Viscous Length Research Articles

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.

Superhydrophobic drag reduction in high-speed towing tank

Abstract

Vibration-based surface treatment considering viscous penetration length

Functional surfaces can be made to produce various effects by modifying the surfaces of materials. To make functional surfaces for various industrial fields various methods have been used to modify and control the wettability of the surface. In this study, we focused on treating the wettability of a liquid film surface by applying vertical high-frequency vibration. Especially, the relationship between the vibration and the coating film thickness was carefully investigated, to ensure the maximum roughness control in thin liquid films. For surface roughness analysis, three methods were used. First, we measured the contact angle using high speed camera. In results, as frequency increases, contact angle decreases while as voltage increases, contact angle increases. Second, we measured surface roughness using displacement sensor. As a result, both surface wavelength and amplitude decreased as frequency increased. Third, we analyzed the surface shapes of the samples produced with differing viscosity, frequency, and voltage of the applied vibration. As a result, as frequency increases, or viscosity or voltage decrease, the change in the surface shape decreases. It means the surface roughness is decreased. We found that it was necessary to optimize the liquid film thickness in consideration of the damping effect or viscous penetration length when performing surface treatment using vibration. These findings confirm that it is necessary to optimize the process by taking into account the vibration, viscosity and film thickness for proper film surface treatment, and that surface treatment using the vibration method can be productively used in various industrial fields.

Micro-Macro Acoustic Modeling of Heterogeneous Foams with Nucleation Perturbation

<div class="section abstract"><div class="htmlview paragraph">The properties of a polyurethane foam are greatly influenced by the addition of graphite particles during the manufacturing process, initially used as a fire retardant. These thin solid particles perturbate the nucleation process by generating bubbles in their immediate vicinity. A large body of work has focused on foams that are reasonably homogeneous. In this work, we propose a modeling approach for inhomogeneous foams that includes membrane effects and allows pore size distributions to be accounted for. The cellular structure of the foam is obtained through a random Laguerre tessellation optimized from experimental properties. The structure of real foam samples is analyzed using X-ray computed tomography and scanning electron microscopy, followed by image processing, to create three-dimensional, digital models of the samples. The corresponding effective material parameters, including the permeability, the tortuosity and the viscous characteristic length, are subsequently computed by applying a numerical homogenization approach. All the numerical data are presented, discussed and gauged against experimental results.</div></div>

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.

Acoustics of monodisperse open-cell foam: An experimental and numerical parametric study.

This article presents an experimental and numerical parametric study of the acoustical properties of monodisperse open-cell solid foam. Solid foam samples are produced with very good control of both the pore size (from 0.2 to 1.0 mm) and the solid volume fraction (from 6% to 35%). Acoustical measurements are performed by the three-microphone impedance tube method. From these measurements, the visco-thermal parameters-namely, viscous permeability, tortuosity, viscous characteristic length, thermal permeability, and thermal characteristic length-are determined for an extensive number of foam samples. By combining Surface Evolver and finite-element method calculations, the visco-thermal parameters of body centered cubic (bcc) foam numerical samples are also calculated on the whole range of solid volume fraction (from 0.5% to 32%), compared to measured values and to theoretical model predictions [Langlois et al. (2019). Phys. Rev. E 100(1), 013115]. Numerical results are then used to find approximate formulas of visco-thermal parameters. A systematic comparison between measurements and predictions of the Johnson-Champoux-Allard-Lafarge (JCAL) model using measured visco-thermal parameters as input parameters, reveals a consistent agreement between them. From this first step, a calculation of the optimal microstructures maximizing the sound absorption coefficient is performed.

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.

