An experimental study on riblet-induced spanwise vortices in turbulent boundary layers
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摘要: 壁湍流中的相干结构与壁面的高摩擦阻力密切相关，研究壁面纵向微小沟槽对展向涡的影响规律，有助于深入认识沟槽壁面的减阻机理。在自由来流速度控制在0.18m/s的水槽中（Reτ=190），采用高时间分辨率粒子图像测速技术，测量光滑平板和沟槽板（s+=2h+=16.3）湍流边界层，分别获得了15998个瞬时速度矢量场。使用λci识别展向涡，比较了2种壁面流动中不同法向位置处展向涡的数量、平均强度、平均尺度及各尺度展向涡所占的数量比例。结果表明：沟槽使近壁区顺向涡的数量减小，逆向涡的数量增大，并削弱了展向涡的强度；沟槽使近壁区小尺度顺向涡和中尺度逆向涡的比例增加，中尺度顺向涡和大尺度逆向涡的比例减小，使得近壁区顺向涡的尺度差异变小，对近壁区逆向涡的尺度差异几乎无影响；沟槽减小了对数律区小尺度顺向涡的数量比例，并增大了大尺度顺向涡的数量比例，对数律区逆向涡数量比例的变化规律和顺向涡正好相反。Abstract: Coherent structure is closely related to the high frictional resistance in wall turbulence.Summarizing the influence rule of vertical micro-grooves on spanwise vortex is helpful for understanding the drag reduction mechanism by riblet surface.15998 instantaneous velocity fields over both riblet (s+=2h+=16.3) and smooth surfaces in turbulent boundary layers (TBL) at a Reynolds number of Reτ=190 were acquired by using time-resolved particle image velocimetry (TRPIV) in a water tunnel.The swirling strength λci was used to reveal spanwise vortices, and we extracted the cores of spanwise vortices by finding swirling strength's local extremum in whole field.Subsequently, the proportion of the spanwise vortex, the average swirl strength, the average diameter of the vortex and the proportion of the each scale vortex were analyzed statistically in flow field over riblet surface.All experimental results were compared with those over a smooth surface.It is found that (1) the number of prograde spanwise vortices is decreased by riblet in near wall region, while retrograde spanwise vortices'number is increased.(2) The average strength of the spanwise vortex is decreased, whether prograde vortex or retrograde vortex.(3) The proportion of small scale prograde vortices and mesoscale retrograde vortices is increased in near wall region, while mesoscale prograde vortices and large scale retrograde vortices'proportion is decreased.(4) The difference in stream-normal scale of the prograde spanwise vortex becomes smaller in inner boundary, but the retrograde spanwise vortex's scale difference without change.(5) The proportion of small scale prograde vortices is decreased in log-law region, while the proportion of large scale prograde vortices is increased.Impact on the proportion of retrograde vortices is exactly opposite of the prograde vortex.
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图 2 光滑壁面与沟槽壁面湍流边界层平均速度剖面
Figure 2. Mean velocity profiles of TBL over the plate and riblet surfaces
图 3 相对湍流度沿法向位置y+的分布(实心：沟槽壁面，空心：光滑壁面)
Figure 3. Distribution of turbulent intensity in wall-normal direction of TBL
图 4 2D PIV瞬时速度场中Λci准则检测出的涡结构(蓝色为顺向涡，红色为逆向涡，A-1为A中顺向涡的局部放大图)
Figure 4. Example of vortex identification and extraction in an instantaneous two-dimensional PIV velocity field by using Λci (Retrograde spanwise vortices are presented in red and prograde vortices in blue, A-1 is a localized enlargement of prograde vortices in A)
图 5 顺向涡(NP)和逆向涡(NR)的比例随法向位置y+的变化
Figure 5. The proportion of prograde (NP) and retrograde (NR) vortex according to y+
图 6 顺向涡(ΛP)和逆向涡(ΛR)涡心的平均强度随法向位置y+的变化
Figure 6. Average swirling-strength of prograde (ΛP) and retrograde (ΛR) vortex core according to y+
图 7 涡尺度的示意图
Figure 7. An example of realizing vortex diameter from a swirling strength (Λci) map
图 8 顺向涡(P-D+)和逆向涡(R-D+)的平均直径随法向位置y+的变化
Figure 8. The average diameters of prograde (P-D+) and retrograde (R-D+) vortex according to y+
图 9 顺向涡(P-a/b)和逆向涡(R-a/b)流向尺度和法向尺度的平均比值随法向位置y+的变化
Figure 9. The ratio of the average scale of stream to normal of prograde (P-a/b) and retrograde (R-a/b) vortex according to y+
图 10 各尺度顺向涡的数量比例随y+的变化云图
Figure 10. Contours of the proportion of each scale prograde vortex according to y+
图 11 各尺度逆向涡的数量比例随y+的变化云图
Figure 11. Contours of the proportion of each scale retrograde vortex according to y+
图 12 沟槽与光滑壁面流场中各尺度涡数量比例的差值随法向位置的变化云图
Figure 12. The difference of the proportion of each scale spanwise vortex between the flow field over plate and riblet
表 1 光滑壁面和沟槽壁面湍流边界层的流动参数
Table 1. Flow parameters of the TBL over the plate and riblet surfaces
U∞/(m·s-1) δ/mm θ/mm u*/(m·s-1) Reθ Reτ Cf DR/% Plate 0.180 18.51 1.88 0.0098 355 190 0.0059 - Riblet 0.181 21.01 2.15 0.0095 400 208 0.0057 6.68% 
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