Explicit approximation of the wavenumber for lined ducts

This work aims to investigate the mode-matching (MM) and low frequency approximation (LFA) solutions of a two dimensional waveguide problem with flanged junction. The relative merits of each approach are compared for the scattering of fluid-coupled wave. The boundary value problem involving higher order derivatives at boundaries becomes a non-Sturm–Liouville problem where the use of standard orthogonality relation (OR) enables the MM solution. The derivation of LFA is made which proves to be surprisingly accurate for structure-borne mode incident. In order to validate the truncated model expansion the distribution of power in duct regions is discussed and Gibbs oscillations are incorporated by reconstruction of the normal velocity field using Lanczos filter. The structural acoustic has become a stimulating and attention-grabbing issue of this era. The interest to minimize the ducted fan noise aero engines, power station and heating, ventilation, and air conditioning (HVAC) system offers a great inspiration to engineers and scientists. Duct work is common feature in engineering structures, air craft and buildings etc. which clearly beneficial but also a channel for unwanted noise. It propagates sound at significant distances by the mechanism of reflection through the internal walls of duct and duct vibration. In order to reduce such noises some dissipative devices likewise expansion chamber, acoustic lining or silencer and absorbent material are useful. Numerous investigations [1–3] have been made to suggest some analysis for the reduction of unwanted noise. Ayub et al. [2] and Huang [3–5] considered the reactive silencer used in HVAC system for reducing ducted tonal fan noise. The duct parallel to x-axis of the inlet/outlet of the expansion chamber was taken to be bounded by membrane with varying height. Because of this variation in height of the membrane the device was tuned which gave stopband for specified frequency. The flexible channels have been discussed by Dowell and Voss [6]. They have analyzed the cavity-backed panel at the low frequency range in the presence of fluid flow. Afterwards Kang and Fuchs [7] has extensively examined their proficiency in the case of cavity-backed micro perforated membrane. Recently Lawrie and Kirby [8,9] investigated the performance of two dimensional modified reactive silencers due to their potential use of hybrid silencers devices in HAVC ducting system. Their investigation proposed that the stopband by the silencer can be broadened and/or shifted with height of the membrane.

Journal of Sound and Vibration, 2001

This paper describes the development and application of a time-domain acoustic liner model which is suitable for the simulation of sound propagation and attenuation in lined ducts. The #uid #ow within the duct domain is represented by the non-linear, unsteady Euler equations while the liner model consists of a resistive frequency-independent part and a reactive part which is obtained by solving the one-dimensional Euler equations within the liner cavity. Specialized boundary conditions are used for matching the 1D cavity #ow and the 2D duct #ow. The liner model has been formulated in order to predict the sound attenuation with or without mean #ow, as well as for linear or non-linear sound propagation. The model has been validated in the case of linear pure-tone and N-wave signals by checking against analytical formulations obtained via eigensolutions of the linearized inviscid #ow equations. Very good agreement was obtained for both zero and subsonic mean #ows.

Boundary Elements and Other Mesh Reduction Methods XXXII, 2010

This paper deals with strategies for computing efficiently the propagation of sound waves in ducts with acoustic lining at its walls. Though efficient these treatments seem to have reach their limit and there is still a need for considering other passive techniques to reduce further the sound radiation at the duct exit. In most cases of practical interest, these added acoustics components can be modelled as acoustic cavities which are connected to the duct and can be either purely reactive or dissipative. The assessment of the efficiency of such a system requires a precise knowledge of the acoustic field in the duct. Though standard Finite Element (FE) software could, in principle, be used for this purpose, a full FE model would be extremely demanding especially in the mid-frequency range and this can have a negative impact when, for instance, some efficient optimizations are needed. In the present work,we present a new numerical procedure that judiciously exploit the benefit of the FEM and the BEM approach. First, a set of FE eigenmode are computed in the cavity to produce a numerical impedance matrix connecting the pressure and the acoustic velocity on the duct wall interface. Then an integral representation for the acoustic pressure in the main duct is used. The presence of acoustic liners on the walls of the duct is taken into account via an appropriate modal decomposition of the Green's function. Typical applications involving Helmholtz resonators and Herschel-Quincke tubes are presented. We show that our algorithm allows a very fast and accurate computation of the scattering matrix of such a system with a numerical complexity that grows very mildly with the frequency.

