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

Shinichiro Yanase, Ryuji Daikai, Tsutomu Morinaga

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)3183-3190
Number of pages8
JournalNippon Kikai Gakkai Ronbunshu, B Hen/Transactions of the Japan Society of Mechanical Engineers, Part B
Volume64
Issue number626
Publication statusPublished - Oct 1998
Externally publishedYes

Fingerprint

ducts
Ducts
tubes
Vortex flow
vortices
diagrams
Newton-Raphson method
secondary flow
spectral methods
Secondary flow
cross sections
Flow patterns
aspect ratio
Aspect ratio
flow distribution
polynomials
curvature
Polynomials
expansion

Keywords

  • Bifurcation
  • Curved duct
  • Dean problem
  • Spectral method

ASJC Scopus subject areas

  • Mechanical Engineering
  • Condensed Matter Physics

Cite this

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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.",
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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

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