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The effect of seam imperfections on the unsteady flow within a fluid-filled torus

Published online by Cambridge University Press:  12 February 2015

Sophie A. W. Calabretto ,
Trent W. Mattner  and
James P. Denier
Sophie A. W. Calabretto
Affiliation:
Department of Engineering Science, The University of Auckland, Auckland 1142, New Zealand
Trent W. Mattner
Affiliation:
School of Mathematical Sciences, The University of Adelaide, Adelaide 5005, Australia
James P. Denier*
Affiliation:
Department of Engineering Science, The University of Auckland, Auckland 1142, New Zealand
*
†Email address for correspondence: [email protected]
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Abstract

We consider the behaviour of the flow within a fluid-filled torus when there is a sudden change in the rotation rate of the torus. Experimental work on this problem by Madden & Mullin (J. Fluid Mech., vol. 265, 1994, p. 217) demonstrated a flow with a rich and complex dynamics. In particular, planar (top-down) flow visualisation images show a well-defined laminar band at both the inner and outer bend of the toroidal pipe. Hewitt et al. (J. Fluid Mech., vol. 688, 2011, pp. 88–119) demonstrated the existence of finite-time singularities in the resulting viscous boundary layers, and linked the post-singularity structure to one of the laminar bands identified in experiments (Madden & Mullin J. Fluid Mech., vol. 265, 1994, p. 217; del Pino et al.Phys. Fluids, vol. 20 (12), 2008, 124104). The second band (or laminar front) identified by Madden & Mullin was conjectured by Hewitt et al. to be the result of a centrifugal instability, perhaps generated by small imperfections in the experimental apparatus. Here we explore this conjecture further, demonstrating that a small seam imperfection can generate substantial secondary motion but with considerably different dynamics than the centrifugally driven instability of Hewitt et al.

JFM classification

Boundary Layers: Boundary Layers Boundary Layers: Boundary layer separation Boundary Layers: Boundary layer stability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 767 , 25 March 2015 , pp. 240 - 253
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Copyright
© 2015 Cambridge University Press 

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