Experimental study of TRPIV for turbulent boundary layer of longitudinal concave curvature wall
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摘要: 带有曲率和压力梯度作用的湍流边界层广泛地存在于各类工程应用中。以带有流向凹曲率的壁面（简称凹壁面）模型为研究对象，利用双相机大小视场的TRPIV系统分别测量了上游和下游两个不同流向位置的瞬时速度场。以光滑平板模型的实验数据为基准，研究了凹壁面上湍流边界层的变化规律。通过对比光滑平板的平均速度剖面和雷诺应力剖面，发现凹壁面情况下的平均速度剖面逐渐偏离了传统对数律，且湍流强度比平板情况下更弱。以
$ {\varLambda _{ci}} $ 准则识别出的顺向涡为条件进行条件相位平均，发现凹壁面中涡上方正脉动的峰值与空间尺度的变化相反，而下方的负脉动比平板情况更强。进一步使用空间两点相关方法提取相干结构，同时利用椭圆拟合的方法计算近壁区相干结构与壁面的倾角，发现凹壁面上相干结构沿流向的空间尺度逐渐增大。结果表明：当湍流边界层受到凹曲率和顺压梯度的共同作用时，近壁附近与尾迹区内湍流强度的差异增大，同时边界层内相干结构的旋涡强度增加；随着向下游的发展，缓冲层附近顺向涡上方正脉动的空间尺度增大，但峰值降低，而在对数律区的上侧则产生了相反的现象；凹壁面湍流边界层内相干结构向更高法向高度迁移的趋势减弱，且相干结构的空间尺度在下游一侧的增长幅度更大。Abstract: Turbulent boundary layers with curvature and pressure gradient are widely used in various engineering applications. A wall model with concave curvature in streamwise was used as the research object, and the instantaneous velocity fields at two different streamwise positions upstream and downstream were measured by TRPIV experiment with dual camera size field of view. Using experimental data from a smooth flat plate as a benchmark, the variation pattern of the turbulent boundary layer on a concave wall is investigated. By comparing the mean velocity profile and the Reynolds stress profile with those of the smooth flat plate, it was found that the mean velocity profile in the concave wall case gradually deviated from the conventional logarithmic law and that the turbulence intensity was weaker than that in the flat plate case. Conditional averaging is carried out under the condition of the prograde vortex identified by$ {\varLambda _{ci}} $ criterion. It is found that the peak of the positive fluctuations above the vortices in the concave wall varies oppositely to the scale range, while the negative fluctuations below the vortices is stronger than that of flat plate. The coherent structures were further extracted using a spatial two-point correlation method and the inclination of the coherent structures in the near-wall region to the wall was calculated using an ellipse fitting method. It was found that the scale range of the coherent structure on the concave wall gradually increases along the streamwise. The results show that when the turbulent boundary layer is subjected to a combination of concave curvature and favorable pressure gradient, the difference in turbulence intensity near the near-wall region and within the wake region increases, along with an increase in the intensity of vortices in the coherent structures within the boundary layer. With development downstream, the scale range of positive fluctuations above the prograde vortex on the buffer layer increases, but the peak value decreases, while the opposite phenomenon occurs on the upper side of logarithmic region. The trend of coherent structure migration to higher normal height in the curved wall turbulent boundary layer is weakened, and scale range of the coherent structures grows mainly towards the downstream side. -
图 7 小视场y*+ ref=30附近顺向涡流向脉动速度的条件平均等值线图
Figure 7. Conditional phase-averaged contour of the fluctuation velocity in the direction of the downward vortex near y*+ ref=30 in a small field
图 8 小视场y*+ ref=80附近顺向涡流向脉动速度的条件平均等值线图
Figure 8. Conditional phase-averaged contour of the fluctuation velocity in the direction of the downward vortex near y*+ ref=80 in a small field
图 9 小视场流向两点相关系数等值线图
Figure 9. The contour of two points correlation coefficient in the streamwise direction in the small field
图 10 大视场流向两点相关系数等值线图
Figure 10. The contour of two points correlation coefficient in the streamwise direction in the large field
表 1 边界层参数
Table 1. Boundary layer parameters
上游（L=2.0 m） 下游（L=2.3 m） 平板实验 U∞/（m·s−1） 0.316 0.328 0.267 uτ,large/（m·s−1） 0.0175～0.0180 0.0196～0.0203 0.0116 uτ,small/（m·s−1） 0.0179 0.0202 0.0116 δ99/mm 36.85 37.29 60.16 Reτ 659.6 753.3 697.9 K 9.03×10−7 1.68×10−6 — 
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