引用本文: 李唯一，王涛，张先念，等. 旋转流体多边形自由表面形成机制研究[J]. 实验流体力学，2022，36（X）：1-10.
LI W Y，WANG T，ZHANG X N，et al. Mechanism study of free-surface polygons formation in rotating fluids[J]. Journal of Experiments in Fluid Mechanics, 2022，36（X）：1-10..
 Citation: LI W Y，WANG T，ZHANG X N，et al. Mechanism study of free-surface polygons formation in rotating fluids[J]. Journal of Experiments in Fluid Mechanics, 2022，36（X）：1-10..

## Mechanism study of free-surface polygons formation in rotating fluids

• 摘要: 针对流体在约束旋转中产生多边形涡流的现象，设计了旋转圆筒实验装置，对不同旋转频率、液面高度及圆筒半径下的旋转流体行为进行了研究。基于实验现象，提出了全局复合波模型，该模型的计算结果与实验现象一致。根据流动相似理论，利用量纲分析法对实验数据进行分析处理；借助黑体辐射模型给出了流体参数在一定范围下的经验公式，该公式在径长比小于4的情况下与实验数据符合程度较好。本文建立的全局复合波模型及相关研究结论可为多边形涡流形成机制与变化规律研究提供理论参考。

Abstract: In order to study the formation mechanism of polygon phenomenon in rotating fluid, a test set-up of rotating cylinder which can produce rotating fluid was designed. Experiments on rotating fluid for different rotational frequency, liquid heights and radiuses of cylinder were performed. Based on experimental results, a composite wave theoretical model of the intersection point between the free surface of fluid and the bottom of the container was established according to the wave equation and ignoring the specific movement inside the fluid. On this basis, the theoretical model was verified by experiments, and the rotation state on the experimental phenomenon was further studied. Based on the experimental data and previous work, this paper made empirical formula fitting to the data, and found that the fitting effect of blackbody radiation model is the best. The main conclusions are shown below: 1）The viscous action caused by the relative motion between the rotating fluid and the wall causes the free surface of the fluid to form a polygon, which is related to the rotation frequency, the radius of the container, the height of the liquid surface, and the density and viscosity of the fluid, which can be shown by the phase change of the wave. 2）The radial motion of the intersection point between the free surface of the fluid and the bottom of the container can be regarded as the result of the interaction between the gravity pressure field, the centrifugal field and the reflected wave of the vessel wall and the viscous force of the vessel wall, and the radial wave equation can be approximately described by simple harmonic motion. after the parameters of the wave equation satisfy certain constraints, the free surface profile can be obtained by near Fourier transform projection. 3）For a single influence factor, the number of polygonal edges on the free surface of the rotating fluid is positively related to the rotation frequency and negatively related to the height of the liquid surface. The larger the radius of the cylinder is, the easier it is to form polygons. 4）For more influencing factors, the angle number of polygons on the free surface of rotating fluid is mainly related to the two dimensionless quantities of R/H and 1/Ek. With the increase of 1/Ek, the number of angles increases, but the range of adjacent transition boundaries decreases gradually. In the experiment, the more the number of corners, the more unstable the polygon. The disturbance caused by a slight change in rotation frequency will change the number of angles. In the experiment, there is a R/H value in the range of 2.4, 2.5, which makes polygons form most easily, and the 1/Ek range of adjacent transition boundaries is also the largest. 5）When R/H∈2.0, 4.0, the relationship between the angle number of the rotating fluid and 1/Ek accords with the blackbody radiation model curve, which indicates that the hypothesis of the fluid complex wave may be related to the harmonic oscillator hypothesis of the blackbody radiation. When R/H>4, the constraint effect of the wall is weakened, and the blackbody radiation model can only be used for qualitative prediction. The phenomenon is explored from the theoretical point of view, and the empirical formula is fitted from the experimental point of view. The results can be further applied to theoretical research to determine the physical mechanism of the phenomenon.

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