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Understanding evolution of vortex rings in viscous fluids

Published online by Cambridge University Press:  13 December 2017

Aashay Tinaikar Open the ORCID record for Aashay Tinaikar [Opens in a new window] ,
S. Advaith  and
S. Basu Open the ORCID record for S. Basu [Opens in a new window]
Aashay Tinaikar*
Affiliation:
Interdisciplinary Centre for Energy Research, Indian Institute of Science, Bangalore-560012, Karnataka, India
S. Advaith
Affiliation:
Interdisciplinary Centre for Energy Research, Indian Institute of Science, Bangalore-560012, Karnataka, India
S. Basu
Affiliation:
Interdisciplinary Centre for Energy Research, Indian Institute of Science, Bangalore-560012, Karnataka, India Department of Mechanical Engineering, Indian Institute of Science, Bangalore-560012, Karnataka, India
*
†Email address for correspondence: tinaikar.aashay@gmail.com
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Abstract

The evolution of vortex rings in isodensity and isoviscosity fluid has been studied analytically using a novel mathematical model. The model predicts the spatiotemporal variation in peak vorticity, circulation, vortex size and spacing based on instantaneous vortex parameters. This proposed model is quantitatively verified using experimental measurements. Experiments are conducted using high-speed particle image velocimetry (PIV) and laser induced fluorescence (LIF) techniques. Non-buoyant vortex rings are generated from a nozzle using a constant hydrostatic pressure tank. The vortex Reynolds number based on circulation $(\unicode[STIX]{x1D6E4}/\unicode[STIX]{x1D708})$ is varied in the range 100–1500 to account for a large range of operating conditions. Experimental results show good agreement with theoretical predictions. However, it is observed that neither Saffman’s thin-core model nor the thick-core equations could correctly explain vortex evolution for all initial conditions. Therefore, a transitional theory is framed using force balance equations which seamlessly integrate short- and long-time asymptotic theories. It is found that the parameter $A=(a/\unicode[STIX]{x1D70E})^{2}$, where $a$ is the vortex half-spacing and $\unicode[STIX]{x1D70E}$ denotes the standard deviation of the Gaussian vorticity profile, governs the regime of vortex evolution. For higher values of $A$, evolution follows short-time behaviour, while for $A=O(1)$, long-time behaviour is prominent. Using this theory, many reported anomalous observations have been explained.

JFM classification

Vortex Flows: Vortex dynamics Vortex Flows: Vortex Flows Wakes/Jets: Vortex streets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 836 , 10 February 2018 , pp. 873 - 909
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Copyright
© 2017 Cambridge University Press 

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