Experimental investigation of the spatial distribution of uniform momentum zones in wall-bounded flow
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摘要: 为深入探索湍流边界层等动量区的空间分布特性，使用大视场粒子图像测速仪在水洞中测量了平板湍流边界层流法向平面内的速度矢量场。通过计算流向速度的概率密度函数，得到不同时刻和空间位置处的等动量区分布，分析不同数量的等动量区沿流向的持续距离以及出现频率。不同等动量区数量下，其对应的流向持续距离和流向间隔具有显著差异。当等动量区数量与其平均值相近时，等动量区在流向的持续距离较长，且流向间隔较小、出现频率较大；反之，当等动量区数量与其平均值相差较大，其对应的流向持续距离较短，且流向间隔较大、出现频率较低。Abstract: Experiments are carried out in a water tunnel to measure the velocity field in the streamwise-wall-normal plane by particle image velocimetry with a large field of view, in order to investigate the spatial distribution of the uniform momentum zones in the turbulent boundary layer. Through calculating the probability density function of the measured streamwise velocity, the temporal and spatial distribution of the uniform momentum zones are achieved. Then the lasting distance and the appearing frequency are analyzed for the uniform momentum zones with different numbers. For different uniform momentum zone numbers, there are apparent differences for both the corresponding lasting distance and appearing frequency. When the number of uniform momentum zones is close to their mean value, the uniform momentum zones can last for long distance along the streamwise direction and have small streamwise separation, appearing more frequently. On the contrary, when the number of uniform momentum zones is far from the mean value, the corresponding uniform momentum zones last for smaller distance along the streamwise direction and have a larger streamwise separation, appearing less frequently.
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图 2 流向瞬时速度平均值随法向高度变化曲线
Figure 2. Distribution of mean streamwise velocity along wall-normal direction
图 3 流向脉动速度均方根值随法向高度变化曲线
Figure 3. Distribution of root-mean-square value of streamwise fluctuation velocity along wall-normal direction
图 4 PIV测量得到的流向瞬时速度等值线图
Figure 4. Iso-contours of instantaneous streamwise velocity measured by PIV
图 5 流向瞬时速度的概率密度分布直方图
Figure 5. Histogram of probability density function of instantaneous streamwise velocity
图 6 由剪切层速度划分得到的瞬时速度场
Figure 6. Instantaneous velocity field obtained by shear layer velocity division
图 7 等动量区数量N的分布图
Figure 7. Distribution of the number N of the detected uniform momentum zones
图 8 等动量区数量平均值与文献数据对比图
Figure 8. Comparison of the mean value of the detected uniform momentum zone number with data in the literature
图 9 不同流向位置处等动量区数量分布
Figure 9. Distribution of the number of uniform momentum zones at different streamwise locations
图 10 流向持续距离$L^+_x $的概率密度分布
Figure 10. Probability density function of the streamwise distance $L^+_x $
图 11 平均流向持续距离随等动量区数量变化
Figure 11. Variation of the mean streamwise distance with the number of uniform momentum zones
图 12 流向间隔$S^+_{x} $的概率密度分布
Figure 12. Probability density function of streamwise separation $S^+_{x} $
图 13 流向间隔平均值随等动量区数量变化
Figure 13. Variation of the mean streamwise separation of uniform momentum zones
图 14 $L^+_{x, {\mathrm{mean}}} S^+_{x, {\mathrm{mean}}} $随等动量区数量N的变化
Figure 14. Variation of $L^+_{x, {\mathrm{mean}}} S^+_{x, {\mathrm{mean}}} $ on the number N of uniform momentum zones
表 1 边界层主要参数
Table 1. Main parameters of the boundary layer
U∞/（m·s−1） uτ/（m·s−1） lν/mm δ/mm θ/mm Reθ Reτ 0.47 0.0189 0.048 47.58 5.40 2740 997 
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