Thermal Characteristic Lengths Research Articles

Experimental characterization of rigid porous material via the first ultrasonic reflected waves at oblique incidence

Enhanced ultrasonic method for the evaluation of acoustic parameters of air-saturated porous material is presented. This method is based on the direct and inverse problem of the reflection of an oblique incident wave from the surface of the porous medium with rigid frame. The interaction of the sound pulse with the porous material is described by the equivalent fluid model using the Johnson-Champoux-Allard approach (JCA) to describe the visco-inertial dissipative effects and the thermal effects inside the porous media. Four parameters are involved in the calculation of the dynamic density and the bulk modulus at high frequencies, namely the porosity ϕ, the high frequency limit of tortuosity α∞, the viscous and thermal characteristic lengths Λ and Λ′. The sensitivity of each parameter on reflected waves from the surface of the porous medium is studied for different oblique angles of incidence. The advantage of the proposed method is that the inverted values of porosity, tortuosity, viscous and thermal characteristic lengths are simultaneously obtained by minimizing between the experimental and simulated reflected signals. Moreover, no relationship is assumed between the viscous and thermal characteristic lengths. The numerical and experimental validation of this method is presented and compared to the theoretical prediction.

Influence of Porosity, Fiber Radius and Fiber Orientation on the Transport and Acoustic Properties of Random Fiber Structures

The ability of air-saturated fibrous media to mitigate sound wavesiscontrolled by their transport properties that are themselves controlled by the geometrical characteristics of their microstructure such as the open porosity,fiber radius, and fiber orientation. Here, micro-macro relationships are proposed to link these microstructural features to the macroscopic transport properties of random fiber structures. These transport properties are the tortuosity, the viscous and thermal static permeabilities, and the viscous and thermal characteristic lengths. First, representative elementary volumes (REVs)ofrandom fiber structures are generated for different triplets of porosity,fiber radius and fiber orientation. The fibers are allowed to overlap and are motionless (rigid-frame assumption). The fiber orientation is derivedf rom as econd order orientation tensor.S econd, the transport equations are numerically solved on the REVs which are seen as periodic unit cells. These solutions yield the transport properties governing the sound propagation and dissipation in the respective fibrous media. From these solutions, micro-macro relationships are derivedt oe stimate the transport properties when the geometry of the fiber structure is known. Finally,these relationships are used to study the influence of the microstructural features on the acoustic properties of random fiber structures.

Acoustic performances of silicone foams for sound absorption

The aim of this study is to investigate the link between the elaboration process, the microstructure and the acoustic behaviour of silicone foams obtained using a two-component silicone. Different parameters such as the ratio of components, the addition of a thinning agent and the curing temperature are varied, with the objective of understanding the influence of each parameter in the foam’s acoustic absorption. The microstructure is analysed using scanning electron microscopy and acoustic properties are measured. Two non-acoustical properties of the porous material are also investigated, namely the porosity and the flow resistivity. Pore cell size and interconnected porosity have great impact on acoustical properties. Significant enhancements of the absorption properties could be obtained in the low-frequency band by increasing the rate of agent B through an increase in the amount of interconnected porous cells. An improvement in absorption is observed in the higher frequency range when a thinning agent is added to the mixture. Representative models of the foam for acoustic simulations are obtained allowing estimation of the tortuosity, viscous and thermal characteristic length from acoustic measurements. These models are able to simulate the acoustic behaviour of the silicone foams when embedded in sound packages.

A semi-analytical model for the influence of temperature on sound propagation in sintered metal fiber materials

A semi-analytical model is developed to predict the influence of temperature on the sound absorbing performance of sintered metal fiber materials (SMFMs) by extending the Johnson-Champoux-Allard-Lafarge (JCAL) model. In this model, three micro-structure factors of the SMFMs – the Kozeny number and the thermal and viscous shape factors – are calculated by applying the multi-scale asymptotic method (MAM), and the temperature effect is taken into account by considering the variations of the thermo-physical parameters of saturated air with temperature. Key transport parameters (e.g., viscous and thermal permeability, tortuosity, viscous and thermal characteristic lengths) are then directly determined by fiber diameter and porosity of the material. High-efficiency of the semi-analytical model is demonstrated for estimating the influence of topological parameters upon sound absorption under different temperatures. The transport parameters obtained by the proposed model agree well with those calculated using fully numerical simulations. Also, the model predictions are in accordance with existing experimental measurements at different temperatures. The model reveals not only the underlying mechanisms of temperature effect on sound propagation in porous metals, but also provides a theoretical guideline for the sound absorption application of SMFMs in high temperature environments.

