Wenping Bi

An improved multimodal method for sound propagation in nonuniform lined ducts

An efficient method is proposed for modeling time harmonic acoustic propagation in a nonuniform lined duct without flow. The lining impedance is axially segmented uniform, but varies circumferentially. The sound pressure is expanded in term of rigid duct modes and an additional function that carries the information about the impedance boundary. The rigid duct modes and the additional function are known a priori so that calculations of the true liner modes, which are difficult, are avoided. By matching the pressure and axial velocity at the interface between different uniform segments, scattering matrices are obtained for each individual segment; these are then combined to construct a global scattering matrix for multiple segments. The present method is an improvement of the multimodal propagation method, developed in a previous paper [Bi et al., J. Sound Vib. 289, 1091-1111 (2006)]. The radial rate of convergence is improved from O(n(-2)), where n is the radial mode indices, to O(n(-4)). It is numerically shown that using the present method, acoustic propagation in the nonuniform lined intake of an aeroengine can be calculated by a personal computer for dimensionless frequency K up to 80, approaching the third blade passing frequency of turbofan noise.

Characteristics of penalty mode scattering by rigid splices in lined ducts

In lined ducts, incident modes are scattered by axially and circumferentially nonuniform impedance. Experiments and numerical calculations have proved that this mode scattering can reduce the liner performance in some cases. This paper is devoted to the characterization of the penalty mode scattering excited by hard-walled splices which often exist in lined ducts. It is shown that, in the range of small splice angles, the transmission loss may decrease sharply with increasing splice angle when one mode, which is near cut-off or has high azimuthal order, is incident. When the incident sound field is composed of several acoustical modes, the phase interferences of incident modes are important for the penalty mode scattering. The effects of other parameters, e.g., liner length, mode quasiresonance on the penalty mode scattering are also presented.

Fano resonance scatterings in waveguides with impedance boundary conditions

The resonance scattering theory is used to study the sound propagation in a waveguide with a portion of its wall lined by a locally reacting material. The objective is to understand the effects of the mode coupling in the lined portion on the transmission. It is shown that a zero in the transmission is present when a real resonance frequency of the open system, i.e., the lined portion of the waveguide that is coupled to the two semi-infinite rigid ducts, is equal to the incident frequency. This transmission zero occurs as a Fano resonance-due to the excitation of a trapped mode in the open system. The trapped mode is formed by the interferences of two neighbored modes with complex resonance frequencies. It is also linked to the avoided crossing of eigenvalues of these two modes that occurs near an exceptional point (a subject that has attracted much attention in recent years in different physical domains). The real and complex resonance frequencies of the open system are determined by an equivalent eigenvalue problem of matrix Heff, which describes the eigenvalue problem defined in the finite lined portion (scattering region). With the aid of the eigenvalues and eigenfunctions of matrix Heff, the usual acoustic resonance scattering formula can be extended to describe the coupling effects between the scattering region and the rigid parts of the waveguide.

Sound Propagation in Varying Cross Section Ducts Lined with Non-uniform Impedance by Multimode Propagation Method

A Multimode Propagation Method (MPM) is proposed to study sound propagation in varying cross section lined ducts. The lined impedance may be arbitrary nonuniform in both axial and circumferential directions. It may be local or bulk reaction (in this paper, only local reaction boundary condition is studied). The cross section variation need not to be slow. The dimensionless wavenumber K (K = kR, where k = !=c, R is the typical radius of ducts) may be high enough to suit for the turbofan duct problem. This method models the above wave propagation as a scattering problem. It decomposes the whole duct into three contiguous regions with respect to axial coordinate z: left and right semiinflnite uniform rigid ducts connected by an arbitrary varying cross section transition lined region. The sound pressure and axial particle velocity are decomposed using the local rigid modes, which are known a priori and correspond to the exact, physical decomposition in the uniform rigid regions, while they provide a coupled, mathematical representation of the total wave fleld in the transition region. Evanescent modes are included. Two stable reformulations, of the Helmholtz wave propagation problem, are obtained accounting for exact boundary conditions and initial conditions by introducing modal impedance Z and an additional operator T. The complicated boundary conditions (varying section with axial and circumferential nonuniform impedance) are included in the formulas naturally. The two difierential matrix equations are integrated simultaneously from the free end (or the output end for flnite duct with known radiation modal impedance) to the source plane. Memory requirement is in the order O(N 2 t ), but not O(N 2 t Nz) where Nt is the number of mode truncation, Nz refers to the number of steps of axial discretization. The modal coe‐cients of re∞ection and transmission are then obtained which means that only one calculation is needed for any kind of source conflguration. This method obeys the energy conservation when the liner is not dissipative and could be generalized to account for the presence of ∞ow.

