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http://dx.doi.org/10.26748/KSOE.2021.070

Analysis of Steady Vortex Rings Using Contour Dynamics Method for Fluid Velocity  

Choi, Yoon-Rak (School of Naval Architecture and Ocean Engineering, University of Ulsan)
Publication Information
Journal of Ocean Engineering and Technology / v.36, no.2, 2022 , pp. 108-114 More about this Journal
Abstract
Most studies on the shape of the steady vortex ring have been based on the Stokes stream function approach. In this study, the velocity approach is introduced as a trial approach. A contour dynamics method for fluid velocity is used to analyze the Norbury-Fraenkel family of vortex rings. Analytic integration is performed over the logarithmic-singular segment. A system of nonlinear equations for the discretized shape of the vortex core is formulated using the material boundary condition of the core. An additional condition for the velocities of the vortical and impulse centers is introduced to complete the system of equations. Numerical solutions are successfully obtained for the system of nonlinear equations using the iterative scheme. Specifically, the evaluation of the kinetic energy in terms of line integrals is examined closely. The results of the proposed method are compared with those of the stream function approaches. The results show good agreement, and thereby, confirm the validity of the proposed method.
Keywords
Norbury-Fraenkel family of vortex rings; Contour dynamics method; Velocity; Integration over the logarithmic-singular segment; Velocities of vortical and impulse centers;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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