Static Flow Resistivity Research Articles

Sound absorption properties of additively manufactured porous materials with minimal surface pore geometries

This study explores the use of additive manufacturing, specifically stereolithography (SLA), to create porous acoustical materials with precise pore geometries for aircraft engine noise reduction. Unlike traditional methods like foaming and fiber-spinning, SLA allows for exact control over pore shapes. Three triply periodic minimal surface (TPMS) pore designs were investigated: split-P, lidinoid, and diamond. These structures were designed through implicit modeling and made from polymeric resin. Their sound absorption capabilities were tested under normal incidence in a two-microphone impedance tube to examine how porosity influences their acoustic performance. Findings revealed unique sound absorption profiles for each geometry, which can be modified by adjusting porosity. Additionally, the static flow resistivity was measured using a raylometer, where results showed that flow resistance is a key factor in their absorption efficiency. Among the three samples, the split-P geometry shows superior sound absorption. This preliminary research highlights the potential of using tailored TPMS geometries in acoustic liners for effective noise control in aerospace applications.

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.

Sound Absorption Performance and Mechanism of Aluminum Foams with Double Main Pore‐Porous Cell Wall Structure

To enhance the sound absorption performance of open‐cell aluminum foam, the double main pores‐porous cell walls (DMP‐PCW) aluminum foams via infiltration casting of preforms mixed with two sizes of NaCl particles are prepared. The pore structure, sound absorption performance, and mechanism of DMP‐PCW aluminum foam are investigated. The pore structure consists of double‐sized main pores similar to the NaCl particles and the cell wall pores formed by the connections between NaCl particles. It is found that the static flow resistivity of DMP‐PCW aluminum foam reaches an optimum value of 28105 Pa.s m−2 when the volume proportion of small main pores increases, the size of cell wall pores decreases, and the number of cell wall pores per unit main pore surface area (NPPA) increases. At 800–6300 Hz, the average absorption coefficient is 0.89. In addition, the Wilson model predicts the sound absorption properties of DMP‐PCW aluminum foam. The predicted values agree well with the measured values. The finite‐element acoustic simulations and dynamic viscous‐thermal permeability calculations reveal that the improved sound absorption performance of DMP‐PCW aluminum foam is correlated to the enhanced sound transmission caused by increased NPPA and increased viscous‐thermal loss due to the double main pore structure.

Sound absorption of a perforated panel backed with perforated porous material: Energy dissipation of Helmholtz resonator cavity

A new type of low-frequency sound absorbing Helmholtz resonator is proposed, which consists of a perforated rigid panel backed with gradually perforated porous material. A theoretical model is developed by dividing the structure into a multi-layer system by using the double porosity theory, which is verified by finite element simulations and experimental measurements. The sound absorption performance of the proposed acoustic metamaterial is studied by applying the theoretical model and numerical model, where the influences of the perforation diameter, panel thickness, back cavity shape and static flow resistivity of the porous material matrix on sound absorption are discussed. The results show that this new metamaterial has better sound absorption performance than the perforated panel and the perforated porous material. Finite element simulations show that this new acoustic metamaterial absorbs sound energy almost entirely through Helmholtz cavity resonance, which accelerates the diffusion of sound into the porous material for dissipation. An energy dissipation compensation mechanism is found between the perforated panel and the perforated porous material, which enables the metamaterial to always achieve near-perfect sound absorption performance over a wide range of neck diameters. This new resonance metamaterial provides another avenue for the design of low-frequency sound absorbers.

