Wall Admittance Research Articles

Modification of the transfer matrix method for the sonic black hole and broadening effective absorption band

Sonic black hole (SBH) is capable of the concentration for the sound energy by the shrinking duct and appropriate wall admittance. However, the concentrated energy cannot be dissipated due to the weak air damping. Meanwhile, when the inserted rings are insufficient, the accuracy of the conventional transfer matrix method (TMM) is less than satisfactory for the simulation of the original SBH. In this study we commit to modify this simulation method and broaden the effective absorption band by using porous materials. First, we derived the acoustic transfer relationship of the conical cavity and the acoustic admittance of the toroidal cavity, via formulating the basic equation. After combining with the two method, the modified TMM (MTMM) results show excellent agreement with the finite element results. The applicability of the derived wall admittance is analyzed in detail. The MTMM has also been applied to obtain the sound absorption of a SBH configuration with embedded porous materials (PMSBH). The proposed PMSBH can effectively dissipate the concentrated sound energy, leading to the ultra-low cut-on frequency of near-perfect absorption. Specifically, the cut-on frequency of the PMSBH is 387 Hz, with the corresponding wavelength being 8.8 times than the structural length. In addition, the parametric analysis shows the near independence of the absorption performance of the PMSBH on the damping loss, so that the PMSBH can achieve excellent absorption without adding other acoustic materials. These appealing characteristic could promote the application of the PMSBH in noise control.

Absorptive nature of scattering coefficients in stress-energy tensor formalism for room acoustics.

In the stress-energy tensor formalism, the symmetry between absorption and scattering coefficients, as proven by measurements combined with simulations, is counterintuitive. By introducing the wall admittance, we show that the scattering coefficient is partly created by the real part of the wall admittance combined with the active intensity, that is, is partly due to absorption. However, for curved surfaces or finite source distances, it also depends on the imaginary part of the wall admittance in combination with the reactive intensity, which confers its genuine scattering properties inversely proportional to the distances to the sources. Thus, for plane waves impinging on plane boundaries, or purely real admittances, scattering reduces to absorption.

Sound waves in continuum models of periodic sonic black holes

In this work we address the study of continuum models of periodic sonic black holes (SBHs) at duct terminations. A conventional SBH combines a decreasing power-law profile with a wall admittance in such a way that sound waves entering the SBH slow down, while their amplitude increases and their wavelength decreases as they approach the duct termination. In an ideal scenario, the wave is trapped and dissipated inside the SBH so that no reflection occurs. Instead of dealing with conventional SBHs, we are interested here in periodic SBHs. These have the potential to extend the application range of SBHs below the cut-on frequency thanks to the formation of stopbands, among other significant aspects. First, the case of an SBH cell placed between semi-infinite ducts is analyzed and it is shown how it reduces not only sound reflection but also sound transmission. The acoustic pressure inside the SBH is governed by a modified Webster equation that is solved in weak form using a basis of Gaussian functions. The dependence of the reflection, transmission and absorption coefficients for different SBH parameters and boundary conditions is analyzed in detail. Next, the case of an infinite periodic SBH lattice is considered. The nullspace method (NSM) is used to impose the periodic boundary conditions of the problem. Complex dispersion curves are computed and the separate roles played by the SBH power-law profile and wall admittance on the dispersion curves and pressure distribution inside the cells are examined. Bragg scattering turns out to be the main mechanism behind bandgap formation and wall admittance is essential to achieve the SBH effect. A parametric study follows, showing the influence of the damping, the residual radius, the SBH order and its length on the imaginary part of the complex dispersion curves. Finally, the reflection, transmission and absorption coefficients for a finite 3-cell SBH are investigated. Although most of the research on SBHs has focused on practical application designs, it is believed that a thorough understanding of the performance of continuum models of SBHs could be very useful for the former.

How the waveguide acoustic black hole works: A study of possible damping mechanisms.

