以直接模擬蒙地卡羅法計算三維微管流場與熱傳特性探討

The Investigation of Fluid dynamics and Heat Transfer Characteristics of 3-D Micro-channel Flows Via DSMC Simulation

林雅茹(Lin Ya-Ju)

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(2007年)

https://doi.org/10.6846/TKU.2007.00704

摘要

本文以直接模擬蒙地卡羅法(Direct Simulation Monte Carlo Method)[1]來模擬三維矩形微管之低流速流場，並改變管口徑大小與比例來探討流場內部的各種熱傳現象，和矩形空管內管角於兩壁作用下的活動情形，而這是在二維模擬場是無法看的結果，也是三維模擬方管存在的價值所在，更趨近於真實。其次是探討微流場內摩擦係數( Cf )、Poiseuille number ( Cf*Re )於管角和管壁面的比較；另外，取Nusselt numbe來探討不同溫度、壓力之熱傳現象。本文所使用的工作流體為氮氣(N2)，分子模型則採用VHS分子模型。
模擬之結果發現，管角於兩壁作用下的活動情形與流體在管壁邊有所差異，對於管角所受的影響還是依然明顯而不同於二維微流場，即使加大寬高比為5倍也是如此；並發現到當流場越稀薄(Kn越大)時，摩擦係數( Cf )會越大，並且在同口徑之微流場(同Kn時)，管長1 的Cf因為分子單位長度所受到壓縮效應的關係會越大；而Poiseuille number則是隨著Kn的增加而降低。由微流場內部來看，其Poiseuille number於流場內跳動幅度會隨著Kn上升由3降到0.04而趨近於穩定；對於改變溫度時，摩擦係數( Cf )、Poiseuille number ( Cf*Re )是隨溫度的升高( 273K~373K )而降低。Nusselt numbe 從22下降到只有0.035，是隨著溫度的升高( 273K~373K )與壓力的下降( 2.5 atm~0.1atm )所導致的。

關鍵字

直接模擬蒙地卡羅法 ； 紐森數 ； 微流場

並列摘要

The Direct Simulation Monte Carlo (DSMC) [1] method is employed to analyze the low-speed fluid dynamics characteristics of a three-dimensional (3-D) microstructure and its heat transfer activities with different diameters and ratios. The 3-D simulation is valuable and more authentic than the 2-D simulation, because the observations of the corner and center of the wall inside the microchannel cannot be made in the 2-D simulation. In addition, The Fanning friction coefficient and Poisseuille number to the corner and the center of the wall in the fluid are compared. Also, Nusselt number is utilized to discuss the heat transfer with different temperature and pressure. The VHS model and nitrogen have been applied to the experiment.
The result showed that the fluid flow to the corner of the wall inside the microchannel was different from the fluid flow to the center of the wall. The influence of fluid flow by the corner of the wall inside the microchannel in 3-D simulation was still different from 2-D simulation. The same result was observed when increasing the width-to-height ratio to five-fold. Furthermore, as the Knudsen number increased in the fluid flow, the friction coefficient (Cf) increased. At the same caliber of microchannel, Cf in the 1 microchannel had risen because of the molecular length per unit received greater pressure from compression. In contrast, the Poissruille number decreased as the Kn number increased. According to the inside of the microchannel, the amplitude of Poiseuille number in fluid flow with arising Kn decreased from 3 to 0.04, and then Poiseuille number became stable. When the temperature increased (273K – 373K), friction coefficient ( Cf ) and Poiseuille number ( Cf*Re ) decreased. Nusselt number decreased from 22 to 0.035 was the result of the increase in temperature (273K – 373K) and decrease in pressure (0.1atm – 0.1atm).

並列關鍵字

DSMC ； MEMS ； Microstructure

參考文獻

[31] 黃盈翔，” 以直接模擬蒙地卡羅法計算三維背向式階梯微流場”， 淡江大學機械與機電工程學系碩士班，台北，2006。

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[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.