Experimental study on the anisotropy in von Kármán swirling flow system
-
摘要: 利用Tomo–PIV测量了冯卡门涡旋流动系统中心区域的三维速度信息，通过2种方法计算得到的速度二阶结构函数，分析了该系统中流动的各向异性特性。实验结果表明：冯卡门涡旋流动系统中心区域的流动均匀性较好，但均方根速度的不同分量间呈现出显著的各向异性，水平分量与竖直分量比值约为1.5。通过2种方法计算得到的速度二阶结构函数结果相近，并给出：经过各个方向分量平均后的速度二阶结构函数各向同性度较高；但其在尺度空间中的分布呈现“水平面内各向同性度高，竖直平面内存在一定各向异性”的特性，且随着尺度的减小，此各向异性会逐渐减弱并接近各向同性。该研究为认识湍流流动以及冯卡门涡旋流动系统提供了基础理解和分析方法。Abstract: The degree of anisotropy in the Von Kármán Swirling (VKS) flow system was experimentally investigated. The three-dimensional velocity near the center of VKS was measured by tomographic PIV and two methods were adopted to calculate the second order Velocity Structure Function (VSF2) in order to study the scale-by-scale anisotropy. It is found that the fluctuation velocity is highly homogeneous. However, the Root-Mean-Square (RMS) velocity in the vertical direction is one-third times smaller than that in the horizontal direction, which characterizes the large-scale anisotropy. This large-scale anisotropy has left its fingerprint on the small scales, which is reflected by the observation that the scale-space distribution of VSF2 is isotropic in the horizontal plane while it is not in the vertical plane. Besides, this anisotropy diminishes as scale decreases, consistent with the local isotropy assumption proposed by Kolmogorov. This experimental study provides new insights into turbulent flows.
-
图 3 方法二计算速度结构函数的步骤（二维情况）
Figure 3. Steps to calculate velocity structure function through method Ⅱ （two-dimensional case）
图 4 时均速度场和湍流强度的空间分布
Figure 4. Spatial distribution of the mean velocity field and turbulence intensity
图 5 方法一计算得到的纵向速度二阶结构函数
Figure 5. Longitudinal second order velocity structure function through method Ⅰ
图 6 方法一计算得到的横向速度二阶结构函数
Figure 6. Transverse second order velocity structure function through method Ⅰ
图 7 方法二计算得到的纵向速度二阶结构函数
Figure 7. Longitudinal second order velocity structure function through method Ⅱ
图 8 纵向速度二阶结构函数在尺度空间的分布（方法二）
Figure 8. Scale-space distribution of longitudinal second order velocity structure function through method Ⅱ
图 9 纵向速度二阶结构函数在不同尺度上的脉动（方法二）
Figure 9. Fluctuations of longitudinal second order velocity structure function among the spherical shell through method Ⅱ
图 10 三维尺度空间内极角和方位角的定义
Figure 10. Definition of polar angle and azimuth angle in three-dimensional scale space
图 11 纵向速度二阶结构函数随极角和方位角的变化（方法二）
Figure 11. Variation of longitudinal second order velocity structure function with polar angle and azimuth angle （method Ⅱ）
-
[1] POPE S B. Turbulent flows[M]. Cambridge: Cambridge University Press, 2000. [2] SCHLICHTING H, GERSTEN K. Fundamentals of boundary–layer theory[M]//Boundary-Layer Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 2016: 29-49. . [3] TAYLOR G I. Statistical theory of turbulence[J]. Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences, 1935, 151(873): 421–444. doi: 10.1098/rspa.1935.0158 [4] BATCHELOR G K. The theory of homogeneous turbu-lence[M]. Cambridge: Cambridge University Press, 1953. [5] ORSZAG S A, PATTERSON Jr G S. Numerical simulation of three-dimensional homogeneous isotropic turbulence[J]. Physical Review Letters, 1972, 28(2): 76–79. doi: 10.1103/physrevlett.28.76 [6] ISHIHARA T, GOTOH T, KANEDA Y. Study of high–Reynolds number isotropic turbulence by direct numerical simulation[J]. Annual Review of Fluid Mechanics, 2009, 41: 165–180. doi: 10.1146/annurev.fluid.010908.165203 [7] KOLMOGOROV A N. