Thermal Characteristic Lengths Research Articles

A machine learning approach for predicting the Johnson-Champoux-Allard parameters of a fibrous porous material

Porous fibrous materials have been widely used as acoustic treatments for noise attenuation. Their acoustic properties are typically characterized by Johnson-Champoux-Allard (JCA) model, which includes five dominant parameters, i.e., open porosity, flow resistivity, tortuosity, viscous characteristic length, and thermal characteristic length. The JCA parameters depend on the microstructure configuration of the material, which can be attained by experimental measurements or numerically analyzing the flow field inside the microstructure, but significant efforts to predict the parameters are typically required. This study proposes a machine learning approach based on an artificial neural network (ANN) for predicting the JCA parameters of a fibrous material. Two geometric parameters that can characterize the fibrous material, i.e., the radius of the fiber and the equivalent throat size between neighbouring fibers, are set as inputs for the prediction model, while the five JCA parameters are set as outputs. The datasets for the network are prepared from finite element simulations. Results confirm that the trained model can predict the JCA parameters accurately and reliably based on the micro-structural geometric parameters. Finally, the model is further validated by the measured acoustic characteristics of a metal-based fibrous material in an impedance tube. The machine learning model opens up possibilities to facilitate the design of advanced porous materials.

Numerical study to investigate the effect of sample size sensitivity on porous materials with respect to different geometrical parameters

Porous materials play a crucial role in various industrial applications, where precise determination of geometric parameters like dynamic tortuosity, as well as viscous and thermal characteristic lengths, is essential for optimizing acoustical performance. Up to this point, there has been no published size sensitivity test that recommends the ideal sample size for analyzing these parameters in an industrial environment. The present article analyzes different reconstructed porous material samples using conventional CFD and coupled FEA-CFD simulations and suggests optimal sample size and specific simulation setup optimized for industrial purposes, which grant high accuracy and reasonable computational cost. The present paper analyzed several samples, which were reconstructed by micro-CT and analyzed in Star-CCM+ simulation environment. It was found that the optimal sample size (1.5×1.5×1.5 mm or 2.5×2.5×2.5 mm) is different for specific average pore sizes. It was proven through various numerical simulations based on reconstructed porous material samples that running only one coupled CFD-FEM simulation is satisfactory to directly determine all investigated parameters. It was demonstrated that the computationally demanding numerical model could be simplified in specific cases using a rigid body and highlight the limitations.

Numerical study to investigate the thermal characteristic length with coupled CFD-FEM simulations

This paper introduces a new technique for directly calculating the thermal characteristic length (Λ′) of porous materials, addressing a critical parameter required for accurate acoustic simulations during vehicle development. The proposed method offers improved practicality over existing approaches. The research seeks to overcome the limitations of current methods, proposing a coupled CFD-FEA approach within a fluid–structure interaction (FSI) simulation framework. By incorporating both fluid temperature and the fundamental definition of characteristic length, this formulation enables the direct calculation of Λ′. The validity of the method is established through specific tests conducted on ten reconstructed material samples. The proposed approach outperforms measurement techniques and established formulas, offering enhanced accuracy while overcoming the limitations of experimental repeatability. The study demonstrates the universal nature of characteristic curves across various flow regimes, ensuring consistent parameter determination under different flow conditions and sample sizes. Additionally, the research highlights the significant influence of structure deformation, regardless of flow regime, sample size, and flow direction. This paper advances the comprehension of characteristic parameters across diverse conditions by presenting a new method that enhances practicality, accuracy, and applicability to vehicle acoustic simulations.

Characterizing high-frequency wave interaction in rigid porous bilayer materials: Insights from acoustic parameter sensitivity analysis

This study aims to investigate the sensitivity of high-frequency acoustic parameters in rigid air-saturated porous bilayer materials using the equivalent fluid theory. The interaction between the fluid and solid phases of the porous medium incorporates visco-inertial and thermal exchange, characterized by two functions: the dynamic tortuosity α(ω) proposed by Johnson etal. and the dynamic compressibility β(ω) proposed by Allard, refined by Sadouki for the low-frequency domain of ultrasound. Various parameters, including porosity, tortuosity, viscous characteristic length, thermal characteristic length, as well as viscous and thermal shape factors, are examined in this study. A 10% variation in these parameters is considered to assess their impact on the amplitudes of transmitted waves. The findings of this study contribute to a deeper understanding of high-frequency wave behavior in porous bilayer materials. The investigation sheds light on the sensitivity of the parameters and provides valuable insights for the design and optimization of such materials in engineering, technology, and applied sciences.