Perfect sound absorption of Helmholtz resonators with embedded channels in petal shape

The acoustic metamaterial in the form of a petal-shaped channel embedded Helmholtz resonator (P-CEHR) is proposed for perfect sound absorption. According to theoretical predictions, numerical simulations, and experiments, the P-CEHR achieves perfect low-frequency (e.g., 200 Hz) sound absorption across a deep subwavelength thickness (e.g., 1/34 of the corresponding acoustic wavelength). Compared with the circular-shaped channel embedded Helmholtz resonator, the sound absorption peak and bandwidth of P-CEHR are significantly improved (e.g., increased by 20.9% and 60.0%, respectively) under fixed overall dimensions. Physically, the introduction of the petal shape changes the fluid dynamic characteristics of the channel, resulting in the periodic distribution of particle velocity along the circumferential direction and the expansion of the area of the viscous boundary layer. By adjusting the morphology of the embedded channel, the tortuosity ratio and the relative static flow resistance of the channel can be regulated appropriately, so that the resonator can meet the acoustic impedance matching condition and achieve excellent sound absorption performance. This work provides a method for improving the performance of acoustic absorption metamaterials with built-in air channels and has guiding significance for the control of low-frequency noise.

Improving and Optimizing Sound Absorption Performance of Polyurethane Foam by Prepositive Microperforated Polymethyl Methacrylate Panel

Sound absorption performance of polyurethane foam could be improved by adding a prepositive microperforated polymethyl methacrylate panel to form a composite sound-absorbing structure. A theoretical sound absorption model of polyurethane foam and that of the composite structure were constructed by the transfer matrix method based on the Johnson–Champoux–Allard model and Maa’s theory. Acoustic parameter identification of the polyurethane foam and structural parameter optimization of the composite structures were obtained by the cuckoo search algorithm. The identified porosity and static flow resistivity were 0.958 and 13078 Pa·s/m2 respectively, and their accuracies were proved by the experimental validation. Sound absorption characteristics of the composite structures were verified by finite element simulation in virtual acoustic laboratory and validated through standing wave tube measurement in AWA6128A detector. Consistencies among the theoretical data, simulation data, and experimental data of sound absorption coefficients of the composite structures proved the effectiveness of the theoretical sound absorption model, cuckoo search algorithm, and finite element simulation method. Comparisons of actual average sound absorption coefficients of the optimal composite structure with those of the original polyurethane foam proved the practicability of this identification and optimization method, which was propitious to promote its practical application in noise reduction.

Preparation and Characterization of Gradient Compressed Porous Metal for High-Efficiency and Thin-Thickness Acoustic Absorber.

Increasing absorption efficiency and decreasing total thickness of the acoustic absorber is favorable to promote its practical application. Four compressed porous metals with compression ratios of 0%, 30%, 60%, and 90% were prepared to assemble the four-layer gradient compressed porous metals, which aimed to develop the acoustic absorber with high-efficiency and thin thickness. Through deriving structural parameters of thickness, porosity, and static flow resistivity for the compressed porous metals, theoretical models of sound absorption coefficients of the gradient compressed porous metals were constructed through transfer matrix method according to the Johnson–Champoux–Allard model. Sound absorption coefficients of four-layer gradient compressed porous metals with the different permutations were theoretically analyzed and experimentally measured, and the optimal average sound absorption coefficient of 60.33% in 100–6000 Hz was obtained with the total thickness of 11 mm. Sound absorption coefficients of the optimal gradient compressed porous metal were further compared with those of the simple superposed compressed porous metal, which proved that the former could obtain higher absorption efficiency with thinner thickness and fewer materials. These phenomena were explored by morphology characterizations. The developed high-efficiency and thin-thickness acoustic absorber of gradient compressed porous metal can be applied in acoustic environmental detection and industrial noise reduction.

Mathematical modeling of Stokes flow in petal shaped pipes

A theoretical model is developed to characterize fully developed laminar flow (Stokes flow) in idealized petal shaped pipes by regarding the pipe wall as a circular boundary having sinusoidal perturbation (or, equivalently, surface roughness). Built upon the method of perturbation, the model quantifies the effects of the relative roughness and wave number of the pipe boundary on the Stokes flow. Approximate solutions of the velocity field, pressure gradient, and static flow resistivity are obtained. The same approach together with the method of Fourier transform is used to deal with low Reynolds flow in pipes having other cross-sectional morphologies such as triangle and square. Results obtained from computational fluid dynamics simulations are used to validate the theoretical model predictions, with good agreement achieved. The presence of surface roughness causes periodic fluctuation and global offset of velocity distribution and enlarges both the pressure gradient and static flow resistivity in petal shaped pipes.