New power-law scaling for friction factor of extreme Reynolds number pipe flows

We report a novel power-law scaling for the friction factor of incompressible Newtonian fluid flows at extreme Reynolds numbers: f = Ce/Re2/13. The formula is based on a new phenomenology for coherent structures that dominate the momentum exchange in meso-layer regions and scales with the geometric mean δδν, where δν is the viscous length scale and δ is the pipe radius. Comparisons with the experimental data from the Princeton Superpipe and the Hi-Reff Facility at the National Metrology Institute of Japan show excellent agreement for a large range of Reynolds numbers. This work, along with the recent empirical evidence, suggests a possible change in the mechanism of turbulent momentum transfer for pipe flows in extreme Reynolds numbers.

Improved Menter’s one-equation turbulence model

Compatible modifications to original Menter model (OMM) are incorporated using an elliptic relaxation approach to accurately accounting non-local characteristics accompanied by near-wall turbulence. Coefficients/functions of improved Menter model (IMM) are parameterized with the elliptic relaxation function to imitate the combined effects of near-wall turbulence and non-equilibrium. The characteristic length scale involved in the elliptic relaxation scheme is constructed in terms of viscous and turbulent length scales in conjunction with a non-singular strain-rate invariant. Non-local effects are consequently reinforced by the mean flow and turbulent variables. A non-linear eddy-viscosity damping function is invoked to relax the viscous length-scale coefficient pertaining to the elliptic relaxation model. Comparisons indicate that the IMM substantially improves the accuracy of flow simulations compared to the OMM and widely used Spalart-Allmaras (SA) model. A good consensus is obtained between IMM and DNS (direct numerical simulation)/measured data.

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.

Mechanism for Increased Viscous Drag over Porous Sheet Acoustic Liners

Traditional acoustic liners used in damping sound in aircraft applications consist of a porous face sheet, honeycomb core, and solid backing. Experiments have observed that, under conditions of high tonal sound levels, there occurs a dramatic increase in the viscous drag in the turbulent boundary layers over these surfaces. The mechanism for this increase in drag is the topic of interest. This involves experiments on a series of acoustic liners with fabricated porous sheets having a range of hole diameters, spacing, and patterns. The hole spacing spanned a range of viscous spanwise length scales from . The boundary-layer measurements include mean velocity and turbulence intensity profiles, velocity spectra, and turbulence burst, ejection, and sweep statistics based on the variable interval time-averaging and -quadrant methods. Coupled with this are direct drag measurements of the acoustic liners. The results show a dramatic increase in drag at frequencies near acoustic resonance and at high sound levels. This is presumed to be driven by net zero mass jets emanating from the porous sheets. For the experimental data available, the largest increase in drag is observed for the smaller spanwise distance between perforations, which is comparable to the typical spanwise wavelength of wall streak structures in turbulent boundary layers. The increase in drag is correlated with an increase in the turbulence wall layer burst and ejection events.

Viscous fluid flow inside an oscillating cylinder and its extension to Stokes’ second problem

We present the analytical solution for the fluid motion inside a cylindrical tank whose angular velocity starts from rest and undergoes a harmonic oscillation. This problem, which has not yet been reported, is an extension to Stokes’ second problem where the fluid motion is governed by an outer moving cylindrical boundary and a zero velocity condition at the cylinder center. Different from the flow on the outside of a cylinder, the cylinder radius has a large influence on the internal fluid motion. We show that the fluid approaches solid body rotation for cylinders with outer radii similar to the characteristic viscous length scale of the flow, whereas the motion approaches that of Stokes’ original flat plate solution within very large cylinders. We detail both the transient starting condition and the quasi-steady fluid motion, which we present along with a particle image velocimetry experiment for validation. After decay of the initial startup transient, both quasi-steady analytical and experimental results predict that the oscillatory flow inside has an amplitude of velocity that decreases toward the center of the cylinder. The thickness of the Stokes layer, which is proportional to the penetration depth of the viscous wave, is altered by the size of the cylinder and/or the frequency of oscillation. We show that the penetration depth of the Stokes layer reaches its maximum thickness at intermediate cylinder sizes. The solution and results presented herein are potentially of value to describe the fluid motion in many applications where fluids are contained within cylindrical geometries.

