Non-uniform Liner Research Articles

Acoustic scattering mechanism and noise attenuation of circumferentially non-uniform liner with spectral-wave guide method

In this paper, a model is established with application of the spectral-wave guide method, which has higher accuracy and can serve as a rapid calculation tool for sound transmission calculations. Based on this calculation model, some numerical results of circumferentially non-uniform lined annular/circular ducts are carried out, and some physical mechanisms can be discovered. The numerical results show that periodical impedance distributions along the circumferential direction will lead to discontinuous scattered modes with regular spacing; and mirror-symmetric structure liner will converge the energy of opposite modes. Relying on this mechanism, the potential of acoustic scattering can be further developed by suppressing lower or enhancing higher order modes with expressly designed segmented liner configurations. In particular, the intrinsic mechanism of mode redistribution brought about by the non-uniform liner can be subtly utilized to attenuate broadband noise. The present work indeed shows that circumferentially non-uniform liner is conducive to the reduction of the practical broadband sound source. Furthermore, the effects of non-uniform flow are considered in the model, then distinction of noise attenuation and scattered modes energy in different flows is shown. A possible mechanism is proposed that refraction effects in complex flows lead to the distinction. These works show that the current model has profound potential and availability for the research and designs of circumferentially non-uniform liner.

Sound wave scattering in a flow duct with azimuthally non-uniform liners

Novel acoustic liner designs often incorporate new materials with non-uniform impedance distributions. Therefore, new methods are required for their modelling and analysis. In this paper, a theoretical model is developed to investigate the scattering of sound waves from an axially symmetrical flow duct with a semi-infinite, azimuthally non-uniform acoustic lining on the duct wall. More specifically, the incorporation of Fourier series expansions into the Wiener–Hopf method leads to an analytical model with a matrix kernel, which is further factorised by using the pole-removal method to obtain a closed-form solution. A new mathematical method is developed to solve the residues associated with the pole-removal technique. The proposed model has been verified and validated by comparing with corresponding computational results. In addition to shedding light on the possible physical effect of azimuthally non-uniform liners along with an axial hard–soft interface, the current model enhances the theoretical modelling capability for a complicated set-up of practical importance, and can be used to investigate new liner designs for passive noise control in flow ducts.

Slow sound in lined flow ducts.

The acoustic propagation in lined flow duct with purely reactive impedance at the wall is considered. This reacting liner has the capability to reduce the speed of sound, and thus to enhance the interaction between the acoustic propagation and the low Mach number flow ( M≃0.3). At the lower frequencies, there are typically four acoustic or hydrodynamic propagating modes, with three of them propagating in the direction of the flow. Above a critical frequency, there are only two propagating modes that all propagate in the direction of the flow. From the exact two-dimensional formulation an approximate one-dimensional model is developed to study the scattering of acoustic waves in a straight duct with varying wall impedance. This simple system, with a uniform flow and with non-uniform liner impedance at the wall, permits to study the scattering between regions with different wave characteristics. Several situations are characterized to show the importance of negative energy waves, strong interactions between acoustic and hydrodynamic modes, or asymmetric scattering.

Using Azo As a Conductive and Adhesive Liner for through Glass Vias Filling By Cu Electroplating

This study introduces a method using aluminum-doped zinc oxide (AZO) as a conductive and adhesive liner for through glass vias (TGVs) filling by Cu electroplating. AZO liner is formed on a glass surface by three steps: AZO sol-gel coating, sol-gel evaporation and annealing. AZO sol-gel evaporation was observed by thermogravimetry-differential thermal analysis (TG-DTA). Surface morphology was observed by OM and SEM, and crystallinity and grain size were measured by XRD. AZO sol-gel evaporation rate is key for forming a conformal AZO liner in TGVs. When AZO sol-gel coating was operated under the condition at lower evaporation rate, it would form thick and non-uniform liner and there was a risk of void formation after copper electrodeposition. On the contrary, when the AZO sol-gel coating was operated under the condition of ultrahigh evaporation rate, a thin and uniform AZO liner was formed on the sidewall of the TGVs. This phenomenon refers to the fast coffee ring effect in TGVs. Cu Electroplating was used after AZO liner was formed in the TGVs. This study combined an alkaline conformal copper plating bath with an acid button-up copper plating bath to fill the TGVs. AZO liner cannot only enhance the adhesive force between the deposited copper and the glass, but also play an important role for direct copper plating in TGVs.

