Narrow sidebranch arrays for low frequency duct noise control

Experimental study of the effects of the long chimney of a closed tonehole on the sound of a bassoon

The bassoon has side holes a few tens of millimeters long, much longer than in other woodwinds. When they are closed, the "quarter-wave" resonances of these "chimneys" create short circuits in parallel with the bore. At these resonance frequencies, near 2 kHz-within the sensitive range of hearing-it is expected that the waves will not propagate beyond the chimney, affecting both the input impedance and the radiated sound. Using parametric studies with varying chimney lengths, these effects on impedance and radiated sound are measured for a French bassoon and a simplified conical model instrument. The effects are clear on the model instrument, especially when several chimneys have equal length. For the bassoon, the passive filter effect remains, but its importance in the sound is blurred due to changes in the oscillation regime and in the directivity, as simulations confirmed. The effect is audible under laboratory conditions, but on the same order of magnitude as the spatial level variations due to the directivity. It is, therefore, unlikely that the difference in timbre between the French and the German bassoon is mainly due to longer tonehole chimneys.

On the length scale and Strouhal numbers for sound transmission across coupled duct cavities at low Mach number

The sound transmission across two coupled cavities along a rectangular duct in the presence of a low Mach number flow is examined experimentally in the present study. An effort is also made for a deeper understanding of how the flow, excitation sound frequency, and excitation level influence the sound transmission loss. The results confirm that the high sound transmission loss across the cavities is associated with the strong out-of-phase pressure fluctuations within the cavities. The sound transmission loss deteriorates significantly once the flow speed exceeds a threshold value. A different length scale is proposed. This length scale, together with the threshold flow speed and the peak sound transmission loss frequency, gives a Strouhal number, which is basically independent of the cavity offset for a fixed cavity length. The present finding extends the previous effort of the authors, enabling the prediction of the flow speed limit and operating frequency of the coupled cavities for duct silencing at a low Mach number.

On sound propagation along an infinite rectangular duct-like structure with a finite slot opening and its modelling

The sound propagation across a sound leaking section along an infinite rectangular duct-like structure near to the lower order duct eigenfrequencies is investigated numerically in the present study. The sound leakage is achieved by finite length rectangular slots located at a corner of the duct-like structure cross section. The finite-element simulations are performed, in the first place, to gain insights into the modal development inside the structure. A semi-analytical model, which considers the wavy air motions along the slots with oblique sound radiation patterns, is developed. An empirical framework is also proposed to estimate the complex longitudinal wavenumber along the slot using the numerical results and dimensional analysis. The performance of the proposed semi-analytical model, together with the complex wavenumber prediction framework, is tested using two duct-like structures with different cross section aspect ratios. The results show that the present proposed approach gives predictions close to the finite-element simulations. The deviations are well within engineering tolerance.

Broadband noise insulation of windows using coiled-up silencers consisting of coupled tubes

It has been demonstrated that a staggered window achieves better noise reduction performance than a traditional single glazing one at middle to high frequencies while maintaining a degree of natural ventilation. There is, however, little improvement in the low frequency range. In contrast, this work proposes to apply coiled-up silencers consisting of coupled tubes on the side walls of staggered windows to obtain noise attenuation in a broad band, especially in the low frequency range. Each element in the silencer consists of two coupled tubes with different cross sections so that noise at more frequencies can be attenuated than that with a uniform cross section. The simulation results show that 8.8 dB overall insertion loss can be obtained between 100 and 500 Hz after applying a combination of silencers designed at 7 different frequencies, and the insertion loss of the staggered window is increased from 6.7 to 15.6 dBA between 100 and 2000 Hz for normal incident traffic noise with the proposed silencers installed. The design is validated by the experiments with a 1:4 scale down model.

Sound transmission across a narrow sidebranch array duct muffler at low Mach number

The sound transmission loss across a duct muffler in the form of a linear array of 11 narrow sidebranches is examined experimentally in the present study. The introduction of a low Mach number duct flow deteriorates the broadband acoustical performance of the muffler and strong sound transmission loss dips and sound amplifications are observed at high flow speeds. It is found that a stronger acoustic pressure magnitude inside the sidebranches improves the muffler's performance in the presence of the duct flow. A theoretical analysis using a 2-sidebranch array muffler is conducted and the results indicate the possibility of increasing the sound pressures inside the sidebranches by locating the shorter sidebranch upstream of the longer one. The results of further experiments validate the theoretical deduction. Results also confirm that the muffler with sidebranches arranged in the order of decreasing acoustic impedance magnitude has stronger resilience against aerodynamic disturbance and gives better performance when the upstream excitation level and the duct flow speed are fixed.

