以直接模擬蒙地卡羅法計算三維背向式階梯微流場

DSMC Simulation of 3-D backward-facing step flow at microscale

黃盈翔(Ying-Hsiang Huang)

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(2006年)

https://doi.org/10.6846/TKU.2006.00678

摘要

本文以直接模擬蒙地卡羅法(Direct Simulation Monte Carlo Method)[1]來模擬改變不同進出口壓力之二維背向式階梯微流場，用以分析不同紐森數對流場現象之影響，接著探討三維背向式階梯微流場的流場現象。本文使用質量流率相等法來修正低速背向式階梯微流場的進出口邊界條件，所模擬的工作流體為氮氣(N2)，分子模型則採用VHS分子模型。
在本文中，由不同紐森數之二維模擬結果，可以發現當流場kn=0.1時渦流現象將消失，而由流場圖中則是發現當kn值越大，也就是流場越稀薄的時候，階梯的影響將不顯著，由於流場稀薄度變大的關係導致流場內的速度梯度變大，發現流場有發散的跡象。而在三維的模擬中，三維之模擬結果與二維之模擬結果有明顯的差異；就速度分佈來看，三維流場之模擬結果比二維流場之模擬結果低了許多，大約只有二維模擬的70％，這是因為三維模擬流場之管壁效應比二維模擬流場大的結果；也由於這個原因，三維流場模擬結果中，渦流消失的流場之kn值與二維流場是不同的，三維模擬時當流場kn=0.02渦流消失。本文也模擬加大寬高比1，3和5倍，其結果顯現在三維的模擬時，寬高比小於3的時候，兩邊壁的效應對流場的影響就相當顯著，隨著寬高比的增加，此時流場性質愈趨近二維模擬時的結果，所以本文發現當管徑之寬高比大於5時，以二維流場模擬三維實例是合理的。

關鍵字

直接模擬蒙地卡羅法 ； 微機電系統 ； 微管

並列摘要

The Direct Simulation Monte Carlo (DSMC) method has been employed to analyze the rationality of the 2-D simplification for a 3-D backward-facing step flow. An mass flux treatment for low-speed inflow and outflow boundaries for the DSMC of the microchannel flow is employed. The VHS model and Nitrogen was employed in the simulation. The 3-D microchannel flows is simulated with the cross aspect ratio 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. It shows 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 increases, the flow pattern and heat transfer characteristics tend to approach that of 2-D results. The 2-D simplification is found to be reasonable only when the cross aspect ratio is larger than 5.
In this paper, the effects of rarefaction on flow characteristics are also analyzed and discussed. It is found that flow separation, recirculation, and reattachment will disappear as Knudsen number, Kn, exceeds 0.1 for 2-D case, and will disappear as Kn exceeds 0.02 for 3-D case.

並列關鍵字

DSMC ； MEMS ； Micro-channel

參考文獻

[2] Bird, G. A. “Molecular Gas Dynamics And The Direct Simulation of Gas Flows,” Oxford University Press, 1994.

[3] Bird, G. A., “Approach to Translational Equilibrium in a Rigid Sphere Gas,” Phys. Fluids Vol. 6, pp. 1518-1519, 1963.

[4] Bird, G. A., “The Velocity Distribution Function Within a Shock Wave,” Journal of Fluid Mechanics, Vol. 30, part 3, pp. 479-487, 1967.

[5] Borgnakke, C., and Larsen, P. S., “Statistical Collision Model for Monte Carlo Simulation of Polyatomic Gas Mixture,” Journal of Computational Physics, Vol. 18, No. 4, pp. 405-420, 1975.

[8] Muntz, E. P., “Rarefied gas dynamics,” Annu. Rev. Fluid Mech. 21, pp. 387-417, 1989.