Velocity measurements for flows around micro-cylinder array based on image overlapping
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摘要: 分析了相关深度对Micro-PIV速度场测量的影响，说明采用低密度粒子图像叠加技术能够有效减小相关深度，提高速度测量的准确性。将该方法应用于微柱群绕流流场的分层测量，雷诺数分别取0.8~3.6，在此基础上计算了空间平均速度。将分层速度场和平均速度廓线与采用平均相关技术获得的结果进行了比较。结果表明，采用低密度粒子图像叠加方法获得的全场绕流速度分布更为合理，通道底部和顶部近壁区的平均“伪滑移速度”分别减小了22.7%和17.2%，通道中心平均速度峰值增加了5.2%。
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关键词:
- 显微粒子图像测速技术 /
- 图像叠加法 /
- 微柱群绕流 /
- 分层测量
Abstract: In this study, the influence of depth of correlation (DOC) on the micro-PIV measurement is analyzed. The method of image overlapping under the low particle density condition can decrease DOC and improve the velocity measurement accuracy. This method is applied to the velocity measurements on multiple fluid planes for the flow around a micro-cylinder array under eight Reynolds numbers from 0.8 to 3.6, and the spatial averaged velocities (SAVs) are calculated based on the velocities. In order to analyze the measurement accuracy, the velocities and SAVs resulting from the method of image overlapping are compared to those obtained by the method of average cross-correlation. The results indicate that of the image overlapping is a more reasonable method under the low particle density condition. The average pseudo-slip velocity decreases by 22.7% for the bottom surface and 17.2% for the top, respectively, and the average peak velocity increases by about 5.2%. -
图 1 相关深度对相关函数的影响示意图。(a)近壁区相关峰值的正偏差，出现“伪滑移速度”; (b)中心层平面相关峰值的负偏差。图中±Δx为位移偏差; Φ, ΦS及ΦB分别为总相关函数, 焦平面粒子及背景粒子图像对相关函数的贡献; Vmeas及Vreal分别为速度测量值和真实值。
Figure 1. The influence of DOC on the correlation function. (a) Positive deviation of correlation peak near wall surface, "pseudo-slip flow"; (b) Negative deviation of correlation peak on center plane. where±Δx is the displacement deviation; Φ, ΦS and ΦB are the total correlation function and correlation function contributed by in-plane particle images and background particle images, respectively; Vmeas and Vreal are the measurement value and real value of velocity, respectively.
图 6 采用低密度粒子图像叠加方法获得的分层速度场分布
Figure 6. Velocity on multi-fluid planes by image overlapping method
图 7 采用平均相关法获得的分层速度场分布
Figure 7. Velocity on multi-fluid planes by correlation averaging method
表 1 2种方法的壁面速度
Table 1. Velocities on two walls by two methods
Re 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 平均值 Q/(μl·s-1) 14.3 21.5 28.6 35.8 42.9 50.1 57.2 64.4 / 底面VS, a/(mm·s-1) 8.6 14.7 18.7 20.5 27.3 25.6 36.0 37.1 / 底面VNDS, a 0.43 0.49 0.47 0.41 0.46 0.37 0.45 0.41 0.44 底面VS, o/(mm·s-1) 5.4 11.5 12.5 18.4 21.2 17.6 30.4 33.5 / 底面VNDS, o 0.27 0.38 0.31 0.37 0.36 0.25 0.38 0.37 0.34 底面δS/% -37.2 -21.8 -33.2 -10.2 -22.3 -31.3 -15.6 -9.7 -22.7 顶面VS, a/(mm·s-1) 10.6 12.3 12.6 21.9 21.3 28.9 29.5 37.6 / 顶面VNDS, a 0.53 0.41 0.32 0.44 0.36 0.41 0.37 0.42 0.41 顶面VS, o/(mm·s-1) 9.1 10.7 13.5 16.3 13.8 20.5 23.2 35.1 / 顶面VNDS, o 0.46 0.36 0.34 0.33 0.23 0.29 0.29 0.39 0.34 顶面δS/% -14.2 -13.0 7.1 -25.6 -35.2 -29.1 -21.4 -6.6 -17.2 
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表 2 2种方法的峰值速度
Table 2. Peak velocities by two methods
Re 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 平均值 Q/(μl·s-1) 14.3 21.5 28.6 35.8 42.9 50.1 57.2 64.4 / VP, a/(mm·s-1) 24.2 31.7 46.3 54.1 66.3 75.3 89.5 98.2 / VNDP, a 1.22 1.06 1.16 1.09 1.11 1.08 1.12 1.10 1.12 VP, o/(mm·s-1) 24.7 35 45.8 58.7 72.2 78.9 93.8 101.3 / VNDP, o 1.24 1.17 1.15 1.18 1.21 1.13 1.18 1.13 1.17 δS/% 2.1 10 -1.1 8.5 8.9 4.8 4.8 3.2 5.2
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