Optimized reactive silencers composed of closely-spaced elongated side-branch resonators

This paper reports a theoretical study of the sound propagation in a rectangular waveguide loaded by closely-spaced elongated side-branch resonators forming a simple low-frequency broadband reactive silencer. Semi-analytical calculations account for the evanescent modes both in the main waveguide and side-branch resonators and for the viscothermal losses in the silencer elements. Reasonable accuracy is maintained in the evaluation of transmission, reflection, and absorption coefficients, while the calculation time is reduced by a few hundred times in comparison with the finite element method. Therefore, the proposed method is particularly suitable for optimization procedure. The lengths of the individual equally spaced side-branch resonators are optimized by a heuristic evolutionary algorithm that maximizes the minimum transmission loss (TL) over a pre-defined frequency range. Numerical results indicate that the minimum TL of the optimized silencers is reduced due to the destructive effect of the evanescent coupling from the resonators of the nearest side-branches. In the opposite, the TL increases linearly with the number of the side-branch resonators.

Optimized reactive silencers with narrow side-branch tubes

This paper presents a theoretical study of the sound propagation in a waveguide loaded by an array of flush-mounted narrow side-branch tubes, forming a simple low-frequency reactive silencer. The individual tube-lengths and the distances between the adjacent tubes are optimized in order to maximize the minimum transmission loss over a given frequency range. The transmission properties of the silencer are calculated using the transfer matrix method, heuristic evolutionary approach is employed for the determination of the optimal parameters. The numerical results are validated against the finite element method simulation. A comprehensive parametric study is performed to demonstrate the optimized silencer performance as a function of the number of side-branch tubes, and the frequency range. It is shown that for the given frequency range, the minimum transmission loss of the optimized silencer increases linearly with the number of the side-branch tubes.

Broadband noise attenuation using a variable locally reacting impedance

Passive control of low-frequency duct noise remains a technical challenge. Traditional noise control devices are either overly bulky or too narrowband. A broadband attenuation mechanism inspired by the mammalian cochlea is presented in this theoretical study. It consists of a parallel arrangement of an array of multiple beams or stretched strips backed by a cavity. The structure vibrates strongly in response to the broadband incident noise and hence creates substantial reflection. If both the media in the cavity and the duct are air, the mass-like load from the fluid in the cavity suppresses the response of the structure and thus lowers the transmission loss. If helium, or some other gas with lower density than air in the duct, fills the cavity, the mass-like reactance of the cavity is reduced and the silencing performance is improved. Then such a silencer can achieve a satisfactory attenuation performance at low frequency range. Multiple adjacent resonant peaks are found in the transmission loss curve and such a silencer has superiority in size and acoustic performance over expansion chamber and duct lining.

Sound transmission in a duct with a side-branch tube array mounted periodically

This paper presents a theoretical study of sound propagation in a duct with a tube array flush-mounted periodically. The underlying wave interaction is analyzed by the transfer matrix method, and validated by the numerical simulation. With identical tubes, a particular situation is observed that the periodic distance and the tube length are "matched," leading to a strong coupling effect by Bragg reflection and tube resonance, resulting in a wide stopband in low frequency. Even when the tubes in the array are not identical, the Bragg reflection can still work to broaden the stopband which was originally contributed by tube resonances.

Acoustic attenuation performance through a constricted duct improved by an annular resonator

Acoustic attenuation performance through a constricted duct is greatly improved by an annular resonator. A method based on the Green's function for a semi-infinite circular duct is proposed to calculate the transmission loss, where the velocity distributions are assumed to be uniform at the constriction inlet/outlets and at the inlet to the annular resonator. From an analogous acoustical circuit, the effect of higher order evanescent modes on the quarter-wave resonance is described by an extra length. The improved acoustic attenuation performance is also confirmed by an experiment.