Role of atom redeposition during rising ion flux in ion-induced nanodot self-assembly on GaSb surfaces

In this study, a bottom-up approach of ion irradiation from hot cathode DC discharge plasma was used to investigate the role of energetic ion flux on the self-assembly of GaSb nanodots (NDs) at normal incidence. It was observed that, when increasing the flux in the range of 1014–1015 ions cm−2 s−1, the lateral dimension and root mean square (RMS) roughness of NDs is reduced even at constant temperature conditions in the ion energy range from 400–800 eV. The evolution of the surface morphology for different flux regimes is observed in a numerical integration simulation using the nonlinear isotropic damped Kuramoto–Sivashinsky (DKS) equation. By introducing a redeposition term, the DKS equation is found to be in good qualitative agreement with the experimental results. We have demonstrated the linear dependency of the redeposition coefficient on the ion flux and also reported the nonlinear dependency on the thermal diffusion coefficient, transition time, and characteristic length with the flux. In accordance with the nonlinearity, we have also discussed the effect of the variation of the ion flux on the RMS roughness and lateral dimension of NDs.

Formulae for predicting non-acoustical parameters of deformed fibrous porous materials.

Formulae to predict non-acoustical parameters (i.e., flow resistivity, tortuosity, and viscous and thermal characteristic lengths) of deformed fibrous porous materials are proposed provided that the original values of these parameters are known in advance. These formulae are developed using numerical fluid analyses. The flow resistivity was calculated by using the finite element method for a two-dimensional incompressible viscous fluid approximated by Oseen flow. The tortuosity and characteristic lengths were calculated by using the complex variable boundary element method for a two-dimensional potential flow. These calculations showed that the flow resistivity was inversely proportional to the porosity multiplied by the three-halves power of the compression ratio, that the tortuosity can be represented by a linear expression of the porosity, and that both characteristic lengths changed in the same manner with respect to the porosity. These tendencies agreed well with measurements of real glass wools of various bulk densities. The proposed prediction formulae for the parameters were then derived from the tendencies obtained from the numerical analyses. The predicted parameter values were compared with the calculated parameters and good agreement was obtained, confirming the validity of the proposed formulae.

Sound propagation in porous materials with annular pores.

Long-wavelength sound propagation in porous materials with annular pores is investigated in this paper. Closed-form analytical expressions for the effective acoustical properties of this type of material were obtained. These are compared with both direct numerical calculations of the effective properties and their calculations obtained by using semi-phenomenological models. Analytical expressions for the input parameters of the latter, i.e., static viscous and thermal permeabilities, viscous and thermal characteristic lengths, and tortuosity, are also provided. The introduced model is successfully validated by comparing its predictions with measured data taken from literature. A parametric analysis that allows highlighting the influence of the different geometrical parameters of porous materials with annular pores on their sound absorptive properties is also presented.

Influence of porosity, fiber radius, and fiber orientation on anisotropic transport properties of random fiber structures

The ability of fibrous media to mitigate sound waves is controlled by their transport properties that are themselves greatly affected by the geometrical characteristics of their microstructure such as porosity, fiber radius, and fiber orientation. Here, the influence of these geometrical characteristics on the anisotropic transport properties of random fiber structures is investigated. First, representative elementary volumes (REVs) of random fiber structures are generated for different triplets of porosity, fiber radius and fiber orientation. The fibers are allowed to overlap and are motionless (rigid-frame assumption). The fiber orientation is derived from a second order orientation tensor. Second, the transport equations are numerically solved on the REVs which are seen as periodic unit cells (PUCs). These solutions yield the transport properties governing the sound propagation and dissipation in the respective fibrous media. These transport properties are the tortuosity, the viscous and thermal static permeabilities, and the viscous characteristic length. Finally, relations are proposed to estimate the transport properties and the thermal characteristic length when the geometry of the fiber structures is known.