The acoustic black hole (ABH) effect in waveguides is studied using frequency-domain finite element simulations of a cylindrical waveguide with an embedded ABH termination composed of retarding rings. This design is adopted from an experimental study in the literature, which surprisingly showed, contrary to the structural counterpart, that the addition of damping material to the end of the waveguide does not significantly reduce the reflection coefficient any further. To investigate this unexpected behavior, we model different damping mechanisms involved in the attenuation of sound waves in this setup. A sequence of computed pressure distributions indicates occurrences of frequency-dependent resonances in the device. The axial position of the cavity where the resonance occurs can be predicted by a more elaborate wall admittance model than the one that was initially used to study and design ABHs. The results of our simulations show that at higher frequencies, the visco-thermal losses and the damping material added to the end of the setup do not contribute significantly to the performance of the device. Our results suggest that the primary source of damping, responsible for the low reflection coefficients at higher frequencies, is local absorption effects at the outer surface of the cylinder.

Resonance tuning in vocal tract acoustics from modal perturbation analysis instead of nonlinear radiation pressure

The analysis of planar wave resonances in ducts of variable cross-section is of importance in many areas of acoustics such as horn theory, the design of musical instruments or the numerical generation of voice. An interesting problem is that of modifying the tube geometry and physical parameters to move its resonances to desired target values. In vowel production, for instance, one can properly adjust the length, cross-sectional area and wall admittance of the vocal tract (VT) to change the frequency of a resonance or to bring together or set apart a group of them for achieving some natural voice effects. An optimization strategy can be implemented to that purpose, which induces small sequential variations of the VT parameters according to sensitivity functions, until one obtains the desired resonance values. The sensitivity functions are usually derived from the work done by variations in the non-linear radiation pressure within the duct. In this paper we will show that, elegant as it may be, there is in fact no need of non-linear phenomena to determine appropriate sensitivity functions. These can readily be obtained from first order modal perturbation analysis. To demonstrate that, we transform the three-dimensional (3D) problem of voice generation into a one-dimensional one (1D), driven by a Webster-type equation. Despite of the latter being 1D, we discretize it using the finite element method (FEM) to benefit from its weak formulation to deduce expressions for the sensitivity functions. The latter are recovered from a perturbation modal analysis of the discrete Webster equation for VT area, length and wall admittance variations. Several examples concerning vowel to vowel transformations are presented to illustrate the potential and limitations of the method. The herein proposed 1D approach for resonance tuning could be easily coupled to 3D FEM codes for expressive vowel production in the future.

Passive volumetric time domain simulation for room acoustics applications.

A major design consideration for volumetric wave-based time-domain room acoustics simulation methods, such as finite difference time domain (FDTD) methods, must be sufficiently general, or robust, to handle irregular room geometries and frequency-dependent and spatially varying wall conditions. A general framework for the design of such schemes is presented here, based on the use of the passivity concept, which underpins realistic wall conditions. This analysis is based on the use of conservative finite volume methods, allowing for a representation of the room system as a feedback connection of a lossless part, corresponding to wave propagation over the interior, and a lossy subsystem, representing the effect of wall admittances. Such a representation includes simpler FDTD methods as a special case, and allows for the determination of stability conditions for a variety of time-stepping strategies.

Transfer matrices to characterize linear and quadratic acoustic black holes in duct terminations

The acoustic black hole (ABH) effect for sound reduction in duct terminations can be accomplished by means of retarding structures. The latter act as waveguides and their performance relies on two factors. First, a power-law decay of the duct radius and, second, an appropriate dependence of the wall admittance with the duct radius. In theory, the ABH can be achieved placing a set of rigid rings inside the duct, with inner radii and inter-spacing decreasing to zero as the tube end section is approached. In this work we focus on the linear and quadratic inner radius decay cases, referred to as the linear and quadratic ABHs. To begin with, analytical expressions are derived for the quadratic ABH and compared to those of the linear one. In both cases the solutions become singular at the final section of the duct. The wall admittance manifests the same behavior. Therefore, one has to deal with imperfect ABHs ending before the singularity, even in the best case scenario. Yet in practice, one may encounter further factors that deteriorate the ABH behavior. The number of rings and cavities between them is finite as it is the ring thicknesses. Damping also plays an important role. It is herein proposed to analyze the influence of all these factors on the reflection coefficient of the ABHs by means of the transfer matrix method (TMM). Transfer matrices are presented which allow one to relate the acoustic pressure and acoustic particle velocity between different sections of the retarding structure. They constitute a quick and valuable tool for an initial design of ABHs.

