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旋转流体多边形自由表面形成机制研究

李唯一 王涛 张先念 李雪琴 孙振生

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 doi: 10.11729/syltlx20220074
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 doi: 10.11729/syltlx20220074
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. doi: 10.11729/syltlx20220074
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. doi: 10.11729/syltlx20220074

旋转流体多边形自由表面形成机制研究

doi: 10.11729/syltlx20220074
基金项目: 国家自然科学基金重大研究计划(91952110),国防科技173基础加强计划(2021-JCJQ-JJ-0424)
详细信息
    作者简介:

    李唯一:(1999—),男,湖北应城人,博士研究生。研究方向:气体动力学。通信地址:西安市灞桥区同心路2号火箭军工程大学(710025)。E-mail:bestleeimpact@163.com

    通讯作者:

    E-mail:wtao009@163.com

  • 中图分类号: O352

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。
  • 图  1  实验室中观察到的六边形涡流现象(上)及其瞬时速度场和涡度图(下)[4]

    Figure  1.  Hexagonal vortex phenomenon observed in the laboratory(up) and Instantaneous velocity field and vorticity map of a hexagonal flow pattern(bottom)[4]

    图  2  旋转圆筒装置示意图与实物图

    Figure  2.  Schematic diagram of rotating cylinder device and view of the perspex cylindrical tank with no working fluid

    图  3  转盘旋转频率与涡流边数的关系

    Figure  3.  The relationship between the frequency of the rotating disk and the number of vortex edges

    图  4  旋转流体自由表面多边形相图

    Figure  4.  Phase diagram for “polygons” on the surface of a fluid on a rotating disk

    图  5  不同圆筒半径下出现椭圆形自由表面时对应的转盘旋转频率

    Figure  5.  The frequency of rotation corresponding to the emergence of elliptical free surface at different cylinder radius

    图  6  对照实验

    Figure  6.  Comparative experimental phenomenon

    图  7  交点在径向上的运动规律

    Figure  7.  Radial motion of intersection points

    图  8  交点侧视图

    Figure  8.  Side view of intersection points

    图  9  由黏滞力引起的波相位差示意图(俯视图)

    Figure  9.  Schematic diagram of wave phase difference caused by viscosity(top view)

    图  10  交点波动方程在给定参数下的可视化图像(ω=π/6)[14-15]

    Figure  10.  Visualization of wave equation at intersection with given parameters(ω=π/6)[14-15]

    图  11  同一N值下R/H与1/Ek的关系

    Figure  11.  The relationship between different N values corresponding to R/H and 1/Ek

    图  12  两种模型的拟合结果

    Figure  12.  The fitting results of the two models

    图  13  黑体辐射模型曲线的检验结果

    Figure  13.  Test results of blackbody radiation model curves

    表  1  实验参数

    Table  1.   Experimental condition parameter setting

    实验名称不变量变量变量取值
    实验1:旋转频率f
    对涡流边数的影响研究
    R=105 mm
    H=44 mm
    f 0~12.5 Hz
    实验2:液面高度H
    对涡流边数的影响研究
    R=105 mm Hf H=18、22、35、45和50 mm
    f=0~11.5 Hz
    实验3:圆筒半径R
    对涡流边数的影响研究
    H=25 mm Rf R=35、50、65、85和105 mm
    f=0~11.7 Hz
    实验4:圆筒与转盘
    共同旋转对照实验
    R=105 mm
    H=44 mm
    f f=0~12.5 Hz
    实验5:固定方向上
    分界面交点运动规律研究
    R=105 mm
    H=44 mm
    f=7.5 Hz
    下载: 导出CSV

    表  2  式(6)各参数取值满足的约束条件

    Table  2.   Constraint conditions of each parameter value in Equation (6)

    NkAεαα区间长度
    2N/24/N[2, R][4, 7]3.0
    3[2.8, R][5.5, 6.8]1.3
    4[4, R][6, 6.8]0.8
    5[6.5, R][5.9, 6.6]0.7
    6[6.5, R][6, 6.6]0.6
    下载: 导出CSV

    表  3  高空核爆电磁脉冲模型拟合结果

    Table  3.   Fitting results of HEMP model

    经验公式过渡界R2系数AIC值
    $1/Ek(\tau \text{,2})=40\;182[{\text{e} }^{-1.681(\tau -2)}-{\text{e} }^{-2.837(\tau -2)}]$两角过渡界0.98397.03
    $1/Ek(\tau \text{,3})=38\;770[{\text{e} }^{-1.293(\tau -2)}-{\text{e} }^{-3.376(\tau -2)}]$三角过渡界0.934111.96
    $1/Ek(\tau \text{,4})=60\;290[{\text{e} }^{-1.388(\tau -2)}-{\text{e} }^{-3.457(\tau -2)}]$四角过渡界0.93498.22
    $1/Ek(\tau \text{,5})=64\;087[{\text{e} }^{-1.299(\tau -2)}-{\text{e} }^{-3.486(\tau -2)}]$五角过渡界0.94498.77
    下载: 导出CSV

    表  4  黑体辐射模型拟合结果

    Table  4.   Fitting results of blackbody radiation model

    经验公式过渡界R2系数AIC值
    $1/Ek(\tau \text{,2})\text{=}\dfrac{1.125\times {10}^{6} }{({\text{e} }^{\frac{0.119}{\tau -2} }){\tau }^{6.845} }$两角过渡界0.99981.314
    $1/Ek(\tau ,\text{3})\text{=}\dfrac{3.434\times {10}^{6} }{({\text{e} }^{\frac{0.168}{\tau -2} }-1){\tau }^{6.980} }$三角过渡界0.980104.875
    $1/Ek(\tau ,\text{4})\text{=}\dfrac{4.865\times {10}^{6} }{({\text{e} }^{\frac{0.148}{\tau -2} }-1){\tau }^{7.110} }$四角过渡界0.97992.476
    $1/Ek(\tau ,\text{5})\text{=}\dfrac{3.910\times {10}^{6} }{({\text{e} }^{\frac{0.137}{\tau -2} }-1){\tau }^{6.824} }$五角过渡界0.98392.880
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-08-08
  • 修回日期:  2022-09-02
  • 录用日期:  2022-09-07
  • 网络出版日期:  2022-10-13

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