Fabien Chevillotte

Dynamic viscous permeability of an open-cell aluminum foam: Computations versus experiments

Is it possible to find a two-dimensional (2D) periodic unit cell representative of the dynamic viscous dissipation properties of a real porous media? This is a challenging question addressed in this paper through a review of tools and methods of experimental and computational micro(poro)mechanics. The combination of advanced experimental imaging and numerical homogenization techniques provides a unique opportunity to understand and assess the limits of two-dimensional models of microstructures, as a potential basis for the engineering prediction of macroscopic properties of acoustical materials. This is illustrated for a real sample of open-cell aluminum foam. The conclusion, based on this analysis, is that the 2D periodic foam model geometry provides a reliable estimate of the dynamic permeability, except in the low frequency range. This is not surprising because in the 2D periodic foam model geometry, ligaments are always perpendicular to the flow direction, thus decreasing artificially the static perme...

Microstructure based model for sound absorption predictions of perforated closed-cell metallic foams

Closed-cell metallic foams are known for their rigidity, lightness, thermal conductivity as well as their low production cost compared to open-cell metallic foams. However, they are also poor sound absorbers. Similarly to a rigid solid, a method to enhance their sound absorption is to perforate them. This method has shown good preliminary results but has not yet been analyzed from a microstructure point of view. The objective of this work is to better understand how perforations interact with closed-cell foam microstructure and how it modifies the sound absorption of the foam. A simple two-dimensional microstructural model of the perforated closed-cell metallic foam is presented and numerically solved. A rough three-dimensional conversion of the two-dimensional results is proposed. The results obtained with the calculation method show that the perforated closed-cell foam behaves similarly to a perforated solid; however, its sound absorption is modulated by the foam microstructure, and most particularly by the diameters of both perforation and pore. A comparison with measurements demonstrates that the proposed calculation method yields realistic trends. Some design guides are also proposed.

A direct link between microstructure and acoustical macro-behavior of real double porosity foams

The acoustical macro-behavior of mineral open-cell foam samples is modeled from microstructure morphology using a three-dimensional idealized periodic unit-cell (3D-PUC). The 3D-PUC is based on a regular arrangement of spheres allowed to interpenetrate during the foaming process. Identification and sizing of the 3D-PUC is made from x-ray computed microtomography and manufacturing process information. In addition, the 3D-PUC used allows to account for two scales of porosity: The interconnected network of bubbles (meso-porosity) and the inter-crystalline porosity of a gypsum matrix (micro-porosity). Transport properties of the micro- and the meso-scales are calculated from first principles, and a hybrid micro-macro method is used to determine the frequency-dependent visco-thermal dissipation properties. Olny and Boutin found that the double porosity theory provides the visco-thermal coupling between the meso- and micro-scales [J. Acoust. Soc. Am. 114, 73-89 (2003)]. Finally, the results are successfully compared with experiments for two different mineral foam samples. The main originality of this work is to maintain a direct link between the microstructure morphology and the acoustical macro-behavior all along the multi-scale modeling process, without any adjusted parameter.

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.

Measurement of the low-wavenumber component within a turbulent wall pressure by an inverse problem of vibration

An experimental validation is implemented for the measurement of a weak acoustic component within a turbulent wall pressure by an inverse problem of vibration. The turbulent flow is generated by a forward-facing step in a wind tunnel. In addition to the flow, an acoustic source with a low level excites the plate and plays the role of an additional acoustic component to be identified. The inverse methods called the force analysis technique and the corrected force analysis technique are used to compute the wall pressure fluctuations from the measurement of the plate vibration using an array of 13 accelerometers. The results show that contrary to the conventional techniques using pressure sensors, the inverse methods have a very good signal-to-noise ratio at the low wavenumbers. Indeed, the plate vibration is much more sensitive to the acoustic component than to the aerodynamic part. Moreover, this study shows that both methods can be used to isolate the weak acoustic part and identify its frequency spectrum.

