Abstract
The laminar flow in a curved rectangular duct for a range of the aspect ratio 1 ≤ l ≤ 12 is investigated by use of the spectral method. The steady solutions are obtained using the Newton-Raphson method with the symmetry condition. As a result, five branches of steady solutions are found. Linear stability characteristics are also investigated for all the steady solutions. It is found that one steady solution is linearly stable for most of l, but two linearly stable steady solutions exist for a region of small l and there are several intervals of l where there is no linearly stable steady solution. We performed time-evolution calculations with and without the symmetry condition, and observed periodic oscillations with the symmetry condition and aperiodic time evolutions without the symmetric condition. Finally, the present results numerically suggest that what determines which solution is realizable may be the maximum of the momentum transfer in the cross section.
| Original language | English |
|---|---|
| Pages (from-to) | 151-183 |
| Number of pages | 33 |
| Journal | Fluid Dynamics Research |
| Volume | 31 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Sep 2002 |
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Keywords
- Bifurcation analysis
- Curved rectangular duct
- Linear stability
- Spectral method
ASJC Scopus subject areas
- Mechanical Engineering
- Statistical and Nonlinear Physics
Cite this
Laminar flows through a curved rectangular duct over a wide range of the aspect ratio. / Yanase, Shinichiro; Kaga, Yoshito; Daikai, Ryuji.
In: Fluid Dynamics Research, Vol. 31, No. 3, 09.2002, p. 151-183.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Laminar flows through a curved rectangular duct over a wide range of the aspect ratio
AU - Yanase, Shinichiro
AU - Kaga, Yoshito
AU - Daikai, Ryuji
PY - 2002/9
Y1 - 2002/9
N2 - The laminar flow in a curved rectangular duct for a range of the aspect ratio 1 ≤ l ≤ 12 is investigated by use of the spectral method. The steady solutions are obtained using the Newton-Raphson method with the symmetry condition. As a result, five branches of steady solutions are found. Linear stability characteristics are also investigated for all the steady solutions. It is found that one steady solution is linearly stable for most of l, but two linearly stable steady solutions exist for a region of small l and there are several intervals of l where there is no linearly stable steady solution. We performed time-evolution calculations with and without the symmetry condition, and observed periodic oscillations with the symmetry condition and aperiodic time evolutions without the symmetric condition. Finally, the present results numerically suggest that what determines which solution is realizable may be the maximum of the momentum transfer in the cross section.
AB - The laminar flow in a curved rectangular duct for a range of the aspect ratio 1 ≤ l ≤ 12 is investigated by use of the spectral method. The steady solutions are obtained using the Newton-Raphson method with the symmetry condition. As a result, five branches of steady solutions are found. Linear stability characteristics are also investigated for all the steady solutions. It is found that one steady solution is linearly stable for most of l, but two linearly stable steady solutions exist for a region of small l and there are several intervals of l where there is no linearly stable steady solution. We performed time-evolution calculations with and without the symmetry condition, and observed periodic oscillations with the symmetry condition and aperiodic time evolutions without the symmetric condition. Finally, the present results numerically suggest that what determines which solution is realizable may be the maximum of the momentum transfer in the cross section.
KW - Bifurcation analysis
KW - Curved rectangular duct
KW - Linear stability
KW - Spectral method
UR - http://www.scopus.com/inward/record.url?scp=0036748609&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0036748609&partnerID=8YFLogxK
U2 - 10.1016/S0169-5983(02)00103-X
DO - 10.1016/S0169-5983(02)00103-X
M3 - Article
AN - SCOPUS:0036748609
VL - 31
SP - 151
EP - 183
JO - Fluid Dynamics Research
JF - Fluid Dynamics Research
SN - 0169-5983
IS - 3
ER -