Generation and breakup of Worthington jets after cavity collapse. Part 1. Jet formation
Generation and breakup of Worthington jets after cavity collapse. Part 1. Jet formation
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DOI：
10.1017/s0022112010003526
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发表时间：
2010-11-01
影响因子：
3.7
通讯作者：
Gordillo, J. M.
中科院分区：
文献类型：
--
作者：
Gekle, Stephan;Gordillo, J. M.
上个世纪初，Worthington和科尔发现，轴对称固体撞击液体表面后喷射出的高速射流与撞击物尾流中产生的空气空腔的形成和塌陷密切相关。在本文中，我们结合联合收割机详细的边界积分模拟与分析建模来描述形成这样的沃辛顿射流后的影响，一个圆盘上的水。我们扩展了Gekle等人（Phys. Rev. Lett.，Vol.102，2009 A，034502），仅对描述射流基础动力学有效，以描述整个射流。我们发现，射流内部的流动结构可以分为三个不同的区域：轴向加速区域，在那里传入的液体的径向动量被转换为轴向动量;弹道区域，在那里流体粒子没有经历进一步的加速和不断移动的速度在加速区域的结束;和射流尖端区域，在那里射流最终打破成液滴。从我们对弹道区域的建模中，我们得出结论，与高速射流也被喷射的其他物理情况相反，这里研究的沃辛顿射流的类型不能使用Longuet-Higgins的双曲射流理论来描述（J. Fluid Mech.，第127卷，1983，第103页）。最重要的是，我们发现，喷射射流的速度和形状可以很好地预测在任何时刻的时间与唯一的知识之前获得的数量夹断发生。这一事实使我们能够提供封闭的表达式的喷射速度和喷射液滴的大小作为速度和尺寸的冲击器的函数。我们表明，我们的研究结果也适用于沃辛顿射流出现后，从水下喷嘴生长的气泡崩溃，虽然这个系统创建较厚的射流比磁盘的影响。
At the beginning of the last century Worthington and Cole discovered that the high-speed jets ejected after the impact of an axisymmetric solid on a liquid surface are intimately related to the formation and collapse of an air cavity created in the wake of the impactor. In this paper, we combine detailed boundary-integral simulations with analytical modelling to describe the formation of such Worthington jets after the impact of a circular disk on water. We extend our earlier model in Gekle et al. (Phys. Rev. Lett., vol. 102, 2009a, 034502), valid for describing only the jet base dynamics, to describe the whole jet. We find that the flow structure inside the jet may be divided into three different regions: the axial acceleration region, where the radial momentum of the incoming liquid is converted to axial momentum; the ballistic region, where fluid particles experience no further acceleration and move constantly with the velocity obtained at the end of the acceleration region; and the jet tip region, where the jet eventually breaks into droplets. From our modelling of the ballistic region we conclude that, contrary to the case of other physical situations where high-speed jets are also ejected, the types of Worthington jets studied here cannot be described using the theory of hyperbolic jets of Longuet-Higgins (J. Fluid Mech., vol. 127, 1983, p. 103). Most importantly, we find that the velocity and the shape of the ejected jets can be well predicted at any instant in time with the only knowledge of quantities obtained before pinch-off occurs. This fact allows us to provide closed expressions for the jet velocity and the sizes of the ejected droplets as a function of the velocity and the size of the impactor. We show that our results are also applicable to Worthington jets emerging after the collapse of a bubble growing from an underwater nozzle, although this system creates thicker jets than the disk impact.