Détermination de l'épaisseur et la résistivité au passage de l'air d'un matériau poreux à structure rigide en utilisant les ondes transmises.

National audienceUne méthode acoustique est proposée pour mesurer la résistivité au passage de l’air et l’épaisseur d’un échantillon poreux à structure rigide. Les méthodes classiques 3,4 permettant la mesure de la résistivité (où la perméabilité visqueuse) nécessitent la connaissance préalable de la porosité. La méthode présentée dans ce travail est basée sur un modèle temporel du problème direct dans lequel une expression simplifiée (indépendante de la fréquence et de la porosité) du coefficient de transmission dans le régime de Darcy (très basses fréquences) est établie. Cette expression ne dépend que de la perméabilité visqueuse (où la résistivité au passage de l’air) et de l’épaisseur d’un échantillon poreux. Le problème inverse est résolu en minimisant, l’écart entre le signal transmis théorique et expérimentale, permettant ainsi la détermination de l’épaisseur et de la perméabilité visqueuse (où la résistivité) d’une mousse en plastique. Cette méthode présente l’avantage d’être simple, rapide et efficace

Characterization of rigid porous medium via ultrasonic reflected waves at oblique incidence

International audienceIn this paper, an enhanced method is proposed for measuring porosity, tortuosity, viscous and thermal characteristic length of porous materials having a rigid frame via reflected ultrasonic waves at oblique incidence using the equivalent fluid model. The advantage of the proposed method is that the four parameters are determined simultaneously just using reflected experimental waves for a porous material saturated by air. The inverse problem is solved based on the least-square numerical method using experimental reflected waves in time domain. Tests are performed using industrial plastic foams. Experimental and numerical validation results of this method are presented

Acoustic propagation in fractal porous media

La méthode de minimisation de l'intégrale d'action (principe variationnel) permet d’obtenir les équations de propagation des ondes. Cette méthode a été généralisée aux milieux poreux de dimensions fractales, pour étudier la propagation acoustique dans le domaine temporel, en se basant sur le modèle du fluide équivalent. L'équation obtenue réécrite dans le domaine fréquentiel représente une généralisation de l'équation d'Helmholtz. Dans le cadre du modèle d'Allard-Johnson, l'équation de propagation a été résolue de manière analytique dans le domaine temporel, dans les régimes des hautes et des basses fréquences. La résolution a été faite par la méthode de la transformée de Laplace, et a porté sur un milieu poreux semi-infini. Il a été trouvé que la vitesse de propagation dépend de la dimension fractale. Pour un matériau poreux fractal d'épaisseur finie qui reçoit une onde acoustique en incidence normale, les conditions d’Euler ont été utilisées pour déterminer les champs réfléchi et transmis. La résolution du problème direct a été faite dans le domaine temporel, par la méthode de la transformée de Laplace, et par l’usage des fonctions de Mittag-Leffler. Le problème inverse a été résolu par la méthode de minimisation aux sens des moindres carrés. Des tests ont été effectués avec succès sur des données expérimentales, en utilisant des programmes numériques développés à partir du formalisme établi dans cette thèse. La résolution du problème inverse a permis de retrouver les paramètres acoustiques de mousses poreuses, dans les régimes des hautes et des basses fréquences.The action integral minimization method (variational principle) provides the wave propagation equations. This method has been generalized to fractal dimensional porous media to study the acoustic propagation in the time domain, based on the equivalent fluid model. The resulting equation rewritten in the frequency domain represents a generalization for the Helmholtz equation. As part of the Allard-Johnson model, the propagation equation was solved analytically in the time domain, for both high and low frequencies fields. The resolution was made by the method of the Laplace transform, and focused on a semi-infinite porous medium. It was found that the wave velocity depends on the fractal dimension.For a fractal porous material of finite thickness which receives an acoustic wave at normal incidence, the Euler conditions were used to determine the reflected and transmitted fields. The resolution of the direct problem was made in the time domain by the method of the Laplace transform, and through the use of the Mittag-Leffler functions. The inverse problem was solved by the method of minimizing the least squares sense. Tests have been performed successfully on experimental data; programs written from the formalism developed in this work have allowed finding the acoustic parameters of porous foams, in the fields of high and low frequencies

