Thermal Characteristic Lengths Research Articles

Possibilities of porous-structure representation – an overview

Porous media can be found in all areas of scientific life, such as medicine, civil engineering, material science, fluid dynamics. Computing has achieved high efficiency and computational capacity – so far. However, three-dimensional Computational Fluid Dynamics (CFD) simulations of microstructure remain significant challenges. Pore-scale simulations can help understand the physical processes and determine macroscopic parameters such as the high-frequency limit of dynamic tortuosity, viscous, and thermal characteristic lengths. Independent of whether the computational problem is two or three-dimensional, the geometry as input parameter must be prepared. For this reason, geometry representation methods play a crucial role in the analysis at the pore-scale, especially in numerical simulations. In this article, an insight into microstructures’ visualization capabilities is provided essentially for CFD simulations.

Improving Sound Absorption coefficient and analysis of polyurethane foam reinforced with wood powder

When it comes to acoustic insulation Polyurethane foam plays a very vital role for various sound absorption applications. The interest of this paper is to spot out the best combination of bio-based porous materials to obtain the best acoustic property. Here the porous materials used are polyurethane foam, pine wood with air gap. The sound absorption depends on the material properties such as Flow resistivity, porosity, tortuosity, thermal characteristic length and physical characteristic length, the different combinations of materials with air gap are being tested for sound absorption coefficient using impendence tube method using COMSOL. The results are being compared with numerical values obtained using impedance tube that helps us to present the best combination which provides the maximum sound absorption.

Experimental characterization of air-saturated porous material via low-frequencies ultrasonic transmitted waves

An improved acoustic method is proposed for measuring the tortuosity and the viscous and thermal characteristic lengths of air-saturated porous materials via low-frequency ultrasonic transmitted waves (70 kHz–110 kHz). The equivalent fluid model is considered. The interaction between the saturated fluid and the structure is taken into account in two frequency response factors: the dynamic tortuosity of the medium and the dynamic compressibility of the air which are described by their high-frequency expansion in powers of the viscous and thermal skin depth, either limiting the expansion to the first two leading terms or the first three leading terms with the introduction of two new viscous and thermal shape factors. These two new factors play an important role in stabilizing and improving the inverted parameters of the tortuosity and the viscous and thermal characteristic lengths in the frequency band considered. The inverse problem is solved numerically in the frequency domain by minimizing the spectrum of simulated and experimental transmitted signals. Optimized parameters of tortuosity, viscous and thermal characteristic lengths, and viscous and thermal shape factors are obtained simultaneously. The tests are carried out with three samples of plastic foam. The results obtained by the two procedures are discussed and compared to those given in the literature.

Application of Acoustical Method to Characterize Nonwoven Material

Some structural parameters, such as tortuosity, viscous and thermal characteristic lengths, are difficult to obtain through direct measurements. Existing indirect methods, i.e. acoustical method, make it possible to estimate these parameters. This paper presents an application of acoustical inversion methods for estimating structural parameters of polyester nonwoven materials. A four-microphone impedance tube was used to measure sound reflection and transmission coefficients. The inversion methods used in this research are least square and Bayesian approaches. The least square method was achieved via Nelder-Mead algorithm. The Bayesian inversion process was conducted with Metropolis-Hastings algorithm and maximum a posteriori. Inversed parameters from two methods as well as front and back sides of nonwoven fabric were compared. Moreover, inversed porosity and airflow resistivity were compared with measured values. The results show that the least square and Bayesian methods has a good agreement. Estimated parameters from Bayesian method were selected for further analysis. A sizable differences on thermal characteristic length were found by comparing the values from two sides, while the differences are relatively small for other parameters. It is also found that the inversed porosity, tortuosity are reasonable. The results suggest that the acoustical inversion methods can be used to accurately characterize polyester fibrous materials.

Buckling of thermalized elastic sheets

Steady progress in the miniaturization of structures and devices has reached a scale where thermal fluctuations become relevant and it is thus important to understand how such fluctuations affect their mechanical stability. Here, we investigate the buckling of thermalized square sheets under either compression or shear. We demonstrate that thermal fluctuations increase the critical buckling load compared to the classical Euler buckling load due to the enhanced scale-dependent bending rigidity for sheets that are much larger than a characteristic thermal length scale. The presented results are universal and apply to a wide range of microscopic sheets. These results are especially relevant for atomically thin 2D materials, where thermal fluctuations can significantly increase the critical buckling load because the thermal length scale is on the order of nanometers at room temperature.

