Parametric study of a drum-like silencer

An optimization study is carried out for a silencer consisting of two side-branch, rectangular cavities covered by membranes highly stretched in the direction of the duct axis. Stopband is defined as the range of frequency where the transmission loss is everywhere higher than the peak value of that in an expansion chamber which occupies three times as much cavity volume as does the present silencer. The logarithmic bandwidth is optimized with respect to the length-to-depth ratio of the cavity, the mass and the tension of the membrane. For two cavities each with a dimensionless volume of 5 (the duct height being the length scale), the optimal cavity aspect ratio is 6.6, and the lower stopband frequency is 0.09 times the first cut-on frequency of the rigid duct. This is compared favourably with the traditional duct lining modelled as an equivalent fluid. As the membrane mass increases, the stopband shifts to lower frequencies but it also narrows. The widest stopband is around 1.6 octaves for a massless membrane. The membrane tension plays a delicate role of setting the intervals between adjacent spectral peaks.     

Time-domain simulation of acoustic wave propagation and interaction with flexible structures using Chebyshev collocation method

A time-domain Chebyshev collocation (ChC) method is used to simulate acoustic wave propagation and its interaction with flexible structures in ducts. The numerical formulation is described using a two-dimensional duct noise control system, which consists of an expansion chamber and a tensioned membrane covering the side-branch cavity. Full coupling between the acoustic wave and the structural vibration of the tensioned membrane is considered in the modelling. A systematic method of solution is developed for the discretized differential equations over multiple physical domains. The time-domain ChC model is tested against analytical solutions under two conditions: one with an initial state of wave motion; the other with a time-dependent acoustic source. Comparisons with the finite-difference time-domain (FDTD) method are also made. Results show that the time-domain ChC method is highly accurate and computationally efficient for the time-dependent solution of duct acoustic problems. For illustrative purposes, the time-domain ChC method is applied to investigate the acoustic performance of three typical duct noise control devices: the expansion chamber, the quarter wavelength resonator and the drum silencer. The time-dependent simulation of the sound-structure interaction in the drum silencer reveals the delicate role of the membrane mass and tension in its sound reflection capability.     

Study on plate silencer with general boundary conditions

A plate silencer consists of an expansion chamber with two side-branch rigid cavities covered by plates. Previous studies showed that, in a duct, the introduction of simply supported or clamped plates into an air conveying system could achieve broadband quieting from low to medium frequencies. In this study, analytical formulation is extended to the plate silencer with general boundary conditions. A set of static beam functions, which are a combination of sine series and third-order polynomial, is employed as the trial functions of the plate vibration velocity. Green?s function and Kirchhoff–Helmholtz integral are used to solve the sound radiation in the duct and the cavity, and then the vibration velocity of the plate is obtained. Having obtained the vibration velocity, the pressure perturbations induced by the plate oscillation and the transmission loss are found. Optimization is carried out in order to obtain the widest stopband. The transmission loss calculated by the analytical method agrees closely with the result of the finite element method simulation. Further studies with regard to the plate under several different classical boundary conditions based on the validated model show that a clamped-free plate silencer has the worst stopband. Attempts to release the boundary restriction of the plate are also made to study its effect on sound reflection. Results show that a softer end for a clamped–clamped plate silencer helps increase the optimal bandwidth, while the same treatment for simply supported plate silencer will result in performance degradation.     

Noise silencer in the form of a Helmholtz resonator at the outlet of an air duct of finite length

A new type of noise silencer with the original design of the air duct-resonator system is proposed. The design is free of the disadvantages that are inherent in the conventional design with a resonator placed inside the air duct. A physical model of the silencer is developed, and its efficiency is calculated for different geometrical and physical parameters of the resonator and the air duct. A comparison between the calculated characteristics and the experimental data is performed, and their agreement is demonstrated.     

