Jade, Nagaraja and B, Venkatesham
(2018)
Vibro-Acoustic behaviour of Flexible Rectangular Ducts.
PhD thesis, Indian institute of technology Hyderabad.
Abstract
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 subsystems. Modal radiation efficiencies of a rectangular duct are estimated and compared to those of simple rectangular plate. This comparison shows a similarity between duct sound radiation behaviours in terms of plate modes. The analytical model results are validated using Finite Element-Boundary Element Method (FEM-BEM) numerical results. As a part of the study, sound radiation behaviour of a duct is studied to understand its equivalence with monopole and dipole sources. As second step, an experimental setup is developed to measure the breakout noise in terms of Transverse Transmission Loss (TTL) and radiation efficiency, by providing a plane-wave excitation. A methodology is developed to calculate input sound power from measured pressure signals inside the cylindrical tube using an autospectrum of a progressive wave. Radiated sound power is measured using two different methods, namely- intensity probe method (P-P method) and Microflown technique (P-U method). Using the measured input and radiated sound power, TTL and radiation efficiency are calculated. These results have been corroborated with analytical results of ‘equivalent plate model’ and FEM-BEM numerical results.
Second part of the current study is to understand the effect of duct joints on modal parameters. In this study, three different rectangular ducts with two types of joints
(welded and adhesive joints) are considered. Pre-test analysis is performed to know the number of measuring points and their locations. Then, Experimental Modal Analysis (EMA) is performed on these three ducts to identify natural frequencies and mode shapes. These EMA (measured) results are compared to Numerical Modal Analysis (NMA) results (predicted). It has been observed from all cases that natural frequencies are in good agreement. Mode shapes of measured and predicted results are compared in terms of Modal Assurance Criteria (MAC) plot, mode pair table and visual inspection. Low MAC values are observed for the duct with welded joints. However, a duct with an adhesive joint similar to the ideal shape has good MAC value. Detailed section analysis is performed on a duct with a two-welded joint configuration to understand mode shape deviation. It is observed from experimental and numerical results that joints play a critical role in deviation of mode shapes for thin flexible structures. Hence, as next part of the study, an analytical model is developed to incorporate joint effects in estimating the modal parameters. Here, the joint condition is represented using linear and rotational spring’s stiffness. Natural frequencies and mode shapes of a rectangular duct are found analytically by Rayleigh-Ritz method using an ‘equivalent plate model’. These results are validated with experimental results for a rectangular duct with Pittsburgh lock joint. Natural frequencies of the duct in both cases are in good agreement. Mode shapes of symmetric modes remained same for both ducts, whereas antisymmetric modes deviated from each other. This deviation is observed only in duct walls next to the joint.
Third part of the study focuses on sound source reconstruction using two inverse techniques such as Inverse Numerical Acoustics (INA) and Near-field Acoustic Holography (NAH) methods. Here, INA is used to reconstruct the vibration velocity on a flexible duct surface in structural-acoustic coupled system. Effect of measurement locations, measurement points and mesh density on reconstruction results is discussed at both coupled and uncoupled frequencies. L-curve regularization parameter selection method is used to overcome the ill-posed problem. It is verified from reconstruction results that vibration velocity can be obtained accurately with less than 10% error.
Four different NAH techniques are used in the present investigation to identify distribution of fan noise source strength and radiation pattern. Firstly, number of reference microphones needed to find the incoherent sources by Singular Value Decomposition (SVD) is evaluated. Later, sound source is reconstructed with measured sound pressure using different NAH techniques. The reconstructed results showed that ESM method is best to reconstruct fan noise sources with minimal error. The behaviour of a fan at blade passing frequency (BPF) is akin to a dipole sound source. A comparison of reconstructed pressures with measured values indicates that reconstructed pressure correlates very well with measured pressure. As part of study, ESM is used to reconstruct sound source at uncoupled and coupled frequencies for a rectangular box with a single compliant wall. Sound pressure data for reconstruction is generated from numerical simulations instead of actual measurements. Reconstructed results are compared to actual results at both frequencies. Effect of noise on accuracy of the reconstruction is studied for different signal to noise ratio (SNR) values. Higher SNR values led to good accuracy in reconstruction. Based on the regularization studies, it can be concluded that L-curve method is better compared to GCV method for reconstruction at uncoupled and coupled frequencies.
Finally, from the present research work it is concluded that vibro-acoustic behaviour of the flexible rectangular ducts is studied effectively using direct (sound intensity method, Microflown technique) and inverse techniques (INA and NAH).
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