On low frequency sound transmission loss of double sidebranches: a comparison between theory and experiment

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.

Data assimilation of flow-acoustic resonance

A data assimilation (DA) strategy was developed for accurate prediction of the flow-acoustic resonant fields within a channel-branch system. The challenges of numerical simulation of such internal aeroacoustic systems are primarily associated with determination of the transfer loss between the acoustic waves and the shear layer vortices. Thus, a data-assimilated momentum loss model that comprises a viscous loss item and an inertial loss item was established and embedded into the Navier-Stokes equations. During the DA, the acoustic pressure pulsations measured from a dynamic pressure array served as the observational data, the ensemble Kalman filter served as the optimization algorithm, and a three-dimensional transient computational fluid dynamics method comprising an explicit algebraic Reynolds stress model (EARSM) served as the predictive model system. EARSM was used because its ability to predict internal flow-acoustic resonances was superior to that of other eddy viscosity models and Reynolds stress models. The data-assimilated flow-acoustic resonant fields were then comprehensively validated in terms of their acoustic fields, time-averaged flow fields, and phase-dependent flow fields. The time-averaged flow fields were obtained from planar particle-image velocimetry (PIV) measurements, and the phase-dependent flow fields were obtained from field programmable gate array-based phase-locking PIV measurements. The results demonstrate that the use of DA afforded an optimal simulation that efficiently decreased the numerical errors in the frequencies and amplitudes of the acoustic pressure pulsations, thereby achieving better agreement between time-averaged flow distributions and fluctuations. In addition, the data-assimilated numerical simulation completely reproduced the spatiotemporal evolution of the shear layer vortices, that is, their formation, developing, transport, and collapsing regions.

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 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.

On sound transmission loss across a Helmholtz resonator in a low Mach number flow duct

A simplified physical model, which described the generation of sound by a Helmholtz resonator upon flow excitation at its neck, was developed in the present investigation to study the drop in sound power transmission loss across such a resonator mounted on the wall of a duct conveying a low Mach number mean flow. Experiments were derived to validate the model. Mitigation methods derived according to the model were also tested experimentally. Results showed that the simplified model gave predictions which agreed with experimental observations. The proposed mitigation methods were also proved to be effective for building services application. It was also found that the sound intensity generated by the flow excited resonator scaled with approximately the ninth power of the flow velocity inside the duct.

Transmission characteristics of a tee-junction in a rectangular duct at higher-order modes

Numerical and experimental studies were undertaken to characterize the noise transmission and scattering properties in higher-order modes across the tee-junction of a rectangular duct used in ventilation and air-conditioning systems. To measure these properties, a formulation of a transmission matrix based on the transfer function and a two-microphone method was devised. The measurement of modal sound transmission and scattering coefficients is demonstrated for a duct element in a rectangular duct. The results of numerical simulations were verified by experiments. The results show that sound transmissions of fundamental mode and higher-order modes across the main duct are high at the eigen-frequencies of the main duct and sidebranch. Weak modal coupling of the branch-modes and the traveling wave in the main duct is observed at or very close to the eigen-frequencies of the sidebranch, which shifts excitation of the higher-order branch-modes at higher frequencies. A decrease in sound transmission and increase in sound scattering into higher-order modes occur with excitation of the axial branch-mode. Excitation of the longitudinal branch-mode due to branch-end reflection also results in lower sound transmission of higher-order modes across the junction along the main duct.

On sound propagation from a slanted side branch into an infinitely long rectangular duct

The transmission of sound from a slanted side branch into an infinitely long rectangular duct is studied numerically using the method of finite element with absorptive domain exit boundaries. The sound transmission coefficients associated with various acoustic modes are investigated in details. The results show that the plane wave assumption is only valid at very low frequency. It is also found that the intensities of the higher modes are stronger than that of the plane wave once they are excited. Besides, a critical side-branch slant angle is found over which a significant change of sound propagation mode takes place. This affects substantially the energy distribution between various acoustic modes inside the main duct. A simplified model is proposed to explain the phenomenon and the relationship of this critical angle with the width ratio between the side branch and the main duct is established.

Sound transmission characteristics of Tee-junctions and the associated length corrections

The sound transmission characteristics of a Tee-junction formed by a sidebranch and an infinitely long duct are investigated numerically using the finite element method. The associated corrections of the branch length and the upstream duct length are also discussed in detail. The types of branch resonance that result in strong or weak sound transmission across the junction are determined and their effects on the length corrections examined. Results suggest that the type of sidebranch, the branch width, the branch length, and the order and the form of the resonance affect more significantly the length corrections of the duct section. The excitation of nonplanar higher branch modes gives rise to rapid increase in the duct length corrections and also results in lower sound transmission.