多孔介質流場定量量測與分析及其應用; Quantitative Measurements and Analyse of Porous Media Flows and their Application

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题名:	多孔介質流場定量量測與分析及其應用;Quantitative Measurements and Analyse of Porous Media Flows and their Application
作者:	陳勇州;Yung-Chou Chen
贡献者:	機械工程研究所
关键词:	DPIV量測;無因次滑移速度;滑移速度;多孔性介質;折射率契合;digital particle image velocimetry;non-dimensional slip velocity;slip velocity;Porous media;index of refractive matching technique
日期:	2008-12-16
上传时间:	2009-09-21 12:02:34 (UTC+8)
出版者:	國立中央大學圖書館
摘要:	本論文定量量測多孔介質(porous media)流道表面及其內部流場之速度分佈，應用數位質點影像測速儀(digital particle image velocimetry, DPIV)，結合折射率契合(index of refractive matching, IRM)技術，針對兩種不同流場，即壓力驅動矩型管流和旋轉圓管壁剪力驅動流場，在不同孔隙率(ε)和不同雷諾數(Re)條件下，定量量測多孔介質速度場之變化，進而評估著名的多孔介質Brinkman方程式中有效黏滯係數(μ)與多孔介質表面滑移係數(???? ，μ為流體動黏滯係數)之關係及其適用性。有關壓力驅動流方面，於多孔介質矩型流道內下方分別放置圓柱陣列或玻璃珠，來模擬不同ε值之多孔性介質。採用不同柱距的透明圓柱陣列，可排列出均質(homogeneous)但不同的ε值(ε = 0.6 ~ 0.9)之多孔介質，而使用玻璃珠(粒徑d = 2mm)作為非均質(non-homogeneous)之多孔介質時，可降低ε值至0.4使其近似於燃料電池多孔電極材料之ε值。由DPIV量測結果顯示，流體與多孔介質表面有明顯之滑移速度(us)，且us與ε和一以流道水力直徑所定義之Re數有重要之關係。藉由一無因次滑移速度us/(γ( )k0.5) ≡ Ûs ≡ 1/?來說明主要結果，其中γ( )為多孔介質表面上的剪應變率而k為滲透率，我們發現，當ε值為一定值(介於0.6 ε 0.9)時，Ûs值會隨Re增加而增加(至少Re 100)，而在固定Re值下，Ûs值也會隨著ε值增加而增加。應用IRM技術於ε = 0.4之玻璃珠多孔介質流場，我們可量測多孔介質從表面滑移速度到內部流場速度漸減至Darcy速度時所需經過之多孔介質厚度，並定義此厚度為轉換層厚度(δ)，實驗結果顯示δ值為定值，不隨Re變化，至少在20 Re 100範圍內，且δ ? 0.75d。再者，量測所得之Ûs值比一般使用Brinkman方程式所假設的Ûs = 1 (或??????)高出5.5~13倍，即Ûs = 5.5 ~ 13與Re數有關。另外，剪力驅動流場乃由兩同心之靜止內圓柱以及一空心可旋轉之外圓柱所構成，內圓柱壁上則裝上許多小圓柱陣列來模擬具不同的ε值(ε = 0.8 ~ 0.9)之多孔介質。實驗結果中顯示，在任一固定ε值下，Ûs值會隨Re增加反而會減少，與壓力驅動流場正好相反，顯示Ûs值與流場型態有關，且Ûs = 0.21?0.29 < 1，與壓力驅動流場顯著不同。綜合以上的結果，顯示一般使用Brinkman方程式所假設之Ûs = 1 (或?????)須再做考慮與修正。 This thesis reports measurements of the velocity distribution across the porous surface and inside using digital particle image velocimetry (DPIV) together with the index of refraction matching (IRM) technique. A pressure-driven rectangular duct and a shear-driven Couette flow, each covering a wide range of flow Reynolds number (Re) and the porosity (ε) of porous media, are studied. The variation of the velocity distribution in porous media is quantitatively measured to identify the relation between the effective viscosity (μ) of the well-known Brinkman equation and the slip coefficient (???? ??μ is fluid dynamic viscosity) at the surface of porous media, so that the applicability of such relation can be evaluated. In the case of pressure-driven flow, the transparent cylinder arrays or glass beads are used to simulate the porous media. The homogeneous porous media with ε varying from 0.6 to 0.9 can be obtained using the cylinder arrays with different gaps among cylinders while the non-homogeneous porous media with ε ? 0.4. Closely matching that of the electrode material in the fuel cell can be established using small glass beads of 2 mm-diameter (d). DPIV measurements show that there are significant slip velocities (us) at the interface of the homogeneous porous media, of which values of us are functions of ε and Re based on the hydraulic diameter of the flow channel. These results are to be demonstrated by a non-dimensional form of the slip velocities, Ûs ≡ us/(γ( )k0.5) ≡ 1/?, where γ( ) and k are the shear stress at the surface and the permeability of porous media, respectively. It is found that values of Ûs increase with Re at a given value of ε (0.6 ? ε ? 0.9) or with ε at a given value of Re (Re ? 100). In non-homogeneous porous media (ε = 0.4) with the IRM method, it is also found that there exists a transition layer with a thickness of δ, through which the slip velocity at the interface of the porous media reduces to the Darcy velocity. Experimental results show that the value of δ is constant nearly and does not vary with Re, at least for 20 ? Re ? 100, where δ ? 0.75d. Moreover, values of Ûs are found to be much greater than that predicted by the Brinkman equation (Ûs = 1 or ??? 1), about 5.5 to 13 times higher, depending on Re. That is, Ûs = 5.5 ~ 13. In the case of shear-driven flow, the flow field is established between a stationary inner cylinder and a concentric rotating outer cylinder. The non-homogeneous porous media with ε varying from 0.8 to 0.9 can be similated by installing arrays of small cylindrical rods on the surface of the inner cylinder. In this case, experimental results show that Ûs decreases with increasing Re at any fixed values of ε. This is opposite to the case of pressure-driven flow, indicating that Ûs depends on the type of flow. Specifically, Ûs = 0.21 ~ 0.29 < 1, depending on Re. These results suggest that the commonly used assumption that is μ* = μ or ??? 1 (Ûs = 1) in the Brinkman equation should be re-considered and modified according to the type of flow, ε and Re.
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