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Flow in a rotating non-aligned straight pipe

Published online by Cambridge University Press:  20 April 2006

J. Berman  and
L. F. Mockros
J. Berman
Affiliation:
The Technological Institute, Northwestern University, Evanston, Illinois Present address: Department of Chemical Engineering, University of Kentucky, Lexington, Kentucky.
L. F. Mockros
Affiliation:
The Technological Institute, Northwestern University, Evanston, Illinois
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Abstract

A third-order regular perturbation solution is developed for laminar flow through a straight pipe that is rotating about an axis not aligned with the pipe axis. Coriolis accelerations produce transverse secondary velocities (similar to those in flow through coiled tubes) and modify the axial-velocity profile. The effects of rotation on the velocity fields are shown to depend on two parameters: (i) the product of axial and rotational Reynolds numbers, and (ii) the square of the rotational Reynolds number itself. Even though their strength increases with increases in parameter magnitudes, transverse circulations are qualitatively insensitive to parametric values. The axial profile, on the other hand, can be significantly modified by the rotation; the zeroth-order parabolic axial profile can be skewed toward the outside, dimpled in the centre with maximums on either side of the centreline, or both, depending on the values of the two parameters. The modification of the axial-velocity profile has important ramifications in the design of heat/mass-transfer devices.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 144 , July 1984 , pp. 297 - 310
Copyright
© 1984 Cambridge University Press

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References

Barua, S. N. 1954 Secondary flow in a rotating straight pipe. Proc. R. Soc. Lond. A 227, 133–139.Google Scholar
Barua, S. N. 1963 On secondary flow in stationary curved pipes. Q. J. Mech. Appl. Maths 16, 61–67.Google Scholar
Benton, G. S. 1956 The effect of the Earth's rotation on laminar flow in pipes. Trans ASME E: J. Appl. Mech. 23, 123–127.Google Scholar
Dean, W. R. 1927 Note on the motions of fluid in a curved pipe. Phil. Mag. 4, 208–223.Google Scholar
Dean, W. R. 1928 The stream-line motion of a fluid in a curved pipe. Phil. Mag. 5, 673–695.Google Scholar
Ito, H. & Motai, T. 1974 Secondary flow in a rotating curved pipe. Rep. Inst. High Speed Mech. 29, 33–57.Google Scholar
Ito, H. & Nanbu, K. 1971 Flow in rotating straight pipes of circular cross section. Trans. ASME D: J. Basic Engng 93, 383–394.Google Scholar
McConalogue, D. J. & Srivastava, R. S. 1968 Motion of a fluid in a curved tube. Proc. R. Soc. Lond. A 307, 37–53.Google Scholar
Manlapoz, R. L. & Churchill, S. W. 1980 Fully developed laminar flow in a helically coiled tube of finite pitch. Chem. Engng Commun. 7, 57–78.Google Scholar
Mansour, K. 1983 Fully developed steady laminar flow through a pipe rotating slowly about a line perpendicular to its own axis. (Personal communication.)
Nandakumar, K. & Masliyah, J. H. 1982 Bifurcation in steady laminar flow through curved tubes. J. Fluid Mech. 119, 475–490.Google Scholar
Van Dyke, M. 1978 Extended Stokes series: laminar flow through a loosely coiled pipe. J. Fluid Mech. 86, 129–145.Google Scholar