On acoustic propagation in three-dimensional rectangular ducts with flexible walls and porous linings

The focus of this article is toward the development of hybrid analytic-numerical mode-matching methods for model problems involving three-dimensional ducts of rectangular cross-section and with flexible walls. Such methods require first closed form analytic expressions for the natural fluid-structure coupled waveforms that propagate in each duct section and second the corresponding orthogonality relations. It is demonstrated how recent theory [Lawrie, Proc. R. Soc. London, Ser. A 465, 2347-2367 (2009)] may be extended to a wide class of three-dimensional ducts, for example, those with a flexible wall and a porous lining (modeled as an equivalent fluid) or those with a flexible internal structure, such as a membrane (the "drum-like" silencer). Two equivalent expressions for the eigenmodes of a given duct can be formulated. For the ducts considered herein, the first ansatz is dependent on the eigenvalues/eigenfunctions appropriate for wave propagation in the corresponding two-dimensional flexible-walled duct, whereas the second takes the form of a Fourier series. The latter offers two advantages: no "root-finding" is involved and the method is appropriate for ducts in which the flexible wall is orthotropic. The first ansatz, however, provides important information about the orthogonality properties of the three-dimensional eigenmodes.     

Theory of the Greenspan viscometer

We present a detailed acoustic model of the Greenspan acoustic viscometer, a practical instrument for accurately measuring the viscosity eta of gases. As conceived by Greenspan, the viscometer is a Helmholtz resonator composed of two chambers coupled by a duct of radius rd. In the lowest order, eta=pi f rho(rd/Q)2, where f and Q are the frequency and quality factor of the isolated Greenspan mode, and rho is the gas density. In this level of approximation, the viscosity can be determined by measuring the duct radius and frequency response of the resonator. In the full acoustic model of the resonator, the duct is represented by a T-equivalent circuit, the chambers as lumped impedances, and the effects of the diverging fields at the duct ends by lumped end impedances with inertial and resistive components. The model accounts for contributions to 1/Q from thermal dissipation (primarily localized in the chambers) and from a capillary used for filling and evacuating the resonator. A robust, prototype instrument is being used for measuring the viscosity of reactive gases used in semiconductor processing. For well-characterized surrogate gases, the prototype viscometer generated values of eta that were within +/-0.8% of published reference values throughout the pressure range 0.2-3.2 MPa. Remarkably, we achieved this level of agreement by only slight adjustment of the numerically calculated inertial and resistive end effect parameters to improve the agreement with helium reference values. No other parameters were adjusted.     

Characteristic study on an ESD suppressor by the FDTD method

The FDTD method was used to study the characteristics of an ESD suppressor filled with air, neon, argon, and helium. Obtained capacitance of the ESD suppressor filled with air was validated by measurement data and TDMM simulations. No large differences are found among the obtained capacitances for the ESD suppressor filled with air, neon, argon, and helium. But the ESD suppressor filled with air has a much higher trigger and clamping voltage than the ESD suppressor filled with neon, argon, or helium. The calculated capacitances are presented for different conditions. The ESD currents, charges, and electric fields are also presented.     

Analysis of the radial and longitudinal effect in a double TE(104) and a single TE(102) rectangular cavity

