### Abstract

Time-periodic vortex flows in an enclosed circular cylinder driven by the rotation of one endwall are investigated experimentally and numerically. This work is motivated partly by the linear stability analysis of Gelfgat [J. Fluid Mech. 438, 363 (2001)], which showed the existence of an axisymmetric double Hopf bifurcation, and the purpose of the experiment is to see if the nonlinear dynamics associated with this double Hopf bifurcation can be captured under laboratory conditions. A glycerin/water mixture was used in a cylinder with variable height-to-radius ratios between Γ =1.67 and 1.81, and Reynolds numbers between Re=2600 and 2800 (i.e., in the neighborhood of the double Hopf). Hot-film measurements provide, for the first time, experimental evidence of the existence of an axisymmetric double Hopf bifurcation, involving the competition between two stable coexisting axisymmetric limit cycles with periods (nondimensionalized by the rotation rate of the endwall) of approximately 31 and 22. The dynamics is also captured in our nonlinear computations, which clearly identify the double Hopf bifurcation as "type I simple," with the characteristic signatures that the two Hopf bifurcations are supercritical and that there is a wedge-shaped region in (Γ, Re) parameter space where both limit cycles are stable, delimited by Neimark-Sacker bifurcation curves.

Original language | English (US) |
---|---|

Article number | 104106 |

Journal | Physics of Fluids |

Volume | 18 |

Issue number | 10 |

DOIs | |

State | Published - Oct 2006 |

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### Keywords

- Bifurcation
- Confined flow
- Flow instability
- Laminar to turbulent transitions
- Numerical analysis
- Pulsatile flow
- Vortices

### ASJC Scopus subject areas

- Mechanics of Materials
- Computational Mechanics
- Physics and Astronomy(all)
- Fluid Flow and Transfer Processes
- Condensed Matter Physics

### Cite this

*Physics of Fluids*,

*18*(10), [104106]. https://doi.org/10.1063/1.2362782

**Experimental and numerical investigation of the competition between axisymmetric time-periodic modes in an enclosed swirling flow.** / Lopez, Juan; Cui, Y. D.; Lim, T. T.

Research output: Contribution to journal › Article

*Physics of Fluids*, vol. 18, no. 10, 104106. https://doi.org/10.1063/1.2362782

}

TY - JOUR

T1 - Experimental and numerical investigation of the competition between axisymmetric time-periodic modes in an enclosed swirling flow

AU - Lopez, Juan

AU - Cui, Y. D.

AU - Lim, T. T.

PY - 2006/10

Y1 - 2006/10

N2 - Time-periodic vortex flows in an enclosed circular cylinder driven by the rotation of one endwall are investigated experimentally and numerically. This work is motivated partly by the linear stability analysis of Gelfgat [J. Fluid Mech. 438, 363 (2001)], which showed the existence of an axisymmetric double Hopf bifurcation, and the purpose of the experiment is to see if the nonlinear dynamics associated with this double Hopf bifurcation can be captured under laboratory conditions. A glycerin/water mixture was used in a cylinder with variable height-to-radius ratios between Γ =1.67 and 1.81, and Reynolds numbers between Re=2600 and 2800 (i.e., in the neighborhood of the double Hopf). Hot-film measurements provide, for the first time, experimental evidence of the existence of an axisymmetric double Hopf bifurcation, involving the competition between two stable coexisting axisymmetric limit cycles with periods (nondimensionalized by the rotation rate of the endwall) of approximately 31 and 22. The dynamics is also captured in our nonlinear computations, which clearly identify the double Hopf bifurcation as "type I simple," with the characteristic signatures that the two Hopf bifurcations are supercritical and that there is a wedge-shaped region in (Γ, Re) parameter space where both limit cycles are stable, delimited by Neimark-Sacker bifurcation curves.

AB - Time-periodic vortex flows in an enclosed circular cylinder driven by the rotation of one endwall are investigated experimentally and numerically. This work is motivated partly by the linear stability analysis of Gelfgat [J. Fluid Mech. 438, 363 (2001)], which showed the existence of an axisymmetric double Hopf bifurcation, and the purpose of the experiment is to see if the nonlinear dynamics associated with this double Hopf bifurcation can be captured under laboratory conditions. A glycerin/water mixture was used in a cylinder with variable height-to-radius ratios between Γ =1.67 and 1.81, and Reynolds numbers between Re=2600 and 2800 (i.e., in the neighborhood of the double Hopf). Hot-film measurements provide, for the first time, experimental evidence of the existence of an axisymmetric double Hopf bifurcation, involving the competition between two stable coexisting axisymmetric limit cycles with periods (nondimensionalized by the rotation rate of the endwall) of approximately 31 and 22. The dynamics is also captured in our nonlinear computations, which clearly identify the double Hopf bifurcation as "type I simple," with the characteristic signatures that the two Hopf bifurcations are supercritical and that there is a wedge-shaped region in (Γ, Re) parameter space where both limit cycles are stable, delimited by Neimark-Sacker bifurcation curves.

KW - Bifurcation

KW - Confined flow

KW - Flow instability

KW - Laminar to turbulent transitions

KW - Numerical analysis

KW - Pulsatile flow

KW - Vortices

UR - http://www.scopus.com/inward/record.url?scp=33750585494&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750585494&partnerID=8YFLogxK

U2 - 10.1063/1.2362782

DO - 10.1063/1.2362782

M3 - Article

AN - SCOPUS:33750585494

VL - 18

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 10

M1 - 104106

ER -