In this study, we analyzed the diffraction of the acoustic dominant mode in a parallel-plate trifurcated waveguide with normal impedance boundary conditions in the case where surface impedances of the upper and lower infinite plates are different from each other. The acoustic dominant mode is incident in a soft/hard semi-infinite duct located symmetrically in the infinite lined duct. The solution of the boundary value problem using Fourier transform leads to two simultaneous modified Wiener–Hopf equations that are uncoupled using the pole removal technique. Two infinite sets of unknown coefficients are involved in the solution, which satisfy two infinite systems of linear algebraic equations. These systems are solved numerically. The new kernel functions are factorized. Some graphical results showing the influence of sundry parameters of interest on the reflection coefficient are presented.

Applied Acoustics, 2014

This paper deals with the effect of the temperature and the frequency on the acoustic behavior of lined duct partially treated with usual material used in acoustic insulation. First, the effect of frequencies and temperature on the acoustic impedance of usual materials used in lined duct such as glass or rock wools in order to reduce acoustic level is investigated. Secondly, the variational formulation of the acoustic duct problem taking into account velocity and temperature effects is established. Then, a numerical model is derived which permits to compute the reflection and the transmission coefficients of such duct for different temperatures and several flow velocities. The acoustic power attenuation is then computed from these coefficients and the effect of the temperature and flow velocities on this energetic quantity is evaluated. The numerical results are obtained for three configurations of a lined duct treated for different temperature ranges and several velocities. Numerical coefficients of transmission and reflection as well as the acoustic power attenuation show the relative influence of temperature.

Journal of Sound and Vibration, 2017

The paper presents derivation of the impedance matrix based on the rigorous solution of the wave equation obtained by the Wiener-Hopf technique for a semi-infinite unflanged cylindrical duct. The impedance matrix allows, in turn, calculate the acoustic impedance along the duct and, as a special case, the radiation impedance. The analysis is carried out for a multimode incident wave accounting for modes coupling on the duct outlet not only qualitatively but also quantitatively for a selected source operating inside. The quantitative evaluation of the acoustic impedance requires setting of modes amplitudes which has been obtained applying the mode decomposition method to the far-field pressure radiation measurements and theoretical formulae for single mode directivity characteristics for an unflanged duct. Calculation of the acoustic impedance for a non-uniform distribution of the sound pressure and the sound velocity on a duct cross section requires determination of the acoustic power transmitted along/radiated from a duct. In the paper, the impedance matrix, the power, and the acoustic impedance were derived as functions of Helmholtz number and distance from the outlet.

Archives of Acoustics, 2012

Numerical methods are mostly used to predict the acoustic pressure inside duct systems. In this paper, the development of a numerical method based on the convected Helmholtz equation to compute the acoustic pressure inside an axisymmetric duct is presented. A validation of the proposed method was done by a comparison with the analytical formulation for simple cases of hard wall and lined ducts. The effect of the flow on the acoustic pressure inside these ducts was then evaluated by computing this field with different Mach numbers.

Journal of Sound and Vibration, 1995

In this paper an approach is presented for obtaining exact analytical solutions for sound propagation in ducts with an axial mean temperature gradient. The one-dimensional wave equation for ducts with an axial mean temperature gradient is derived. The analysis neglects the effects of mean flow, and therefore the solutions obtained are valid only for mean Mach numbers that are less than 0•1. The derived wave equation is then transformed to the mean temperature space. It is shown that by use of suitable transformations, the derived wave equation can be reduced to analytically solvable equations (e.g., Bessel's differential equation). The applicability of the developed technique is demonstrated by obtaining a solution for ducts with a linear temperature profile. This solution is then applied to investigate the dependence of sound propagation in a quarter wave tube upon the mean temperature profile. Furthermore, the developed analytical solution is used to extend the classical impedance tube technique to the determination of admittances of high temperature systems (e.g., flames). The results obtained using the developed analytical solution are in excellent agreement with experimental as well as numerical results. Analytical solutions were also obtained for a duct with an exponential temperature profile and also for a temperature profile that corresponds to a constant convective heat transfer coefficient at the wall.

ASME 2020 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, 2020

The SALUTE project aims at evaluating performance of metacomposites for acoustic smart lining in grazing turbulent flow. Theoretical and numerical investigations are carried out for designing innovative specimen. A specific focus is placed in the realization of prototypes for evaluating the metacomposite liner performances in 2D and 3D liners, its process complexity and robustness. The insight gain in this project is new tools for obtaining innovative samples; the acoustical experimental tests demonstrate efficiency and robustness of such technology for controlling UHBR noise emission. This paper is focused on parametric study based on the maximization of the absorption coefficient in a duct by optimizing the impedance of a treated area.

