A generalized vortex ring model
A generalized vortex ring model
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DOI：
10.1017/s0022112008005168
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发表时间：
2009-03
影响因子：
3.7
通讯作者：
By Felix Kaplanski;S. Sazhin;Y. Fukumoto;S. Begg;M. Heikal
中科院分区：
文献类型：
--
作者：
By Felix Kaplanski;S. Sazhin;Y. Fukumoto;S. Begg;M. Heikal
通过假设涡环厚度的时间依赖性由关系式给出，其中a是正数且1/4 ≤ B ≤ 1/2，将传统的层流涡环模型推广。在$a=\sqrt{2\nu}$的情况下，其中ν是层流运动粘度，B = 1/2，广义模型的预测与传统层流模型的预测相同。在B = 1/4的情况下，它的某些预测与湍流涡环模型相似，假定与时间有关的有效湍流粘度ν ε等于τ ε ′。在固定涡环半径R 0和增加涡环半径的情况下都进行这种推广。在后一种情况下，所谓的第二Saffman公式被修改。在固定R 0的情况下，预测的涡度分布短时间内显示出密切的协议与高斯形式的所有B和比较有利的可用的实验数据。分析了最大涡量区和流体在参考系中随涡环质心运动的速度为零的区域的位置随时间的演化。注意到两个区域的位置都取决于B，后一个区域总是比第一个区域更远离涡轴。结果表明，在第一区域中的流体的轴向速度总是大于在第二区域中的轴向速度。两个速度都强烈地依赖于B。虽然这两个区域中速度的径向分量都等于零，但这两个区域的位置都随时间而变化。这导致引入有效径向速度分量;后一种情况取决于B。该模型的预测与文献报道的涡环参数的实验测量结果进行了比较。
A conventional laminar vortex ring model is generalized by assuming that the time dependence of the vortex ring thickness ℓ is given by the relation ℓ = atb, where a is a positive number and 1/4 ≤ b ≤ 1/2. In the case in which $a=\sqrt{2\nu}$, where ν is the laminar kinematic viscosity, and b = 1/2, the predictions of the generalized model are identical with the predictions of the conventional laminar model. In the case of b = 1/4 some of its predictions are similar to the turbulent vortex ring models, assuming that the time-dependent effective turbulent viscosity ν∗ is equal to ℓℓ′. This generalization is performed both in the case of a fixed vortex ring radius R0 and increasing vortex ring radius. In the latter case, the so-called second Saffman's formula is modified. In the case of fixed R0, the predicted vorticity distribution for short times shows a close agreement with a Gaussian form for all b and compares favourably with available experimental data. The time evolution of the location of the region of maximal vorticity and the region in which the velocity of the fluid in the frame of reference moving with the vortex ring centroid is equal to zero is analysed. It is noted that the locations of both regions depend upon b, the latter region being always further away from the vortex axis than the first one. It is shown that the axial velocities of the fluid in the first region are always greater than the axial velocities in the second region. Both velocities depend strongly upon b. Although the radial component of velocity in both of these regions is equal to zero, the location of both of these regions changes with time. This leads to the introduction of an effective radial velocity component; the latter case depends upon b. The predictions of the model are compared with the results of experimental measurements of vortex ring parameters reported in the literature.