| 摘要(英) |
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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簡奇偉 “平板式固態氧化物燃料電池氣態多孔管道之速度量測”，國立中央大學機械工程系，碩士論文 (2006)。
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