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Evolution of the Lagrangian drift and vortex added-mass of a growing vortex ring

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Abstract

The vortex-based propulsive systems’ enhanced performance greatly contributes to the vortex added-mass effect, which was initially developed to explain the added drag when a solid body accelerates in fluids. However, the solution of the instantaneous vortex added-mass coefficient is still remaining a question because vortices always do not have a stable geometric shape like solid bodies. In this paper, the formation of a canonical vortex ring is performed to investigate the nature of vortex added-mass and explore a solution for estimating the vortex added-mass coefficient. The vortex ring is generated by a piston-cylinder apparatus, and the time-dependent flow fields are recorded by particle image velocimetry technique. The ridges of finite-time Lyapunov exponent are applied to identify the Lagrangian boundary of the vortex ring. It is found that a part of the ambient fluids is entrained by the vortex ring when it propagates downstream, resulting in the growth of the vortex ring. Besides, a significant drift of the ambient fluid is observed to bypass the Lagrangian boundary of the vortex ring and reveals the nature of the vortex added-mass. Thus, the added-mass coefficient of the vortex is redefined as the ratio of the volume of the Lagrangian drift fluids in finite time interval step to the vortex volume at that instant. By referring to McPhaden’s method to estimate the added-mass of a solid body, a method based on the multiple material lines with relative-timestep is developed to estimate the volume of Lagrangian drift fluids induced by the vortex added-mass. Then, an empirical criterion for determining the material line number and the finite time interval step is suggested for the vortex ring flow, and the eventual vortex added-mass coefficient calculated by the volume of Lagrangian drift fluids is found to well agree with the results of Brennen. Moreover, the method based on multiple material lines for calculating Lagrangian drift fluids’ volume suggests a potential solution for estimating the added-mass coefficient of arbitrary vortex structures.

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Authors and Affiliations

  1. School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai, 200240, China

    Shu-jia Lin, Yang Xiang, Zhuo-qi Li, Fu-xin Wang & Hong Liu

Authors
  1. Shu-jia Lin
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  2. Yang Xiang
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  3. Zhuo-qi Li
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  4. Fu-xin Wang
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  5. Hong Liu
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Corresponding author

Correspondence to Yang Xiang.

Additional information

Projects supported by the National Natural Science Foundation of China (Grant Nos. 91441205, 91941301), the China Postdoctoral Science Foundation (Grant No. 2018M642007).

Biography: Shu-jia Lin (1995-), Female, Master

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Lin, Sj., Xiang, Y., Li, Zq. et al. Evolution of the Lagrangian drift and vortex added-mass of a growing vortex ring. J Hydrodyn 33, 725–735 (2021). https://doi.org/10.1007/s42241-021-0064-2

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  • DOI: https://doi.org/10.1007/s42241-021-0064-2

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