Acoustical behaviour of purely reacting liners

This paper investigates the acoustical behavior of a purely reacting liner in presence of a grazing flow. This device exhibits an unusual acoustical behavior: for a certain range of frequencies, no wave can propagate against the flow. The effect of shear flow is investigated by the Chebyshev Spectral Method, which provides detailed information near the wall. A negative group velocity is found in a range of frequencies and it is demonstrated that the sound can be stopped.

Trapped modes at acoustically rigid splices

The presences of subwavelength rigid splices are typical configurations in acoustic lined ducts, e.g., in the acoustic treated nacelles of an aeroengine, where the liners are usually manufactured in sections and the sections are jointed together by longitudinal acoustically rigid splices. In general, those small splices just perturb the sound fields and their roles are neglect. But sometimes, e.g., in the intakes of an aeroengine, they may produce important effects. We show numerically that there exist a new kind of mode in a lined duct in presence of the subwavelength rigid splices. Different from the modes in a uniform lined duct, the new kind of mode is formed by the presences of subwavelength acoustically rigid splices, whose widths are much smaller than the radius of the lined duct and the acoustic wavelength, which trap the surface waves and guide modes of the corresponding uniform lined duct as local oscillations in the vicinities of the small splices.

Sound propagation in ducts lined with porous materials by a Multi-Modal Marching Method

An efficient Multi-Modal Marching Method (MMM) was recently developed for sound propagation in non-uniform waveguides (including the effect of non-uniform locally reacting lining, and n on-uniform duct t ransverse dimensions). It was s hown to deal with realistic turbofan engine configurations with spliced liners up to relatively high reduced wavenumbers K~50. Here, the principle of MMM is given and applied to the case of a duct with non-locally reacting lining.

Sound attenuation optimization using metaporous materials tuned on exceptional points

A metamaterial composed of a set of periodic rigid resonant inclusions embedded in a porous lining is investigated to enhance the sound attenuation in an acoustic duct at low frequencies. A transmission loss peak is observed on the measurements and corresponds to the crossing of the lower two Bloch modes of an infinite periodic material. Numerical parametric studies show that the optimum modal attenuation can be achieved at the exceptional point in the parameter plane of inclusion position and frequency, where the two lower modes merge.

Modeling of sound propagation in nonuniform waveguides

Sound propagation in waveguides is modeled by a Multimodal Method. The waveguides geometries may involve bends, variable cross‐sections, or their combinations. The waveguide boundaries may involve axially or circumferentially nonuniform impedance conditions or acoustically rigid conditions. Uniform flow may also be included for a simple uniform geometry. The pressure (displacement potential for uniform flow) is expanded in terms of the modes of acoustically rigid waveguides and an additional function that carries the information about the impedance boundary. The rigid waveguide modes and the additional function are known a priori so that calculations of the true modes of waveguides with impedance boundary, which are difficult, are avoided. By matching the pressure and axial velocity (displacement potential and axial derivative for uniform flow) at the interface between different axially uniform segments, scattering matrices are obtained for each individual segment; these are then combined to construct a g...