Design, fabrication and sound absorption test of composite porous metamaterial with embedding I-plates into porous polyurethane sponge

Nowadays the use of porous polyurethane sponge (PPS) is very common for sound absorption, thanks to its light-weight feature and easy fabrication. However, in many circumstances the traditional PPS has very limited absorption capabilities, due to the slow wave phenomenon and/or to insufficient sub-wavelength sound absorption. In this paper, we propose a composite porous metamaterial (CPM) consisting in a porous polyurethane sponge with embedded multi-layer I-plates to mitigate this problem. To characterize the sound absorption coefficient of the proposed CPM, we resort to the Johnson-Champoux-Allard (JCA) model, where five acoustic parameters, namely porosity, flow resistivity, tortuosity, viscous, and thermal characteristic lengths, are determined by acoustic test methods. Numerical and experimental results show that the sound absorption performance of PPS in the CPM is remarkably improved, compared to a contrast structure and a pure porous material, taking advantage of a twofold mechanism of local acoustic energy dissipation of the I-plates and the slow wave phenomenon cancellation inside the structure. Finally, the effects of the geometrical parameters on average sound absorption coefficient are presented and discussed in detail. The scheme of this paper possesses potential application value for the design of broadband and efficient sound absorbers, providing a reference for researches of new acoustic functional devices with high absorption performances.

Characterization on Polyester Fibrous Panels and Their Homogeneity Assessment.

Nowadays, fibrous polyester materials are becoming one of the most important alternatives for controlling reverberation time by absorbing unwanted sound energy in the automobile and construction fields. Thus, it is worthy and meaningful to characterize their acoustic behavior. To do so, non-acoustic parameters, such as tortuosity, viscous and thermal characteristic lengths and thermal permeability, must be determined. Representative panels of polyester fibrous material manufactured by perpendicular laying technology are thus tested via the Bayesian reconstruction procedure. The estimated porosity and airflow resistivity are found in good agreement with those tested via direct measurements. In addition, the homogeneity of polyester fibrous panels was characterized by investigating the mean relative differences of inferred non-acoustic parameters from the direct and reverse orientation measurements. Some parameters, such as tortuosity, porosity and airflow resistivity, exhibit very low relative differences. It is found that most of the panels can be assumed homogeneous along with the panel thickness, the slight inhomogeneity mostly affecting the thermal characteristic length.

Sound propagation in porous materials containing rough tubes

A theoretical model is developed to quantify the influence of surface roughness on sound propagation in porous materials containing rough tubes by extending the Johnson–Champoux–Allard–Lafarge (JCAL) model. The five transport parameters of the JCAL model, including the viscous permeability, thermal permeability, tortuosity, viscous characteristic length, and thermal characteristic length, are calculated by modeling the rough tubes in the porous material as parallel rough tubes having idealized sinusoidal morphologies. The transport parameters obtained using the proposed model are validated by full finite element simulations. Based on these transport parameters, the sound absorption coefficient of the porous material containing idealized rough tubes is calculated, which agrees well with the FE result. The roughness effect is investigated by comparing sound absorption performance between parallel smooth tubes and parallel rough tubes. The existence of tube roughness weakens the thermal effect but dramatically strengthens the viscous effect in sound energy dissipation, resulting in enhanced sound absorption. This work provides fundamental insights on how surface roughness affects the acoustic performance of sound-absorbing porous materials.

