Measurements and empirical model of the acoustic properties of reticulated vitreous carbon

Reticulated vitreous carbon (RVC) is a highly porous, rigid, open cell carbon foam structure with a high melting point, good chemical inertness, and low bulk thermal conductivity. For the proper design of acoustic devices such as acoustic absorbers and thermoacoustic stacks and regenerators utilizing RVC, the acoustic properties of RVC must be known. From knowledge of the complex characteristic impedance and wave number most other acoustic properties can be computed. In this investigation, the four-microphone transfer matrix measurement method is used to measure the complex characteristic impedance and wave number for 60 to 300 pore-per-inch RVC foams with flow resistivities from 1759 to 10,782 Pa s m(-2) in the frequency range of 330 Hz-2 kHz. The data are found to be poorly predicted by the fibrous material empirical model developed by Delany and Bazley, the open cell plastic foam empirical model developed by Qunli, or the Johnson-Allard microstructural model. A new empirical power law model is developed and is shown to provide good predictions of the acoustic properties over the frequency range of measurement. Uncertainty estimates for the constants of the model are also computed.     

Sound absorption characteristics of a high-temperature sintering porous ceramic material

This article is dedicated to sound absorption properties of porous zeolite with macropores, a ceramic material fabricated by high-temperature sintering. Acoustical properties of this ceramic material are studied by two analytical models, Delany–Bazley model and Johnson–Allard model, where the latter one shows a better fit to the experimental results. Moreover increasing the thickness of samples would improve the sound absorption in the low frequency ranges. Raising the porosity could increase the highest sound absorption coefficient. The resonance frequencies of the materials with 3–5 mm particles are more obvious. Comparing with glass wool, porous zeolite has a better sound absorption.     

An experimental study on the acoustic absorption of sand panels

Potentially sand panels could be used as novel sound absorbing materials that are fire resistant, environmentally friendly, mechanically strong and have good durability. However, the performance of sand panels as sound absorbers has not yet been studied. Results of measurements in a reverberation chamber of the random-incidence absorption coefficients of 13 different sand panel compositions and configurations with air gaps are reported. Also the flow resistivities and bulk densities have been measured. The results prove that sand panels could offer effective and wide-band acoustic absorption. As is the case with conventional sound absorbing materials, adding an air space is found to be the most effective way to widen the absorption bands and improve the overall absorption. Comparisons of the measured sand panel absorption data with predictions of the Delany and Bazley and Voronina models reveal that, while neither model is very accurate, the former gives more accurate predictions especially for sand panels with lower flow resistivity and smaller thickness.     

材料吸声系数双传声器测量的参数识别方法

本文提出了在普通房间中利用双传声器对多孔性和纤维性吸声材料吸声系数测量时的参数识别方法。利用Delany&Bazley经验模型对测量数据进行了参数识别,建立了材料的阻抗模型,并计算出材料全频带的吸声系数。与驻波管方法得到的吸声系数相比,在0～3000Hz范围内,二者都能较好地吻合。通过在不同的环境中进行对比测试,说明该方法具有较好的重复性和准确性。     

On the modification of Delany and Bazley fomulae

It is well known that the formulae developed by Delany and Bazley for characterising the acoustic properties of porous materials should not be extended to low frequencies. Accordingly, a low frequency correction is required when finding the surface impedance or absorption coefficient of a porous material. This article reviews corrections of a type originally proposed by Miki [J. Acoust. Soc. Japan, 1990;11:19–24] and concludes that there is no physical basis behind these methods and that they should not be used. Instead, a number of alternative methods are available that maintain the correct limiting behaviour for the fundamental properties of a porous material at low frequencies, and two of these methods are briefly reviewed here.     

