多腔體消音器之聲學性能設計與分析

Design and Analysis of Acoustic Performance of Multi-chamber Muffler

林迺凱(Nai-Kai Lin)

指導教授 ： 王昭男

國立臺灣大學/工學院/工程科學及海洋工程學研究所/碩士(2022年)

https://doi.org/10.6342/NTU202200145

摘要

本研究著重於多腔體消音器之小型船消音器（Alpha）、大型船艦消音器（Bata、Gamma）聲學性能設計與分析。首先，利用相關文獻來驗證本文之傳輸矩陣法與有限元素法所計算的傳輸損失之正確性，並進行聲學性能的定性、定量分析，接著，將傳輸矩陣法用於Alpha消音器的初步變更設計，並使用有限元素法相互比較；而最佳化是利用Nelder-Mead Method，結合有限元素法迭代至最佳相對公差，並求出Beta消音器優化後的尺寸與傳輸損失。
利用傳輸矩陣法進行的Alpha消音器初步變更設計時，當計算頻率接近非平面波之激發頻率，或接近Karal Factor可修正頻率之上限時，傳輸矩陣法就會失去準確度。因此，膨脹管直徑很大的消音器，傳輸矩陣法可用頻率會受限於很低的頻率範圍。
Beta消音器之優化設計，是先將腔體體積縮小至原始設計腔體體積的72.9%後，並期望在分析內的所有頻率皆呈現較為均勻的傳輸損失。以全頻段優化結果來說，Beta消音器之前、後消音器的傳輸損失在頻率140赫茲以上皆至少有10分貝效果。不過，在低頻段（50赫茲到180赫茲）與高頻段（900赫茲到2850赫茲）之傳輸損失，與頻率在180赫茲到900赫茲（中頻段）相比，仍有待提升。因此，如果僅優化低頻段與高頻段之頻率，其傳輸損失的優化結果在頻率高於90赫茲時皆優於全頻段優化設計，且在頻率高於180赫茲以上時，也皆優於Gamma消音器。
最後，低頻、高頻段之優化，驗證了中頻段的頻率較容易透過不同的優化方式，而保持相對優異的傳輸損失，因此將來進行優化設計時，僅需要針對低頻、高頻段之頻率，來進行目標函數的計算，不僅可以節省許多計算成本，也可以得到相對於全頻段優化的優異成果。

關鍵字

傳輸矩陣法 ； 有限元素法 ； 消音器設計 ； Nelder-Mead方法 ； 最佳化設計

並列摘要

This research focuses on design and analysis of acoustic performance of small ship muffler (Alpha) and large ship muffler (Beta, Gamma) which are multi-chamber muffler. First, use related paper to verify correctness of Transmission Loss (TL) calculated by Transfer Matrix Method (TMM) and Finite Element Method (FEM) in this article, and conduct qualitative and quantitative analysis of acoustic performance. Next, TMM is used to design the initial alteration of Alpha muffler, and FEM is used to compare with each other. The optimization used Nelder-Mead Method, combined with FEM to iterate to the best relative tolerance, and found optimized size and TL of Beta muffler.
When using TMM to design the initial alteration of Alpha muffler, if the frequency is close to the excitation frequency of the non-plane wave or the upper limit of the Karal Factor correction, TMM will lose its accuracy. Therefore, TMM can only be used at very low frequency if mufflers have a large diameter.
The optimized design of Beta muffler is reducing its cavity volume to 72.9% of the original cavity volume, and presenting a relatively uniform TL at all frequency within the analysis. In terms of full-bands optimization results, the front and back muffler have at least 10 dB of TL above 140 Hz. However, TL between low frequency bands (50Hz to 180Hz) and high frequency bands (900 Hz to 2850 Hz) still need to be improved compared with frequency at 180 Hz to 900 Hz (middle frequency bands). Therefore, if only optimize TL of the low frequency bands and the high frequency bands, the results of optimization are better than full-bands optimization when frequency is higher than 90 Hz, and it is also better than the Gamma muffler when frequency is higher than 180 Hz.
Finally, the optimization of low frequency bands and high frequency bands verify that it is easier to maintain relatively excellent TL through different optimization methods in middle frequency bands. In the future, when optimization design is carried out, the calculations of objective function only need to be performed for the frequencies of the low and high bands, which can not only save lots of calculation costs, but also obtain excellent results compared to full-bands optimization.

並列關鍵字

Transfer Matrix Method ； Finite Element Method ； Muffler Design ； Nelder-Mead Method ； Design optimization

參考文獻

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