Microstructure-based calculations and experimental results for sound absorbing porous layers of randomly packed rigid spherical beads

Abstract

Acoustics of stiff porous media with open porosity can be very effectively modelled using the so-called Johnson-Champoux-Allard-Pride-Lafarge model for sound absorbing porous media with rigid frame. It is an advanced semi-phenomenological model with eight parameters, namely, the total porosity, the viscous permeability and its thermal analogue, the tortuosity, two characteristic lengths (one specific for viscous forces, the other for thermal effects), and finally, viscous and thermal tortuosities at the frequency limit of 0 Hz. Most of these parameters can be measured directly, however, to this end specific equipment is required different for various parameters. Moreover, some parameters are difficult to determine. This is one of several reasons for the so-called multiscale approach, where the parameters are computed from specific finite-element analyses based on some realistic geometric representations of the actual microstructure of porous material. Such approach is presented and validated for layers made up of loosely packed small identical rigid spheres. The sound absorption of such layers was measured experimentally in the impedance tube using the so-called two-microphone transfer function method. The layers are characterised by open porosity and semi-regular microstructure: the identical spheres are loosely packed by random pouring and mixing under the gravity force inside the impedance tubes of various size. Therefore, the regular sphere packings were used to generate Representative Volume Elements suitable for calculations at the micro-scale level. These packings involve only one, two, or four spheres so that the three-dimensional finite-element calculations specific for viscous, thermal, and tortuous effects are feasible. In the proposed geometric packings, the spheres were slightly shifted in order to achieve the correct value of total porosity which was precisely estimated for the layers tested experimentally. Finally, in this paper some results based on the self-consistent estimates are also provided. V C 2014 AIP Publishing LLC. [http://dx.

Sound absorption and compressive property of PU foam‐filled composite sandwiches: Effects of needle‐punched fabric structure, porous structure, and fabric‐foam interface

“…Hence, PU0 wt% revealed a better sound absorption efficiency at low frequencies between 200 and 600 Hz (Figure B). With water content exceeding 0.75 wt%, foam cells continued to grow, and air flow resistivity descended during which the presence of irregularly merged pores adversely affected sound absorption . Despite low foaming density, numerous small cells contributed to sound absorption efficiency, In addition, the compressive property of flexible PU foam was also highly correlated with the cell structure.…”

Generation of random microstructures and prediction of sound velocity and absorption for open foams with spherical pores

“…37 Thus, the result of the viscous flow analysis shown in Fig. 9 allowed to determine the parameter of static (viscous) permeability k 0 and the low-frequency limit a 0 (i.e., at 0 Hz) of the viscous dynamic tortuosity aðxÞ.…”

“…The transport parameters are computed from three steady, static (i.e., non-harmonic) analyses defined on the fluid domain of representative volume element; they are the following scaled boundary value problems (BVPs): 4,26,31,37 (1) the viscous flow problem: the Stokes flow caused by a unit pressure gradient, with no-slip boundary conditions on the fluid-solid interface; (2) the thermal conduction problem: a steady heat transfer caused by a unit heat source, with isothermal boundary conditions on the fluid-solid interface; (3) the electric conduction problem: the electric field distribution in the fluid domain of porous medium made up of electrically insulating solid filled with a conductive fluid, caused by a unit electric potential gradient; in fact, the scaled electric conduction problem corresponds to the inertial flow in the high-frequency regime, 4 and it can be eventually reduced to the Laplace problem for the unknown (electric) potential field.…”

“…The regular sphere packings have also been used in the microstructure-based modeling of porous media made up of rigid spheres, 31,36-38 for which-in the case when the spheres are identical-even some analytical estimations of the relevant transport parameters are possible. 37,39 The present work is organized as follows. First, the procedure for a controlled random generation of periodic microstructures representative for open-cell foams with spherical pores is presented.…”

Benchmarks for microstructure-based modelling of sound absorbing rigid-frame porous media

“…This approach is less computationally intensive, since it uses the computed eight (or fewer) parameters as inputs to the semi-analytical formulas of the JCALP model (or its variations). Such a hybrid approach has been used to investigate the acoustical properties of fibrous materials [37][38][39][40][41][42][43], granular media [33,37,[44][45][46][47], various polymeric and open-cell foams [34,35,[48][49][50][51][52][53][54][55][56][57][58][59], ceramic foams with spherical pores [60], metallic foams [36], and syntactic hybrid foams, i.e. open-cell polyurethane foams with embedded hollow microbeads [61].…”