An application of Kozeny–Carman flow resistivity model to predict the acoustical properties of polyester fibre

Modelling of the acoustical properties of polyester fibre materials is usually based on variations of the Bies and Hansen empirical model [1], which allows the calculation of the air flow resistivity of a porous material. The flow resistivity is the key non-acoustical parameter which determines the ability of this kind of materials to absorb sound. The main scope of this work is to illustrate that an alternative theoretical model based on the Kozeny–Carman equation can be used to predict more accurately the flow resistivity from the fibre diameter and bulk material density data. In this paper the flow resistivity is retrieved from the acoustic absorption coefficient data for polyester fibre samples of different densities and fibre diameters. These data agree closely with the flow resistivity predicted with the proposed Kozeny–Carman model.     

Experimental determination of the micro- and macrostructural parameters influencing the acoustical performance of fibrous media

Measurements of the two characteristic lengths of 6 glass wool samples (with flow resistivities between 11,900 and 69,900 Pa s m⁻²) and 6 polyester fibre samples (with flow resistivities between 4100 and 51,000 Pa s m⁻²) have been made. These data have been used to determine the cross-sectional shape factors which are related to the characteristic lengths introduced by Allard. By using the formulas due to Bies and Allard, it has been found that the two characteristic lengths of the glass wool samples can be independently predicted from the glass fibre diameter. In respect to polyester fibre samples, a new relation between the flow resistivity, the fibre diameter and the bulk density has been proposed and examined. The accuracy of the predictions of the non-acoustical parameters has been confirmed by the measurements and predictions of the absorption coefficient using the Delany and Bazley and Allard models.     

Measurement of the acoustic properties of a sound absorbing material at high temperatures

Measurements have been made of the acoustic properties of a typical mineral wool fibrous material at temperatures up to 500C. In addition to acoustic impedance and propagation constant the flow resistance of the material was measured over the same temperature range. With use of a modified form of the Delany-Bazley empirical formula good agreement was found between predicted and measured values of the acoustic impedance and propagation constant at various temperatures up to 500°C.     

A transfer-matrix approach for estimating the characteristic impedance and wave numbers of limp and rigid porous materials

A method for evaluating the acoustical properties of homogeneous and isotropic porous materials that may be modeled as fluids having complex properties is described here. To implement the procedure, a conventional, two-microphone standing wave tube was modified to include: a new sample holder; a section downstream of the sample holder that accommodated a second pair of microphone holders and an approximately anechoic termination. Sound-pressure measurements at two upstream and two downstream locations were then used to estimate the two-by-two transfer matrix of porous material samples. The experimental transfer matrix method has been most widely used in the past to measure the acoustical properties of silencer system components. That procedure was made more efficient here by taking advantage of the reciprocal nature of sound transmission through homogeneous and isotropic porous layers. The transfer matrix of a homogeneous and isotropic, rigid or limp porous layer can easily be used to identify the material's characteristic impedance and wave number, from which other acoustical quantities of interest can be calculated. The procedure has been used to estimate the acoustical properties of a glass fiber material: good agreement was found between the estimated acoustical properties and those predicted by using the formulas of Delany and Bazley.     

Measuring flow resistivity of porous materials at low frequencies range via acoustic transmitted waves

An acoustic transmissivity method is proposed for measuring flow resistivity of porous materials having rigid frame. Flow resistivity of porous material is defined as the ratio between the pressure difference across a sample and the velocity of flow of air through that sample per unit cube. The proposed method is based on a temporal model of the direct and inverse scattering problem for the diffusion of transient low-frequency waves in a homogeneous isotropic slab of porous material having a rigid frame. The transmission scattering operator for a slab of porous material is derived from the response of the medium to an incident acoustic pulse. The flow resistivity is determined from the solution of the inverse problem. The minimization between experiment and theory is made in the time domain. Tests are performed using industrial plastic foams. Experimental and numerical results, and prospects are discussed.     

