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The Dean equations extended to a helical pipe flow

Publication ,  Journal Article
Germano, M
Published in: Journal of Fluid Mechanics
January 1, 1989

In this paper the Dean (1928) equations are extended to the case of a helical pipe flow, and it is shown that they depend not only on the Dean number K but also on a new parameter λ/ where λ is the ratio of the torsion τ to the curvature κ of the pipe axis and the Reynolds number referred in the usual way to the pipe radius a and to the equivalent maximum speed in a straight pipe under the same axial pressure gradient. The fact that the torsion has no first-order effect on the flow is confirmed, but it is shown that this is peculiar to a circular cross-section. In the case of an elliptical cross-section there is a first-order effect of the torsion on the secondary flow, and in the limit λ/ → ∞ (twisted pipes, provided only with torsion), the first-order ‘displacement’ effect of the walls on the secondary flow, analysed in detail by Choi (1988), is recovered. Different systems of coordinates and different orders of approximations have recently been adopted in the study of the flow in a helical pipe. Thus comparisons between the equations and the results presented in different reports are in some cases difficult and uneasy. In this paper the extended Dean equations for a helical pipe flow recently derived by Kao (1987) are converted to a simpler form by introducing an appropriate modified stream function, and their equivalence with the present set of equations is recovered. Finally, the first-order equivalence of this set of equations with the equations obtained by Murata et al. (1981) is discussed. © 1989, Cambridge University Press. All rights reserved.

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Published In

Journal of Fluid Mechanics

DOI

EISSN

1469-7645

ISSN

0022-1120

Publication Date

January 1, 1989

Volume

203

Issue

7

Start / End Page

289 / 305

Related Subject Headings

  • Fluids & Plasmas
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences
 

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Germano, M. (1989). The Dean equations extended to a helical pipe flow. Journal of Fluid Mechanics, 203(7), 289–305. https://doi.org/10.1017/S0022112089001473
Germano, M. “The Dean equations extended to a helical pipe flow.” Journal of Fluid Mechanics 203, no. 7 (January 1, 1989): 289–305. https://doi.org/10.1017/S0022112089001473.
Germano M. The Dean equations extended to a helical pipe flow. Journal of Fluid Mechanics. 1989 Jan 1;203(7):289–305.
Germano, M. “The Dean equations extended to a helical pipe flow.” Journal of Fluid Mechanics, vol. 203, no. 7, Jan. 1989, pp. 289–305. Scopus, doi:10.1017/S0022112089001473.
Germano M. The Dean equations extended to a helical pipe flow. Journal of Fluid Mechanics. 1989 Jan 1;203(7):289–305.
Journal cover image

Published In

Journal of Fluid Mechanics

DOI

EISSN

1469-7645

ISSN

0022-1120

Publication Date

January 1, 1989

Volume

203

Issue

7

Start / End Page

289 / 305

Related Subject Headings

  • Fluids & Plasmas
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences