本文研究的重點，著重於在車輛排氣管尾端所引發出來的流場與噪音分析，汽機車排氣管所排放的廢氣是一種具有脈衝式爆炸波的流體，它是非穩態及非線性的，不易以傳統的線性聲學理論來預測的。此脈衝式的流體流過排氣管出口之後會有一系列複雜的震波繞射現象發生，例如：繞射震波、渦漩的和膨脹波反射等現象。我們藉由高階的軸對稱尤拉與那維亞史託克解子，求解這些由震波與渦漩交互作用所引發出來的複雜的現象。為了節省計算的時間，我們在高階解子內加入了平行運算的技術。在數值方法上，使用由Jiang and Shu兩人所提出的五階準確度的加權基本不震盪法做為空間差分的方法，在時間的積分上則是採用四階準確度的 Runge-Kutta 方法。
為了有效降低在排氣管口處由震波與渦漩交互作用所產生的噪音，我們設計了一個尾部平滑彎曲且漸擴的排氣管來代替傳統的直管排氣管。在文章中，詳細地研究排氣管下游的流場與聲場，並分析其噪音等級。當排氣管流場達到假穩態時，發現聲波會朝著某些主要的方向傳遞。在直管的例子中，最主要的聲波是朝著六十度角方向傳遞；在曲管的例子中，最主要的聲波是朝著零度角方向傳遞。
為了去估算脈衝式流體對排氣管流場和噪音的影響，我們在排氣管的入口處設置一週期性的入口邊界條件，這週期性的派衝波是經由實驗量測所獲得的，所量測的是三陽如意125機車，在測量時車子引擎的轉速是固定在每分鐘五千轉，車身是靜止不動。數值模擬的結果顯示，這週期性的入口脈衝波對於排氣管下游的流場及聲場有很大的影響，這些影響包括渦漩環的大小、渦漩中心的渦量值以及噪音量的等級。此外，為了考慮人耳對於聲音的響應頻率，A加權的噪音等級方法是被應用在分析噪音等級上。最後，對實驗量測的聲壓等級數據和數值模擬的聲壓等級值做比較。結果顯示，在直管例子中最大A加權的噪音等級誤差是0.8dBA；在曲管例子中最大A加權的噪音等級誤差是1.4dBA。再對最小噪音標準值做比較，結果顯示，在直管例子中最小A加權的噪音等級誤差是1.7dBA；在曲管例子中最小A加權的噪音等級誤差是0.9dBA。結果證實尾部彎曲且漸擴外形的排氣管確實達到縮小排氣管下游噪音範圍。

The present study focuses on the noise problem associated with a vehicle’s exhaust pipe. A pulsated flow with weak pulsating blast waves from a vehicle engine is discharged out of the vehicle’s exhaust pipe. The discharged pulsated flow and the induced shock/vortex interactions that result in radiated noise are numerically investigated by the axi-symmetric Euler/Navier-Stokes solver with the parallel computational technology. The numerical method used is a fifth-order weighted essentially non-oscillation scheme of Jiang and Shu for spatial discretization and a fourth-order non-TVD Runge-Kutta method for time integration.
In order to effectively reduce the radiated noise due to shock/vortex interactions near the pipe exit, the pipe shape near the exit is redesigned by using a smoothed curved, expanding shape near the pipe exit, instead of the traditional straight shape. The detailed flow field downstream of the pipe and its sound pressure level are studied. When the flow field has become a quasi-steady state, the major propagation direction of sound wave for the straight-pipe case is found in the 60° direction, which is different from the 0° direction for the curved-pipe case. Moreover, noise produced by the straight- and curved-shape pipe with periodic pulsating blast waves are analyzed and compared. The periodic pulsating wave is obtained by fitting the measured pressure data from a motorcycle exhaust pipe at an engine speed of 5000rpm at an idle condition. It is found that the periodic pulsating waves can greatly influence the downstream flow and sound fields such as the vortex–ring size, vortex-center vorticity and sound pressure level (SPL). In consideration of the frequency response of the human ear, the A-scale SPL method is applied to analyze sound pressure level. Experimental and simulated sound pressure levels are computed and compared. The results of sound pressure levels for experiment and simulation show that their absolute error in the maximum A-weighting SPL is 0.8dBA for the curved-pipe case and 1.4dBA for the straight-pipe case. Moreover, their absolute error in the minimum A-weighting SPL is 1.7dBA for the curved-pipe case and 0.9dBA for the straight-pipe case. It is proved that the partially curved, expanding pipe can reduce the noise region downstream of the pipe.

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