Modeling of surface roughness effects on Stokes flow in circular pipes

Fluid flow and pressure drop across a channel are significantly influenced by surface roughness on a channel wall. The present study investigates the effects of periodically structured surface roughness upon flow field and pressure drop in a circular pipe at low Reynolds numbers. The periodic roughness considered exhibits sinusoidal, triangular, and rectangular morphologies, with the relative roughness (i.e., ratio of the amplitude of surface roughness to hydraulic diameter of the pipe) no more than 0.2. Based upon a revised perturbation theory, a theoretical model is developed to quantify the effect of roughness on fully developed Stokes flow in the pipe. The ratio of static flow resistivity and the ratio of the Darcy friction factor between rough and smooth pipes are expressed in four-order approximate formulations, which are validated against numerical simulation results. The relative roughness and the wave number are identified as the two key parameters affecting the static flow resistivity and the Darcy friction factor.

Microstructure-based experimental and numerical investigations on the sound absorption property of open-cell metallic foams manufactured by a template replication technique

The current study investigates the acoustic absorption property of nickel-based superalloy open-cell foams manufactured by a newly developed template replication process. Inconel 625 open cell foams with controllable porosities (92%–98%) and cell sizes (300μm–900μm) have been successfully produced and tested for their sound absorption performance. It is evident that foam samples with the smallest cell size among them exhibit the best acoustic absorption performance, with sound absorption coefficient>0.9 at frequencies >1500Hz for 50mm thick sample. In the numerical simulation, the classical Delany­Bazley model is employed to predict the acoustic absorption property across a broad frequency range, and it requires knowledge of foam's static air flow resistivity, which, as proposed in this work, can be analytically expressed as a function of foam's microstructure parameters. A good agreement between such microstructure-based numerical model and experimental results was obtained. The proposed model can be utilized as a material design tool to guide the production of foam with optimal microstructure for sound absorption through the controllable template replication process.

Modeling of roughness effects on acoustic properties of micro-slits

An analytical model is developed to predict the effects of surface roughness on the acoustic properties of micro-slits. Periodic (sinusoidal) roughness distributed with relatively small amplitude on slit surface is assumed, enabling small parameter analysis. Within the incompressible creeping flow regime, the dependence of key fluidic and acoustic properties including static flow resistivity, tortuosity, effective density and compressibility on relative roughness and wave number of roughness is quantified. For validation, analytical predictions are compared with numerical simulation results based on the method of finite elements, with good agreement achieved. The presence of surface roughness is shown to increase both static flow resistivity and tortuosity, causing a significant increase in the effective density of the micro-slits, but has little effect on effective compressibility.

End correction model for the transfer impedance of microperforated panels using viscothermal wave theory.

Microperforated panels (MPPs) are efficient sound absorbers featuring microperforations with low porosity. Sound absorption occurs inside the perforations and their vicinity as well, which is represented with an end correction in the transfer impedance of the MPPs. Many empirical models for the end correction were derived from experiment or numerical simulation data. In order to validate these models, this paper presents an analytical solution of the end correction for sharp-edged circular perforations using viscothermal wave theory. The perforations are assumed to be periodically distributed and each perforation is associated with a square duct resulting from a periodic spatial partition. The velocity profile and the temperature field in each perforation are derived from the low reduced frequency model, which pose the boundary conditions to determine the modal coefficients of the acoustic, entropy, and viscous waves in the duct. An impedance end correction model is derived from the asymptotic expansion of the modal solution. It improves the conventional model by introducing a static flow resistance term to describe the energy dissipation due to the acoustic flow distortion outside the perforations. Numerical and experimental examples validate that the proposed model offers better prediction for the transfer impedance and the sound absorption of the MPPs.

