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Aspect Ratio Effect on Laminar Flow Bifurcations in a Curved Rectangular Tube Driven by Pressure Gradients

Published online by Cambridge University Press:  30 October 2017

K. T. Chen ,
K. F. Yarn ,
H. Y. Chen ,
C. C. Tsai ,
W. J. Luo  and
C. N. Chen
K. T. Chen
Affiliation:
Department of Applied MathematicsNational Chung Hsing UniversityTaichung, Taiwan
K. F. Yarn
Affiliation:
Department of Electronic EngineeringFar East UniversityTainan, Taiwan
H. Y. Chen
Affiliation:
Department of Applied MathematicsNational Chung Hsing UniversityTaichung, Taiwan
C. C. Tsai
Affiliation:
Department of Applied MathematicsNational Chung Hsing UniversityTaichung, Taiwan
W. J. Luo*
Affiliation:
Graduate Institute of Precision ManufacturingNational Chin-Yi University of TechnologyTaichung, Taiwan
C. N. Chen
Affiliation:
Department of PhysicsTamkang UniversityNew Taipei, Taiwan
*
*Corresponding author (wjluo@ncut.edu.tw)
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Abstract

This study investigated the flow bifurcations of flows driven by a pressure gradient in a rectangular curved tube. When fluid flows within a curved tube, due to the centrifugal effect, secondary vortices can be induced in the cross section of the tube. The secondary flow states are dependent on the magnitude of the pressure gradient (q) and the aspect ratio (γ). In this study, the continuation method was applied to investigate the flow bifurcations in a curved tube with increasing pressure gradient (1 < q < 6000) and aspect ratio (0.9 < γ < 1.4).

The bifurcation diagrams are composed of solution branches, which are linked by limiting points or bifurcation points. The flow states in a solution branch belong to the same group. The ranges of the flow states and the relationship between the states can also be derived from the bifurcation diagrams. In this study, two types of bifurcation were found, one in the range of 0.9 < γ < 1.17, and another in the range of 1.18 < γ < 1.4. The ranges of stable flow solutions and the distributions of limit and bifurcation points in both pressure gradient and aspect ratio are derived in this study.

Keywords

Pressure gradientRectangular curved tubeFlow bifurcationAspect ratio effect
Type
Research Article
Information
Journal of Mechanics , Volume 33 , Issue 6 , December 2017 , pp. 831 - 840
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2017 

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