 15 kHz. A description of the related Zenneck wave is performed, at high and low frequencies.

Ultrasonic surface waves above a doubly periodic grating

Ultrasonic surface waves above a layer indented by a doubly periodic set of holes having a square-shaped cross section are studied experimentally. Measurements are compared with predictions obtained from a modal model inspired by the theory of the diffraction of electromagnetic waves. Predictions obtained with the modal model and a simplified model where the periodic structure is replaced by an impedance plane are compared.

Transmission of ultrasonic waves through porous layers of high flow resistivity saturated by air

Transmission of ultrasonic waves through porous materials of high flow resistivity and porosity (in contact with air at both faces) is modelled and measured for an open-bubble foam at normal and oblique incidence. The importance of the airborne wave and the differences with the case of an elastic nonporous solid are demonstrated. A simple method to measure the shear modulus and the Poisson coefficient of the frame is suggested for similar materials.