Ultrathin multi-slit metamaterial as excellent sound absorber: Influence of micro-structure

An ultrathin (subwavelength) hierarchy multi-slit metamaterial with simultaneous negative effective density and negative compressibility is proposed to absorb sound over a wide frequency range. Different from conventional acoustic metamaterials having only negative real parts of acoustic parameters, the imaginary parts of effective density and compressibility are both negative for the proposed metamaterial, which result in superior viscous and thermal dissipation of sound energy. By combining the slit theory of sound absorption with the double porosity theory for porous media, a theoretical model is developed to investigate the sound absorption performance of the metamaterial. To verify the model, a finite element model is established to calculate the effective density, compressibility, and sound absorption of the metamaterial. It is theoretically and numerically confirmed that, upon introducing micro-slits into the meso-slits matrix, the multi-slit metamaterial possesses indeed negative imaginary parts of effective density and compressibility. The influence of micro-slits on the acoustical performance of the metamaterial is analyzed in the context of its specific surface area and static flow resistivity. This work shows great potential of multi-slit metamaterials in noise control applications that require both small volume and small weight of sound-absorbing materials.

Analysis of Static Flow Resistivity of a Modified Impedance Tube

The static flow resistivity is a fundamental parameter for measuring and classifying the sound absorption behavior of various types of materials. Several methods have been developed for measuring the static flow resistivity acoustically. Most of these methods cannot be implemented directly in the standard tubes which are widely used for measurements of sound absorption coefficients and impedance as defined in ISO 10534.2. The accuracy of the proposed method and the tube is verified through finite element analysis and the feasibility to determine the static flow resistivity is validated through experiments. It is validated that the accuracy of the proposed method is highly dependent on the position of the acoustic center of the measurement microphones and the accuracy can be enhanced by increasing the back cavity depth and/or decreasing the measurement frequency.

Fractal Model for Acoustic Absorbing of Porous Fibrous Metal Materials

To investigate the changing rules between sound absorbing performance and geometrical parameters of porous fibrous metal materials (PFMMs), this paper presents a fractal acoustic model by incorporating the static flow resistivity based on Biot-Allard model. Static flow resistivity is essential for an accurate assessment of the acoustic performance of the PFMM. However, it is quite difficult to evaluate the static flow resistivity from the microstructure of the PFMM because of a large number of disordered pores. In order to overcome this difficulty, we firstly established a static flow resistivity formula for the PFMM based on fractal theory. Secondly, a fractal acoustic model was derived on the basis of the static flow resistivity formula. The sound absorption coefficients calculated by the presented acoustic model were validated by the values of Biot-Allard model and experimental data. Finally, the variation of the surface acoustic impedance, the complex wave number, and the sound absorption coefficient with the fractal dimensions were discussed. The research results can reveal the relationship between sound absorption and geometrical parameters and provide a basis for improving the sound absorption capability of the PFMMs.

Static flow resistivity measurements based on the ISO 10534.2 standard impedance tube

Static flow resistivity is a fundamental parameter governing the sound absorption behavior of different materials, and several methods based on the use of impedance tubes have been developed for measuring the flow resistivity acoustically. However, these methods cannot be directly implemented in the standard impedance tubes that are widely used for measurements of sound absorption coefficients and impedance as defined in ISO 10534.2, because the termination conditions of impedance tubes and the placement of microphones in these existing methods are different. In this paper, a new acoustic method based on the impedance transfer function is proposed to determine the static flow resistivity with a standard impedance tube that complies with ISO 10534.2. The accuracy and the robustness of the proposed method are investigated through the finite element analysis and the feasibility of determining the static flow resistivity is validated through experiments. It is found that the accuracy of the proposed method is sensitive to the acoustic center position of the measurement microphones and the accuracy can be enhanced by increasing the back cavity depth or decreasing the measurement frequency.