Computation of acoustic properties and design guidelines of periodic Biot-modeled foams

This paper aims at consolidating research dealing with vibroacoustics of periodic media. The main goal of this work is to develop and to validate tools for the design of global vibroacoustic treatments based on periodic patterns, allowing passive control of acoustic paths in layered concepts. To this aim, some enhancements are introduced to the state of the art on the study and the design of Biot-modeled foams, in order to obtain desired acoustics performances through embedded periodic inclusions. At first, the properties of the studied acoustic package, constituted by a poro-elastic 3D unit cell, is introduced. Successively, through the use of the acoustic-structure coupling that comes from the implementation of Biot model, a non-rigid inclusion test campaign is carried out by considering some solid (but still non-perfectly-rigid) inclusions in a 3D-modeled unit cell; in particular, six setups are discussed herein. Then, some design guidelines are provided in order to predict at which frequency the first performance peak appears, together with its amplitude, as functions of unit cell dimensions, airflow resistivity, tortuosity, viscous and thermal characteristic lengths, frame density, Young modulus and loss factor; conversely, it is shown also the link between the unit cell dimensions and the first performance peak amplitude as functions of the design frequency.

Investigation of Sound Absorption Characteristics of Polypropylene Nanofiber Nonwoven Fabric Focusing on Flow Resistance in Biot Acoustic Parameters

We proposed a novel nanofiber manufacturing technology by melt-blowing process. In the present report, we focused on manufactured polypropylene nanofiber nonwoven fabric as a novel sound absorbing material, measuring its Biot acoustic parameters, and also performed its CFD (Computational Fluid Dynamics)analysis to discuss flow resistance in them. Especially, we looked at the influence of the gap ratio (the ratio of the fiber gab between fibers and fiber diameter, which was related to the porosity), Knudsen number and the thermal characteristic length on the sound absorption coefficient and the flow resistance. As a result, it can be seen that the sound absorption coefficient and the flow resistance are greatly affected by the gap between the fibers. Moreover, the gap ratio and the thermal characteristic length are found to be essential parameters under the constant gap between fibers.

Sound absorption performance of sustainable foam materials: Application of analytical and numerical tools for the optimization of forecasting models

Traditional models used to predict acoustic properties of poroelastic materials are usually applied to fibrous layers or polyurethane foams. However, for new materials like complex cellular foams these procedures may not be applied due to the different cell microstructure. To this aim, the sound absorbing properties of novel sustainable foam materials are investigated as a function of the nature and loading of waste powders and their effects on the microstructure and the acoustic properties. The foams are prepared from naturally occurring alginates that are in situ polymerized. The morphology and the acoustic properties of the foam-cells appear linked to the particle size distribution of the starting powder. Determination of the parameters of Johnson–Champoux–Allard acoustic model (tortuosity, viscous characteristic length, thermal characteristic length, porosity and flow resistivity) was performed using five different forecasting methods, including traditional analytical model for fibrous materials as well as inverse procedure. A new procedure for tortuosity computation of foam is proposed and validated. Transfer Matrix Method calculation of the absorption coefficient was performed and compared with the experimental data, in order to assess the validity of the model. Indirect method technique is demonstrated to be dependent on experimental measurement of thermal characteristic length.

Computational Investigations on Soundproof Applications of Foam-Formed Cellulose Materials

Recent studies have highlighted an innovative way to produce highly porous materials based on cellulose fibers. These studies have focused on the foam-forming process, where the cellulose fibers and other components are mixed with foam. In the authors’ previous research, the foam-formed cellulose materials (FCM) were obtained by mixing a surfactant with cellulose fibers, taken from virgin pulp and recovered papers. In the present paper, the authors performed additional experimental and computational analyses in order to evaluate the sound insulation capabilities of these FCM beyond the initial impedance of tube investigations. The poroacoustics computational methodology parameters—i.e., airflow resistivity, porosity, tortuosity, viscous, and thermal characteristic lengths—were herein evaluated. This analysis was performed using both a theoretical/empirical approach from the specialized literature and an experimental investigation developed by the authors. The computational investigations were conducted in two stages: First, we evaluated the approximation of the experimentally gained normal incidence parameters, in terms of absorption and reflection, respectively, relative to the estimated ones. The second stage of analysis consists of a parametrical estimation of sound insulation characteristics concerning the incidence angle of sound hitting the porous layer. The results presented in this paper are in agreement with the computational experimental results, providing extended soundproof characteristics to the incidence angle of the acoustic field. Further, this study supplies additional information useful for future analyses regarding the influences of random geometry air inclusions into the FCM layer.