The response of the cavity to the rotation of a point-like sample in the horizontal (y-z) plane passing through the center of the Bruker double TE(104) and single TE(102) rectangular cavities in concentric circles of radii rho = 0, 1, 2, 3, 4, and 5 mm from the cavity center (radial effect) has been analyzed. The experimentally observed dependencies of the EPR signal intensity, I(pp), showed the following: (i) for rho = 0 mm (a sample position in the cavity center), I(pp) is independent of the angle of rotation; (ii) for rho = 1, 2, and 3 mm, the I(pp) dependence progressively changes from circular to oval; (iii) when the radius is further increased to rho = 4 and 5 mm, the I(pp) dependence changes dramatically, giving a figure eight shape. These experimental observations are in very good agreement with the theoretical calculations, in which the response is modeled using modified Cassinian curves, K(rho, phi). Similar trends were observed for any position of the horizontal (y-z) plane at which the sample is situated along the vertical x axis of the cavity; however, the amplitude of the signal decreases with increase in the absolute value of the x coordinate, ||x ||. The variation in the signal amplitude along the cavity x axis (longitudinal effect) can be calculated theoretically using a modified sine-squared curve, G(x). In general, the response of the cavity to a point-like sample situated at any position, P(rho, phi, x), can be represented as a product of the mentioned Cassinian curve, K(rho, phi), and sine-squared curve, G(x), giving for the signal intensity I(pp)(rho, phi, x) approximately K(rho, phi)G(x). The response to a large cylindrical sample which is concentrically situated on the cavity x axis can then be obtained by integrating the above product, K(rho, phi)G(x), over the sample volume. The nonlinear radial effect may give rise to a serious source of systematic error in quantitative EPR spectroscopy and shows that accurate and precise positioning of the sample in the microwave cavity is essential.     

A Super-Wide Bore DNP System for Multiple Sample Polarization: Cryogenic Performance and Polarization at Low Temperature

The volume of polarized sample and the delay required between successive polarizations of samples represent serious constraints for dynamic nuclear polarization (DNP) applications. With these limitations in mind, a DNP polarizer, based on a super-wide bore (150-mm diameter) vertical magnet operating at 3.35?T, was designed. The working diameter for loading/unloading samples is equal to 46?mm and the microwave cavity can accommodate up to three samples. The cryostat can be cooled to 4.2?K in typically 2?h and filled with liquid helium in 1?h. Once filled with liquid helium, the cryostat hold time is on the order of 4?h and a minimum temperature of 1.19?K can be reached. In situ polarization levels at low temperature were measured between 5 and 10?% in single and multiple samples of ¹³C-labeled urea and glycine.     

Reexploration of interacting holographic dark energy model: cases of interaction term excluding the Hubble parameter

In this paper, we make a deep analysis for the five typical interacting holographic dark energy models with the interaction terms \(Q=3\beta H_{0}\rho _\mathrm{{de}}\), \(Q=3\beta H_{0}\rho _\mathrm{{c}}\), \(Q=3\beta H_{0}(\rho _\mathrm{{de}}+\rho _\mathrm{c})\), \(Q=3\beta H_{0}\sqrt{\rho _\mathrm{{de}}\rho _\mathrm{c}}\), and \(Q=3\beta H_{0}\frac{\rho _\mathrm{{de}}\rho _{c}}{\rho _\mathrm{{de}}+\rho _\mathrm{c}}\), respectively. We obtain observational constraints on these models by using the type Ia supernova data (the Joint Light-Curve Analysis sample), the cosmic microwave background data (Planck 2015 distance priors), the baryon acoustic oscillations data, and the direct measurement of the Hubble constant. We find that the values of \(\chi _\mathrm{min}^2\) for all the five models are almost equal (around 699), indicating that the current observational data equally favor these IHDE models. In addition, a comparison with the cases of an interaction term involving the Hubble parameter H is also made.     

Enhancement of the quantum-liquid phase by increased resistivity in thick a-MoxSi1-x films

Effects of normal-state resistivity rho(n) on the vortex phase diagram at low temperature T have been studied based on dc and ac complex resistivities for thick amorphous MoxSi(1-x) films. It is commonly observed irrespective of rho(n) that, in the limit T=0, the vortex-glass-transition line B(g)(T) is independent of T and extrapolates to a field below the T=0 upper critical field B(c2)(0), indicative of the quantum-vortex-liquid (QVL) phase in the regime B(g)(0)相似文献   