Transient ultrasonic wave propagation in porous material of non-integer space dimension

Acoustic propagation in a self-similar porous medium having a rigid frame is studied. A fractional propagation equation in a porous material of non-integer dimension is established using the variational method (Stillinger–Palmer–Stavrinou formalism). The wave equation is solved analytically in the time domain using the Laplace transform method. The analytical solution of the propagation equation shows the existence of a supersonic wave whose front wave velocity depends on the non-integer dimension and the tortuosity of the self-similar porous material. Numerical simulations of the amplitude of the ultrasonic wave inside the material show the sensitivity of the main important parameters describing the propagation (non-integer dimension, tortuosity, viscous and thermal characteristic lengths). The non-integer dimension seems to be the only parameter which acts on both the amplitude and the velocity of the acoustic wave.

Flame Spread over Liquid Fuel on a Water Layer-Basic Research on Tsunami Fire

The purpose of this study is to reveal the flame spreading mechanism of tsunami fire. But the mechanism of tsunami fire is so complex that we couldn’t assess qualitatively. So the basic research on tsunami fire is needed. As a first step, we did flame spread experiment on only liquid fuel and liquid fuel/water layer under static liquid fuel. We measured flame spread rate. As a result, fuel thickness is in range of 5 - 15 mm, and flame spread rate over only liquid fuel is faster than liquid fuel/water layer’s at same fuel thickness. To reveal the gap of the flame spread rate at same liquid fuel thickness, we visualized current distribution by PIV and thermal boundary layer by shadowgraph method. By these results, we revealed that the thermal characteristic length is longer and the current characteristic depth of liquid fuel/water is deeper than that of liquid only fuel.

Acoustic media with pore size distribution and assignment of the pore characteristic lengths and permeabilities

The model by Champoux and Allard [J. Appl. Phys. 70(4), 1975-1979 (1991)] is used extensively for research and development of new porous media solutions and for predicting sound propagation in the presence of porous media. Four key non-acoustical parameters in this model which are rarely measured non-acoustically are: the viscous and thermal characteristic lengths, thermal permeability and Pride parameter Pride et al [Phys. Rev. B 47, 4964-4978 (1993)]. In this work we show how these parameters unambiguously relate to the pore size distribution which is a characteristic measured nonacoustically and more routinely. We compare the predictions by this model against the log-normal pore size distribution model by Horoshenkov et al. [J. Acoust. Soc. Am. 104, 1198-1209 (1998)] and show that these two models provide very close predictions when the four non-acoustic parameters are expressed through the mean pore size and its standard deviation. We also confirm these results through a 4-microphone impedance tube experiment in which we determine the dynamic density and complex bulk modulus of a range of porous media. We also study the values of the viscous and thermal characteristic lengths and viscous and thermal permeabilities which fit our acoustic data.

Inverse acoustical characterization of natural jute sound absorbing material by the particle swarm optimization method

Abstract For modeling of jute as acoustic material, knowledge of its non-acoustical parameters like porosity, tortuosity, air flow resistivity, thermal and viscous characteristic lengths is a prime requisite. Measurement of these non-acoustical parameters is not straightforward and involves a dedicated measurement setup. So in order to overcome this issue, the inverse acoustical characterization can be used. In this paper, the particle swarm optimization method (PSO) is used as an optimization method. This method estimates the non-acoustical parameters of jute material in felt form by minimizing the error between experimental and theoretical sound absorption data. In this work, the impedance prediction models for fibrous materials like Johnson–Champoux–Allard model with rigid and limp frame and Garai–Pompoli model is used for sound absorption coefficient calculation by the transfer matrix method along with the PSO. The inverse estimated non-acoustical parameters for jute material are then compared with estimated and experimentally measured parameters for jute felts. Using these inversely predicted parameters, sound absorption of multilayer sound absorbers is also studied.

