Experimental study of the mechanism of drag reduction in turbulent boundary layers on the superhydrophobic structured wall with microstructure
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摘要: 对超疏水微沟槽和微凸柱面湍流边界层的减阻机理进行了实验研究。使用高时间分辨率粒子图像测速仪（TRPIV），测量了亲水壁面、超疏水微沟槽壁面和超疏水微凸柱壁面湍流边界层内的瞬时速度场，对比分析了3种壁面的壁面摩擦切应力，发现超疏水壁面都产生了减阻效果，但超疏水微沟槽壁面的减阻率（13.8%）要大于超疏水微凸柱壁面（10.2%）。通过对比分析湍流边界层内3种壁面对应的平均速度剖面、湍流脉动强度和雷诺切应力剖面，证实流体在超疏水壁面具有滑移速度，且在$15 < {y^ + } < 100$区域的同一法向高度上，亲水壁面、超疏水微沟槽及超疏水微凸柱壁面对应的流向湍流脉动强度依次减弱；同时在$30 < {y^ + } < 80$区域的同一法向高度上，超疏水微凸柱壁面、亲水壁面和超疏水微沟槽壁面对应的法向湍流脉动强度依次减弱。在整个法向高度上，亲水壁面、超疏水微凸柱壁面和超疏水微沟槽壁面的雷诺切应力的最大值依次减小。以${\Lambda _{{\text{ci}}}}$准则识别出的顺向涡为条件进行条件采样和相位平均，并分别与亲水壁面对比，发现在${y^ + } \approx 63$附近，超疏水微沟槽壁面展向涡诱导的第四象限事件幅值减弱，其构成的扫掠事件强度减小，进而实现减阻。为进一步分析湍流脉动能量，使用本征正交分解，将湍流边界层内全场的瞬时脉动速度在时间上和流−法向空间进行求和并进行无量纲化，用来表征流场的脉动程度。结果表明：超疏水微凸柱壁面的展向滑移的增阻特性，削弱了其流向滑移带来的减阻效果。超疏水微沟槽壁面的流向滑移特性能有效地抑制湍流脉动，从而达到更好的减阻效果。Abstract: The drag reduction mechanism of the wall turbulent boundary layer with superhydrophobic micro-riblets and micro-convex posts is studied experimentally. The instantaneous velocity field in the turbulent boundary layer of the hydrophilic wall, superhydrophobic micro-riblets wall and micro-convex posts wall is measured by high time resolution particle image velocimetry (TRPIV). The frictional shear stress of the three kinds of walls is compared and analyzed. It is found that the superhydrophobic walls achieve drag reduction effect. However, the drag reduction rate of the superhydrophobic micro-riblets wall is higher than that of the superhydrophobic micro-convex posts wall, and the drag reduction rate of the superhydrophobic micro-riblets wall is 13.8%, while the drag reduction rate of the superhydrophobic micro-convex posts wall is 10.2%. Through comparison and analysis on the three kinds of wall corresponding average velocity profile in the turbulent boundary layer, turbulence intensity and Reynolds shear stress profile, it is found that the fluid indeed has sliding speed in the superhydrophobic wall, and in the area of the same normal height at $15 < {y^ + } < 100$, the streamwise turbulence intensity corresponding to the hydrophilic wall, superhydrophobic micro-riblets and micro-convex posts wall decreases successively. At the same time, in the area of the same normal height at $30 < {y^ + } < 80$,the wall-normal turbulence intensity of the superhydrophobic micro-convex posts, hydrophilic wall and superhydrophobic micro-riblets wall decrease successively. Over the whole wall-normal height, the maximum values of Reynolds shear stress on the hydrophilic wall, superhydrophobic micro-convex posts and micro-riblets wall decrease successively. Based on the conditional sampling and phase averaging of the spanwise vortex identified by the ${\Lambda _{{\text{ci}}}}$criterion, it is found that the amplitude of the fourth quadrant event induced by the spanwise vortex of the superhydrophobic micro-riblets wall weakens nearby at ${y^{\text{ + }}} \approx 63$, which leads to the intensity of its sweep events decreasing, and then the drag reduction is realized. In order to further analyze the turbulent fluctuation energy, the instantaneous fluctuation velocity of the whole turbulent boundary layer is summed in time and over the streamwise-normal space by using Proper Orthogonal Decomposition and it is dimensionless to characterize the fluctuation degree of the flow field. The results show that the spanwise slip characteristics of the superhydrophobic micro-convex posts increase the drag and weaken the drag reduction effect caused by the streamwise slip. The streamwise slip characteristics of the superhydrophobic micro-riblets wall can effectively suppress turbulence fluctuation and achieve better drag reduction effects.
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图 3 结构壁面：（a）无微结构（b）微沟槽结构；（c）微凸柱结构
Figure 3. Structured walls: (a) no microstructure; (b) micro-riblets structure; (c) micro-convex posts structure
图 7 ${\Lambda _{{\text{ci}}}}$识别结果
Figure 7. The results of ${\Lambda _{{\text{ci}}}}$ recognition
图 9 y+≈63附近展向涡相位平均流向脉动速度云图
Figure 9. Conditional phase averaged contour of the spanwise vortex with streamwise fluctuation velocity at y+≈63
图 10 y+≈63附近展向涡相位平均法向脉动速度云图
Figure 10. Conditional phase averaged contour of the spanwise vortex with wall-normal fluctuation velocity at y+≈63
图 11 y+≈63附近大尺度展向涡相位平均流向脉动速度云图
Figure 11. Conditional phase averaged contour of the large scale spanwise vortex with streamwise fluctuation velocity at y+≈63
图 12 ${\Lambda _{{\text{ci}}}}$随${y^ + }$的变化曲线
Figure 12. Variation of ${\Lambda _{{\text{ci}}}}$in boundary layer
表 1 基本湍流减阻参数
Table 1. Basic turbulent drag reduction parameters
参数 亲水壁面 超疏水微沟槽壁面 超疏水微凸柱壁面 自由来流速度${U_\infty }/\left( {{\text{m}} \cdot {{\text{s}}^{ - 1}}} \right)$ 0.35 0.35 0.35 壁面摩擦速度
${u_\tau }/\left( {{\text{m}} \cdot {{\text{s}}^{ - 1}}} \right)$0.0153 0.0142 0.0145 内尺度雷诺数
$R{e_\tau }$657 642 629 壁面摩擦切应力
${\tau _w}/\left( {kg \cdot {m^{ - 1}} \cdot {s^{ - 2}}} \right)$0.232915 0.200818 0.209132 壁面摩擦系数
${C_f}$0.003698 0.003149 0.003277 减阻率
$\eta $13.8% 10.2% 
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表 2 各壁面湍动能的前10阶模态的能量贡献
Table 2. Energy contributions of the first 10 POD modes to the TKE of all surface
态 亲水壁面 合计 超疏水微沟槽
壁面合计 超疏水微凸柱
壁面合计 1 0.175 0.175 0.185 0.185 0.180 0.180 2 0.088 0.264 0.097 0.282 0.103 0.282 3 0.057 0.321 0.054 0.336 0.057 0.339 4 0.047 0.369 0.045 0.382 0.054 0.393 5 0.036 0.404 0.034 0.416 0.039 0.433 6 0.029 0.433 0.029 0.445 0.030 0.462 7 0.027 0.461 0.028 0.473 0.027 0.489 8 0.024 0.485 0.021 0.494 0.023 0.513 9 0.020 0.505 0.019 0.514 0.020 0.533 10 0.018 0.523 0.019 0.532 0.018 0.550
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