Elliptic Blending with One-Equation Model

A wall-distance-free modification to Wray-Agarwal (WA) one-equation turbulence model is convoked using an elliptic relaxation approach to accurately accounting for non-local characteristics of near-wall turbulence. Model coefficients/functions are parameterized with the elliptic relaxation function to preserve the combined effects of near-wall turbulence and nonequilibrium. The characteristic length scale associated with the elliptic relaxation equation is formulated in terms of viscous and turbulent length scales in conjunction with the invariant of strain-rate tensor. Consequently, non-local effects are explicitly influenced by the mean flow and turbulent variables. A near-wall damping function is introduced to relax the viscous length-scale coefficient adhering to the elliptic relaxation model. Comparisons indicate that the new model improves the accuracy of flow simulations compared to the widely used Spalart-Allmar as model and remains competitive with the SST model.A good correlation is obtained between the current model and DNS/experimental data.

RETRACTED: Experimental characterization of human cancellous bone via the first ultrasonic reflected wave – Application of Biot’s theory

Abstract In this paper, enhanced characterization of human cancellous bone using reflected ultrasound waves is proposed using the Biot theory modified by the Johnson et al. model for viscous exchange between the structure and the saturating fluid. A simplified expression of the reflection coefficient at the first surface is obtained in the frequency domain. This expression is based on the three physical parameters which are porosity, tortuosity and viscous characteristic length, as well as on the mechanical parameters: Young modulus and poison ratio of the skeleton part. The reflected signal is calculated in the frequency domain by the product of the spectrum of the incident signal with the reflection coefficient. In the time domain, the reflected wave is obtained by taking the inverse Fourier transform of the reflected frequency signal. The inverse problem is solved numerically by minimizing between simulated and experimental reflected signals. Three physical parameters are inverted simultaneously: porosity, tortuosity and viscous characteristic length. Tests are performed using two samples of trabecular bone. Experimental results are compared with theoretical predictions, giving a good correlation.

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.

The Role of Wettability on the Response of a Quartz Crystal Microbalance Loaded with a Sessile Droplet

In this work, the interaction between a sessile droplet’s contact angle and a quartz crystal microbalance (QCM) is elucidated. We differentiate the QCM’s frequency response to changes in the droplet contact area from variations in the dynamic contact angle. This is done by developing a computational model that couples the electrical and mechanical analysis of the quartz substrate with the visco-acoustic behavior of the sessile droplet. From our analysis, we conclude that changes in the contact angle have an effect on the frequency response of the QCM when the droplet height is on the order of the viscous decay length or smaller. On the other hand, changes in the interfacial contact area of the sessile droplets have a significant impact on the frequency response of the QCM regardless of the droplet size.

Bayesian inference of a human bone and biomaterials using ultrasonic transmitted signals.

Ultrasonic techniques could be good candidates to aid the assessment of osteoporosis detection, due to their non-intrusiveness and low cost. While earlier studies made use of the measured ultrasonic phase velocity and attenuation inside the bone, very few have considered an inverse identification of both the intrinsic pore microstructure and the mechanical properties of the bone, based on Biot's model. The main purpose of this work is to present an in vitro methodology for bone identification, adopting a statistical Bayesian inference technique using ultrasonic transmitted signals, which allows the retrieval of the identified parameters and their uncertainty. In addition to the bone density, Young's modulus and Poisson's ratio, the bone pore microstructure parameters (porosity, tortuosity, and viscous length) are identified. These additional microstructural terms could improve the knowledge on the correlations between bone microstructure and bone diseases, since they provide more information on the trabecular structure. In general, the exact properties of the saturating fluid are unknown (bone marrow and blood in the case of bone study) so in this work, the fluid properties (water) are identified during the inference as a proof of concept.

