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

Volume | 64 |

Issue number | 626 |

Publication status | Published - Oct 1998 |

Externally published | Yes |

### Fingerprint

### Keywords

- Bifurcation
- Curved duct
- Dean problem
- Spectral method

### ASJC Scopus subject areas

- Mechanical Engineering
- Condensed Matter Physics

### Cite this

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

*64*(626), 3183-3190.

**Multiple solution of a flow in a curved rectangular tube (1st report, symmetric steady solutions and their stability).** / Yanase, Shinichiro; Daikai, Ryuji; Morinaga, Tsutomu.

Research output: Contribution to journal › Article

*Nippon Kikai Gakkai Ronbunshu, B Hen/Transactions of the Japan Society of Mechanical Engineers, Part B*, vol. 64, no. 626, pp. 3183-3190.

}

TY - JOUR

T1 - Multiple solution of a flow in a curved rectangular tube (1st report, symmetric steady solutions and their stability)

AU - Yanase, Shinichiro

AU - Daikai, Ryuji

AU - Morinaga, Tsutomu

PY - 1998/10

Y1 - 1998/10

N2 - 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.

AB - 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.

KW - Bifurcation

KW - Curved duct

KW - Dean problem

KW - Spectral method

UR - http://www.scopus.com/inward/record.url?scp=33746614206&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33746614206&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33746614206

VL - 64

SP - 3183

EP - 3190

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

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

SN - 0387-5016

IS - 626

ER -