以直接模擬蒙地卡羅法模擬微流道之氣體流場與熱傳特性分析探討

The Investigation of Fluid Dynamics and Heat Transfer of Micro-channel Flows using DSMC Simulation

潘穎哲(Ying-Jhe Pan)

指導教授 ： 洪祖昌

淡江大學/工學院/機械與機電工程學系碩士班/碩士(2009年)

https://doi.org/10.6846/TKU.2009.00769

摘要

近年來由於工業的發展及半導體工業的成熟，相關領域的產品與物件都具有低成本、高精確度與運作快速等特性。微機電系統(Micro-Electro-Mechanical Systems, MEMS)的尺寸都與分子平均自由徑同等級甚至更小。在稀薄度氣體流場得分析中數值模型須考慮分子觀點。直接模擬蒙地卡羅(Direct simulation Monte Carlo, DSMC)法是目前被認為較精確且使用最廣泛的方法。
本文以DSMC法分析在微機電系統中十分重要的幾何微管。首先利用DSMC法模擬一簡單二維矩形微管，將其結果與Navier-Stokes方程搭配滑移(Slip)邊界條件的分析之結果做比較，以探討氣體稀薄(Rarefaction)效應對流場性質所造成之影響。當流場稀薄度較高時，可觀察到DSMC模擬結果與Navier-Stokes方程的解有明顯的差異，故在分析稀薄度較高之流場時，應使用DSMC法會有較準確之結果。
為減少計算時間與記憶體，常會以二維模擬做為代表。在實際工程應用中應以三維分析作為研發參考，故本文探討三維以及二維之矩形維管、微結構管與背向式階梯管流場，比較二維與三維結果，由比較結果可知寬高比大於五時，其流場性質趨近二維結果比率有98％，當寬高比小於五時，三維流場與熱傳性質會與二維結果產生較大差距，故在近壁面流場或寬高比小於5之三維流場模擬會偏離二維結果。

關鍵字

直接模擬蒙地卡羅法 ； 微機電系統 ； 微管

並列摘要

Due to the development and maturation of the semiconductor industry in recent year, the products of related fields are low-cost, high-accurate and high-speed. The characteristic size of Micro-Electro-Mechanical Systems (MEMS) is in the same order as or even smaller than the mean free path (MFP) of gas molecules. In rarefied-gas flow, a mathematical model, which bases on the molecular point of view, has to be considered in the predictions of flow dynamics. The direct simulation Monte Carlo (DSMC) method is a popular and accurate simulation technique for rarefied-gas flows.
In this thesis, the DSMC method was applied to analyze microchannels which are the most important elements of MEMS. At first, we simulate a 2-D straight rectangular cross-section microchannel using the DSMC method. To study the influence of rarefaction effects on the flow properties, the DSMC results are compared with the numerical solutions of Navier-Stokes equations with slip boundary conditions. The discrepancy between the DSMC results and the Navier-Stokes solutions becomes more obvious when the degree of rarefaction increases. The results show that we must use the DSMC method in rarefied-gas flows to get more accurate results.
In order to reduce the computation time and memory requirement, the 2-D simplification of a 3-D flow problem is often used in the DSMC simulation. In practical engineering applications, this simplification, however, is inappropriate as the cross-section aspect ratio of the 3-D structure decreases. We simulated the 3-D straight rectangular cross-section microchannels, the 3-D microchannels with microstructures and the 3-D microchannels with backward-facing steps. The results of the 3-D structures are compared with those of 2-D simplifications. It is found that the approaching level of the 3-D results to those of the 2-D simplification is over 98 % when the cross-section aspect ratio is greater than 5. When the cross aspect ratio is less than 5, the influence of 3-D effect can no longer be ignored and it is necessary to use a full 3-D simulation in the analysis of microchannel flows.

並列關鍵字

DSMC ； MEMS ； microchannel

參考文獻

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