Acoustic wave propagation in a macroscopically inhomogeneous porous medium saturated by a fluid

Ryck, Laurent De; Groby, Jean‐Philippe; Leclaire, Philippe; Lauriks, Walter; Wirgin, Armand; Fellah, Zine El Abiddine; Dépollier, Claude

doi:10.1063/1.2431570

Cited by 40 publications

(43 citation statements)

References 22 publications

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“…In an equivalent fluid medium, [17] the appropriate conservation of momentum and constitutive relations take the form: [24] being two relaxation functions given by…”

Section: Outline Of the Numerical Proceduresmentioning

confidence: 99%

“…In [17], it is shown that the wave equation describing the propagation in a macroscopicallyinhomogeneous porous medium in the rigid frame approximation can formally take the form of the usual acoustic wave equation in a macroscopically-inhomogeneous fluid (in which the microscopic features of the porous medium are homogenized) with spatial (and frequency) dependent compressibility κ e (x, ω) and density ρ e (x, ω).…”

Section: Introductionmentioning

confidence: 99%

“…The wave equation in an inhomogeneous medium can be solved in a variety of manners: via the wave splitting method [33,17,30], the transfer matrix method [28,4] (for piecewise constant media), integral methods [20,39,37], or purely numerical (e.g., finite-element [19] or finite-difference [5]) methods. The methods dedicated to inverse problems are wave splitting and linearisation [38,39] techniques deriving from the integral formalism.…”

Section: Introductionmentioning

confidence: 99%

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Use of specific Green's functions for solving direct problems involving a heterogeneous rigid frame porous medium slab solicited by acoustic waves

Groby

Ryck

Leclaire

et al. 2006

Math Methods in App Sciences

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A domain integral method employing a specific Green's function (i.e., incorporating some features of the global problem of wave propagation in an inhomogeneous medium) is developed for solving direct and inverse scattering problems relative to slab-like macroscopically inhomogeneous porous obstacles. It is shown how to numerically solve such problems, involving both spatially-varying density and compressibility, by means of an iterative scheme initialized with a Born approximation. A numerical solution is obtained for a canonical problem involving a two-layer slab. IntroductionThis work was initially motivated by two problems: i) the design problem connected with the determination of the optimal profile of a continuous and/or discontinuous spatial distribution of the material/geometric properties of porous materials for the absorption of sound [7] and ii) the retrieval of the spatially-varying mechanical and geometrical parameters of bone for the diagnosis of diseases such as osteoporosis [10].Such inverse problems [20] can be decomposed into two sub-problems: i) the determination of the constitutive and conservation relations linking the various spatially-variable mechanical parameters of the porous medium to its response to an acoustic solicitation, and ii) the resolution of the * Correspondence to: J.-P. Groby, Akoestieke en Thermische Fysica, KULeuven, Celestijnenlaan 200D , 3001 Heverlee, Belgium † E-mail: jeanphilippe.groby@fys.kuleuven.be 1 wave equation in an inhomogeneous porous medium (for instance, within the Biot, or rigid frame approximations). Here we focus on the second point.In [17], it is shown that the wave equation describing the propagation in a macroscopicallyinhomogeneous porous medium in the rigid frame approximation can formally take the form of the usual acoustic wave equation in a macroscopically-inhomogeneous fluid (in which the microscopic features of the porous medium are homogenized) with spatial (and frequency) dependent compressibility κ e (x, ω) and density ρ e (x, ω).The present work deals with a method of resolution of direct problems involving acoustic wave propagation in a macroscopically-inhomogeneous fluid medium, whose density and compressibility are both space dependent, this being a prerequisite to the resolution of related inverse problems.This topic is also of great interest in quantum physics (inverse potential scattering [2,37,38,39]), ocean acoustics [9,8,32,11,36,12] (detection of inhomogeneities, sediment exploration, influence of seawater and seafloor composition and heterogenity on the long-range propagation of acoustic waves in the sea, ...), seismology [1,40,42] (determination of the internal structure and composition of the Earth via seismic waves,...), geophysics [42,25,48,44] (characterization of soil, detection of geological features such as hydrocarbon reservoirs, ...), optics and electromagnetism [47,41] (design and characterization of materials having specified response to waves, detection of flaws,...).The wave equation in an inhomogeneous medi...

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“…In an equivalent fluid medium, [17] the appropriate conservation of momentum and constitutive relations take the form: [24] being two relaxation functions given by…”

Section: Outline Of the Numerical Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Use of specific Green's functions for solving direct problems involving a heterogeneous rigid frame porous medium slab solicited by acoustic waves

Groby

Ryck

Leclaire

et al. 2006

Math Methods in App Sciences

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“…[8][9][10] These methods are usually simpler to implement than methods based on a Green's function approach. [11][12][13][14] The accuracy can be set to any desired level, by choosing a sufficiently large number of layers.…”

Section: A Feasibility Of Saw Elastic Depth Profilingmentioning

confidence: 99%

Surface acoustic wave depth profiling of a functionally graded material

Goossens

Leclaire

et al. 2007

Journal of Applied Physics

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The potential and limitations of Rayleigh wave spectroscopy to characterize the elastic depth profile of heterogeneous functional gradient materials are investigated by comparing simulations of the surface acoustic wave dispersion curves of different profile-spectrum pairs. This inverse problem is shown to be quite ill posed. The method is then applied to extract information on the depth structure of a glass-ceramic ͑ alumina͒ functionally graded material from experimental data. The surface acoustic wave analysis suggests the presence of a uniform coating region consisting of a mixture of Al 2 O 3 and glass, with a sharp transition between the coating and the substrate. This is confirmed by scanning electron microscope with energy dispersive x-ray analysis.

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“…[1][2][3][4][5][6] In particular, airframe noise, which is generated through the interaction between the turbulent flow and the solid bodies on the aircraft, has been identified as an "aircraft noise barrier" since the early seventies. 7 Therefore, considering the interdisciplinary challenge between fluid mechanics and acoustics arising from this noise effect, airframe noise reduction has become a major concern for stakeholders within the aviation sector, acoustic experts, fluid mechanics engineers and researchers.…”

Section: Introductionmentioning

confidence: 99%

Use of dual planar jets for the reduction of flow-induced noise

et al. 2017

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The planar jet has been proposed to reduce the flow-induced noise. However, the self-noise emission from a single planar jet is a limiting factor on the performance based characteristics of this technology. Therefore, this research paper reports an alternative dual planar jets geometry in an attempt to minimize the self-noise of the single planar jet, thus, further enhancing total noise reduction in the application. Tandem cylinders are considered as the generic bluff body, which represents the source of flow-induced noise. Tests are conducted to capture noise reduction effects when using a single planar jet geometry. Subsequently, two different configurations of the dual planar jets geometry were tested in comparison. It is observed that the dual jets geometry achieves more noise reduction when compared to the single jet. Moreover, conclusions are made on the most efficient configuration in the dual jets geometry.

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Acoustic wave propagation in a macroscopically inhomogeneous porous medium saturated by a fluid

Cited by 40 publications

References 22 publications

Use of specific Green's functions for solving direct problems involving a heterogeneous rigid frame porous medium slab solicited by acoustic waves

Use of specific Green's functions for solving direct problems involving a heterogeneous rigid frame porous medium slab solicited by acoustic waves

Surface acoustic wave depth profiling of a functionally graded material

Use of dual planar jets for the reduction of flow-induced noise

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