A framework for studying the effect of compliant surfaces on wall turbulence

This paper extends the resolvent formulation proposed by McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) to consider turbulence–compliant wall interactions. Under this formulation, the turbulent velocity field is expressed as a linear superposition of propagating modes, identified via a gain-based decomposition of the Navier–Stokes equations. Compliant surfaces, modelled as a complex wall admittance linking pressure and velocity, affect the gain and structure of these modes. With minimal computation, this framework accurately predicts the emergence of the quasi-two-dimensional propagating waves observed in recent direct numerical simulations. Further, the analysis also enables the rational design of compliant surfaces, with properties optimized to suppress flow structures energetic in wall turbulence. It is shown that walls with unphysical negative damping are required to interact favourably with modes resembling the energetic near-wall cycle, which could explain why previous studies have met with limited success. Positive-damping walls are effective for modes resembling the so-called very-large-scale motions, indicating that compliant surfaces may be better suited for application at higher Reynolds number. Unfortunately, walls that suppress structures energetic in natural turbulence are also predicted to have detrimental effects elsewhere in spectral space. Consistent with previous experiments and simulations, slow-moving spanwise-constant structures are particularly susceptible to further amplification. Mitigating these adverse effects will be central to the development of compliant coatings that have a net positive influence on the flow.

The Green’s function in a channel with a sound-absorbing cover in the case of a uniform flow

We study the modal structure of an acoustic field of a point source as function of channel wall admittance in the case of a two-dimensional channel. The characteristic equation for determining the eigen-values corresponding to the boundary problem is studied in the form of this equation’s dependence on the admittance, which varies in the entire complex plane. All modes, without exception, existing in the channel and forming the source field are classified based on the obtained topography of the characteristic equation. The expressions that describe the amplitudes and spatial distribution of the hydrodynamic modes, attenuation rate (for stable modes), or increment (for unstable modes) were obtained as functions of the wall admittance and flow velocity. It is shown that in addition to the hydrodynamic unstable modes existing downstream from the source, hydrodynamic unstable modes exist upstream from the source at any admittance. They appear only when the admittance has an elastic character. It is shown that hydrodynamic modes are induced only in the case when the source is located close to the wall or on the wall. The amplitude of these modes decreases exponentially with distance from the wall.

Prediction of Breakout Noise from Acoustically Lagged Rectangular HVAC Ducts

Heating, ventilation and air-conditioning (HVAC) ducts are often lagged on the outside of the duct wall with a highly porous material, covered in turn with a thin impervious jacket. This arrangement is used to provide thermal insulation as well as the breakout noise reduction. In this paper, a prediction method based on the four-pole parameters is discussed to evaluate the lagged duct performance in terms of the breakout noise reduction in the plane-wave frequency range. Transfer matrix of the inner and outer duct walls in the transverse direction is calculated using the wall admittance as a function of the axial wave number. Assuming a common axial wave number ensures coupling between the acoustic waves and structural waves. It is a function of the wall admittance. Considerable difference between common axial wave number and the air acoustic wave number is observed near the coupling frequency region of the duct wall. The overall transfer matrix is developed in order to relate the inside plane wave pressure to the outer acoustic particle velocity. This is combined with the radiation impedance of the duct to predict the transverse transmission loss. Net Insertion loss of the lagged duct is calculated using the difference of the transverse transmission loss of the lagged duct and the corresponding bare duct. Predicted values of the insertion loss are compared with the measured values from literature. Finally, results of parametric studies are presented.

EDITORIAL: SPECIAL ISSUE "EFFICIENT NUMERICAL METHODS"