Acoustic attenuation of hybrid silencers

The acoustic attenuation of a single-pass, perforated concentric silencer filled with continuous strand fibers is investigated first theoretically and experimentally. The study is then extended to a specific type of hybrid silencer that consists of two single-pass perforated filling chambers combined with a Helmholtz resonator. One-dimensional analytical and three-dimensional boundary element methods (BEM) are employed for the predictions of the acoustic attenuation in the absence of mean flow. To account for the wave propagation in absorbing fiber, the complex-valued characteristic impedance and wave number are measured. The perforation impedance facing the fiber is also presented in terms of complex-valued characteristic impedance and wave number. The effects of outer chamber diameter and the fiber density are examined. Comparisons of predictions with the experiments illustrate the need for multi-dimensional analysis at higher frequencies, while the one-dimensional treatment provides a reasonable accuracy at lower frequencies, as expected. The study also shows a significant improvement in the acoustic attenuation of the silencer due to fiber absorption. Multi-dimensional BEM predictions of a hybrid silencer demonstrate that a reactive component such as a Helmholtz resonator can improve transmission loss at low frequencies and a higher duct porosity may be effective at higher frequencies.     

Whispering-gallery-bottle microcavities: the three-dimensional etalon

In a tapered optical fiber there exist localized light structures that, in analogy to the magnetic bottles used in plasma fusion, can be called whispering-gallery bottles (WGBs). These essentially three-dimensional structures are formed by the spiral rays that experience total internal reflection at the fiber surface and that also bounce along the fiber axis in response to reflection from the regions of tapering. It is shown that the Wentzel-Kramers-Brillouin quantization rules for the strongly prolate WGBs can be inversed exactly, thus determining the cavity shape from its spectrum. The approximation considered allows one to find the shape of the etalon bottle, which, similar to the one-dimensional Fabry-Perot etalon, contains an unlimited number of equally spaced wave-number eigenvalues. The problem of determining such a non-one-dimensional cavity is not trivial, because such a cavity does not exist among the uniformly filled cavities such as rectangular boxes, cylinders, and spheroids that allow separation of variables. The etalon cavity corresponds to the fiber radius variation p(z) = rho0/cos(deltakz)/, where deltak is the wave-number spacing. The latter result is in excellent agreement with ray-dynamics numerical modeling.     

A mode matching method for modeling dissipative silencers lined with poroelastic materials and containing mean flow

A mode matching method for predicting the transmission loss of a cylindrical shaped dissipative silencer partially filled with a poroelastic foam is developed. The model takes into account the solid phase elasticity of the sound-absorbing material, the mounting conditions of the foam, and the presence of a uniform mean flow in the central airway. The novelty of the proposed approach lies in the fact that guided modes of the silencer have a composite nature containing both compressional and shear waves as opposed to classical mode matching methods in which only acoustic pressure waves are present. Results presented demonstrate good agreement with finite element calculations provided a sufficient number of modes are retained. In practice, it is found that the time for computing the transmission loss over a large frequency range takes a few minutes on a personal computer. This makes the present method a reliable tool for tackling dissipative silencers lined with poroelastic materials.     

Broadband noise reduction by circular multi-cavity mufflers operating in multimodal propagation conditions

In this study, sound propagation through a circular duct with non-locally lining is investigated both numerically and experimentally. The liner concept is based on perforated screens backed by air cavities. Dimensions of the cavity are chosen to be of the order or bigger than the wavelength so acoustic waves within the liner can propagate parallel to the duct surface. This gives rise to complex scattering mechanisms among duct modes which renders the muffler more effective over a broader frequency range. This work emanates from the Cleansky European HEXENOR project which aim is to identify the best multi-cavity muffler configuration for reduction of exhaust noise from helicopter turboshaft engines. Here, design parameters are the cavity dimensions in both longitudinal and azimuthal directions. The best cavity configuration must in addition fit weight specifications which implies that the number of walls separating each cavity should be chosen as small as possible. To achieve these objectives, the scattering matrix of the lined duct section is obtained experimentally for two specific muffler configurations operating in multimodal propagation conditions. The good agreement with numerical predictions serves to validate the perforate plate impedance model used in our calculation. Finally, given an incident acoustic pressure which is representative of typical combustion noise spectrum, the best cavity configuration achieving the maximum overall acoustic Transmission Loss is selected numerically. The study also illustrates how the acoustic performances are dependent on the nature of the incident field.     