Sound absorption properties of a sunflower composite made from crushed stem particles and from chitosan bio-binder

A recent study investigated the mechanical, thermal and acoustical properties of a bio-based composite made from crushed particles of sunflower stalks binded together by chitosan, a bio-based binder. The acoustical performance in absorption was found to be poor as the material was highly compacted and with low porosity. The present study focuses on the acoustical properties of a higher porosity composite, with lower density while the mechanical rigidity remains fairly high. A higher absorption coefficient is obtained. The experimental results on the absorption coefficient are compared to the prediction of a model involving 5 physical parameters (porosity, tortuosity, airflow resistivity, thermal and viscous characteristic lengths). The characterization methods to determine these parameters are described. The comparison between experimental and theoretical results shows that this material exhibits peculiar microstructural features. It is found that the sound absorption properties can involve dead-end pores or clusters and multiple porosity scales in the material.

Asymptotic limits of some models for sound propagation in porous media and the assignment of the pore characteristic lengths.

Modeling of sound propagation in porous media requires the knowledge of several intrinsic material parameters, some of which are difficult or impossible to measure directly, particularly in the case of a porous medium which is composed of pores with a wide range of scales and random interconnections. Four particular parameters which are rarely measured non-acoustically, but used extensively in a number of acoustical models, are the viscous and thermal characteristic lengths, thermal permeability, and Pride parameter. The main purpose of this work is to show how these parameters relate to the pore size distribution which is a routine characteristic measured non-acoustically. This is achieved through the analysis of the asymptotic behavior of four analytical models which have been developed previously to predict the dynamic density and/or compressibility of the equivalent fluid in a porous medium. In this work the models proposed by Johnson, Koplik, and Dashn [J. Fluid Mech. 176, 379-402 (1987)], Champoux and Allard [J. Appl. Phys. 70(4), 1975-1979 (1991)], Pride, Morgan, and Gangi [Phys. Rev. B 47, 4964-4978 (1993)], and Horoshenkov, Attenborough, and Chandler-Wilde [J. Acoust. Soc. Am. 104, 1198-1209 (1998)] are compared. The findings are then used to compare the behavior of the complex dynamic density and compressibility of the fluid in a material pore with uniform and variable cross-sections.

Characterization of compressed earth blocks using low frequency guided acoustic waves.

The objective of this work was to analyze the influence of compaction pressure on the intrinsic acoustic parameters (porosity, tortuosity, air-flow resistivity, viscous, and thermal characteristic lengths) of compressed earth blocks through their identification by solving an inverse acoustic wave transmission problem. A low frequency acoustic pipe (60-6000 Hz of length 22 m, internal diameter 3.4 cm) was used for the experimental characterization of the samples. The parameters were identified by the minimization of the difference between the transmissions coefficients data obtained in the pipe with that from an analytical interaction model in which the compressed earth blocks were considered as having rigid frames. The viscous and thermal effects in the pores were accounted for by employing the Johnson-Champoux-Allard-Lafarge model. The results obtained by inversion for high-density compressed earth blocks showed some discordance between the model and experiment especially for the high frequency limit of the acoustic characteristics studied. This was as a consequence of applying high compaction pressure rendering them very highly resistive therefore degrading the signal-to-noise ratios of the transmitted waves. The results showed that the airflow resistivity was very sensitive to the degree of the applied compaction pressure used to form the blocks.

Agricultural by-products for building insulation: Acoustical characterization and modeling to predict micro-structural parameters

The acoustical characteristics for building insulation of five largely available plant particles (hemp shiv, sunflower bark and pith, flax shiv and rape straw) without binder were investigated. Results show that they can all be used for acoustical absorption. Measurements were then analyzed to estimate not only the sound absorption coefficient, but also the particles intrinsic properties such as porosities (i.e. total, inter- and intra-particles porosities) and densities (i.e. bulk and skeletal). An equivalent fluid model is then used to predict the sound absorption. From acoustical measurements, simple analytical equations allow to estimate key micro-structural parameters such as tortuosity, viscous and thermal characteristic lengths and resistivity.