On Sound Radiation from an Open-Ended Non-Uniformly Lined Cylindrical Nozzle

Acoustic liners are widely used in jet engine inlet and exhaust ducts, as a passive means of noise reduction. One possible way of liner optimization is the use of a non-uniform acoustic impedance distribution. It has been shown that such a liner can lead to an attenuation in the acoustic amplitude of some of the modes present in the duct. However, the sound attenuation perceived by an observer in the far-field is arguably the most important effect to be achieved. These issues may be illustrated by considering the radiation of sound from a cylindrical duct with impedance varying circumferentially, axially or in both directions and the acoustic pressure at the far-field in each situation. The radiation of sound from an open pipe is represented by a pressure distribution on a disk, viz. the exit plane. The radiation of sound in free space, i.e. without obstacles, is specified by a Kirchhof integral. The source distribution on the duct exit plane, which allows the evaluation of radiation integrals, is specified by the radial, axial, and circumferential modes, in the cylindrical nozzle. The evaluation of the radiation integrals show that (i) the total acoustic field consists of a spherical wave multiplying a sum of radial modes n = 1, . . . ,∞ and azimuthal modes of odd order only m = 1,3,5, . . . ; (ii) each mode consists of a monopole term and a dipole term and depend on the frequency and the radial wavenumbers, determined by the boundary condition at the duct wall. When the impedance distribution varies circumferentially or axially, the evaluation of the wavenumbers involves the determination of the roots of an infinite determinant, while when the impedance aries both axially and circumferentially, the roots of a doubly infinite determinant have to be calculated. In the case of external noise of an aircraft, the observer is on the ground, at a distance much greater than the duct diameter, and the radiation integrals for an observer in the far-field can be simplified, since the dipole term is weak. The evaluation of the acoustic pressure for an observer in the far-field, shows that it depends on the radial wavenumbers in the nozzle, which are specified by the wall boundary conditions, and thus depend on the acoustic impedance distribution. This allows comparison of hard-walled nozzles, with liners with constant impedance and non-uniform liners, the latter with impedance distribution varying circumferentially, axially or in both directions. The far-field acoustic pressure is specified by a directivity factor that is calculated for several values of the parameters for each of the cases mentioned above.

On Sound Generation in Cylindrical Flow Ducts with Non-Uniform Wall Impedance

The use of acoustic liners is a common means of noise reduction in jet engine exhausts. The quest for more effective sound absorption mechanisms in cylindrical ducts has led to the consideration of non-uniform liners, with impedance varying circumferentially, axially, or in both directions. The present paper is based on the theory of mode coupling in a non-uniformly lined cylindrical duct and considers the complementary problem of generation of sound or excitation of coupled modes by a source distribution. The sound field due to an arbitrary source distribution is obtained as a superposition of eigenfunctions corresponding to complex eigenvalues for the radial wavenumbers and natural frequencies taking into account that the radial, axial and azimuthal modes are coupled by the non-uniform wall impedance, and including resonant and non-resonant cases. The waveforms are illustrated for point monopole, dipole and quadrupole sources and a continuous monopole distribution. It is shown that a non-uniform liner provides a greater attenuation than a uniform liner with the same average impedance if it is ‘well-matched’ to the sound field, that is, if it has higher impedance at the peaks and lower at the nodes of the standing modes.

A Conformal Oxide Liner for Through Silicon Vias by Pulsed SA-CVD Deposition

In 3D integration technology, TSVs (Through Silicon Via) are used to electrically interconnect stacked chips. The preferred isolation process is SA-CVD O3/TEOS based oxide because it is conformal and has a high deposition rate at low temperature. A drawback is a high TSV density dependency that leads to a non-uniform liner thickness across the chip and along the whole wafer. Using a pulsed flow 400{degree sign}C O3/TEOS process, we obtained a superior result in terms of conformality and structure density dependency for via's with aspect ratio 10 (2x20 and 5x50μm). The process strongly outperforms standard processes without pulsing.

Modelling of sound propagation in a non-uniform lined duct using a Multi-Modal Propagation Method

Liner non-uniformities, such as distributed impedances, may have a direct influence on the performance of turbofan engine liners. A relevant problem to study these effects is that of sound propagation in a hard-walled duct of circular cross-section, fitted with a region of non-uniform liner. Given the complex modal input amplitudes at one end of the hard-walled duct, the problem is to compute the complex modal output amplitudes at the other end. In the present paper, a Multi-Modal Propagation Method (MMPM) is proposed to solve this problem in the absence of mean flow. For simplicity, the liner impedance is set piecewise constant along the duct, while being arbitrarily variable along the circumference of each segment. The principle of the method is to expand the sound pressure and axial velocity into double infinite series using the rigid duct modal basis, and then to follow the projection coefficients evolution along the duct axis. Scattering matrices are obtained for individual segments and then combined to construct a global scattering matrix. It is numerically shown that the convergence rate of the infinite series is at least O ( M - 2 ) and O ( N - 1.5 ) , where M and N refer to the maximum circumferential and radial mode orders, respectively. Validation of the method is done in 2D by comparison with FEM. The present MMPM is shown to deal with realistic turbofan engine configurations with spliced liners, up to relatively high reduced wavenumbers K ∼ 50 .

Use of nonuniform liners as sound suppressors

It is desirable in many practical situations to design a liner for a duct while maintaining the shape of its cross section intact. When these cross-sectional areas are large, a lot of the acoustical energy could stay unaffected by the wall treatment. Experimental results are presented which indicate that this problem might be remedied by means of an axially nonuniform treatment of the duct. In the case of an exponentially lined duct, some evidence that sound energy would flow away from the center of the duct is obtained. Also included in this paper is a theoretical discussion supporting the possibility of the modal conversion in presence of nonuniform liners. [Work partly supported by NASA Lewis.]