Prediction of effective properties and sound absorption of random close packings of monodisperse spherical particles: Multiscale approach

The transport and sound absorption properties of random close packings of monodisperse spherical particles are explored following a multiscale approach. First, the discrete element method is used to simulate the free fall of the monodisperse particles in a bounded domain to create virtual samples that are representative of real samples. Different particle diameters ranging from 1 to 16 mm are studied. From the virtual samples, representative volume elements (RVEs) are defined. Local partial differential equations governing the transport properties are numerically solved on the RVEs. From the discretized RVEs and the numerical solutions, eight transport properties (porosity, tortuosity, and viscous and thermal static tortuosities, permeabilities, and characteristic lengths) are derived. Micro-macro relationships between these properties and the particle diameter are developed. They are validated against experimental measurements of the open porosity and sound absorption coefficients. The relationships are used to analyze the salient sound absorption features of such media, notably the resonant sound absorption behavior. Expressions allowing identification of the optimal particle diameter for a given thickness, or conversely, the optimal thickness for a given particle diameter, for achieving 100% absorption at the first resonant absorption are derived.

Acoustic properties of periodic micro-structures obtained by additive manufacturing

Periodic acoustic structures of rigid micro-rods produced via additive manufacturing were analyzed using an impedance tube in the 500 Hz–6000 Hz frequency range. The acoustical properties such as the porosity, the airflow resistivity, the tortuosity, the viscous characteristic length and the thermal characteristic length were determined by comparing an analytical model and the experimental results. The model which takes into account the interaction between the acoustic wave and a rigid periodic structure was proven to be an effective tool to correlate the final acoustic performance of the structure and the printing parameters. It was shown that broadband acoustic capabilities can be improved over the studied frequency range with the smallest filament possible or by reducing the lattice parameter and/or by changing the orientation of the filament from one layer to the next. This work was motivated by the need to control the manufacturing parameters of acoustic materials with broadband absorption capabilities. Furthermore the present investigation paves the way to explore new avenues to replace stochastic porous materials by new structures with combined mechanical and acoustic properties.

Calculation of the temperature field of the material in the thermal model of laser ablation

The mechanisms of laser ablation of materials under the interaction of powerful pulsed laser radiation with a material coated with a thin film system were studied. One of the first models of such interaction of high-power laser radiation with matter was the thermal model. A onetemperature thermal model was used when considering the interaction of laser radiation with dielectrics, and a two-temperature model was used when considering the interaction of laser radiation with metals. When studying the processes of laser ablation within the framework of the thermal model, the method of moments with a special selection of the test function was chosen. Computer simulation was conducted to study the dependence of the surface temperature and the characteristic thermal length on the radiant flux. Variants with both constant and variable optophysical characteristics of the phenomenon were considered. Calculations were performed for different time ranges under different initial conditions. The results of the numerical experiment agree well with the data of other authors.

Experimental measurement of tortuosity, viscous, and thermal characteristic lengths of rigid porous material via ultrasonic transmitted waves

An inverse method is proposed for measuring tortuosity, viscous, and thermal characteristic lengths of air-saturated porous material with rigid frame via ultrasonic transmitted waves at normal incidence. The equivalent fluid model is considered. The interaction between the fluid saturated the pores and the structure are taken into account in two frequency response factors: the dynamic tortuosity of the medium introduced by Johnson et al. and the dynamic compressibility of the air introduced by Allard. Simplified expression of the transmission coefficient is obtained in frequency domain, and this expression depends on the porosity, tortuosity, viscous, and thermal characteristic lengths. The inverse problem is solved numerically in time domain by minimizing between simulated and experimental transmitted waves. The inverted parameters are in good agreement with those obtained using conventional methods. Simulated signals are reconstructed using the optimized values found and compared with the experimental signals. Tests are performed using three different plastic foam samples having low flow resistivity. The proposed technique has the advantage of being simple, fast, and not expensive.An inverse method is proposed for measuring tortuosity, viscous, and thermal characteristic lengths of air-saturated porous material with rigid frame via ultrasonic transmitted waves at normal incidence. The equivalent fluid model is considered. The interaction between the fluid saturated the pores and the structure are taken into account in two frequency response factors: the dynamic tortuosity of the medium introduced by Johnson et al. and the dynamic compressibility of the air introduced by Allard. Simplified expression of the transmission coefficient is obtained in frequency domain, and this expression depends on the porosity, tortuosity, viscous, and thermal characteristic lengths. The inverse problem is solved numerically in time domain by minimizing between simulated and experimental transmitted waves. The inverted parameters are in good agreement with those obtained using conventional methods. Simulated signals are reconstructed using the optimized values found and compared with the experimental s...