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers[J]. Proceedings of the Royal Society of London Series A: Mathematical and Physical Sciences, 1991, 434(1890): 9–13. doi: 10.1098/rspa.1991.0075 [8] FRISCH U, KOLMOGOROV A N. Turbulence: the legacy of A. N. Kolmogorov[M]. Cambridge: Cambridge University Press, 1995. [9] MONIN A S, YAGLOM A M. Statistical fluid mechanics, volume Ⅱ: mechanics of turbulence[M]. New York: Dover Publications, 2013. [10] ZANDBERGEN P J, DIJKSTRA D. Von Kármán swirling flows[J]. Annual Review of Fluid Mechanics, 1987, 19: 465–491. doi: 10.1146/annurev.fl.19.010187.002341 [11] DOUADY S, COUDER Y, BRACHET M E. Direct observation of the intermittency of intense vorticity filaments in turbulence[J]. Physical Review Letters, 1991, 67(8): 983–986. doi: 10.1103/physrevlett.67.983 [12] VOTH G A, SATYANARAYAN K, BODENSCHATZ E. Lagrangian acceleration measurements at large Reynolds numbers[J]. Physics of Fluids, 1998, 10(9): 2268–2280. doi: 10.1063/1.869748 [13] VOTH G A, LA PORTA A, CRAWFORD A M, et al. Measurement of particle accelerations in fully developed turbulence[J]. Journal of Fluid Mechanics, 2002, 469: 121–160. doi: 10.1017/s0022112002001842 [14] BOURGOIN M, OUELLETTE N T, XU H T, et al. The role of pair dispersion in turbulent flow[J]. Science, 2006, 311(5762): 835–838. doi: 10.1126/science.1121726 [15] TOMS B A. Some observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers[C]//Proc. of In. Cong. On Rheology, 1948. [16] WHITE C M, MUNGAL M G. Mechanics and prediction of turbulent drag reduction with polymer additives[J]. Annual Review of Fluid Mechanics, 2008, 40: 235–256. doi: 10.1146/annurev.fluid.40.111406.102156 [17] CRAWFORD A M, MORDANT N, XU H T, et al. Fluid acceleration in the bulk of turbulent dilute polymer solutions[J]. New Journal of Physics, 2008, 10(12): 123015. doi: 10.1088/1367-2630/10/12/123015 [18] OUELLETTE N T, XU H T, BODENSCHATZ E. Bulk turbulence in dilute polymer solutions[J]. Journal of Fluid Mechanics, 2009, 629: 375–385. doi: 10.1017/s0022112009006697 [19] XI H D, BODENSCHATZ E, XU H T. Elastic energy flux by flexible polymers in fluid turbulence[J]. Physical Review Letters, 2013, 111(2): 024501. doi: 10.1103/physrevlett.111.024501 [20] ZHANG Y B, BODENSCHATZ E, XU H T, et al. Experimental observation of the elastic range scaling in turbulent flow with polymer additives[J]. Science Advances, 2021, 7(14): eabd3525. doi: 10.1126/sciadv.abd3525 [21] 陈正云, 张清福, 潘翀, 等. 超疏水旋转圆盘气膜层减阻的实验研究[J]. 实验流体力学, 2021, 35(3): 52–59. doi: 10.11729/syltlx20200025CHEN Z Y, ZHANG Q F, PAN C, et al. An experimental study on drag reduction of superhydrophobic rotating disk with air plastron[J]. Journal of Experiments in Fluid Mechanics, 2021, 35(3): 52–59. doi: 10.11729/syltlx20200025 [22] OUELLETTE N T, XU H T, BOURGOIN M, et al. Small-scale anisotropy in Lagrangian turbulence[J]. New Journal of Physics, 2006, 8(6): 102. doi: 10.1088/1367-2630/8/6/102 [23] SREENIVASAN K R. On the universality of the Kolmogorov constant[J]. Physics of Fluids, 1995, 7(11): 2778–2784. doi: 10.1063/1.868656 [24] YEUNG P K, ZHOU Y. Universality of the Kolmogorov constant in numerical simulations of turbulence[J]. Physical Review E, 1997, 56(2): 1746–1752. doi: 10.1103/physreve.56.1746 [25] MONCHAUX R, RAVELET F, DUBRULLE B, et al. Properties of steady states in turbulent axisymmetric flows[J]. Physical Review Letters, 2006, 96(12): 124502. doi: 10.1103/physrevlett.96.124502 [26] KNUTSEN A N, BAJ P, LAWSON J M, et al. The inter-scale energy budget in a von Kármán mixing flow[J]. Journal of Fluid Mechanics, 2020, 895: A11. doi: 10.1017/jfm.2020.277 [27] TAYLOR M A, KURIEN S, EYINK G L. Recovering isotropic statistics in turbulence simulations: the Kolmo-gorov 4/5th law[J]. Physical Review E, 2003, 68(2): 026310. doi: 10.1103/PhysRevE.68.026310 -
下载:
点击查看大图
计量
- 文章访问数: 75
- HTML全文浏览量: 27
- PDF下载量: 7
- 被引次数: 0