極細繊維材の吸音率予測手法の開発

This report deals with sound absorption coefficient prediction technique of ultrafine fiber. As the sound absorption material used for the interior noise reduction of the automobile, the fiber with a diameter of several μm is considered. When a fiber diameter becomes small, usually a sound absorption coefficient increases. But predictive precision was bad by the conventional performance prediction technique. I developed the technique to predict a sound absorption coefficient from the fiber diameter and the fiber density and the material thickness and the material density. The experiment expression of relations was drawn from the experimental results about the flow resistivity and the thermal characteristic length. And I introduce the technique used Limp frame model to predict a sound absorption coefficient for the ultrafine fiber. There diameters are 1-4μm. This paper shows comparison of the experimental results and the calculation results, and this technique is useful.

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

In 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.

Experimental measurements of acoustical properties of snow and inverse characterization of its geometrical parameters

Snow is a sound absorbing porous sintered material composed of solid matrix of ice skeleton with air (+water vapour) saturated pores. Investigation of snow acoustic properties is useful to understand the interaction between snow structure and sound waves, which can be further used to devise non-destructive way for exploring physical (non-acoustic) properties of snow. The present paper discusses the experimental measurements of various acoustical properties of snow such as acoustic absorption coefficient, surface impedance and transmission losses across different snow samples, followed by inverse characterization of different geometrical parameters of snow. The snow samples were extracted from a natural snowpack and transported to a nearby controlled environmental facility at Patsio, located in the Great Himalayan range of India. An impedance tube system (ITS), working in the frequency range 63–6300Hz, was used for acoustic measurements of these snow samples. The acoustic behaviour of snow was observed strongly dependent upon the incident acoustic frequency; for frequencies smaller than 1kHz, the average acoustic absorption coefficient was found below than 0.4, however, for the frequencies more than 1kHz it was found to be 0.85. The average acoustic transmission loss was observed from 1.45dBcm−1 to 3.77dBcm−1 for the entire frequency range. The real and imaginary components of normalized surface impedance of snow samples varied from 0.02 to 7.77 and −6.05 to 5.69, respectively. Further, the measured acoustic properties of snow were used for inverse characterization of non-acoustic geometrical parameters such as porosity, flow resistivity, tortuosity, viscous and thermal characteristic lengths using the equivalent fluid model proposed by Johnson, Champoux and Allard (JCA). Acoustically derived porosity and flow resistivity were also compared with experimentally measured values and good agreement was observed between them.

Further investigations of empirical improvements to the Johnson–Champoux–Allard model

Non-acoustical physical parameters (tortuosity, viscous characteristic length, thermal characteristic length, porosity and flow resistivity) of glass fibre, melamine foam, compressed melamine foam and reticulated polyurethane foam materials have been measured. Also tortuosity and two characteristic lengths have been deduced from impedance tube measurements using commercial software (Foam-X). Between 200Hz and 5kHz sound velocities in the materials have been deduced from impedance tube measurements. Between 79kHz and 1MHz they have been deduced from ultrasonic measurements.Predictions of sound velocities based on the Johnson–Champoux–Allard (JCA) model using measured non-acoustical physical parameters and, at high frequency, using ultrasonically-measured non-acoustical physical parameters (tortuosity, viscous characteristic length and thermal characteristic length) are found to be in good agreement with the ultrasonically-measured sound velocities above 100kHz thereby confirming the accuracy of the JCA model at ultrasonic frequencies.Differences in values of the two characteristic lengths between the Foam-X outputs and the results of ultrasonic measurements, using the slope method, and the important role of two correction factors in Kino’s empirical modification of the JCA model are explored in detail. It is shown that the values of characteristic lengths required to fit data using the original JCA model in the audible frequency range differ significantly from the ultrasonically-measured values. However it is shown that the Foam-X and the Kino model methods yield similar values for the two characteristic lengths in the audible frequency range. Further modifications of the JCA model to make it valid over a wider frequency range are proposed.