Oscillatory instability of a three-dimensional lid-driven flow in a cube

Yuri Feldman; Alexander Yu Gelfgat

doi:10.1063/1.3487476

Oscillatory instability of a three-dimensional lid-driven flow in a cube

Yuri Feldman, Alexander Yu Gelfgat

Research output: Contribution to journal › Article › peer-review

79 Scopus citations

Abstract

A series of time-dependent three-dimensional (3D) computations of a lid-driven flow in a cube with no-slip boundaries is performed to find the critical Reynolds number corresponding to the steady-oscillatory transition. The computations are done in a fully coupled pressure-velocity formulation on 104³, 152³, and 200³ stretched grids. Grid-independence of the results is established. It is found that the oscillatory instability of the flow sets in via a subcritical symmetry-breaking Hopf bifurcation at Re_cr≈1914 with the nondimensional frequency ω=0.575. Three-dimensional patterns in the steady and oscillatory flow regimes are compared with the previously studied two-dimensional configuration and a three-dimensional model with periodic boundary conditions imposed in the spanwise direction.

Original language	English
Article number	093602
Journal	Physics of Fluids
Volume	22
Issue number	9
DOIs	https://doi.org/10.1063/1.3487476
State	Published - 30 Sep 2010
Externally published	Yes

ASJC Scopus subject areas

Computational Mechanics
Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering
Fluid Flow and Transfer Processes

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10.1063/1.3487476

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abstract = "A series of time-dependent three-dimensional (3D) computations of a lid-driven flow in a cube with no-slip boundaries is performed to find the critical Reynolds number corresponding to the steady-oscillatory transition. The computations are done in a fully coupled pressure-velocity formulation on 1043, 1523, and 2003 stretched grids. Grid-independence of the results is established. It is found that the oscillatory instability of the flow sets in via a subcritical symmetry-breaking Hopf bifurcation at Recr≈1914 with the nondimensional frequency ω=0.575. Three-dimensional patterns in the steady and oscillatory flow regimes are compared with the previously studied two-dimensional configuration and a three-dimensional model with periodic boundary conditions imposed in the spanwise direction.",

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AU - Gelfgat, Alexander Yu

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N2 - A series of time-dependent three-dimensional (3D) computations of a lid-driven flow in a cube with no-slip boundaries is performed to find the critical Reynolds number corresponding to the steady-oscillatory transition. The computations are done in a fully coupled pressure-velocity formulation on 1043, 1523, and 2003 stretched grids. Grid-independence of the results is established. It is found that the oscillatory instability of the flow sets in via a subcritical symmetry-breaking Hopf bifurcation at Recr≈1914 with the nondimensional frequency ω=0.575. Three-dimensional patterns in the steady and oscillatory flow regimes are compared with the previously studied two-dimensional configuration and a three-dimensional model with periodic boundary conditions imposed in the spanwise direction.

AB - A series of time-dependent three-dimensional (3D) computations of a lid-driven flow in a cube with no-slip boundaries is performed to find the critical Reynolds number corresponding to the steady-oscillatory transition. The computations are done in a fully coupled pressure-velocity formulation on 1043, 1523, and 2003 stretched grids. Grid-independence of the results is established. It is found that the oscillatory instability of the flow sets in via a subcritical symmetry-breaking Hopf bifurcation at Recr≈1914 with the nondimensional frequency ω=0.575. Three-dimensional patterns in the steady and oscillatory flow regimes are compared with the previously studied two-dimensional configuration and a three-dimensional model with periodic boundary conditions imposed in the spanwise direction.

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Oscillatory instability of a three-dimensional lid-driven flow in a cube

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