## Abstract

This study seeks to characterise the stability of a two-dimensional channel flow involving a 180-degree sharp bend, to infinitesimal three-dimensional disturbances by way of a linear stability analysis. A highly accurate global linear stability analysis of the flow is presented via the Reynolds number Re varies in the range 100 ≤ Re ≤ 700, this Re range produces steady-state two-dimensional flow solutions for bend opening ratio (ratio of bend width on inlet height) β = 1. The two-dimensional base flow solutions demonstrate that as β decreases, the transition from steady to unsteady occurs at lower Reynolds number. The stability analysis shows that the flow first becomes unstable to a synchronous three-dimensional instability mode with span-wise wavenumber k = 2 at approximately Re = 400, whereas the two-dimensional solution branch undergoes transition to unsteady flow somewhere near Re ≈ 800. Instability mode structures associated with the leading eigenvalues are localized at the re-attachment point of the first separation bubble and the separation point of the second separation bubble. The stability analysis is used to produce neutral stability curves, and visualisations of the global modes of the system for typical Reynolds number are also presented.

Original language | English |
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Title of host publication | Proceedings of the 19th Australasian Fluid Mechanics Conference, AFMC 2014 |

Publisher | Australasian Fluid Mechanics Society |

Number of pages | 4 |

ISBN (Electronic) | 9780646596952 |

Publication status | Published - 2014 |

Event | 19th Australasian Fluid Mechanics Conference, AFMC 2014 - Melbourne, Australia Duration: 8 Dec 2014 → 11 Dec 2014 Conference number: 19 |

### Publication series

Name | Proceedings of the 19th Australasian Fluid Mechanics Conference, AFMC 2014 |
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### Conference

Conference | 19th Australasian Fluid Mechanics Conference, AFMC 2014 |
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Country/Territory | Australia |

City | Melbourne |

Period | 8/12/14 → 11/12/14 |

## ASJC Scopus subject areas

- Fluid Flow and Transfer Processes