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The influence of imperfections on the flow structure of steady vortex breakdown bubbles

Published online by Cambridge University Press:  26 April 2007

MORTEN BRØNS ,
WEN ZHONG SHEN ,
JENS NØRKÆR SØRENSEN  and
WEI JUN ZHU
MORTEN BRØNS
Affiliation:
Department of Mathematics, Technical University of Denmark, DK-2800 Lyngby, Denmark
WEN ZHONG SHEN
Affiliation:
Department of Mechanics, Technical University of Denmark, DK-2800 Lyngby, Denmark
JENS NØRKÆR SØRENSEN
Affiliation:
Department of Mechanics, Technical University of Denmark, DK-2800 Lyngby, Denmark
WEI JUN ZHU
Affiliation:
Department of Mathematics, Technical University of Denmark, DK-2800 Lyngby, Denmark Department of Mechanics, Technical University of Denmark, DK-2800 Lyngby, Denmark
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Abstract

Vortex breakdown bubbles in the flow in a closed cylinder with a rotating end-cover have previously been successfully simulated by axisymmetric codes in the steady range. However, high-resolution experiments indicate a complicated open bubble structure incompatible with axisymmetry. Numerical studies with generic imperfections in the flow have revealed that the axisymmetric bubble is highly sensitive to imperfections, and that this may resolve the apparent paradox. However, little is known about the influence of specific, physical perturbations on the flow structure. We perform fully three-dimensional simulations of the flow with two independent perturbations: an inclination of the fixed cover and a displacement of the rotating cover. We show that perturbations below a realistic experimental uncertainty may give rise to flow structures resembling those obtained in experiments, that the two perturbations may interact and annihilate their effects, and that the fractal dimension associated with the emptying of the bubble can quantitatively be linked to the visual bubble structure.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 578 , 10 May 2007 , pp. 453 - 466
Copyright
Copyright © Cambridge University Press 2007

