Breakout Noise From The Coupled Acoustic-Structural HVAC Systems
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Noise control in the heating, ventilation and air-conditioning (HVAC) systems is one of the critical design parameters in measuring the occupant comfort. The noise generated by air-handling units propagates through the ducts in the axial as well as transverse direction. Noise radiated in the transverse direction from the duct walls excited by the internal sound field is called the breakout noise. An analytical formulation has been developed in this thesis in order to predict the breakout noise by incorporating three-dimensional effects along with the acoustical and structural wave coupling phenomena. The first step in the breakout noise prediction is to calculate the interior acoustic response and flexural vibration displacement of the compliant walls. Dynamic interaction between the internal acoustic subsystem and flexible structural subsystem has been expressed in terms of the modal characteristics of the uncoupled response of the acoustic and structural sub-systems. Solutions of the inhomogeneous wave equation are rearranged in terms of impedance and mobility, and the equations describing the complete system are expressed in terms of matrices, which result in a compact matrix formulation. Examples of the formulation are a rectangular cavity with one flexible wall and a rectangular cavity with four-flexible walls. The formulation is modified to incorporate complex boundary conditions by means of appropriate Green’s functions. It is implemented for flexible wall duct using the modified cavity Green’s function. Another objective of the present investigation is to understand the coupling phenomenon and its effect on the compliant wall vibration displacement. The developed three-dimensional analytical analysis of the breakout noise is convenient to implement on the computer, and also to extend the sub-system level model to the system level model in order to analyze a complex acoustic-structural system for the breakout noise problem. The extent of coupling is calculated using a transfer factor based on the uncoupled natural frequencies of the acoustic and structural subsystems. It is observed from the free vibration analysis that a coupling between the cavity and the flexible panel exists in the vicinity of an uncoupled acoustic natural frequency. If a strong coupling occurs between an acoustic mode and a panel mode, then damping of structural subsystem would control it. The cavity volume changes stiffness of the panel, which in turn affects noise radiation in the stiffness-controlled region. The second step is to calculate the sound power radiated from complaint wall. The wall vibration velocity is a linear combination of the uncoupled flexural modes of the structural subsystem. It is substituted into the Rayleigh integral and Kirchhoff– Helmholtz (KH) integral formulation to predict the sound pressure radiated by the vibrating duct wall. The radiated sound power can be obtained by integrating the acoustic intensity over the surface of the flexible duct wall making use of appropriate expressions for radiation impedance. The radiation impedance terms involve a quadruple integral. Evaluation of this integral is quite complex and poses formidable computational challenges. These have been overcome by means of a co-ordinate transformation. Sound power radiation from flexible walls of the plenum and duct walls has been calculated using an equivalent plate model. Analytical results are corroborated with numerical models. The second part of thesis deals with a one-dimensional model to predict the breakout noise from a thin rectangular duct with different end conditions like anechoic termination, rigid-end termination, and the open-end termination. This model incorporates acoustic reflection effects in the duct internal sound field by using standing wave pattern by means of the transfer matrix approach. A one-dimensional prediction method based on the four-pole parameters has been developed to evaluate the lagged duct performance in terms of the breakout noise reduction. Radiation impedance of a duct is calculated by three different methods: (i) finite line source model (ii) finite cylinder model, and (iii) equivalent plate model based on fundamental bending mode of the duct. It is observed that the proposed model that uses the equivalent plate model for the lagged duct and the line source model for the bare duct is appropriate to predict the transverse insertion loss of the lagging, particularly at the lower frequencies that are of primary interest for reducing the breakout noise of rectangular ducts. The bare duct breakout noise results are compared with those of the corresponding 3-D analytical models. It shows that the one-dimensional model captures the overall mean pattern of breakout noise very well. The third part of the thesis examines the internal acoustic field and thence the transmission loss (TL) of a rectangular expansion chamber, the inlet and outlet of which are situated at arbitrary locations of the chamber; i.e., the sidewall or the face of the chamber. The four-pole parameters have been expressed in terms of an appropriate Green’s function of a rectangular cavity with homogeneous boundary conditions. A transfer matrix formulation has been developed for the yielding-wall rectangular chambers by considering structural-acoustic coupling. It may be combined readily with the transfer matrices of the other constituent elements upstream and downstream in order to compute the overall transmission loss or insertion loss. Wherever applicable, parametric studies have been conducted to evolve the design guidelines for minimizing the breakout noise from the HVAC ducts, plenums and cavities.