Journal of Acoustical Society of America, 1992

The acoustic impedance studies in duct systems are important for a complete analysis and design in acoustical transmission lines and filters such as mufflers and silencers. The analysis of standing waves in a duct with passive termination is well known. In this paper, the formulation for acoustic impedance in a finite length duct with dynamic termination is presented. The boundary-element method was used to verify the formulation. The studies can be applied to source characterization and active noise control in duct systems. PACS numbers' 43.20. Mv, 43.20.Rz, 43.55.Ev

The Journal of the Acoustical Society of America, 2014

A fully three-dimensional coupled mode approach is used in this paper to describe the physics of low frequency acoustic signals propagating through a train of internal waves at an arbitrary azimuth. A three layer model of the shallow water waveguide is employed for studying the properties of normal modes and their coupled interaction due to the presence of nonlinear internal waves. Using a robust wave number integration technique for Fourier transform computation and a direct global matrix approach, an accurate three-dimensional coupled mode full field solution is obtained for the tonal signal propagation through straight and parallel internal waves. This approach provides accurate results for arbitrary azimuth and includes the effects of backscattering. This enables one to provide an azimuthal analysis of acoustic propagation and separate the effects of mode coupled transparent resonance, horizontal reflection and refraction, the horizontal Lloyd's mirror, horizontal ducting and anti-ducting, and horizontal tunneling and secondary ducting.

2018

Ducts are extensively used in Heating, Ventilation and Air Conditioning (HVAC) applications and gas industries for transmission of substance, especially liquid or gas. These ducts carry the noise generated by Air-Handling Units (AHU) in axial and transverse directions. Sound radiated in the transverse direction due to acoustic excitation of duct walls is known as ‘Breakout noise’. Sound radiation from duct depends on its structural properties as well as the medium’s acoustic properties. The present research interest is to study sound radiation and vibration characteristics of rectangular ducts using direct and inverse techniques. First part of the work describes analytical, experimental and numerical models to understand sound radiation characteristics of a flexible rectangular duct. Firstly, an analytical model is developed based on an ‘equivalent plate model’ of the rectangular duct. This model has considered the coupled and uncoupled behaviour of both, acoustic and structural sub...

2009

An understanding of the multi-modal propagation of acoustic waves in ducts is of practical interest for use in the control of noise in, for example, aero-engines, automotive exhaust and ventilation systems. In this paper, the propagation of sound from point sources in hard-...

The propagation of unsteady disturbances in ducts of slowly-varying geometry, such as those typical of an aero-engine, can be successfully modelled using a multiple scales approach. The multiple-scales approach has a number of distinct advantages over full numerical methods. The accuracy and usefulness of the multiple scales approach has been validated against finite element methods, using realistic aero-engine configurations. Cut-on cut-off transition of acoustic modes in hard-walled ducts with irrotational mean flow is well understood. However, previous finite-element simulations of this phenomenon appear to indicate the possibility of energy scattering into neighbouring modes at large Helmholtz numbers. In this thesis, an attempt is made to explain such scattering phenomena in slowly varying aero-engine ducts using multiple-scales techniques. In order to model modal scattering a good understanding of cut-on cut-off transition is necessary. Here, the well known single turning point is revisited, and our understanding of cut-on cut-off transition is extended to include an analysis of a double turning point. Then using a similar apparatus, modal scattering in the case where a mode undergoes cut-on cut-off transition is investigated. It is found that, for sufficiently high frequencies, a mechanism exists whereby a propagating incident mode can be scattered into neighbouring modes provided that a mean flow exists within the duct. An asymptotic analysis of this mechanism is presented and, by solving numerically a composite solution, results in a duct of rectangular cross section are obtained. The energy distribution of the incident and neighbouring scattered modes reveals an interaction and exchange of energy with the mean flow. This work now allows greater insight as well as more accurate and fast computations of high frequency mode propagation in slowly-varying hard walled ducts using multiple-scales approaches.

Vibrations in Physical Systems, 2020

External boundaries of acoustic devices can channel sound propagation, and in some cases can create buildup or attenuation of acoustic energy within a confined space. In this paper, it is proposed an efficient practical numerical method (based on FEM) of calculation of attenuation of sound power transmission through ducts. The method shows its viability by presenting the reasonably consistent anticipation of the experimental result. One can observe the mechanical behaviour of the duct’s medium for lower frequencies (high transmission loss) and wave behaviour for higher frequencies (small or zero attenuation). The authors proved that mechanical vibrations of medium reduce the possibility of acoustic energy transmission in duct systems. The radiation impedance for the duct is calculated as well.