Between September 19th and 23rd, 2005, the International Conference of Theoretical and Computational Acoustics (ICTCA) took place in Hangzhou, Zhejing, China. Greater Hangzhou is a beautiful place south-west of Shanghai located on the delta of river Qiantang (Hangzhou Wan). Prof. Ding Lee, Editor-in-Chief of JCA and Honorary Chair of ICTCA 2005, had been living there before he moved to the USA. It was Prof. Lee, who again encouraged us to invite scientists to contribute papers for a new special issue of this journal. Following his advice, we decided to collect papers from participants of our session at the ICTCA conference and from researchers working on related topics. Altogether we received fifteen scientific papers. Because of this strong interest it was decided to split these papers into two special issues. This is the first part and it starts with a paper by D. Givoli et al. D. Givoli was one of the two key note speakers at ICTCA 2005. His research activities on absorbing boundary condition as well as on Dirichlet-to-Neumann operators are leading guides for the treatment of exterior problems. Then, in a contribution on a fluid-structure interaction written by N. J. Kessissoglou et al. the application of the finite element and the boundary element method to the lower frequency range are combined. The authors are extending this method towards higher frequencies and larger structures, such as submarines. Fourier Acoustics or Near-Field Acoustic Holography (NAH ), as it is also called, has been of interest to researchers for the last two or two and a half decades. It is nowadays one of the tools to identify sound sources or so-called hot spots on vibrating structures; in other words: sound source reconstruction. The current research of Sung-Il Ki et al. focuses on the reduction of the measurement effort and costs by means of the implementation of additional rigid reflectors in the sound field. The following two papers treat inverse acoustics problems as well. R. Anderssohn et al. present an identification method to obtain the complex boundary or wall admittance, whereas Sean Wu et al. suggest a new alternative integral-formulation for the prediction of acoustic fields in exterior as well as interior regions. A contribution to the wide field of scattering phenomena has been received from L. Hervella-Nieto et al., who applied the Perfectley Matched Layers (PML), introduced by Berenger in 1994 to simulate an infinite domain for electromagnetic fields, to time harmonic dissipative acoustics problems.

Acoustic characterization and prediction for fan-duct-plenum-room integrations

This paper investigates mutual influence of duct and room acoustics in the whole fan-duct-plenum-room integrations. Applying the parametric design language of finite element software ANSYS (APDL), dimensional and positional influence on system acoustics has been studied. Models with different room dimensions, duct lengths, duct cross-sections, duct locations, duct discharges and duct elbow were constructed, and their characteristics were compared qualitatively. Results show that small rooms, short ducts, large duct cross-sections and bell mouth duct discharges help to increase room sound pressure levels (SPLs); SPLs in ducts and plenums are sensitive to duct dimensions and duct discharge types but insensitive to duct locations and room dimensions; duct elbows have relatively indistinct acoustic influence in each component. Based on the calculation results, a semi-experimental method was proposed for simply and approximately evaluating indoor acoustic spectra of fan-duct-plenum-room integrations, then an example was used to demonstrate the prediction process. Finally, by adopting several ideal models, sound field constitutions, duct and room wall admittances and duct end reflection were explored quantitatively. This study may give a detailed understanding of fan-duct-plenum-room acoustics for researchers, also it might provide a new, simple and approximate prediction method for professionals to evaluate and improve fan-ducted acoustics.

Analyses of radiation impedances of finite cylindrical ducts

To aid in understanding the characteristics of acoustic radiation from finite cylindrical ducts with infinite flanges, mathematical expressions of generalized radiation impedances at the open ends have been developed. Newton's method is used to find the complex wavenumbers of radial modes for the absorption boundary condition. The self-radiation impedances and mutual impedances for some acoustic modes are calculated for the ducts with rigid and absorption walls. The results show that the acoustical conditions of the duct walls have a significant influence on the radiation impedance. The acoustical interaction between the two open ends of the ducts cannot be neglected, especially for plane waves. To increase the wall admittance will reduce this interference effect. This study creates the possibility for simulating the sound field inside finite ducts in future work.

Analysis of a circular patch antenna radiating in a parallel-plate radial guide

This paper investigates the use of a coaxially fed patch as a feeding element in a single-layer radial line slot antenna (RLSA) array. A field matching method is described to analyze a recessed circular cavity radiating into a radial waveguide. Using the wall impedance approach, the analysis is divided into two separate problems of the cavity and its external environment. Based on this analysis, a computer algorithm is developed for determining wall admittances as seen at the edge of the patch in the cavity, the radial admittance matrix for the two-probe feed arrangement, and the input impedance as observed from the coaxial line feeding the cavity. This algorithm is tested against the general-purpose Hewlett-Packard finite-element high frequency structure simulator as well as against measured results. Good agreement in all considered cases is noted.