Development of a thermal aging model for sound-absorbing polyurethane foam

This research aims to establish a reliable thermal aging model of sound-absorbing polyurethane foam (PUF). To achieve this objective, accelerated testing was conducted in a heat chamber under various conditions. The transport parameters (open porosity, high-frequency limit of the dynamic tortuosity, viscous characteristic length, thermal characteristic length, and static thermal permeability) of original and aged PUF were characterized and investigated. Curve fitting was performed to predict the value of each transport parameters corresponding to the level of thermal aging from the collected data. The thermal aging model of PUF was constructed using the Layton model and Arrhenius equations, which showed good agreement with the measured data. By employing the proposed thermal aging model, it became possible to forecast the acoustic behavior of PUF at different aging temperatures and aging periods. Subsequent testing of PUF sample materials confirmed the validity and efficiency of the developed aging model. These findings provide a crucial reference for creating a predictive model for the acoustic behavior of PUFs undergoing thermal aging and offer valuable insights for designing an accelerated testing approach.

Simulation Analysis of Acoustic Radiation from Force Excitation of Foam-Filled Stiffened Sandwich Panels

To tackle the influence of foam filling on the sound radiation performance of reinforced sandwich panels, this study employs a combined approach of experiments and simulations to investigate the factors that impact the sound radiation performance in the 1–2000 Hz mid–low frequency range. The aim is to determine how the parameters of foam impact the sound radiation performance of foam-filled reinforced sandwich panels. The results indicate that changes in the acoustic parameters of the foam have a weak effect on the frequency corresponding to the peak sound radiation power and the non-peak frequency range sound radiation performance of the sandwich panel, while significantly impacting the peak sound radiation power. Among them, porosity has the least influence on sound radiation performance, whereas static flow resistivity and tortuosity factors have a greater influence on peak sound radiation performance. The reduction in thermal characteristic length and the increase in static flow resistivity can both enhance the sound radiation performance of the panel, while the impact of tortuosity factor and viscous characteristic length on panel sound radiation performance depends on the frequency range.

Experimental and Semi-Phenomenological Investigation on Sound Absorption Performance of Natural Granular Sound Absorber: A Case Study on Rice Bran Composites

The sound absorption performance of rice bran composites was quantitatively investigated through an improved semi-phenomenological approach. Rice bran (RB) was employed as the primary and structural component in the creation of granular-type sound absorbers with urea-formaldehyde (UF) adhesive. The sound absorption coefficient (SAC) was measured by the two-microphone impedance tube method. Samples with a rice bran per volume ratio lower than 253 kg/m3 show peak-valley characteristics in the saturation region of their SAC spectrum. Five non-acoustic parameters for each sample were obtained by direct measurement and fitting the experimental SACs to the semi-phenomenological Johnson-Champoux-Allard (JCA) equivalent fluid model using the least-squares fitting method. Samples with higher proportions of RB demonstrate lower porosity (ϕ), viscous characteristic length (Λ), and thermal characteristic length (Λ'). Flow resistivity (σ) was the only parameter that noticeably increases when RB increased while tortuosity (α_∞) did not show a strong correlation. For the uncertainty analysis of the experimental SAC, multivariate method was used in this study. A new model (NM) was predicated on the power-law relation introduced by Delany and Bazley, in which the SAC was a function of flow resistivity alone. The new model predicted the SAC of RB composites more precisely than the standard Delany-Bazley model (¯Δ_"abs(DBM)" ≈4.0¯Δ_"abs(NM)" ). The proposed model had the potential to be extended into a more unified empirical model of SAC for granular-typed sound absorbers in future investigations with a broader spectrum of granular materials.

