Circulation and formation number of laminar vortex rings
Circulation and formation number of laminar vortex rings
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DOI：
10.1017/s0022112098003115
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发表时间：
1998-12
影响因子：
3.7
通讯作者：
M. Rosenfeld;E. Rambod;M. Gharib
中科院分区：
文献类型：
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作者：
M. Rosenfeld;E. Rambod;M. Gharib
对较长放电时间下轴对称涡环的形成时间尺度进行了数值研究。关于形成时间尺度的存在和普遍性的实验结果得到了证实，该形成时间尺度被称为“形成数”。形成数表示涡环达到最大环流的时间。对于活塞冲击运动产生的涡环，其形成数约为4个，这与实验结果非常吻合。将实验研究扩展到其他情况，包括厚剪切层的情况，结果表明，夹断涡的尺度环流对形成过程的细节，如速度方案、速度剖面、涡生几何形状和雷诺数，相对不敏感。这一发现也可能表明，定常涡环的适当尺度环流变化很小。队形数确实取决于速度剖面。非脉冲速度方案略微增加了编队数，而非均匀速度剖面可能会显著减少编队数。例如，在泄流的抛物线速度剖面的情况下，形成数减少多达四倍。这些发现表明，实验发现的形成数微小变化的一个主要来源是排出流速度剖面的不同演变。
The formation time scale of axisymmetric vortex rings is studied numerically for relatively long discharge times. Experimental findings on the existence and universality of a formation time scale, referred to as the ‘formation number’, are confirmed. The formation number is indicative of the time at which a vortex ring acquires its maximal circulation. For vortex rings generated by impulsive motion of a piston, the formation number was found to be approximately four, in very good agreement with experimental results. Numerical extensions of the experimental study to other cases, including cases with thick shear layers, show that the scaled circulation of the pinched-off vortex is relatively insensitive to the details of the formation process, such as the velocity programme, velocity profile, vortex generator geometry and the Reynolds number. This finding might also indicate that the properly scaled circulation of steady vortex rings varies very little. The formation number does depend on the velocity profile. Non-impulsive velocity programmes slightly increase the formation number, while non-uniform velocity profiles may decrease it significantly. In the case of a parabolic velocity profile of the discharged flow, for example, the formation number decreases by a factor as large as four. These findings indicate that a major source of the experimentally found small variations in the formation number is the different evolution of the velocity profile of the discharged flow.