Effect and importance of static-load on airflow resistivity determination and its consequences on dynamic stiffness

Airflow resistivity is a physical parameter which characterizes porous and fibrous sound absorbent materials. It is well-known that such property allows the evaluation of the acoustic behaviour of sound absorbent materials in various fields of application, including automotive noise mitigation, architectural acoustics and building acoustics. In structure-borne sound insulation, airflow resistivity is essential for the evaluation of the dynamic stiffness of porous and fibrous resilient insulating materials used as underlay in floating floors.However, an inconsistency between the dynamic stiffness and the airflow resistivity test conditions can be recognized. In order to evaluate dynamic stiffness of a resilient material, a static load of about 2 kPa is applied, while in airflow resistivity determination this condition is not explicitly required. As a result, the density of analyzed material, in dynamic stiffness and airflow measurements, is different. Since these two quantities are correlated, it is necessary to measure materials under the same conditions of applied static load.In this work the effects of static load (or density after compression) in airflow resistivity determination of various porous and fibrous resilient materials are investigated, and the consequent influence on dynamic stiffness is discussed. A simply empirical relation between density and airflow resistivity is also put forth.The main focus of this paper is to propose an harmonization among requirements of the Standards in order to prevent significant errors in dynamic stiffness determination and incorrect evaluations of the acoustic behaviour.     

Use of a hybrid adaptive finite element/modal approach to assess the sound absorption of porous materials with meso-heterogeneities

The paper discusses the sound absorptive performance of a porous material with meso-perforations inserted in a rectangular waveguide using a numerical hybrid adaptive finite element-modal method. Two specific applications are investigated: (i) the improvement of porous materials noise reduction coefficient using meso-perforations (ii) the effects of lateral air gaps on the normal incidence sound absorption of mono-layer and two-layer porous materials. For the first application, a numerical design of experiments is used to optimize the sound performance of a porous material with meso-perforations with a reduced number of numerical simulation. An example in which the optimization process is carried out on the thickness and size of the perforation is presented to illustrate the relevance of the approach. For the second application, a set of twenty fibrous materials spanning a large flow resistivity range is used. Practical charts are proposed to evaluate the influence of air gaps on the average sound absorption performance of porous materials. This is helpful to both the experimenter regarding characterization of porous material based on Standing Wave Tube measurements and for the engineer to quantifying the impact of air gaps and for designing efficient absorbers.     

Evaluation of the acoustic and non-acoustic properties of sound absorbing materials using a three-microphone impedance tube

This paper presents a straightforward application of an indirect method based on a three-microphone impedance tube setup to determine the non-acoustic properties of a sound absorbing porous material. First, a three-microphone impedance tube technique is used to measure some acoustic properties of the material (i.e., sound absorption coefficient, sound transmission loss, effective density and effective bulk modulus) regarded here as an equivalent fluid. Second, an indirect characterization allows one to extract its non-acoustic properties (i.e., static airflow resistivity, tortuosity, viscous and thermal characteristic lengths) from the measured effective properties and the material open porosity. The procedure is applied to four different sound absorbing materials and results of the characterization are compared with existing direct and inverse methods. Predictions of the acoustic behavior using an equivalent fluid model and the found non-acoustic properties are in good agreement with impedance tube measurements.     

The acoustical properties of consolidated expanded clay granulates

The paper presents a systematic study of acoustic and non-acoustic properties of consolidated porous samples of expanded clay granulates. The effect of the particle size on the acoustic performance of consolidated expanded clays is investigated experimentally and theoretically. This work involves a comparison of the measured and predicted values of the absorption coefficient and normalised acoustic surface impedance data. It is demonstrated that the values of tortuosity and standard deviation in the pore size distribution do not depend significantly on the size of the material aggregate. An empirical expression which links the flow resistivity of the consolidated granular mix has been derived from the measured data. These results pave the way for the development of a simple practical model which will be able to link the acoustic properties of a consolidated granular mix with the characteristic particle dimension and the porosity data. These materials are structurally robust and easy to integrate in buildings and highway structures to control the levels of environmental noise and improve the acoustic quality of spaces.     

Theoretical analysis and experiment study on the acoustic parameters of metal rubber materials

The acoustic parameters of metal rubber materials were theoretically and experimentally investigated. Under the assumption that metal rubber materials were homogenous, isotropic and porous structures, formulas were deduced for the calculations of effective sound velocity, characteristic impedance, propagation constant, structural constant and flow resistivity. The structural constant of metal rubber materials with different structural parameters were obtained and analyzed by using experiments. The experimental and theoretical values of characteristic impedance and propagation constant were compared and analyzed. It is shown that the proposed theoretic method based on the homogenous, isotropic and porous material model is suitable to calculate the acoustic parameters of metal rubber materials.     