Imaging based pore network modeling of acoustical materials

The acoustical behavior of porous materials is dictated by their underlying pore network geometry. Given the complexity of accurately characterizing the various pore network features, current acoustical models instead rely on indirectly incorporating these features by accounting for them within acoustical transport properties, such as tortuosity, viscous and thermal characteristic lengths, and flow resistivity. In turn, these transport properties are currently identified using inverse characterization techniques or using multiphysics modeling techniques. Here, we propose the use of advanced image processing methods to characterize the pore network of acoustical materials and allow the direct calculation of their transport and acoustical properties. To establish the feasibility of this idea, we create 3D printable CAD models of porous materials with controlled pore geometries and use a Matlab-based watershed segmentation technique to calculate their effective pore and throat size distributions. These distributions are then used to calculate their transport properties and predict their sound absorption coefficients using the Johnson–Champoux–Allard model. For comparison, we calculate the transport properties using the hybrid multiphysics modeling technique and the inverse characterization method. The predictions from the three different methods are then compared with experimental measurements obtained by printing and testing the models using an impedance tube.

Brownian motion with radioactive decay to calculate the dynamic bulk modulus of gases saturating porous media according to Biot theory

We present a new stochastic simulation method for determining the long-wavelength effective dynamic bulk modulus of gases, such as ambient air, saturating porous media with relatively arbitrary microgeometries, i.e., simple enough to warrant Biot’s simplification that the fluid and solid motions are quasi-incompressible motions at the pore scale. The simulation method is based on the mathematical isomorphism between two different physical problems. One of them is the actual Fourier heat exchange problem between gas and solid in the context of Biot theory. The other is a diffusion-disintegration-controlled problem that considers Brownian motion of diffusing particles undergoing radioactive-type decay in the pore volume and instant decay at the pore walls. By appropriately choosing the decay time and the diffusion coefficient, the stochastic algorithm we develop to determine the average lifetime of the diffusing particles, directly gives the effective apparent modulus of the saturating fluid. We show how it leads to purely geometric stochastic constructions to determine a number of geometrical parameters. After validating the algorithm for cylindrical circular pores, its power is illustrated for the case of fibrous materials of the type used in noise control. The results agree well with a model of the effective modulus with three purely geometric parameters of the pore space: static thermal permeability divided by porosity, static thermal tortuosity, and thermal characteristic length.

Effects of urea–formaldehyde and polyvinyl acetate adhesive on sound absorption coefficient and sound transmission loss of palmyra palm fruit fiber composites

Composite materials made from palmyra palm fruit fiber (PPFF) were formed using urea–formaldehyde (UF) and polyvinyl acetate (PVAc). We prepared two sets of five different cylindrical samples with varying PPFF contents. The PPFF composites’ normal-incident sound absorption coefficient (SAC) and transmission loss (TL) were measured by using the impedance tube method. The sample with higher PPFF content shows a lower SAC spectrum. It is the opposite for the TL, where a sample with high PPFF content demonstrates a higher TL spectrum. We conducted the least-square fitting method on the experimental SAC and TL spectra utilizing the Johnson-Champoux-Allard (JCA) equivalent fluid model. Non-acoustic parameters were acquired from the fitting. The optimized porosity (ϕ), viscous characteristic length (Λ), and thermal characteristic length (Λ′) are inversely proportional to the PPFF content. The airflow resistivity (σ) and tortuosity (α∞), on the other hand, demonstrate a direct correlation with the PPFF content. Even though the UF samples have an average density of 14.7 % higher than the PVAc samples, their σ,Λ′, and α∞ are just 7.7 %, 4.5 %, and 0.39 % higher than PVAc samples. On the other hand, PVAc samples show higher average Λ and ϕ of 1.4 % and 0.73 %, respectively. The optimized porosity values obtained from the JCA model (ϕJCA) are coherent with ones from the direct estimation method assuming adhesive-coated fiber (ϕfa). It can be concluded that the adhesive’s quantity and density contribute to the composites’ porosity value, ultimately affecting material acoustic properties. Researchers can control and predict how the SAC and TL of fibrous sound absorbers would behave by varying the quantity and density of an adhesive.

