Numerical Study of a Vortex Ring Interacting with a Three-dimensional Convex Surface

Heng Ren,Hongshan Guan,Xianfeng Zhang,Genxuan Zhang,Wanjun Liu

doi:10.19026/rjaset.8.1174

Abstract

A vortex ring impinging on a three-dimensional bump is studied using Large Eddy Simulation (LES) for a Reynolds number Re = 4×10 4 based on the initial diameter and translational speed of the vortex ring. The evolution of vortical structures are investigated and an array of flow phenomena are discovered, such as the generation and deformation of secondary vortex ring, formation of loop-like vortices, interaction of vortex rings and the instability and breakdown of vortical structures. The total enstrophy of the flow reasonably elucidates some typical phases of flow evolution. Based on the Fourier analysis of the vertical vorticity, the azimuthal instabilities of the primary vortex ring are studied. Furthermore, the mechanism of vorticity generation on the bump surface has been revealed based on analysis of the boundary vorticity flux.

Highlights

As one of the simplest and important forms of vortex motion, vortex rings widely exist in nature and engineering
By means of Fourier analysis of the azimuthal perturbation, it is identified that the wave number of the most unstable mode for the primary ring is k = 11, consistent with the theoretical estimate of the dominant mode k = 2.26/σ0 approximately by Maxworthy (1972) and the number of the wavy-like structures observed at t = 17.5 and 20.0
After the primary ring collides with the bump surface, the secondary ring generated lifts up from the surface and moves over the primary vortex ring

Summary

Introduction

As one of the simplest and important forms of vortex motion, vortex rings widely exist in nature and engineering. The interaction of vortex rings with solid or fluid boundaries is a fundamental problem in fluid dynamics and has received considerable attention recent years. The interest in this subject is mainly due to its significant practical applications, such as cavitated rings being used for underwater drilling (Chahine and Genoux, 1983), vortex rings extinguishing gas and oil well fires (Akhmetov et al, 1980) and modeling the interaction between the downburst and the aircraft (Lundgren and Mansour, 1991). Vortex rings interacting with a flat wall has been extensively studied. The instability of vortex rings should be considered when the Reynolds number becomes large enough

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Conclusion