Measurement of tortuosity and viscous characteristic length of double-layered porous absorbing materials with rigid frames via transmitted ultrasonic wave

International audienceMeasurement of tortuosity and viscous characteristic length of Double-layered porous absorbing materials with rigid-frames via transmitted ultrasonic-wave-Manuscript Draft-Manuscript Number: Full Title: Measurement of tortuosity and viscous characteristic length of Double-layered porous absorbing materials with rigid-frames via transmitted ultrasonic-wave Abstract: In this work, an indirect method is proposed for measuring simultaneously acoustic parameters describing the ultrasonic propagation in double-layered porous medium. The porous media consist of two slabs of homogeneous isotropic porous materials with a rigid frame. Each porous slab is described by equivalent fluid model, in which the acoustic wave propagates only in the fluid saturating the material. The inverse problem is solved numerically using experimental transmitted waves in time domain. Four parameters are inverted: tortuosity and viscous characteristic lengths of the two layers. Tests are performed using industrial plastic foams. Experimental and numerical validation results of this method are presented

Ultrasonic Measurement of Tortuosity and Viscous Characteristic Length of Double-Layered Porous Absorbing Materials with rigid frames.

International audienceWe propose an indirect method for measuring simultaneously acoustic parameters describing the ultrasonic propagation in double-layered porous material. The porous media consist of two slabs of homogeneous isotropic porous materials with a rigid frame. Each porous slab is described by an equivalent fluid model, in which the acoustic wave propagates only in the fluid saturating the material. The inverse problem is solved numerically using experimental transmitted waves in time domain. The direct problem is solved in frequency domains. Four parameters are inverted : tortuosity and viscous characteristic lengths of the two layers. Tests are performed using industrial plastic foams. Inverted values of acoustic parameters are close to those measured by conventional methods. Experimental and numerical validation results of this method are presented, which show the advantage of using the transmission for measuring the characteristic lengths, unlike the reflection

Full characterization of rigid porous material through ultrasonic reflected waves at oblique incidence.

International audienceAn improved method is proposed for measuring porosity, tortuosity, viscous and thermal characteristic length of porous materials having a rigid frame via reflected ultrasonic waves at oblique incidence. The conventional ultrasonic approach can be used to determine all the parameters via transmitted waves [1] or using the rst and second reflected waves at normal incidence[2] (the ratio between the viscous and thermal characteristic lengths is xed as in classical acoustic methods [3,4]). The advantage of the proposed method is that the four parameters are determined simultaneously just using reflected experimental waves for a porous material saturated by air. In addition, no relationship is assumed between the two characteristic lengths. The inverse problem is solved based on the least-square numerical method using experimental refllected waves in time domain. Tests are performed using industrial plastic foams. Experimental and numerical validation results of this method are presented.Reference[1] ZEA Fellah, M Sadouki, M Fellah, F. G Mitri, E Ogam, C Depollier." Simultaneous determination of porosity, tortuosity, viscous and thermal characteristic lengths of rigid porous materials" J. Appl. Phys, 114, 204902 (2013); [2] Z. E. A. Fellah, M. Fellah, W. Lauriks, and C. Depollier, "Direct and inverse scattering of transient acoustic waves by a slab of rigid porous material" J. Acoust. Soc. Am. 113, 61-73 (2003). [3] C. Ayrault, A. Moussatov, B. Castagnede, and D. Lafarge, "Ultrasonic characterization of plastic foams via measurements with static pressure variations" Appl. Phys. Lett. 74, 3224-3226 (1999). [4] A. Moussatov, C. Ayrault, and B. Castagne`de, "ultrasonic method for estimation of tortuosity and characteristic length using a barometric chamber"Ultrasonics 39, 195-202 (2001)

Ultrasonic propagation in fractal porous material

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Acoustic wave propagation in fractal porous material

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Acoustic characterization of air-saturated porous materials by solving the inverse problem

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Acoustic characterization of air-saturated porous materials by solving the inverse problem

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