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Transport and stirring induced by vortex formation

Published online by Cambridge University Press:  23 November 2007

S. C. SHADDEN ,
K. KATIJA ,
M. ROSENFELD ,
J. E. MARSDEN  and
J. O. DABIRI
S. C. SHADDEN
Affiliation:
Control and Dynamical Systems, California Institute of Technology, Pasadena, CA 91125, USA
K. KATIJA
Affiliation:
Graduate Aeronautical Laboratories & Bioengineering, California Institute of Technology, Pasadena, CA 91125, USA
M. ROSENFELD
Affiliation:
Department of Fluid Mechanics and Heat Transfer, Tel Aviv University, Ramat Aviv, 69978, Israel
J. E. MARSDEN
Affiliation:
Control and Dynamical Systems, California Institute of Technology, Pasadena, CA 91125, USA
J. O. DABIRI
Affiliation:
Graduate Aeronautical Laboratories & Bioengineering, California Institute of Technology, Pasadena, CA 91125, USA
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Abstract

The purpose of this study is to analyse the transport and stirring of fluid that occurs owing to the formation and growth of a laminar vortex ring. Experimental data was collected upstream and downstream of the exit plane of a piston-cylinder apparatus by particle-image velocimetry. This data was used to compute Lagrangian coherent structures to demonstrate how fluid is advected during the transient process of vortex ring formation. Similar computations were performed from computational fluid dynamics (CFD) data, which showed qualitative agreement with the experimental results, although the CFD data provides better resolution in the boundary layer of the cylinder. A parametric study is performed to demonstrate how varying the piston-stroke length-to-diameter ratio affects fluid entrainment during formation. Additionally, we study how regions of fluid are stirred together during vortex formation to help establish a quantitative understanding of the role of vortical flows in mixing. We show that identification of the flow geometry during vortex formation can aid in the determination of efficient stirring. We compare this framework with a traditional stirring metric and show that the framework presented in this paper is better suited for understanding stirring/mixing in transient flow problems. A movie is available with the online version of the paper.

JFM classification

Vortex Flows: Vortex Flows Mixing: Mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 593 , 25 December 2007 , pp. 315 - 331
Copyright
Copyright © Cambridge University Press 2007

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References

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Shadden et al. supplementary movie

Movie 1. Forward-time finite-time Lyapunov exponent (FTLE) field computed from axisymmetric CFD vortex formation data for L/D = 2. The revealed Lagrangian coherent structures show how fluid is entrained into the vortex. Also apparent is the rear boundary to the stopping vortex. The integration time used to compute the FTLE was T = 3, and the x- and y-axes are plotted in metres. The location of the cylinder is represented by the solid rectangle. The movie spans from τ = 0 to τ = 1.725.

Download Shadden et al. supplementary movie(Video)
Video 674 KB

Shadden et al. supplementary movie

Movie 1. Forward-time finite-time Lyapunov exponent (FTLE) field computed from axisymmetric CFD vortex formation data for L/D = 2. The revealed Lagrangian coherent structures show how fluid is entrained into the vortex. Also apparent is the rear boundary to the stopping vortex. The integration time used to compute the FTLE was T = 3, and the x- and y-axes are plotted in metres. The location of the cylinder is represented by the solid rectangle. The movie spans from τ = 0 to τ = 1.725.

Download Shadden et al. supplementary movie(Video)
Video 751.1 KB