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    题名: 不可壓縮流在具截面變化之矩形微流道之數值模擬
    其它题名: Numerical simulation of incompressible flow in rectangular microchannel with variable cross section
    作者: 陳韻婷;Chen, Yun-ting
    贡献者: 淡江大學航空太空工程學系碩士班
    陳慶祥;Chen, Ching-shung
    关键词: 三維微流道;截面變化;不可壓縮流;數值模擬;three-dimensional microchannel;variable cross section;incompressible flow;Numerical Simulation
    日期: 2009
    上传时间: 2010-01-11 06:46:47 (UTC+8)
    摘要: 以往微流道流場研究之幾何外型結構大多是長直管道,而本研究程式是利用數值模擬程式來分析簡化的Navier-Stokes方程式,探討其應用於三維不可壓縮流體在不同的截面變化下的適用性,並利用商用套裝軟體Fluent來驗證簡化的N-S方程式的準確性。簡化的N-S方程式,因為具有拋物線型的數學特性,用於計算完全發展後的流體,對現今的電腦設備來說,可以節省許多運算時間,比起解完整的N-S方程式快上數十到數百倍,是非常有效率又不失準確性的運算工具。
    本研究程式用Poisson equation來算出垂直於管道軸向的平面之壓力修正,而三維管道的求解過程在大部分的CFD軟體是非常耗費時間,但本研究程式可以利用掌握Poisson equation的運算區間,來省下龐大的運算時間。
    簡化的N-S方程式忽略軸向的擴散項。由於動量和能量的擴散在垂直軸向的平面比軸向強許多,因此這樣的假設在微流道上的適用性更好。目前的數值模擬結果也是顯現出微管道的結果好於傳統管道。
    當漸縮漸擴段的漸縮比繼續加大後,在漸擴處將會產生小迴流,本研究程式在計算迴流處沒有很順利,但初步了解應該是在計算時,需要將方程組組合起來使用隱性方法(coupled scheme),本研究程式將方程組使用顯性方法逐條分開來解(segregated scheme),可能造成本研究程式爆掉的原因。
    本研究程式使用Fluent相互驗證,在Fluent的網格裡使用局部加密來增加準確度,在沒有變化的截面上可以減少網格數,可以節省運算時間,在經相互驗證後,發現本研究程式的準確度相當高,在出口雷諾數上的比對皆在0.5%以內,運算時間也比Fluent快上數十到數百倍,如此有效率又不失準確性的模擬結果,相當令人滿意。
    In the past few years most studies on microchannel flows focus on channels with uniform cross-section. This study simulated three-dimensional microchannel flows with variable cross sections. A set of reduced incompressible Navier-Stokes equations were applied to model the flows. A finite-difference method was used to solve the governing equations. The commercial software package, Fluent, was used to verify the present numerical procedure. The reduced N-S equations are a set of parabolic equations in the axial direction of the channel. An efficient space marching scheme can be applied to solve them.
    In the present study the Poisson equation was solved for the pressure correction in the plane perpendicular to the channel axis. This process is the most time consuming part in computing three-dimensional flows in most CFD softwares. In this study we can control the computational range of Poisson equation so that a great deal of computing time can be saved.
    The reduced N-S equations ignore the diffusion terms in the axial direction. This assumption is better suited for microchannel flows because momentum and energy diffusions are much stronger in the plane perpendicular to the channel axis than that in the axial direction. The predicted results made by the present numerical procedure therefore are better for microchannels than for conventional channels.
    As the nozzle ratio becomes larger a reverse flow forms downstream of the nozzle throat. The present numerical procedure has not worked for reverse flows yet. Our experience suggests that a coupled numerical procedure may have to be used instead of the segregated procedure employed in the present study.
    The commercial software package, Fluent, was used to validate the predicted results made by our numerical procedure. The comparisons were very good. The errors in the exit Reynolds numbers were all less than 0.5%. Yet our program is two to three orders of magnitude faster than Fluent
    显示于类别:[航空太空工程學系暨研究所] 學位論文

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