Image-based modelling of the skin-friction coefficient in compressible boundary-layer transition

We develop a model of the skin-friction coefficient based on scalar images in the compressible, spatially evolving boundary-layer transition. The images are extracted from a passive scalar field by a sliding window filter on the streamwise and wall-normal plane. The multi-scale and multi-directional geometric analysis is applied to characterize the averaged inclination angle of spatially evolving filtered component fields at different scales ranging from a boundary-layer thickness to several viscous length scales. In general, the averaged inclination angles increase along the streamwise direction, and the variation of the angles for large-scale structures is smaller than that for small-scale structures. Inspired by the coincidence of the increasing averaged inclination angle and the rise of the skin-friction coefficient, we propose a simple image-based model of the skin-friction coefficient. The model blends empirical formulae of the skin-friction coefficient in laminar and fully developed turbulent regions using the normalized averaged inclination angle of scalar structures at intermediate and small scales. The model prediction calculated from scalar images is validated by the results from the direct numerical simulation at two Mach numbers, 2.25 and 6, and the relative error can be less than 15 %.

Stoneley wave attenuation and dispersion and the dynamic permeability correction

Stoneley waves induce fluid pressure gradients in a permeable formation surrounding the borehole. These gradients are equilibrated through pressure diffusion, that is to say, slow P-waves in the context of Biot’s poroelasticity theory. Because slow P-waves are strongly sensitive to the formation permeability, the Stoneley-slow P-wave interaction can be used to retrieve the formation permeability from the attenuation and dispersion of Stoneley waves. The accuracy of this established technique in high-permeability formations deteriorates when slow P-waves are not pure diffusion waves; hence, the permeability dependence is more complicated. This effect on Stoneley waves is captured by applying the Johnson-Koplik-Dashen dynamic permeability model. Their model depends on a viscous relaxation length. However, in the estimation of formation permeability from Stoneley waves, this parameter is typically not measured but is estimated from an empirical equation, wherein material properties and microstructural descriptors are lumped together. When the so-calculated relaxation length is erroneous, the inverted formation permeability from the Stoneley wave is not correct either. To overcome this limitation and to provide a versatile alternative, the dynamic permeability problem is reformulated within the viscosity-extended Biot framework. Its physical basis is the conversion scattering in random media from slow P- to slow S-waves. The correlation length of this so-called stochastic dynamic permeability model can be derived from pore-scale images, and it also captures the effect of pore interface roughness. This model is then combined with the simplified Biot-Rosenbaum model to predict Stoneley wave attenuation and dispersion. We have applied this hybrid model to interpret laboratory measurements for which the previously suggested choice of the viscous relaxation length does not provide an accurate prediction. The results indicate that the hybrid model can provide another approach to model Stoneley wave attenuation and dispersion across the entire frequency range.

Stratification Effects in the Turbulent Boundary Layer beneath a Melting Ice Shelf: Insights from Resolved Large-Eddy Simulations

AbstractOcean turbulence contributes to the basal melting and dissolution of ice shelves by transporting heat and salt toward the ice. The meltwater causes a stable salinity stratification to form beneath the ice that suppresses turbulence. Here we use large-eddy simulations motivated by the ice shelf–ocean boundary layer (ISOBL) to examine the inherently linked processes of turbulence and stratification, and their influence on the melt rate. Our rectangular domain is bounded from above by the ice base where a dynamic melt condition is imposed. By varying the speed of the flow and the ambient temperature, we identify a fully turbulent, well-mixed regime and an intermittently turbulent, strongly stratified regime. The transition between regimes can be characterized by comparing the Obukhov length, which provides a measure of the distance away from the ice base where stratification begins to dominate the flow, to the viscous length scale of the interfacial sublayer. Upper limits on simulated turbulent transfer coefficients are used to predict the transition from fully to intermittently turbulent flow. The predicted melt rate is sensitive to the choice of the heat and salt transfer coefficients and the drag coefficient. For example, when coefficients characteristic of fully developed turbulence are applied to intermittent flow, the parameterized three-equation model overestimates the basal melt rate by almost a factor of 10. These insights may help to guide when existing parameterizations of ice melt are appropriate for use in regional or large-scale ocean models, and may also have implications for other ice–ocean interactions such as fast ice or drifting ice.