### Abstract

Flows through a curved rectangular duct for the aspect ratio l = 2 are numerically studied by use of the spectral method with and without a temperature difference between the vertical outer and inner sidewalls. We find three branches of steady solutions for the case without the temperature difference (isothermal case). Then we investigate linear stability of the steady solutions and find that only a portion of one steady solution branch is linearly stable but other branches are unstable. We obtain five branches of steady solutions for the case with the temperature difference (non-isothermal case) for the Grashof number Gr = 100. Linear stability shows that only a portion of one of them is linearly stable while other branches are unstable like the isothermal case. The change of the flow state, as the Dean number Dn is increased, obtained by time evolution calculations, is found to be similar for both the isothermal and nonisothermal cases. When there is no stable steady solution, the time evolution calculations show that typical transition occurs from a steady flow to a chaotic state through a periodic flow when Dn is increased whether the system is isothermal or non-isothermal.

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

Pages (from-to) | 345-358 |

Number of pages | 14 |

Journal | Journal of the Physical Society of Japan |

Volume | 74 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2005 |

### Fingerprint

### Keywords

- Curved rectangular duct
- Dean number
- Grashof number
- Linear stability
- Non-isothermal flow
- Steady solutions

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal of the Physical Society of Japan*,

*74*(1), 345-358. https://doi.org/10.1143/JPSJ.74.345

**Transition from steady to chaotic states of isothermal and non-isothermal flows through a curved rectangular duct.** / Yanase, Shinichiro; Mondal, Rabindra Nath; Kaga, Yoshito; Yamamoto, Kyoji.

Research output: Contribution to journal › Article

*Journal of the Physical Society of Japan*, vol. 74, no. 1, pp. 345-358. https://doi.org/10.1143/JPSJ.74.345

}

TY - JOUR

T1 - Transition from steady to chaotic states of isothermal and non-isothermal flows through a curved rectangular duct

AU - Yanase, Shinichiro

AU - Mondal, Rabindra Nath

AU - Kaga, Yoshito

AU - Yamamoto, Kyoji

PY - 2005/1

Y1 - 2005/1

N2 - Flows through a curved rectangular duct for the aspect ratio l = 2 are numerically studied by use of the spectral method with and without a temperature difference between the vertical outer and inner sidewalls. We find three branches of steady solutions for the case without the temperature difference (isothermal case). Then we investigate linear stability of the steady solutions and find that only a portion of one steady solution branch is linearly stable but other branches are unstable. We obtain five branches of steady solutions for the case with the temperature difference (non-isothermal case) for the Grashof number Gr = 100. Linear stability shows that only a portion of one of them is linearly stable while other branches are unstable like the isothermal case. The change of the flow state, as the Dean number Dn is increased, obtained by time evolution calculations, is found to be similar for both the isothermal and nonisothermal cases. When there is no stable steady solution, the time evolution calculations show that typical transition occurs from a steady flow to a chaotic state through a periodic flow when Dn is increased whether the system is isothermal or non-isothermal.

AB - Flows through a curved rectangular duct for the aspect ratio l = 2 are numerically studied by use of the spectral method with and without a temperature difference between the vertical outer and inner sidewalls. We find three branches of steady solutions for the case without the temperature difference (isothermal case). Then we investigate linear stability of the steady solutions and find that only a portion of one steady solution branch is linearly stable but other branches are unstable. We obtain five branches of steady solutions for the case with the temperature difference (non-isothermal case) for the Grashof number Gr = 100. Linear stability shows that only a portion of one of them is linearly stable while other branches are unstable like the isothermal case. The change of the flow state, as the Dean number Dn is increased, obtained by time evolution calculations, is found to be similar for both the isothermal and nonisothermal cases. When there is no stable steady solution, the time evolution calculations show that typical transition occurs from a steady flow to a chaotic state through a periodic flow when Dn is increased whether the system is isothermal or non-isothermal.

KW - Curved rectangular duct

KW - Dean number

KW - Grashof number

KW - Linear stability

KW - Non-isothermal flow

KW - Steady solutions

UR - http://www.scopus.com/inward/record.url?scp=24644487861&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24644487861&partnerID=8YFLogxK

U2 - 10.1143/JPSJ.74.345

DO - 10.1143/JPSJ.74.345

M3 - Article

AN - SCOPUS:24644487861

VL - 74

SP - 345

EP - 358

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 1

ER -