多孔型热致变色材料表面辐射特性研究

分别采用固相反应法和胶晶模板法制备出了块状和多孔型的钙钛矿锰热致变色材料。研究了不同制备工艺对材料居里温度的影响,探讨了不同掺杂比例、表面粗糙度和表面微结构对材料表面辐射特性的影响。结果表明,由于制备工艺不同,两种不同结构钙钛矿锰材料的居里温度相差较大,但其发射率均随温度升高而增大;而在室温以上,多孔材料的发射率明显比块状材料要大。同时,表面粗糙度对材料表面辐射特性的影响较大。     

The sound speed and attenuation in loose and consolidated granular formulations of high alumina cements

Clinkers of high alumina cements are separated into three granular formulations with particle sizes in the range 0.6-0.71 mm, 0.71-1.18 mm and greater than 1.18 mm. These are used to manufacture consolidated samples of porous concrete in an autoclave. The acoustic and microscopic properties of loose and consolidated porous samples of concrete are investigated using both experimental methods and mathematical modelling. Values of porosity, flow resistivity, tortuosity and parameters of the pore size distribution are determined and used to predict closely the sound speed, acoustic attenuation and normal incidence absorption coefficient of these materials. It is shown that high alumina cements do not require additional binders for consolidation and that the structural bonds in these cements are developed quickly between individual clinkers in the presence of water. The hydration product build-up during the consolidation process is insignificant which ensures good acoustic performance of the consolidated samples resulting from a sufficient proportion of the open pores. The value of porosity in the consolidated samples was found to be around 40%, which is close to that measured in some commercial acoustic absorbers. This work provides a foundation for the development of acoustically efficient and structurally robust materials, which can be integrated in environmentally sustainable concrete and masonry structures.     

Boundary element analysis of packed silencers with protective cloth and embedded thin surfaces

Bulk-reacting porous materials are often used as absorptive lining in packed silencers to reduce broadband noise. Modelling the entire silencer domain with a bulk-reacting material will inevitably involve two different acoustic media, air and the bulk-reacting material. A so-called direct mixed-body boundary element method (BEM) has recently been developed to model the two-medium problem in a single-domain fashion. The present paper is an extension of the direct mixed-body BEM to include protective cloth and embedded rigid surfaces. Protective cloth, an absorptive material itself with a higher flow resistivity than the primary lining material, is usually sandwiched between a perforated metal surface and the lining to protect the lining material from any abrasive effect of the grazing flow. Two different approaches are taken to model the protective cloth. One is to approximate sound pressure as a linear function across the cloth thickness and then use the bulk-reacting material properties of the cloth to obtain the transfer impedance. The other is to measure the transfer impedance of the cloth directly by an experimental set-up similar to the two-cavity method. As for an embedded thin surface, it is a rigid thin surface sandwiched between two bulk-reacting linings. Numerical modelling of an embedded thin surface is similar to the modelling of a rigid thin surface in air. Several test cases are given and the BEM results for transmission loss (TL) are verified by experimental TL measurements.     

A simple empirical model of polyester fibre materials for acoustical applications

A new empirical model has been developed by the authors to predict the flow resistivity, acoustic impedance and sound absorption coefficient of polyester fibre materials. The parameters of the model have been adjusted to best fit the values of airflow resistivity and sound absorption coefficient measured over a set of 38 samples. Calculated results are compared with normal incidence measurements carried out using two different techniques: the transfer-function method in an impedance tube (ISO 10534-2) and the free-field impulse response method (ISO 13472-1). Measurements performed on polyester fibre materials with different density and thickness values, and diameter ranging from 18 to 48 μm, are in good agreement with the predictions of the new model. It is concluded that the new model can predict the basic acoustic properties of common polyester fibre materials with any practical combination of thickness and density².