Modelling of confined vortex rings
Modelling of confined vortex rings
复制标题
DOI：
10.1017/jfm.2015.261
复制
发表时间：
2015-07-01
影响因子：
3.7
通讯作者：
Sazhin, Sergei
中科院分区：
文献类型：
--
作者：
Danaila, Ionut;Kaplanski, Felix;Sazhin, Sergei
本文研究了管内涡环的演化规律。本文提出了一种新的轴对称封闭涡环理论模型。该模型的预测结果与现有的实验数据和数值模拟结果一致。该模型结合了Kaplanski & Rudi（Phys. Fluids，vol. 17，2005，087101）开发的粘性涡环模型和Brasseur（斯坦福大学博士论文）推导壁诱导流函数修正的方法。利用涡环粘性长度随时间变化的幂律假设，得到了涡环的主要积分特征、环量、动能和平动速度随时间的变化。直接数值模拟（DNS）被用来测试模型的适用范围，并调查新的物理特性的限制涡环最近报道的实验研究斯图尔特等人。Fluids，第53卷，2012年，pp. 163-171）。该模型示出导致一个非常好的近似的斯托克斯流函数的空间分布，通过DNS获得。该模型还准确地预测了涡旋特征和涡旋能量的时间演化。提出了用DNS得到的真实涡环拟合模型的方法。这为实际工程应用开辟了道路。
This paper is focused on the investigation of vortex rings evolving in a tube. A new theoretical model for a confined axisymmetric vortex ring is developed. The predictions of this model are shown to be in agreement with available experimental data and numerical simulations. The model combines the viscous vortex ring model, developed by Kaplanski & Rudi (Phys. Fluids, vol. 17, 2005, 087101), with Brasseur's (PhD thesis, Stanford University) approach to deriving a wall-induced streamfunction correction. Using the power-law assumption for the time variation of the viscous length of the vortex ring, the time variations of the main integral characteristics, circulation, kinetic energy and translational velocity are obtained. Direct numerical simulation (DNS) is used to test the range of applicability of the model and to investigate new physical features of confined vortex rings recently reported in the experimental study by Stewart et al. (Exp. Fluids, vol. 53, 2012, pp. 163-171). The model is shown to lead to a very good approximation of the spatial distribution of the Stokes streamfunction, obtained by DNS. The vortex signature and the time evolution of the energy of the vortex are also accurately predicted by the model. A procedure for fitting the model with realistic vortex rings, obtained by DNS, is suggested. This opens the way to using the model for practical engineering applications.