Effect of the three-dimensional microstructure on the sound absorption of foams: A parametric study

The purpose of this work is to systematically study the effect of the throat and the pore sizes on the sound absorbing properties of open-cell foams. The three-dimensional idealized unit cell used in this work enables to mimic the acoustical macro-behavior of a large class of cellular solid foams. This study is carried out for a normal incidence and also for a diffuse field excitation, with a relatively large range of sample thicknesses. The transport and sound absorbing properties are numerically studied as a function of the throat size, the pore size, and the sample thickness. The resulting diagrams show the ranges of the specific throat sizes and pore sizes where the sound absorption grading is maximized due to the pore morphology as a function of the sample thickness, and how it correlates with the corresponding transport parameters. These charts demonstrate, together with typical examples, how the morphological characteristics of foam could be modified in order to increase the visco-thermal dissipation effects.

Identification of Boundary Pressure Field Exciting a Plate Under Turbulent Flow

The characterisation of the aeroacoustic wall pressure field generated by turbulent flow is a difficult task that often requires instrumented panels and huge facilities like wind tunnels. In situ and non-intrusive experiments are rather not possible. In addition, the pressure field is dominated by the aerodynamic component and the experimental dynamics are not sufficient to measure correctly spectra in low wavenumbers by microphones. The present chapter deals with such a separation method by using the Force Analysis Technique (FAT). FAT is based on the use of the equation of motion of the structure (here a plate) and on the approximation of the fourth derivatives by a finite difference scheme. In the case of turbulent flow, the force auto-spectrum can be deduced at one point of the structure by measuring the velocity at 13 points synchronously. To this purpose, an array of 13 pU (acoustic pressure/particle velocity) probes has been made up. This array is moved in the near-field of the plate to identify map of the wall pressure level applied on the surface of the plate. In the present application, it is shown that FAT only identifies the component of the excitation with wavenumber lower than the natural flexural wavenumber of the plate, due to filtering effect of the plate and of the finite difference scheme. In most cases, the convective peak is then canceled and only the acoustic part of the turbulent flow is identified. This property can be of great interest for vehicle manufacturers to quantify the part of the wall pressure that is responsible of the radiated noise or to use FAT as a source separation technique.

An Overview of Microstructural Approaches for Modelling and Improving Sound Proofing Properties of Cellular Foams: Developments and Prospects

Significant advances have been made over the last 15 years in the field of modelling the acoustic properties of foams from the description of their microstructures. It entails a multidisciplinary work at the junction between physico-chemistry and mechanics of porous media, which involves a dialogue between different disciplines and requires the joint development of several techniques (imaging, upscaling, numerical computations, and experimental identification). It seems to be of timely interest to take stock of the methodological developments that have provided guidance on how to manufacture the new generation of foams with enhanced properties and to identify possible future methodological developments.

Rolling noise modeling in buildings

New buildings in urban areas are divided in commercial and living surfaces. This usage has revealed critical disturbances due to the noise of the trolleys delivering at time where the buildings are mostly occupied, e.g., early times in the morning. Rolling trolleys indeed generate low frequency vibrations (below 100 Hz) which propagate easily in the entire building structure and in upper storeys. This work presents an original model for rolling noise in buildings. The developed model is able to account for the ground surface roughness as well as the rolling wheel asperity profile. It also enables to consider the mechanical impedance of the ground including some possible flooring noise treatment. It is shown that the model is able to correctly reproduce the measured level of vibrations and measured noise levels. It is also proved to accurately predict the sensitivity to different types of rolling noise and floorings having various properties, based on a single layer or a multi-layer construction.

On the modeling of visco-thermal dissipations in heterogeneous porous media

Based on a modified equivalent fluid model, the present work proposes a composite model which analytically includes the shape of the inclusions, whether they are porous or not. This model enables to describe the acoustic behavior of a large range of media from perforated plates to arbitrarily shaped porous composites including configurations of porous inclusions in solid matrix or double porosity media. In addition, possible permeability interactions between the substrate material and the inclusions are accounted for.