### Abstract

We present a detailed numerical investigation of three unsteady incompressible flow problems involving periodic arrays of staggered cylinders. The first problem is a uniperiodic flow with two cylinders in each cell of periodicity. The second problem is a biperiodic flow with two cylinders in each cell, and the last problem is a uniperiodic flow with ten cylinders. Both uniperiodic flows are periodic in the direction perpendicular to the main flow direction. In all three cases, the Reynolds number based on the cylinder diameter is 100, and initially the flow field has local symmetries with respect to the axes of the cylinders parallel to the main flow direction. Later on, these symmetries break, vortex shedding is initiated, and gradually the scale of the shedding increases until a temporally periodic flow field is reached. We furnish extensive flow data, including the vorticity and stream function fields at various instants during the temporal evolution of the flow field, time histories of the drag and lift coefficients, Strouhal number, initial and mean drag coefficients, amplitude of the drag and lift coefficient oscillations, and the phase relationships between the drag and lift oscillations associated with each cylinder. Our data confirms that, at this Reynolds number, there are no stable steady-state solutions with local symmetries. Of course, one can obtain such unphysical solutions by assuming symmetry conditions along the axes of the cylinders parallel to the main flow direction and taking half of the computational domain needed normally. In such cases, the "steady-state" flow fields obtained would be identical to the flow fields observed at the initial stages of our computations. However, we show that such flow fields do not represent the temporally periodic flow fields even in a time-averaged sense, because, in all three cases, the initial drag coefficients are different from the mean drag coefficients. Therefore, we conclude that stability studies involving periodic arrays of cylinders should be carried out, as it is done in this work, with the true implementation of the spatial periodicity.

Original language | English |
---|---|

Pages (from-to) | 371-383 |

Number of pages | 13 |

Journal | Computational Mechanics |

Volume | 11 |

Issue number | 5-6 |

DOIs | |

Publication status | Published - 1993 Sep |

Externally published | Yes |

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### ASJC Scopus subject areas

- Applied Mathematics
- Safety, Risk, Reliability and Quality
- Mechanics of Materials
- Computational Mechanics

### Cite this

*Computational Mechanics*,

*11*(5-6), 371-383. https://doi.org/10.1007/BF00350094

**Numerical simulation of flows past periodic arrays of cylinders.** / Johnson, A. A.; Tezduyar, Tayfun E.; Liou, J.

Research output: Contribution to journal › Article

*Computational Mechanics*, vol. 11, no. 5-6, pp. 371-383. https://doi.org/10.1007/BF00350094

}

TY - JOUR

T1 - Numerical simulation of flows past periodic arrays of cylinders

AU - Johnson, A. A.

AU - Tezduyar, Tayfun E.

AU - Liou, J.

PY - 1993/9

Y1 - 1993/9

N2 - We present a detailed numerical investigation of three unsteady incompressible flow problems involving periodic arrays of staggered cylinders. The first problem is a uniperiodic flow with two cylinders in each cell of periodicity. The second problem is a biperiodic flow with two cylinders in each cell, and the last problem is a uniperiodic flow with ten cylinders. Both uniperiodic flows are periodic in the direction perpendicular to the main flow direction. In all three cases, the Reynolds number based on the cylinder diameter is 100, and initially the flow field has local symmetries with respect to the axes of the cylinders parallel to the main flow direction. Later on, these symmetries break, vortex shedding is initiated, and gradually the scale of the shedding increases until a temporally periodic flow field is reached. We furnish extensive flow data, including the vorticity and stream function fields at various instants during the temporal evolution of the flow field, time histories of the drag and lift coefficients, Strouhal number, initial and mean drag coefficients, amplitude of the drag and lift coefficient oscillations, and the phase relationships between the drag and lift oscillations associated with each cylinder. Our data confirms that, at this Reynolds number, there are no stable steady-state solutions with local symmetries. Of course, one can obtain such unphysical solutions by assuming symmetry conditions along the axes of the cylinders parallel to the main flow direction and taking half of the computational domain needed normally. In such cases, the "steady-state" flow fields obtained would be identical to the flow fields observed at the initial stages of our computations. However, we show that such flow fields do not represent the temporally periodic flow fields even in a time-averaged sense, because, in all three cases, the initial drag coefficients are different from the mean drag coefficients. Therefore, we conclude that stability studies involving periodic arrays of cylinders should be carried out, as it is done in this work, with the true implementation of the spatial periodicity.

AB - We present a detailed numerical investigation of three unsteady incompressible flow problems involving periodic arrays of staggered cylinders. The first problem is a uniperiodic flow with two cylinders in each cell of periodicity. The second problem is a biperiodic flow with two cylinders in each cell, and the last problem is a uniperiodic flow with ten cylinders. Both uniperiodic flows are periodic in the direction perpendicular to the main flow direction. In all three cases, the Reynolds number based on the cylinder diameter is 100, and initially the flow field has local symmetries with respect to the axes of the cylinders parallel to the main flow direction. Later on, these symmetries break, vortex shedding is initiated, and gradually the scale of the shedding increases until a temporally periodic flow field is reached. We furnish extensive flow data, including the vorticity and stream function fields at various instants during the temporal evolution of the flow field, time histories of the drag and lift coefficients, Strouhal number, initial and mean drag coefficients, amplitude of the drag and lift coefficient oscillations, and the phase relationships between the drag and lift oscillations associated with each cylinder. Our data confirms that, at this Reynolds number, there are no stable steady-state solutions with local symmetries. Of course, one can obtain such unphysical solutions by assuming symmetry conditions along the axes of the cylinders parallel to the main flow direction and taking half of the computational domain needed normally. In such cases, the "steady-state" flow fields obtained would be identical to the flow fields observed at the initial stages of our computations. However, we show that such flow fields do not represent the temporally periodic flow fields even in a time-averaged sense, because, in all three cases, the initial drag coefficients are different from the mean drag coefficients. Therefore, we conclude that stability studies involving periodic arrays of cylinders should be carried out, as it is done in this work, with the true implementation of the spatial periodicity.

UR - http://www.scopus.com/inward/record.url?scp=0027277839&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027277839&partnerID=8YFLogxK

U2 - 10.1007/BF00350094

DO - 10.1007/BF00350094

M3 - Article

AN - SCOPUS:0027277839

VL - 11

SP - 371

EP - 383

JO - Computational Mechanics

JF - Computational Mechanics

SN - 0178-7675

IS - 5-6

ER -