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The wake of falling disks at low Reynolds numbers

ISSN号：0567-7718
期刊名称：Acta Mechanica Sinica
时间：0
页码：367-371
分类：O322[理学—一般力学与力学基础;理学—力学] V231.3[航空宇航科学与技术—航空宇航推进理论与工程;航空宇航科学技术]
作者机构：[1]Aero Science Key Lab of High ReynoldsAerodynamic Force at High Speed,AVIC Aerodynamics Research Institute,No. 701 PO-Box, 110034 Shenyang, China, [2]State Key Laboratory of Turbulence and Complex Systems,College of Engineering, Peking University, 100871 Beijing, China
相关基金：The project was supported by the National Natural Science Fun- dation of China （10910301062, 11102197）, the National Climb-B Plan （2009CB724100）, the National Foundation for Distinguished Young Scholar of China （10525208）, and the Science Fund for Creative Research Groups （10921202）.Acknowledgement The authors are grateful to Prof. Jun Zhang at New York University for helpful discussions.
相关项目：可压缩湍流的机理、模式及实验研究

关键词：低雷诺数, 磁盘, Hopf分岔, 临界雷诺数, 尾流结构, 流动模式, 高雷诺数, 旋涡结构, Flow visualization- Transition , Wake

中文摘要：

我们设想了垂直地掉在静止的水里的圆形的磁盘的 wake 结构。wake 的进化被显示类似于在一个固定磁盘后面的流动模式。雷纳兹数字， Re =Ud/ ，在 40200 的范围。与雷纳兹数字的上升，常规分叉发生在第一批评雷纳兹数字 Rec1 Re_{ c_1 } ，从 axisymmetric 导致转变弄醒结构到一架飞机对称的；Hopf 分叉发生在第二批评雷纳兹数字 Rec2 Re_{ c_2 } ， wake 结构变得不稳定。当周期的旋涡流出现了， wake 结构的飞机对称首先被失去，但是在更高级的雷纳兹数字恢复了。当我们为另外的掉落的身体为薄磁盘把我们的结果与那些作比较，二个批评雷纳兹数字之间的差别被发现是形状依赖者，例如范围和锥。这观察能以旋涡的结构的不稳定性机制被理解。

英文摘要：

We visualized the wake structure of circular disks falling vertically in quiescent water. The evolution of the wake was shown to be similar to the flow patterns behind a fixed disk. The Reynolds number, Re = Ud/v, is in the range of 40 - 200. With the ascension of Reynolds numbers, a regular bifurcation occurred at the first critical Reynolds number Reel, leading to a transition from an axisymmetric wake structure to a plane symmetric one; A Hopf bifurcation took place at the second critical Reynolds number Rec2, as the wake structure became unsteady. Plane symmetry of the wake structure was first lost as periodic vortex shedding ap- peared, but recovered at higher Reynolds number. The differ- ence between the two critical Reynolds numbers was found to be shape-dependent, as we compared our results for thin discs with those for other falling bodies, such as spheres and cones. This observation could be understood in terms of the instability mechanism of the vortical structure.

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