Prediction of Breakout Noise from a Rectangular Duct using SEA and Deterministic methods

Madhuranthakam, Yoganandh and B, Venkatesham (2018) Prediction of Breakout Noise from a Rectangular Duct using SEA and Deterministic methods. Masters thesis, Indian Institute of Technology Hyderabad.

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Abstract

Sound radiated in the transverse direction due to exural vibration of the duct walls excited by the internal sound �eld is called the breakout noise. Breakout noise is predominant in the exible rectangular ducts compared to other shapes due to lower stiffness. The prediction of sound radiated from the duct walls helps to understand the breakout noise phenomena. The modal density of large ducts is higher when compared to small ducts. In this paper, Statistical Energy Analysis(SEA) is used to predict breakout noise from a rectangular HVAC duct. Deterministic methods like Finite Element Method(FEM), Boundary Element Method(BEM), Wave based methods, etc., can predict the breakout noise. However, these methods have limitations to handle the systems with high modal density because of their long computational time and excessive memory requirement. On the other hand, SEA is an impressive technique to solve those systems. For this work, the selected duct is divided into six subsystems which are four duct walls, internal air cavity, external airspace. The power ow analysis is performed on all the subsystems to calculate Transverse Transmission loss of the unlined duct and the Insertion loss of lagging of the lagged duct. For the lagged duct all the duct walls are treated outside with acoustic material. Theoretical methods are developed to implement Statistical Energy Analysis on the unlined and the lagged rectangular ducts. All the parameters essential for the analysis are discussed in this paper. Transverse Transmission loss values are val- idated with ASHRAE data and Insertion loss values with literature. The results obtained are in good agreement. In literature, various deterministic analytical models are available to predict sound radiation from the rectangular duct such as �nite-length line source, equivalent cylindrical and an equivalent plate model (EPM). In EPM, modal radiation efficiencies and total radiation efficiency of the duct is cal- culated by assuming it as an equivalent rectangular plate. The length and breadth of the plate are represented by the length of the duct and perimeter of the cross-section of the duct. In the present research work, transmission loss (TL) of the rectangular duct is predicted by using total radiation efficiency calculated by equivalent plate model. TL of the rectangular duct is also calculated with modal radiation efficiency of the breathing mode (Dominant Mode). The values obtained from both the results are compared with the TL predicted from the �nite-length source model, and all the three models are in good agreement. However, the prediction of total radiation efficiency and modal radiation efficiency of the duct in equivalent plate model (EPM) involves solving complex mathe- matical equations. Hence, a simpli�ed model is proposed to predict the total radiation efficiency of the duct by using the modal radiation efficiency of simple plate mode. The major contributing mode for the sound radiation in the duct is the breathing mode, i.e., dominant symmetric mode on the four walls. This mode is equivalent to the (4,1) mode of the simple plate. The modal radiation efficiency of simple plate mode (4,1) is used for the TL calculations. From the comparison study, it is observed that below the cut-on frequency the predicted results from the proposed model are in reasonable agreement with the exact model.

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