Analytical method for a circularly polarised rectangular microstrip antenna

The paper proposes a formulation method for the wall admittance of an arbitrarily shaped microstrip antenna using spectral domain analysis. In the paper, the wall admittance of the circularly polarised rectangular microstrip antenna is calculated. The circularly polarised rectangular microstrip antenna is analysed using the cavity model. The electromagnetic fields within the antenna cavity are expanded in terms of the eigenfunctions in the cavity with sides extended by the edge extension length. The edge extension length is determined so that the eigenfunctions satisfy the Helmholtz equation at all frequencies. Their expansion coefficients are determined by the impedance boundary condition at the aperture. The calculated input impedance and axial ratio of the antenna agree fairly well with the measured data.

Effects of Wall Admittance Changes on Aeroelastic Stability of Turbomachines

In the present investigation a kind of new lifting surface model has been suggested based on the application of generalized Green’ sfunction theory anddoubleFouriertransformation technique, which issuitableforsupersonic cascadewithsubsonicleading-edgelocus.Thetheoreticalanalysisshowsthatthechangeofwallboundarycondition not only affects the eigenvalues of the system but also the eigenfunction normalizing factor in comparison with a rigid boundary condition, and it is these variations that affect the e ow and acoustic e eld. On the other hand, through the present numerical simulation the change of wall admittance leads to very remarkable effects on both the lift and moment coefe cients, which will determine whether a nonrigid wall has a positive effect on suppressing blade e utter or not. This means that if one aims at suppressing cascade e utter by use of a nonrigid wall one of the best ways is to e nd soft wall with a controllable acoustic admittance. Nomenclature Aab = periphery of a blade Ab = upper or lower surface of a blade b = blade semichord CFqi, CFa i = imaginary part of blade lift coefe cient CFqr, CFa i = real part of blade lift coefe cient CMqi, CMa i = imaginary part of blade moment coefe cient CMqr, CMa r = real part of blade moment coefe cient H = height from the hub to the tip side h = height from the hub to the tip side in the transformed space h1 = stagger distance, measured parallel to chord h2 = gap distance, measured normal to chord i = p i 1 kb

Effects of wall admittance changes on aeroelastic stability of turbomachines

Effects of wall admittance changes on aeroelastic stability of turbomachines

Input impedance of a probe‐fed cylindrical annular‐ring microstrip antenna

An analysis using a generalized transmission line model (GTLM) for a probe-fed cylindrical annular-ring microstrip antenna is presented. The equivalent circuit elements for the microstrip antenna modeled as a transmission line loaded with wall admittances are derived, and the expression for the input impedance is given. Numerical results for the antenna excited at the TM12 mode are also calculated and compared with the measured ones, and the effects of different feed positions and cylinder radii on the input impedance are analyzed. Good agreement of the GTLM solutions with the experimental results is observed. © 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 16: 41–44, 1997.

Wall parameters by time domain methods : Part 2—The conduction transfer coefficients a, b, c and d

It is shown that the heat transfer behaviour of a wall subjected to random excitation can be expressed by four series of coefficients, ao, a 1, ..., aN, and similar series bn, c n and dn. The number N of such coefficients, typically 4, depends upon the thickness and weight of the wall. The values of dn derive from the first few values of the wall decay times together with the choice of a time interval, typically one hour. an values depend further upon the series of response factors ϕ eeJ, bn on ϕre j and cn on ϕrr j. Values of the wall cyclic transmittance and admittance such as are used in the CIBSE Guide can readily be found from the transfer coefficients. The example given in Part 1 is extended to provide these values.

Generalized transmission‐line model for cylindrical‐rectangular microstrip antennas

AbstractAn analysis using a generalized transmission‐line model (GTLM)for a probe‐fed cylindrical‐rectangular microstrip antenna is presented. The equivalent circuit elements for the microstrip antenna modeled as a transmission line loaded with wall admittances are derived, and the expression for the input impedance is given. Numerical results of the input impedance are calculated and presented as a function of the cylinder radius and the substrate thickness. Excellent agreement of the GTLM solutions with the experimental results is observed. © 1994 John Wiley & Sons, Inc.