Refinements to the relaxation model for sound propagation in porous media

The relaxation formulation for sound propagation in porous media [D. K. Wilson, J. Acoust. Soc. Am. 94(2), 1136–1145 (1993)] was intended to provide a phenomenologically correct model with relatively simple equations. This paper presents several refinements, which connect the relaxation model more clearly to others in the literature, and clarify interpretation of the parameters. In particular, the relaxation function is applied to the dynamic tortuosity (rather than the inverse of the complex density), and the vorticity and thermal relaxation times are related directly to the length scales of Allard and Champoux [J.-F. Allard and Y. Champoux, J. Acoust. Soc. Am. 91(6), 3346–3353 (1992)]. When formulated in this manner, the relaxation and Allard-Champoux models coincide exactly in the low-frequency/small-pore and high-frequency/large-pore limits, although interpolation between these limits differs somewhat. The revised relaxation model can be readily transformed into a causal time-domain model, involving convolutions between the acoustic fields and a relaxation response function. The basic formulation has five parameters: porosity, static flow resistivity, tortuosity, and two relaxation times. A sequence of model reductions is described, leading finally to two-parameter (porosity and static flow resistivity) equations for the impedance and complex wavenumber, which provide a useful generalization of the Delany-Bazley equations.

Acoustic performance of aluminum foams with semiopen cells

To evaluate the effects of structural parameters on sound absorption performance of the aluminum foams with semiopen cells, a generalized regression neural network (GRNN) model has been utilized. In this paper, parameters of bulk density, static flow resistivity were analyzed. Results indicate that the effects of bulk density on sound absorption properties of the semiopen-celled foams are limited. On the contrary, the effects of static flow resistivity on absorption coefficients are complicated. When frequency is 500Hz, there has no significant relationship between static flow resistivity and sound absorption coefficients. When the frequency is higher than 1000Hz, with flow resistivity increasing, absorption coefficients of the aluminum foams increased significantly from 0.2 to exceed 0.8. However, when the static flow resistivity reaches 140kPas/m2, still increasing static flow resistivity could not improve the acoustic performance. Analysis revealed that the GRNN model provides a robust method for predicting acoustic absorption properties.

Transfer impedance of microperforated materials with tapered holes.

It has been previously shown that relatively simple computational fluid dynamics (CFD) models can be used to calculate the transfer impedances, including the associated end corrections, of microperforated panels. The impedance is estimated by first calculating the pressure difference across a single hole when a transient input velocity is imposed, and then Fourier transforming the result to obtain the impedance as a function of frequency. Since the size of the hole and the dimensions of the inlet and outlet channels are very small compared to a wavelength, the flow through the hole can be modeled as incompressible. By using those procedures, Bolton and Kim extended Maa's classical theory to include a resistive end correction for sharp-edged cylindrical holes which differs from those previously proposed by the inclusion of a static component. Here it is shown that CFD models can also be used to compute end corrections for tapered holes. Since practical experimental characterization of perforated materials often involves measurement of the static flow resistance, a closed form empirical equation for that quantity has been developed. Finally, it is shown that configurations having equivalent static flow resistances can yield different acoustic absorptions.

Thermal and acoustic properties of aluminium foams manufactured by the infiltration process

Metallic foams can be classified into closed-cell and open-cell foams depending on the connectivity between the cells. Currently, the majority of metallic foams on the market are closed-cell aluminium foams. However, open-cell aluminium foams are more appropriate for some applications. In this work, we analyze the thermal and acoustic properties, sound absorption coefficient at normal incidence and static flow resistivity of aluminium foams manufactured by means of the infiltration process. We have produced aluminium foams with similar porosity but with three different cell diameters: 0.5, 1 and 2mm. The results reveal the important role of the cell diameter in fixing the physical properties of these materials. The foams manufactured by the infiltration technique are characterized by a highly homogeneous structure and by a high sound absorption coefficient at low frequencies when they are backed by an air gap. Specifically, its thermal and acoustic properties make the 0.5mm cell diameter aluminium foam a good candidate for applications in the construction sector, for example.