### Abstract

The flow through a curved rectangular duct with the curvature = 0.1 is investigated numerically at the Dean number Dn = 100 for various aspect ratio of the duct cross section by use of the spectral method of the polynomial function expansion. The flow is assumed to be uniform in the direction of the duct axis. Steady solutions which are symmetric with respect to the mid-horizontal plane of the duct cross section are obtained by the Newton-Raphson's method and their linear stability is studied. The bifurcation diagram of the solution shows that there exist three solution branches, the main vortex solution, the multi-vortex solution and the singular vortex solution. Some of the secondary flow patterns found by Akiyama et al.^{(1)} are allotted to the solutions in the bifurcation diagram.

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

Pages (from-to) | 3183-3190 |

Number of pages | 8 |

Journal | Nihon Kikai Gakkai Ronbunshu, B Hen/Transactions of the Japan Society of Mechanical Engineers, Part B |

Volume | 64 |

Issue number | 626 |

DOIs | |

Publication status | Published - Oct 1998 |

Externally published | Yes |

### Keywords

- Bifurcation
- Curved duct
- Dean problem
- Spectral method

### ASJC Scopus subject areas

- Condensed Matter Physics
- Mechanical Engineering

## Fingerprint Dive into the research topics of 'Multiple solution of a flow in a curved rectangular tube (1st report, symmetric steady solutions and their stability)'. Together they form a unique fingerprint.

## Cite this

*Nihon Kikai Gakkai Ronbunshu, B Hen/Transactions of the Japan Society of Mechanical Engineers, Part B*,

*64*(626), 3183-3190. https://doi.org/10.1299/kikaib.64.3183