正弦壓力作動下非對稱分岔微流道之整流性分析

Flow Rectification of an Asymmetric Bifurcation Microchannel under Sinusoidal Pressure Actuation

陳詠翔(Yung-Hsiang Chen)

指導教授 ： 孫珍理

國立臺灣大學/工學院/機械工程學研究所/碩士(2014年)

https://doi.org/10.6342/NTU.2014.00617

摘要

本研究藉由動量方程式的推導，設計了16種壁面承受流體施力最小的非對稱分岔微流道，並利用模擬與實驗兩種方式，觀察在正弦壓力的驅動下，流場與整流性受到流道幾何形狀與頻率等參數改變的影響。非對稱分岔微流道的幾何參數有3個：較寬的子流道1分岔角度θ1、較窄的子流道2分岔角度θ2以及子流道寬度比W2/W1。其中，θ1 = 10˚、20˚、40˚、60˚，θ2 = 20˚、60˚，W2/W1 = 0.4、0.6，共有16種變化。由結果發現，不論是模擬或實驗，整流性的方向不會隨著任何參數而改變，淨流率皆是往母流道方向流動。
在數值模擬中，我們設置了兩種不同的頻率大小，分別為0.96 Hz與100 Hz。由模擬結果發現，當θ1增大時，淨流率也會隨之上升，整流效果變得愈好，但當θ2增大時，淨流率會下降，整流性變差，且下降的幅度會隨著θ1增加而變大。此外，當子流道寬度比W2/W1增大，即兩子流道寬度愈接近時，淨流率會下降，整流性變差。當驅動頻率上升時，Womersley number由0.3增加至3，流場由準穩態變得具有暫態的特性，使得速度分佈出現Richardson’s annular effect的特徵，且流場與壓力震盪產生了超過π/4的相位延遲，使得淨流率隨著頻率增加而驟降，整流性變得很差。
在實驗中，將頻率固定為0.5 Hz, 0.7 Hz與0.96 Hz進行μPIV與淨流率量測。由實驗結果發現，當頻率上升後，淨流率會明顯下降，此現象與模擬結果相同，當任一子流道分岔角度增大，雖然低速區會往相對應的子流道方向移動，但是θ1的改變對淨流率並沒有明顯的影響，而θ2的增加則是會讓淨流率上升。當子流道寬度比W2/W1增大，即兩子流道寬度變得愈接近時，低頻狀況下的淨流率會上升，高頻狀況下的淨流率則會變小，然而對流場低速區並沒有太大的影響。

關鍵字

整流性 ； 非對稱分岔微流道 ； 週期性震盪流動

並列摘要

In this work, we employ both numerical and experimental study to investigate the flow rectification of an asymmetric bifurcating microchannel. Three parameters are considered: bifurcation angles (θ1 = 10˚, 20˚, 40˚, 60˚ and θ2 = 20˚, 60˚), width ratio of two daughter channels (W2/W1 = 0.4 and 0.6) and excitation frequency (f = 0.96 Hz and 100 Hz). The design of the branching structure is based on the concept of minimal forces exerted on the bifurcation, which is derived from the linear momentum equation. When a time-dependent sinusoidal pressure is imposed, flow resistances in opposite directions of the bifurcating microchannel differentiate such that a net flow toward the mother channel is attained regardless of the variations of the parameters.
From the simulation, flow rectification improves with the increase of the bifurcation angle of the wider daughter channel. On the contrary, when the bifurcation angle of the narrower daughter channel widens, the flow rectification deteriorates. Moreover, this reduction in net flow rate becomes more severe with increasing the bifurcation angle of the wider daughter channel. Interestingly, we also find that flow rectification enhances slightly when the width difference of the two daughter channels grows. This suggests that asymmetry actually helps to increase flow rectification of a bifurcating microchannel. Moreover, the excitation frequency plays a profound role in the flow rectification. As the Womersley number increases from 0.3 to 3, the attainable net flow rate diminishes significantly due to the emergence of Richardson’s annular effect. A phase lag of π/4 is found between the flow rate and the imposed pressure at f = 100 Hz.
We carry out the μPIV diagnosis at f = 0.96 Hz and measure the net flow rate at f = 0.5 Hz, 0.7 Hz and 0.96 Hz. The results show that increasing either bifurcation angle, low-velocity zone near the fork moves into the corresponding daughter channel. However, rectification improves obviously as the bifurcation angle of narrower daughter channel grows while it has a hardly change after the angle of wider one varies. We also find that the effect of width ratio of two daughter channels alters under different excitation frequency. As the width of both daughter channels becomes more comparable, rectification grows at lower frequency while it deteriorates at higher frequency.

並列關鍵字

Flow rectification ； asymmetric bifurcating microchannel ； oscillatory flow

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