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Laminar flow in a curved pipe with varying curvature

Published online by Cambridge University Press:  29 March 2006

S. Murata ,
Y. Miyake  and
T. Inaba
S. Murata
Affiliation:
Department of Mechanical Engineering, Osaka University, Japan
Y. Miyake
Affiliation:
Department of Mechanical Engineering, Osaka University, Japan
T. Inaba
Affiliation:
Department of Mechanical Engineering, Osaka University, Japan
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Abstract

The steady laminar motion of fluid through pipes of circular cross-section, the curvature of whose centre-line varies locally, is analysed theoretically. The flow in three kinds of pipes whose centre-lines are specified by \[ \hat{y} = a(1+\kappa^2\hat{x}^2)^{\frac{1}{2}},\quad\hat{y} = a\tan h\kappa\hat{x}\quad{\rm and}\quad\hat{y} = a\sin\kappa\hat{x} \] are treated as the examples of once-, twice- and periodically-curved pipes, respectively. The analysis is valid for any other two-dimensionally curved pipes, when centre-line curvature is small. At very small Reynolds number, the position of maximum axial velocity shifts towards the inner side of the pipe section; at large Reynolds number, on the contrary, it tends to the outer side, owing to centrifugal force. Furthermore, in the latter case, adaptation of the flow follows the change of mean-flow direction, with a phase lag.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 73 , Issue 4 , 24 February 1976 , pp. 735 - 752
Copyright
© 1976 Cambridge University Press

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