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

  • Sophie A. W. Calabretto (a1), Trent W. Mattner (a2) and James P. Denier (a1)

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.

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Corresponding author

Email address for correspondence: j.denier@auckland.ac.nz

References

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Banks, W. H. H. & Zaturska, M. B. 1979 The collision of unsteady laminar boundary layers. J. Engng Maths 13 (3), 193212.
Blackburn, H. M. & Sherwin, S. J. 2004 Formulation of a Galerkin spectral element-Fourier method for three-dimensional incompressible flows in cylindrical geometries. J. Comput. Phys. 197, 759778.
Boirin, O., Deplano, V. & Pelissier, R. 2006 Experimental and numerical studies on the starting effect on the secondary flow in a bend. J. Fluid Mech. 574, 109129.
Denier, J. P., Hall, P. & Seddougui, S. O. 1991 On the receptivity problem for Görtler vortices: vortex motions induced by wall roughness. Phil. Trans. R. Soc. Lond. 335 (1636), 5185.
Dennis, S. C. R. & Duck, P. W. 1988 Unsteady flow due to an impulsively started rotating sphere. Comput. Fluids 16 (3), 291310.
Hall, P. 1990 Görtler vortices in growing boundary layers: the leading edge receptivity problem, linear growth and the nonlinear breakdown stage. Mathematika 37, 151189.
Hewitt, R. E., Hazel, A. L., Clarke, R. J. & Denier, J. P. 2011 Unsteady flow in a rotating torus after a sudden change in rotation rate. J. Fluid Mech. 688, 88119.
Kluwick, A. & Wohlfahrt, H. 1986 Hot-wire-anemometer study of the entry flow in a curved duct. J. Fluid Mech. 165, 335353.
Madden, F. N. & Mullin, T. 1994 The spin-up from rest of a fluid-filled torus. J. Fluid Mech. 265, 217244.
Mangalam, S. M., Dagenhart, J. R. & Meyers, J. F. 1985 The Görtler instability on an airfoil. AIAA Paper 85-0491.
Noskov, V., Stepanov, R., Denisov, S., Frick, P., Verhille, V., Pilhon, N. & Pinton, J.-F. 2009 Dynamics of a turbulent spin-down flow inside a torus. Phys. Fluids 21, 045108.
Pedley, T. J. 2003 Mathematical modelling of arterial fluid dynamics. J. Engng Maths 47, 419444.
del Pino, C., Hewitt, R. E., Clarke, R. J., Mullin, T. & Denier, J. P. 2008 Unsteady fronts in the spin-down of a fluid-filled torus. Phys. Fluids 20 (12), 124104.
Riley, N. 1998 Unsteady fully-developed flow in a curved pipe. J. Engng Maths 34, 131141.
Schrader, L., Brandt, L. & Zaki, T. A. 2011 Receptivity instability and breakdown of Görtler flow. J. Fluid Mech. 682, 362396.
Stewartson, K., Cebeci, T. & Chang, K. C. 1980 A boundary-layer collision in a curved duct. Q. J. Mech. Appl. Maths 33 (1), 5975.
Walbran, S. H., Cater, J. E. & Clarke, R. J. 2013 Cross-sectional flow measurements during spin-down of a rotating torus. In PIV2013: 10th International Symposium on Particle Image Velocimetry, Delft, The Netherlands.
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The effect of seam imperfections on the unsteady flow within a fluid-filled torus

  • Sophie A. W. Calabretto (a1), Trent W. Mattner (a2) and James P. Denier (a1)

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