Sound absorption of two-dimensional rough tube porous materials

In this paper, a theoretical model for predicting the sound absorption performance of two-dimensional rough tube porous materials is established based on the Johnson–Champoux–Allard–Lafarge equivalent fluid model. The shape of the two-dimensional rough tube is approximated by trigonometric functions, and the theoretical expressions of its fluid transport parameters are given, including viscous permeability, thermal permeability, tortuosity, viscous characteristic length, and thermal characteristic length. In addition, the influence of shape factor is considered when calculating the thermal permeability and the viscous characteristic length, and its theoretical expression is given. The theoretical model is verified by a numerical simulation model based on the multi-scale asymptotic method, and good agreement is achieved. Compared with smooth tubes, circumferential rough tubes and axial rough tubes, the two-dimensional rough tubes not only enhance the viscous dissipation effect but also enhance the thermal dissipation effect during the propagation of sound waves, thus, realizing the high-efficiency sound absorption at lower frequencies. This work further develops the sound absorption theory of porous materials considering the roughness effect and enriches the research and design ideas of porous materials.

A microstructure-based model of transport parameters and sound absorption for woven fabrics

A microstructure-based model is proposed to describe the transport parameters and sound absorption performance of idealized periodic woven fabrics. With proper hypotheses and simplifications, transport parameters, including permeability, tortuosity, viscous characteristic length and thermal characteristic length, are explicitly expressed as functions of fiber diameter and porosity. The unknown control coefficients introduced in the analytical model are fitted by performing multiscale numerical simulations over the representative unit cells. Subsequently, these transport parameters are submitted into the well-established Johnson-Champoux-Allard (JCA) model of porous media to calculate the acoustic impedance and sound absorption coefficient of the woven fabric. Compared with the corresponding transport parameters of a non-crimp fabric, the tortuosity is enlarged and viscous characteristic length decreases significantly, while the viscous permeability and thermal characteristic length remain almost unchanged, resulting in slightly improved performance in sound absorption. The fiber diameter, porosity, and thickness of a woven fabric comprehensively determine its capability to absorb sound. For enhanced energy dissipation (and hence sound absorption) via viscous-thermal boundary layers on fiber surfaces, the fiber diameter and porosity should be selected from an appropriate range such that the characteristic pore size of the woven fabric lies in the order of submillimeter. With the increase of sheet thickness, the sound absorption coefficient in the low frequency band is significantly improved.

Experimental and modeling investigation of the acoustic behavior of sustainable kenaf/yucca composites

The increased awareness of environmental issues has motivated researchers and manufacturers towards the use of natural acoustic absorbers, which are environmentally friendly, sustainable, and relatively cheap. One approach in this direction is to explore the use of waste fibers for potential applications in sound absorption. This study investigates the acoustic behavior of kenaf and yucca waste fiber composites. To this end, yucca and kenaf waste fibers were collected. The separation and extraction of fibers from non-fibrous tissues and woody parts were carried out using the water retting technique. Afterward, yucca and kenaf fibers were blended with a mass ratio of 70:30, 50:50, and 30:70. Polyvinyl alcohol (PVA) was used as the binder to fabricate the composite samples. The acoustic performance of the composites was evaluated using the impedance tube technique. The frequency-dependent absorption behavior of the samples was also investigated using the Delany-Bazley (D-B), Garai-Pompoli (G-P), and Johnson-Champoux-Allard (JCA) models. An in-house developed Matlab code was used for the simulation of the 3D structure of the specimens, and flow resistivity was calculated by simulation of the airflow through the structure. Additionally, tortuosity, viscous, and thermal characteristic lengths were calculated by an inverse technique. It was found that samples of 100% kenaf fibers have the highest flow resistivity values. Flow resistivity decreased with decreasing the kenaf content in the composite samples. It was found that samples of 100% kenaf fibers exhibit promising performance at the low- and mid-frequency bands. A decrease in the amount of kenaf content led to the shift of absorption peak towards the high-frequency region. It was also found that the JCA model closely follows the trend of experimental data for the frequency range of 80–6300 Hz.

