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On the effect of torsion on a helical pipe flow

Published online by Cambridge University Press:  20 April 2006

M. Germano
M. Germano
Affiliation:
Institute of Applied Mechanics, Politecnico of Torino, Italy
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Abstract

An orthogonal coordinate system along a generic spatial curve has been introduced, and the Navier-Stokes equations for a steady incompressible viscous flow have been explicitly written in this frame of reference. As an application the flow in a helical pipe has been studied, and, formdii 5f curvature and torsion small compared with the radius of the pipe, the flow has been considered as a perturbed Poiseuille flow. The result is that for curvatures and torsions of the same order and for low Reynolds number the curvature induces on the flow a first-order effect on the parameter ε =κa, where κ is the curvature and a the radius of the pipe, while the effect of the torsion on the flow is of the second order in E. This last result disagrees with those of Wang (1981), who, adopting a non-orthogonal coordinate system, found a first-order effect of torsion on the flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 125 , December 1982 , pp. 1 - 8
Copyright
© 1982 Cambridge University Press

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References

Batchelor, G. K. 1967 An Introduction to Fluid Mechanics, app. 2. Cambridge University Press.
Dean, W. R. 1927 Note on the motion of fluid in a curved pipe. Phil. Mag. 4 (7), 208–223.Google Scholar
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Wang, C. Y. 1981 On the low-Reynolds-number flow in a helical pipe. J. Fluid Mech. 108, 185–194.Google Scholar
Ward-Smith, A. J. 1980 Internal Fluid Flow, E (Bends). Clarendon.