由於引擎的作動行程依序為進氣、壓縮、點火爆炸、排氣，因此連接著引擎的排氣管其內部的氣流具有許多脈衝波，並為高溫的振盪流體。脈衝波的移動速度相當快但是振盪流體與熱傳的過程相當緩慢。本文以數值方法研究考慮熱傳效應與壁摩擦效應的震盪流體。為了快速且準確的計算震盪流體，運用複合時間尺度的方法求解質量守恆式、動量守恆式與能量守恆式。固定引擎轉速下，不加入脈衝波並且考慮熱散逸的穩態排氣氣流，採用其中一種時間無因次變數。此種計算的穩態流場歸類為基本流場包含溫度、流速等。利用計算之後的基本流場，於管口加入爆震波，此時排氣管內非穩態的振盪流體則採用另一種時間無因次變數。

　　在數值模擬方面，高階解子建立在五階基本加權不振盪法(5th-order WENO scheme)與四階Runge-Kutta時間積分之上，求解尤拉方程式(Euler equations)，並且考慮排氣管截面積的變化、摩擦效應以及熱傳效應。我們發現比較計算的結果與實驗數據，在某些確認點上有良好的結果。此外利用管長以及入口平均流速作時間無因次化，可以快速且準確的計算基本流場；以管長和入口平均聲速作時間無因次化，可以有效率地預期非穩態流之流場。

　　Due to the process of fuel ignition and explosion inside a vehicle’s engine, the flow inside the exhaust pipe that connects with the engine is a pulsating high- temperature flow with impulsive waves. The impulsive waves move fast, but the pulsating flow and the process of heat transfer are slow. In this study we numerically investigate the pulsating flow with the effects of heat transfer and wall friction. In order to fast and accurately calculate the pulsating flow, a combined time-scaling method is employed for solving the governing equations of the mass, momentum and energy conservations. A steady exhaust-gas flow under the condition of heat loss without impulsive waves at a fixed engine speed is computed by one dimensionless time variable. The computed steady flow is referred as a basic flow with the temperature and flow velocity information. With the computed basic flow, an unsteady pulsating flow inside the exhaust pipe with an imposed blast wave at the pipe inlet is computed by using another dimensionless time variable.
　　
　　The high-resolution solver is established by using 5th-order WENO scheme and 4th-order Runge-Kutta method for solving the Euler equations with the source terms of the variation of pipe’s cross-sectional area and the effects of wall friction and heat transfer. We found that the computed results at different engine speeds are compared well with the experimental data at some checking points. Moreover, the time variable normalized by the ratio of the pipe length to the time-average inlet flow velocity is appropriate for fast and accurately acquiring the basic flow, and the time variable normalized by the ratio of the pipe length to the time-average inlet sound speed for efficiently predicting the unsteady flow.

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