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Turbulence characteristics in open channel with glass-sphere quincunx arrays
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摘要: 梅花形阵列粗糙是常见的床面粗糙形态，但其水流紊动特性参数在颗粒间的沿程变化和不同象限间的分布差异等研究仍较薄弱。采用不同颗粒大小和排列间距的圆形玻璃珠制作了3种梅花形阵列粗糙床面，基于明渠紊流的PIV水槽试验资料，探讨了无量纲纵向紊动强度Tu（请用一个字母（可加下标）表示，全文替换???）、雷诺应力R和紊动能E的分布规律。结果表明：① 颗粒顶部以上区域的Tu、R、E沿程基本呈条带状变化，受颗粒影响较小，而颗粒顶部以下区域则受颗粒影响明显，沿程变化相对复杂，表现出一定的周期性和分区性，并可分为颗粒区和粒间区。② 颗粒顶部以上区域Tu、R、E的垂线分布基本重合，颗粒顶部以下区域则波动明显，分布曲线呈“S”和倒“L”等形状。③ 粒间区各象限的R、E沿程变化较为平缓，接近水平线，第2、4象限的R、E总体大于第1、3象限；颗粒区各象限的R、E沿程分布呈“∪”状并在沿程位置参数x+ = 0附近有最小值。研究成果对鱼道及航道工程设计等具有一定的指导意义。Abstract: The quincunx array is a common structure appearing on rough bed surfaces. However, the study on the variation of flow turbulence characteristics between particles and the distribution of different quadrants is still weak. Using round glass beads of different sizes, three different quincunx arrays with arrangements of different intervals were made. From the particle-image-velocimetry (PIV) data of turbulent flow over these arrays in an open channel flume, the distributions of the dimensionless longitudinal turbulence intensity Tu, Reynolds stress R, and turbulent kinetic energy E were analyzed. They show that the area above the top of the beads features a strip-shaped change indicating the beads have little influence, whereas in the area below the tops, the beads have greater influence. The vertical distribution of Tu, R and E is relatively complex displaying a certain periodicity and regionality that permits a classification into sphere region (SR) and inter-sphere region (ISR). The vertical distribution of Tu, R and E above the top of the particle basically coincides with each other, while the vertical distribution of Tu, R and E below the top of the particle fluctuates obviously, and the distribution curve are shaped like an “S” and an inverted “L”. The longitudinal variations of R and E of different quadrants in the ISR are smooth and close to constant, the values of R and E in the 2nd, 4th quadrant are generally greater than that of the 1st, 3rd quadrant. However, in the SR, the distribution of R and E showed a ∪-like shape and there are minimum values near the position of x+ = 0. The research results have certain guiding significance for the design of fishway and waterway engineering.
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图 7 各象限雷诺应力垂线平均值的沿程变化（0.0??）
Figure 7. Longitudinal variation of vertical average Reynolds stress in different quadrants
图 8 各象限紊动能垂线平均值的沿程变化(0.0???)
Figure 8. Longitudinal variation of vertical average turbulence kinetic energy in different quadrants
图 9 紊动参数垂线平均值的沿程变化(R??)
Figure 9. Longitudinal varation of vertical average turbulence parameters
表 1 试验工况参数
Table 1. Summary data of experimental run
工况 床面 d/mm Q/(L·s-1) h/cm i υ/(10-6·m2·s-1) Um/(cm·s-1) $\overline {{u_*}} $ /(cm·s-1)B/h h/d Fr Re Re* 床面类型 1 B1 6 2.5 4.49 0.001 1.109 22.26 1.800 5.57 7.49 0.34 6631 97.3 粗糙 2 B2 6 2.5 4.37 0.001 1.109 22.90 1.781 5.72 7.28 0.35 6680 96.3 粗糙 3 B3 9 2.5 4.48 0.001 1.135 22.32 1.798 5.58 4.98 0.34 6484 142.5 粗糙 注：d为颗粒直径；Q为流量；h为从光滑床面起算的试验段水深；i为底坡；υ为水的运动黏度；Um为断面平均流速； $\overline {{u_*}} $ 为试验段平均摩阻流速；B为水槽宽度；Fr为弗劳德数；Re为水流雷诺数；Re*为粗糙雷诺数(${\operatorname{Re} _*} = \overline {{u_*}} d/\upsilon $ ???)。
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