直接模擬蒙地卡羅法於高低速流場之模擬

Monte Carlo Simulations of High and Low-Speed Rarefied Gas Flows

鄭朝恩(Chaw-En Zhen)

指導教授 ： 楊建裕

國立中央大學/工學院/機械工程學系/博士(2007年)

摘要

本文以直接模擬蒙地卡羅法計算並分析極音速稀薄氣體中平行混合流之動量以及熱量傳輸現象。另外本文亦針對三維低流速微矩形管來探討以二維模擬取代三維模擬之合理性。
本文計算極音速稀薄氣體中平行混合流之速度、壓力、溫度、密度之流場性質，亦計算混合層中各階速度脈動相關函數、速度與溫度脈動相關函數 和 、機率密度函數f(u'')、f(v'') 、 f(t'')以及聯合機率密度函數f(u'',v'') 、f(u'',t'') 和f(v'',t'') 以對稀薄氣體混合層之內在結構、動量、熱量傳輸有所了解。本文首先觀察其流場特性以及兩自由流分別為不同速度比0.3、0.45以及0.6時自由剪力流混合結構之差異，發現極音速稀薄氣體中平行混合流之流場結構與高速連性紊流混合層類似。接著以機率密度函數f(u'')、f(v'') 、 f(t'')及聯合機率密度函數f(u'',v'') 、f(u'',t'') 和f(v'',t'') 之分佈來解釋和了解其所相對應之各階速度脈動相關函數以及速度與溫度脈動相關函數的統計內涵。
本文亦以直接蒙地卡羅法搭配隱性邊界處理來模擬三維低流速微矩形管，並改變矩形管口徑寬高比為1、1.5、3和5來探討三維矩形管模擬加大口徑寬高比以漸近二維模擬之情形。在三維矩形管口徑寬高比為1、1.5、3和5之算例與二維模擬結果之比較中，發現當矩形管口徑寬高比小於3時，兩側管璧對於流場性質以及熱傳現象有很大的影響。但是當矩形管口徑寬高比越大時，則其模擬結果與二維模擬結果越相近，且當矩形管口徑寬高比大於5時，以二維模擬來取代三維模擬則可視為合理的。

關鍵字

機率密度函數 ； 脈動相關函數 ； 自由剪力層 ； 直接模擬蒙地卡羅法

並列摘要

The Direct Simulation Monte Carlo (DSMC) method has been employed to analyze the transport phenomena in a 2-D rarefied free shear layer at hypersonic speed and the rationality of the 2-D simplification for a 3-D low-speed rectangular cross-sectional microchannel.
The mixing properties of various fluctuation correlations are investigated in the present thesis for a rarefied gas free shear layer at hypersonic speed. The Reynolds average process is assumed when obtaining the correlation functions. Results show that the flow field structure was very similar to that of continuum flow ones at high Reynolds numbers. The higher order correlations are discussed to manifest that the statistical characteristics of these correlations can be realized via its corresponding pdfs, f(u’), f(v’), and jpdf, f(u’,v’), in velocity space. The heat transfer due to momentum and temperature fluctuation correlations, and , are calculated and try to discern its statistical characteristics via the revealed corresponding pdf, f(t’), and jpdfs, f(u’,t’), f(v’,t’), in velocity and temperature space. The calculated distributions of those correlation functions behave as momentum and heat transfer phenomena in the rarefied free shear layer which play a similar role as the turbulent transport in the continuum flow ones.
The Direct Simulation Monte Carlo (DSMC) method has also been employed to analyze the rationality of the 2-D simplification for a 3-D straight rectangular cross-sectional microchannel. An implicit treatment for low-speed inflow and outflow boundaries of the DSMC method for the microchannel flow is employed. The 3-D microchannel flows are simulated with cross aspect ratios in the range of 1 and 5. The calculated flow properties in the 3-D cases are compared with the results of the 2-D case. They show that when the aspect ratio < 3, the two extra side walls in the 3-D case have significant effects on the heat transfer and flow properties. When the aspect ratio is increased, the flow pattern and heat transfer characteristics tend to approach those of 2-D results. The 2-D simplification is found to be reasonable only when the cross aspect ratio is greater than 5.

並列關鍵字

Fluctuation correlation function ； DSMC ； Free shear layer ； Microchannel flow ； Pdf

參考文獻

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