三維微矩腔長寬高比對Rayleigh-Bénard對流效應的DSMC法研究

DSMC Investigation of Aspect Ratio Effect on Rayleigh-Bénard Convection in Three-Dimensional Micro Enclosures

曾培元(Pei-Yuan Tzeng) ； 周貽灣(I-Wan Chou) ； 林宗漢(Tsung-Han Lin) ； 劉中和(Chung-Ho Liu)

《航空太空及民航學刊.系列B》 44卷1期 (2012/04) Pp. 9-19

https://doi.org/10.6124/JAAA.201204_44(1).02

摘要

本研究應用直接模擬蒙地卡羅（Direct Simulation Monte Carlo, DSMC）法對不同外形長寬高比（Aspect Ratio, AR）之三維微矩腔稀薄氣體Rayleigh-Bénard（RB）自然對流流場進行模擬計算。三維RB對流較二維RB對流有更豐富的流動型態和較接近實際情況。研究重點包含應用改良型非時間計數器法提昇三維DSMC計算效率，以利加速三維計算，進而觀察並探討三維熱對流不穩定、複雜的空間流動型態及壁面邊界條件的影響等。壁面邊界條件在上下壁設定為散反射（等溫），左右壁設定為鏡反射而前後壁設定為等向性散射（Isotropic Scattering, IS）邊界條件以模擬絕熱側壁，應用於三維長方體微矩腔四種長寬高比分別為2:2:1、3:3:1、4:4:1、5:5:1之模擬，研究在固定瑞利數（Rayleigh number）Ra = 6643，而不同長寬高比對三維微矩腔稀薄氣體RB自然對流流動型態影響。研究結果顯示四種不同的長寬高比模擬案例呈現出以渦卷（Rolls）及穴渦（Cells）為主的流動型態，渦卷與穴渦的數目和形狀受到三維側壁邊界的影響並隨長寬高比的不同而改變。

關鍵字

直接模擬蒙地卡羅法 ； 絕熱壁 ； 稀薄氣體 ； Rayleigh-Bénard對流 ； 長寬高比

並列摘要

In this study, Direct Simulation Monte Carlo (DSMC) method is used for the simulation of rarefied gas Rayleigh-Bénard (RB) convection in different aspect ratio (AR) of three-dimensional (3D) micro enclosures. In 3D micro enclosures the flow patterns are potentially far richer than those in two dimensions, and where simulations are more closely related to real situations. The major concerns are the application of Modified No Time Counter (MNTC) method to improve the 3D DSMC computational efficiency, the investigation of heat convective flow instability, complex spatial flow patterns and the influences of wall boundary conditions. The newly developed isotropic scattering boundary conditions (IS-BC) for modeling adiabatic walls is applied. The diffuse reflection boundary conditions (DR-BC) are applied on the top and bottom walls, the IS-BC are specified to the front and back walls and specular reflection boundary conditions (SR-BC) to the left and right walls. Four cases with fixed Rayleigh number, Ra = 6643 and different AR of 2:2:1, 3:3:1, 4:4:1, and 5:5:1 are calculated to investigate the effects of AR on the flow patterns of rarefied gas RB convection in 3D rectangular micro enclosures. Results show a dominant convection flow patterns in the form of rolls and cells from four simulation cases. The number and shape of rolls and cells change with the different AR and side wall boundary effects.

並列關鍵字

DSMC ； Adiabatic wall ； Rarefied gas ； Rayleigh-Bénard convection ； Aspect ratio