Effect of fiber cross-section on the transport and acoustic properties of fibrous materials

Fibrous materials can efficiently dissipate acoustic energy, and their intrinsic properties are determined by fiber geometries (microscale). In this study, the effect of cross-sections of fibers on the transport and acoustic properties of fibrous materials was investigated. First, fibers of various cross-sections were modeled by adjusting their open porosity. The representative elementary volumes of fiber structures were generated to describe the periodic unit-cell structures. Next, the transport properties (such as static airflow resistivity, high-frequency limit of the dynamic tortuosity, viscous characteristic length, thermal characteristic length, and static thermal permeability) of fibrous materials were calculated by solving numerical problems using the finite element method. These properties of fibrous materials with complex cross-sections were compared with those with circular cross-sections. Finally, the sound absorption coefficients were predicted using the Johnson-Champoux-Allard-Lafarge (JCAL) model and rigid frame approximation, and the differences in sound-absorbing behavior were analyzed. This study can provide insights into the design of lightweight fibrous materials while maintaining optimal sound absorption performance.

Acoustic Characterization of Some Steel Industry Waste Materials

From a circular economy perspective, the acoustic characterization of steelwork by-products is a topic worth investigating, especially because little or no literature can be found on this subject. The possibility to reuse and add value to a large amount of this kind of waste material can lead to significant economic and environmental benefits. Once properly analyzed and optimized, these by-products can become a valuable alternative to conventional materials for noise control applications. The main acoustic properties of these materials can be investigated by means of a four-microphone impedance tube. Through an inverse technique, it is then possible to derive some non-acoustic properties of interest, useful to physically characterize the structure of the materials. The inverse method adopted in this paper is founded on the Johnson–Champoux–Allard model and uses a standard minimization procedure based on the difference between the sound absorption coefficients obtained experimentally and predicted by the Johnson–Champoux–Allard model. The results obtained are consistent with other literature data for similar materials. The knowledge of the physical parameters retrieved applying this technique (porosity, airflow resistivity, tortuosity, viscous and thermal characteristic length) is fundamental for the acoustic optimization of the porous materials in the case of future applications.

Sound absorption of petal shaped micro-channel porous materials

Experiments demonstrated that surface roughness could significantly improve the sound absorption performance of porous materials. In this study, to quantitatively explore the underlying physical mechanisms, porous materials with roughened pore surfaces are modeled as a bundle of parallel petal shaped tubes, so that relevant acoustic transport parameters, namely, viscous permeability, thermal permeability, tortuosity, viscous characteristic length, and thermal characteristic length, can be theoretically predicted. Multi-scale numerical simulations are implemented to validate the theoretical predictions, with good agreement achieved. Compared with smooth tubes, petal shaped tubes reduce the viscous and thermal characteristic lengths as well as the viscous and thermal permeabilities, resulting in enhanced sound absorption over a wide frequency band.

Natural fibro-granular composite as a novel sustainable sound-absorbing material

An innovative natural fibro-granular composite made of kenaf fibers and waste rice husk granules is developed and presented in this paper. The optimization of the sound absorption coefficient (SAC) of the composites was investigated through the impedance tube method. The central composite design (CCD) technique with response surface methodology (RSM) was used to design the experiments. A quadratic model was established to identify the effects of independent variables, including the thickness (20–60 mm), density (100–300 kg/m3), binder content (10–30 %w/w), and fiber to granule ratio (0.33–3) on the sound absorption average. The accuracy of the proposed model was assessed using ANOVA, and the results demonstrated that all the independent variables were significantly associated with sound absorption. The RSM-CCD model provided the combination for the optimized composite, i.e. thickness of 50 mm, density of 200 kg/m3, binder content of 15 %w/w, and fiber to granule ratio of 2.33. The fibro-granular composite prepared using the optimized results was further characterized in terms of SAC, airflow resistivity, tortuosity, and viscous and thermal characteristic lengths. The results pointed to the promising acoustic behavior of the optimized fibro-granular material. Results show that at all frequencies, the optimized fibro-granular sample provides higher sound absorption compared with samples made of 100% kenaf or 100% rice husk. The frequency-dependent SAC of the optimized material was also predicted by the empirical Delany-Bazley model and the phenomenological model of Johnson-Champoux-Allard, although this last model showed superior prediction performance.

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.