Study on Discharge Coefficients of Drain Orifices in Closed Cavities
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摘要:
该文利用数值方法模拟了封闭腔体的排液流动，获取了排液孔的流量系数。通过量纲分析法研究了小孔流量系数的主要影响因素，拟合了计算小孔流量系数的经验公式。结果表明：当水头高度小于200 mm时，小孔流量系数随水头高度的增加而减小；当水头高度大于200 mm时，小孔流量系数稳定在0.61附近。不同厚径比的小孔流量系数表现为两种不同的形式：小厚径比的小孔呈现薄孔流动特性，流量系数为0.6左右；大厚径比的小孔呈现厚孔流动特性，流量系数为0.8左右。
Abstract:The discharge flow was numerically simulated to obtain discharge coefficients. The main factors influencing the discharge coefficients of orifices were studied by dimensional analysis, and the empirical fitting formulas for calculating discharge coefficients were given. The results show that, with a water head height less than 200 mm, the discharge coefficient decreases with the increase of the head height. With a water head height more than 200 mm, the discharge coefficient keeps stable around 0.61. The discharge coefficients with different thickness to diameter ratios show 2 different forms: the orifices with small thickness-diameter ratios show thin orifice flow characteristics, and the discharge coefficient is about 0.6; the orifices with big thickness to diameter ratios show thick orifice flow characteristics, and the discharge coefficient is about 0.8.
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Key words:
- numerical simulation /
- discharge coefficient /
- dimensional analysis /
- empirical formula
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图 1 封闭腔体简化模型及排液孔局部的网格拓扑结构
Figure 1. The simplified model for the closed cavity and the mesh topology of the drain orifice
图 3 小孔流量系数随孔厚度的变化
Figure 3. Evolution of the discharge coefficient with the orifice thickness
图 4 小孔流量系数随水头高度的变化
Figure 4. Evolution of the discharge coefficient with the head height
图 5 小孔流量系数随水力直径的变化
Figure 5. Evolution of the discharge coefficient with the hydraulic diameter
图 6
$h/d \geqslant 40$ 时小孔流量系数随厚径比$l/d$ 和Reynolds数$Re$ 的变化：（a） 厚径比l/d；（b） ReFigure 6. Evolution of the discharge coefficient with thickness to diameter ratio
$l/d$ and Reynolds number$Re$ for$h/d \geqslant 40$ : （a） thickness to diameter ratio l/d；（b） Re
图 7 利用流线和压力云图描述的小孔附近流动拓扑结构：(a) l/d=0.4；(b) l/d=2
注 为了解释图中的颜色，读者可以参考本文的电子网页版本。
Figure 7. The flow topology near the orifice of plotted streamlines and contours of pressure: (a) l/d=0.4; (b) l/d=2
图 8 涡量厚度沿分离剪切层的分布
Figure 8. Distribution of the vorticity thickness along the separated shear layer
表 1 圆形排液孔的几何参数
Table 1. Geometric parameters of circular drain orifices
d/mm l/mm l/d 5 2, 5, 10, 15, 20 0.4, 1, 2, 3, 4 10 2, 5, 10, 15, 20 0.2, 0.5, 1, 1.5, 2 15 2, 5, 10, 15, 20 0.13, 0.3, 0.67, 1, 1.3 20 2, 5, 10, 15, 20 0.1, 0.25, 0.5, 0.75, 1 
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