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References

REFRENCES

Bak, P. 1986 The Devil's staircase. Physics Today 39 (12), 38–45.CrossRefGoogle Scholar
Bröns, M., Voigt, L. K. & Sörensen, J. N. 1999 Streamline topology of steady axisymmetric vortex breakdown in a cylinder with co- and counter-rotating end-covers. J. Fluid Mech. 401, 275–292.CrossRefGoogle Scholar
Daube, O. 1991 Numerical simulations of axisymmetric vortex breakdown in a closed cylinder. In Vortex Dynamics and Vortex Methods (ed. Anderson, C. R. & Greengard, C.). Lectures in Applied Mathematics, vol. 28, pp. 131–152. American Mathematical Society.Google Scholar
Escudier, M. P. 1984 Observations of the flow produced in a cylindrical container by a rotating endwall. Exps. Fluids 2, 189–196.CrossRefGoogle Scholar
Gelfgat, A. Y. 2002 Three-dimensionality of trajectories of experimental tracers in a steady axisymmetric swirling flow: Effect of density mismatch. Theor. Comput. Fluid Dyn. 16, 29–41.CrossRefGoogle Scholar
Gelfgat, A. Y., Bar-Yoseph, P. Z. & Solan, A. 1996 Stability of confined swirling flow with and without vortex breakdown. J. Fluid Mech. 311, 1–36.CrossRefGoogle Scholar
Gelfgat, A. Y., Bar-Yoseph, P. Z. & Solan, A. 2001 Three-dimensional instability of axisymmetric flow in a rotating lid-cylinder enclosure. J. Fluid Mech. 438, 363–377.CrossRefGoogle Scholar
Guckenheimer, J. & Holmes, P. 1983 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer.CrossRefGoogle Scholar
Hartnack, J. N., Bröns, M. & Spohn, A. 2000 The role of asymmetric perturbations in steady vortex breakdown bubbles. DCAMM Report 628. Technical University of Denmark.Google Scholar
Holmes, P. 1984 Some remarks on chaotic particle paths in time-periodic, three-dimensional swirling flows. Contemp. Maths 28, 393–404.CrossRefGoogle Scholar
Leibovich, S. 1984 Vortex stability and breakdown: Survey and extension. AIAA J. 22, 1192–1206.CrossRefGoogle Scholar
Lopez, J. M. 1990 Axisymmetric vortex breakdown part 1. Confined swirling flow. J. Fluid Mech. 221, 533–552.CrossRefGoogle Scholar
Lopez, J. M., Cui, Y. D. & Lim, T. T. 2006 Experimental and numerical investigation of the competition between axisymmetric time-periodic modes in an enclosed swirling flow. Phys. Fluids 18, 104016.CrossRefGoogle Scholar
Lopez, J. M. & Perry, A. D. 1992 a Axisymmetric vortex breakdown part 3. Onset of periodic flow and chaotic advection. J. Fluid Mech. 234, 449–471.CrossRefGoogle Scholar
Lopez, J. M. & Perry, A. D. 1992 b Periodic axisymmetric vortex breakdown in a cylinder with a rotating end wall. In Gallery of Fluid Motion (ed H. L.Reed). Phys. Fluids A 4, 1869–1881.Google Scholar
Lugt, H. J. & Abboud, M. 1987 Axisymmetric vortex breakdown in a container with a rotating lid. J. Fluid Mech. 179, 179–190.CrossRefGoogle Scholar
Michelsen, J. A. 1992 Basis3D – a platform for development of multiblock PDE solvers. AFM 92-05. Department of Fluid Mechanics, Technical University of Denmark.Google Scholar
Rom-Kedar, V., Leonard, A. & Wiggins, S. 1990 An analytical study of transport, mixing and chaos in an unsteady vortical flow. J. Fluid Mech. 214, 347–395.CrossRefGoogle Scholar
Ronnenberg, B. 1977 Ein selbstjustierendes 3-Komponenten-Laserdoppler-Anemometer nach dem Vergleichsverfaren, angewandt auf Untersuchungen in einer stationären zylindersymmetrischen Drehströmung mit einem Rückströmgebiet. Bericht 19. Max-Planck-Institut für Strömungsforschung, Göttingen.Google Scholar
Serre, E. & Bontoux, P. 2002 Vortex breakdown in a three-dimensional swirling flow. J. Fluid Mech. 459, 347–370.CrossRefGoogle Scholar
Shen, W. Z., Michelsen, J. A., Sφrensen, H. N. & Sφrensen, J. N. 2003 An improved SIMPLEC method on collocated grids for steady and unsteady flow computations. Numer. Heat Transfer B 43 (3), 221–239.CrossRefGoogle Scholar
Shen, W. Z., Michelsen, J. A. & Sφrensen, J. N. 2001 Improved Rhie-Chow interpolation for unsteady flow computations. AIAA J. 39 (12), 2406–2409.CrossRefGoogle Scholar
Sφrensen, J. N. & Loc, T. P. 1989 High-order axisymmetric Navier-Stokes code: Description and evaluation of boundary conditions. Intl J. Numer. Meth. Fluids 9, 1517–1537.CrossRefGoogle Scholar
Sφrensen, J. N., Naumov, I. & Mikkelsen, R. 2006 Experimental investigation of three-dimensional flow instabilities in a rotating lid-driven cavity. Expts. Fluids 41, 425–440.CrossRefGoogle Scholar
Sφrensen, N. N. 1995 General-purpose flow solver applied over hills. RISφ!-R-827-(EN). RISφ National Laboartory.Google Scholar
Sotiropoulos, F. & Ventikos, Y. 1998 Transition from bubble-type vortex breakdown to columnar vortex in a confined swirling flow. Intl J. Heat Fluid Flow 19, 446–458.CrossRefGoogle Scholar
Sotiropoulos, F. & Ventikos, Y. 2001 The three-dimensional structure of confined swirling flows with vortex breakdown. J. Fluid Mech. 426, 155–175.CrossRefGoogle Scholar
Sotiropoulos, F., Ventikos, Y. & Lackey, T. C. 2001 Chaotic advection in three-dimensional stationary vortex-breakdown bubbles: Sil'nikov's chaos and the devil's staircase. J. Fluid Mech. 444, 257–297.CrossRefGoogle Scholar
Sotiropoulos, F., Webster, D. R. & Lackey, T. C. 2002 Experiments on Lagrangian transport in steady vortex-breakdown bubbles in a confined swirling flow. J. Fluid Mech. 466, 215–248.CrossRefGoogle Scholar
Spohn, A., Mory, M. & Hopfinger, E. J. 1998 Experiments on vortex breakdown in a confined flow generated by a rotating disc. J. Fluid Mech. 370, 73–99.CrossRefGoogle Scholar
Stevens, J. L., Lopez, J. M. & Cantwell, B. J. 1999 Oscillatory flow states in an enclosed cylinder with a rotating endwall. J. Fluid Mech. 389, 101–118.CrossRefGoogle Scholar
Thompson, M. C. & Hourigan, K. 2003 The sensitivity of steady vortex breakdown bubbles in confined cylinder flows to rotating lid misalignment. J. Fluid Mech. 496, 129–138.CrossRefGoogle Scholar
Tsitverblit, N. 1993 Vortex breakdown in a cylindrical container in the light of continuation of a steady solution. Fluid Dyn. Res. 11, 19–35.CrossRefGoogle Scholar
Ventikos, Y. 2002 The effect of imperfections on the emergence of three-dimensionality in stationary vortex breakdown bubbles. Phys. Fluids 14 (3), L13–L16.CrossRefGoogle Scholar
Vogel, H. U. 1968 Experimentelle Ergebnisse über die laminäre Strömung in einem zylindriche Gehäuse mit darin rotierender Scheibe. Bericht 6. Max-Planck-Institut für Strömungsforschung, Göttingen.Google Scholar
Wiggins, S. 1990 Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer.CrossRefGoogle Scholar