本研究的目的在於以數值方法研究在矩形截面流道中佈置反自然蓮葉結構之超疏水表面減阻效應。在計算中我們以下列方式模擬該超疏水表面：液氣界面設為平滑之零剪力區域，固液界面則設為無滑移區域。藉由改變高寬比與零剪力面積比例Fc，探討其阻力係數與雷諾數乘積fRe之變化，並且對這些流場作進一步之分析。

研究結果顯示，不同Fc之流道在相同高寬比下減阻效應隨Fc遞增；而在相同Fc下，減阻效應並沒有與高寬比有線性關係。由Fc=0.5與Fc=0.9之流場分析可知流體流經零剪力區域時，速度受到會週期壓力變化所產生之助力與阻力而有先升後降之變化。進一步分析流場會發現造成週期壓力梯度變化是由於流道中形成二次流，亦即促使流體偏離主要流動方向所形成之側向流動現象。透過二次流分析，可以知道高寬比極低（10-2）之流道中，因為流體皆朝向主要流動方向流動，較不會有二次流現象之存在，超疏水表面對於流體而言較能夠完全產生減阻之效應；而在高寬比較低（0.05~0.3）之流道中，二次流現象隨著高寬比增加而有大幅度增加，減阻效應在此會大幅度下降；在高寬比較大（0.3~1）之流道中，二次流強度變化漸緩，不再隨著流道高寬比增加而大幅度增加，故減阻效應並不明顯。

The purpose of this work is to study numerically the drag reduction in rectangular duct flow with superhydrophobic surface, which is produced by manufacturing “negative lotus structure” on the surface. In the numerical calculations herein, we simulate the superhydrophobic surface in the following way: the liquid–gas interface in the surface structure is set as a shear-free planar surface, and the solid–liquid interface as a no-slip surface. By varying the aspect ratio (AR) of the duct cross-section and the proportion (Fc) of the surface area that has zero shear, we investigate the corresponding variation of the fRe product (f being the friction factor of the duct flow, and Re the Reynolds number) in fully-developed flow, and analyze the flow field in detail.

The results show that, typically, the extent of drag reduction increases with Fc for a fixed AR of the duct. Also, for a given Fc, the drag reduction extent depends nonlinearly on AR. From the flow field analysis for Fc = 0.5 and Fc = 0.9, we discover that when the liquid flow passes through the shear-free region, its velocity will first increase and then decrease, accompanied with a periodic variation in the otherwise constant pressure gradient. Moreover, the flow-field analysis suggests that the periodic variation of the pressure gradient is associated with a secondary flow that causes the fluid to deviate from the main current direction in the duct. When the duct has an extremely low AR (say 10-2), there is no significant secondary flow, and the superhydrophobic surface produces significant drag reduction. For AR in the range of about 0.05~0.3, the secondary flow would increases in magnitude with increasing AR, therefore reducing the extent of drag reduction. At even larger AR (in the range of about 0.3~1), the magnitude of the secondary flow does not change much, and the drag reduction effect produced by the surface pattern also becomes less significant.

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