### Abstract

A continuation method has been used with a finite element grid and a geometric perturbation to compute two successive symmetry breaking flow transitions with increasing Reynolds number in flow of generalized Newtonian fluids through a sudden planar expansion. With an expansion ratio of 16, the onset Reynolds number is particularly sensitive to small geometric asymmetry and the critical Reynolds numbers for the two successive flow transitions are found to be very close. These transitions are delayed to higher onset Reynolds numbers by increasing the degree of pseudoplasticity. This trend is observed experimentally as well in this work and may be attributed to the competing effects of shear thinning and inertia on the size of the corner vortex before the symmetry breaking flow transition. After the second transition with an expansion ratio of 16, the two large staggered vortices on opposite walls occupy most of the transverse dimension so that the core flow between the vortices appears as a thin jet oscillating along the flow direction. This is more pronounced for the pseudoplastic liquid. After the second transition, the degree of flow asymmetry at a given location downstream of the expansion plane is larger for the pseudoplastic liquid than for the Newtonian liquid at comparable Reynolds numbers. The last feature is also evident in the experimentally observed velocity profiles.

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

Pages (from-to) | 945-962 |

Number of pages | 18 |

Journal | International Journal for Numerical Methods in Fluids |

Volume | 38 |

Issue number | 10 |

DOIs | |

State | Published - Apr 10 2002 |

### Profile

### Keywords

- Asymmetric flow
- Bifurcation
- Instability
- Sudden expansion
- Transition

### ASJC Scopus subject areas

- Condensed Matter Physics
- Safety, Risk, Reliability and Quality
- Applied Mathematics
- Computational Theory and Mathematics
- Computer Science Applications
- Computational Mechanics
- Mechanics of Materials

### Cite this

*International Journal for Numerical Methods in Fluids*,

*38*(10), 945-962. DOI: 10.1002/fld.242

**Asymmetric flows in planar symmetric channels with large expansion ratio.** / Mishra, Sanjay; Jayaraman, K.

Research output: Contribution to journal › Article

*International Journal for Numerical Methods in Fluids*, vol 38, no. 10, pp. 945-962. DOI: 10.1002/fld.242

}

TY - JOUR

T1 - Asymmetric flows in planar symmetric channels with large expansion ratio

AU - Mishra,Sanjay

AU - Jayaraman,K.

PY - 2002/4/10

Y1 - 2002/4/10

N2 - A continuation method has been used with a finite element grid and a geometric perturbation to compute two successive symmetry breaking flow transitions with increasing Reynolds number in flow of generalized Newtonian fluids through a sudden planar expansion. With an expansion ratio of 16, the onset Reynolds number is particularly sensitive to small geometric asymmetry and the critical Reynolds numbers for the two successive flow transitions are found to be very close. These transitions are delayed to higher onset Reynolds numbers by increasing the degree of pseudoplasticity. This trend is observed experimentally as well in this work and may be attributed to the competing effects of shear thinning and inertia on the size of the corner vortex before the symmetry breaking flow transition. After the second transition with an expansion ratio of 16, the two large staggered vortices on opposite walls occupy most of the transverse dimension so that the core flow between the vortices appears as a thin jet oscillating along the flow direction. This is more pronounced for the pseudoplastic liquid. After the second transition, the degree of flow asymmetry at a given location downstream of the expansion plane is larger for the pseudoplastic liquid than for the Newtonian liquid at comparable Reynolds numbers. The last feature is also evident in the experimentally observed velocity profiles.

AB - A continuation method has been used with a finite element grid and a geometric perturbation to compute two successive symmetry breaking flow transitions with increasing Reynolds number in flow of generalized Newtonian fluids through a sudden planar expansion. With an expansion ratio of 16, the onset Reynolds number is particularly sensitive to small geometric asymmetry and the critical Reynolds numbers for the two successive flow transitions are found to be very close. These transitions are delayed to higher onset Reynolds numbers by increasing the degree of pseudoplasticity. This trend is observed experimentally as well in this work and may be attributed to the competing effects of shear thinning and inertia on the size of the corner vortex before the symmetry breaking flow transition. After the second transition with an expansion ratio of 16, the two large staggered vortices on opposite walls occupy most of the transverse dimension so that the core flow between the vortices appears as a thin jet oscillating along the flow direction. This is more pronounced for the pseudoplastic liquid. After the second transition, the degree of flow asymmetry at a given location downstream of the expansion plane is larger for the pseudoplastic liquid than for the Newtonian liquid at comparable Reynolds numbers. The last feature is also evident in the experimentally observed velocity profiles.

KW - Asymmetric flow

KW - Bifurcation

KW - Instability

KW - Sudden expansion

KW - Transition

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U2 - 10.1002/fld.242

DO - 10.1002/fld.242

M3 - Article

VL - 38

SP - 945

EP - 962

JO - International Journal for Numerical Methods in Fluids

T2 - International Journal for Numerical Methods in Fluids

JF - International Journal for Numerical Methods in Fluids

SN - 0271-2091

IS - 10

ER -