Reynolds-number Effect on Vortex Ring Evolution
An analytical model describing a vortex ring for low Reynolds numbers (Re) proposed previously by Kaplanski and Rudi Phys. Fluids,17, 087101 (2005), is extended to a vortex rings for higher Reynolds numbers. The experimental results show that the vortex ring core takes the oblate ellipsoidal shape with increasing Re. In order to model this feature, we suggest an expression for the vorticity distribution, which corrects the linearized solution of the Navier-Stokes equation, with two disposable nondimensional parameters λ and β governing the shape of the vortex core, and derive the new expressions for the streamfuction, circulation, energy and translation velocity on the basis of it. The appropriate values of λ and β are calculated by equating the nondimensional energy Γd and circulation Gd of the theoretical vortex to the corresponding values obtained from the experimental or numerical vortex ring. To validate the model, the data adapted from the numerical study of a vortex ring at Re= 1 400 performed by Danaila and Helie Phys. Fluids, 20, 073602 (2008), is applied. It is shown that the predicted temporal evolution of the translation velocity at high Reynolds numbers matches very well with the experiments and numerical simulations.
vortex ring translation velocity postformation evolution
F. Kaplanski Y. Fukumoto Y. Rudi
Laboratory of Multiphase Media Physics, Tallinn University of Technology, Tallinn, 12618 Estonia Graduate School of Mathematics and Mathematical Research Centre for Industrial Technology, Kyushu Un
国际会议
广州
英文
57-60
2011-06-30（万方平台首次上网日期，不代表论文的发表时间）