Finite element modeling of fluid-saturated metallic foams from micro-computed tomography

Open-cell metallic foams are high stiffness-to-weight cellular materials whose microstructure allows for saturation of viscous liquid. Such a composite has advantages for underwater sound absorption over traditional rubbers due to minimal compression from hydrostatic pressure, composite tunability, and potential for specific gravity less than one. Semi-phenomenological and hybrid numerical models have been shown to predict sound absorption performance of metallic foams, however difficulty arises in determining parameters for the numerical models such as tortuosity, viscous characteristic length, thermal characteristic length, and flow resistivity. Such models also assume that the porous frame is rigid, an assumption valid for only a limited frequency range. In this presentation, finite element models of fluid-saturated metallic foams are created from micro-computed tomography scans and analyzed to determine sound absorption performance. The advantage of this method is that the entire foam microstructure and surrounding fluid can be accurately modeled through a finite element mesh. In addition, experimental measurement of model parameters is not required and the rigid frame assumption can be removed.

Bayesian inference for the ultrasonic characterization of rigid porous materials using reflected waves by the first interface.

The purpose of this paper is to present a method for the ultrasonic characterization of air-saturated porous media, by solving the inverse problem using only the reflected waves from the first interface to infer the porosity, the tortuosity, and the viscous and thermal characteristic lengths. The solution of the inverse problem relies on the use of different reflected pressure signals obtained under multiple obliquely incident waves, in the time domain. In this paper, the authors propose to solve the inverse problem numerically with a first level Bayesian inference method, summarizing the authors' knowledge on the inferred parameters in the form of posterior probability densities, exploring these densities using a Markov-Chain Monte-Carlo approach. Despite their low sensitivity to the reflection coefficient, it is still possible to extract the knowledge of the viscous and thermal characteristic lengths, allowing the simultaneous determination of all the physical parameters involved in the expression of the reflection operator. To further constrain the problem and guide the inference, the knowledge of a particular incident angle is used at one's advantage in order to more precisely define the thermal length, by effectively yielding a statistical relationship between tortuosity and characteristic length ratio.

Gold Nanoparticles as a Photothermal Agent in Cancer Therapy: The Thermal Ablation Characteristic Length.

In cancer therapy, the thermal ablation of diseased cells by embedded nanoparticles is one of the known therapies. It is based on the absorption of the energy of the illuminating laser by nanoparticles. The resulting heating of nanoparticles kills the cell where these photothermal agents are embedded. One of the main constraints of this therapy is preserving the surrounding healthy cells. Therefore, two parameters are of interest. The first one is the thermal ablation characteristic length, which corresponds to an action distance around the nanoparticles for which the temperature exceeds the ablation threshold. This critical geometric parameter is related to the expected conservation of the body temperature in the surroundings of the diseased cell. The second parameter is the temperature that should be reached to achieve active thermal agents. The temperature depends on the power of the illuminating laser, on the size of nanoparticles and on their physical properties. The purpose of this paper is to propose behavior laws under the constraints of both the body temperature at the boundary of the cell to preserve surrounding cells and an acceptable range of temperature in the target cell. The behavior laws are deduced from the finite element method, which is able to model aggregates of nanoparticles. We deduce sensitivities to the laser power and to the particle size. We show that the tuning of the temperature elevation and of the distance of action of a single nanoparticle is not significantly affected by variations of the particle size and of the laser power. Aggregates of nanoparticles are much more efficient, but represent a potential risk to the surrounding cells. Fortunately, by tuning the laser power, the thermal ablation characteristic length can be controlled.

Temperature Field under Laser Ablative Destruction of Target at Low Temperatures

A thermal model of the laser ablative destruction of materials is considered. The method of moments is used to numerically solve nonstationary heat-conduction equation for 1D system. The solution makes it possible to analyze the dynamics of several parameters that characterize the laser ablation, in particular, surface temperature and characteristic thermal length.