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.     

Effect of Mean Flow on Acoustic Wave Propagation in a Duct with a Periodic Array of Helmholtz Resonators

Sound propagation properties of a duct system with Helmholtz resonators(HRs) are affected by mean flow.Previous studies have tended to focus on the effects of mean flows on acoustic response of a duct system with a finite number of HRs. Employing an empirical impedance model, we present a modified transfer matrix method for studying the effect of mean flow on the complex band structure of an air duct system with an infinite periodic array of HRs. The efficiency of the modified transfer matrix is demonstrated by comparison between an example of transmission response calculation for a finite single HR loaded duct and the finite element simulation result calculated using the COMSOL software. Numerical results are presented to analyze the effect of mean flow on the band structure and transmission loss of the sound wave in the duct system. It is hoped that this study will provide theoretical guidance for acoustic wave propagation of HR silencer in the presence of mean flow.     

A direct mixed-body boundary element method for packed silencers

Bulk-reacting sound absorbing materials are often used in packed silencers to reduce broadband noise. A bulk-reacting material is characterized by a complex mean density and a complex speed of sound. These two material properties can be measured by the two-cavity method or calculated by empirical formulas. Modeling the entire silencer domain with a bulk-reacting lining will involve two different acoustic media, air and the bulk-reacting material. Traditionally, the interior silencer domain is divided into different zones and a multi-domain boundary element method (BEM) may be applied to solve the problem. However, defining different zones and matching the elements along each interface is tedious, especially when the zones are intricately connected. In this paper, a direct mixed-body boundary element method is used to model a packed silencer without subdividing it into different zones. This is achieved by summing up all the integral equations in different zones and then adding the hypersingular integral equations at interfaces. Several test cases, including a packed expansion chamber with and without an absorbing center bullet, and a parallel baffle silencer, are studied. Numerical results for the prediction of transmission loss (TL) are compared to experimental data.     

Design of high-Q cavities in 2D photonic crystals air holes filled with polymer

We design novel photonic crystal heterostructure, substituting the air in the holes with materials of refractive index higher than n = 1. This can be achieved by infiltrating the photonic crystal (PC) with polymer. We theoretically investigate the L₂ cavity with two missing holes in the center, where the six holes surrounding the cavity are locally filled with polymer. We show that cavity modes can be differently tuned depending on the size and the position of the first hole adjacent to the cavity. A photonic microcavity with a high Q factor of 5.5 × 10⁶ and a modal volume V of 0.1919 is demonstrated. We demonstrate that the calculated Q factor for the designed cavity increases by a factor of 22 relative to that for a cavity without displaced and reduced air holes, while the modal volume remains almost constant.     

Screening in ionic systems: simulations for the Lebowitz length

Simulations of the Lebowitz length, xiL (T, rho), are reported for the restricted primitive model hard-core (diameter a) 1:1 electrolyte for densities rho approximately < 4rho(c) and T(c) approximately < T approximately < 40T(c). Finite-size effects are elucidated for the charge fluctuations in various subdomains that serve to evaluate xiL. On extrapolation to the bulk limit for T approximately > 10T(c) the exact low-density expansions are seen to fail badly when rho > 1/10 rho(c) (with rho(c)a3 approximately = 0.08). At higher densities xiL rises above the Debye length, xiD proportional to square root(T/rho), by 10%-30% (up to rho approximately =1.3rho(c)); the variation is portrayed fairly well by the generalized Debye-Hückel theory. On approaching criticality at fixed rho or fixed T, xiL (T, rho) remains finite with xiL(c) approximately = 0.30a approximately = 1.3xiD(c) but displays a weak entropylike singularity.