Dean Equations Extended to a Rotating Helical Pipe Flow
Publication: Journal of Engineering Mechanics
Volume 129, Issue 7
Abstract
In this paper, the fully developed laminar flow in a rotating helical elliptical pipe is examined theoretically. This study focuses on the combined effects of the rotation, the curvature, the torsion, and the shape of cross section. The secondary flow and the fluid particle trajectory are discussed for different elliptical cross sections in the range of −2⩽σ⩽1, where σ represents the ratio of the Coriolis force to the centrifugal force.
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References
Bolinder, C. J.(1996). “First- and higher-order effects of curvature and torsion on the flow in a helical rectangular duct.” J. Fluid Mech., 314, 113–138.
Chen, W. H., and Jan, R.(1992). “The characteristics of laminar flow in a helical circular pipe.” J. Fluid Mech., 244, 241–256.
Dean, W. R.(1927). “Note on the motion of fluid in a curved pipe.” Philos. Mag., 4, 208–223.
Dean, W. R.(1928). “The stream-line motion of fluid in a curved pipe.” Philos. Mag., 5, 673–695.
Germano, M.(1982). “On the effect of torsion on a helical pipe flow.” J. Fluid Mech., 125, 1–8.
Germano, M.(1989). “The Dean equations extended to a helical pipe flow.” J. Fluid Mech., 203, 289–305.
Huttl, T. J., Wagner, C., and Friedrich, R.(1999). “Navier-Stokes solutions of laminar flows based on orthogonal helical coordinates.” Int. J. Numer. Methods Eng., 29, 749–763.
Ishigaki, H.(1996). “Laminar flow in rotating curved pipes.” J. Fluid Mech., 329, 373–388.
Ito, H., and Motain, (1974). “Secondary flow in a rotating curved pipe.” Rep. Inst. High Speed Mech., 29, 33–57.
Ito, H., Komaki, H., Hasegawa, S., and Suzuki, M.(1987). “Numerical and experimental study on laminar flow in a rotating curved pipe (1. constant Dean number).” Mem. Inst. High Speed Mech., 58, 185–235.
Kao, H.(1987). “Torsion effect on fully developed flow in a helical pipe.” J. Fluid Mech., 184, 335–356.
Kotorynski, W. P.(1986). “Steady laminar flow through a twisted pipe of elliptical cross section.” Comput. Fluids, 14, 433–444.
Ludwieg, H.(1951). “Die Ausgebildete Kanalstromung in einem rotierenden system.” Ingenieur-Archiv., 19, 296–308.
Miyazaki, H.(1971). “Combined free and force convective heat transfer and fluid flow in rotating curved circular tube.” Int. J. Heat Mass Transfer, 14, 1295–1309.
Miyazaki, H.(1973). “Combined free and forced convective heat transfer and fluid flow in a rotating curved rectangular tube.” Trans. ASME C: J. Heat Transfer, 95, 64–71.
Selmi, M., and Nandakumar, K.(1999). “Bifurcation study of flow through rotating curved duct.” Phys. Fluids, 11(8), 2030–2043.
Thomas, R. H., and Walters, K.(1965). “On the flow of an elastico-visicous liquid in a curved pipe of elliptic cross section under a pressure gradient.” J. Fluid Mech., 21, 173–182.
Topakoglu, H. C., and Ebadian, M. A.(1985). “On the steady laminar flow of an incompressible viscous fluid in a curved pipe of elliptical cross section.” J. Fluid Mech., 158, 329–340.
Topakoglu, H. C., and Ebadian, M. A.(1987). “Viscous incompressible flow in a curved pipe with elliptical cross section.” J. Fluid Mech., 184, 571–580.
Tuttle, E. R.(1990). “Laminar flow in twisted pipes.” J. Fluid Mech., 219, 545–570.
Wang, C. Y.(1981). “On the low-Reynolds-number flow in a helical pipe.” J. Fluid Mech., 108, 185–194.
Yamamoto, K., Yanase, S., and Alam, M. M.(1999). “Flow through a rotating curved duct with square cross section.” J. Phys. Soc. Jpn., 68(4), 1173–1184.
Yamamoto, K., Alam, M. M., Yasuhara, J., and Aribowo, A.(2000). “Flow through a rotating helical pipe with circular cross section.” Int. J. Heat Fluid Flow, 21, 213–220.
Zhang, J., and Zhang, B.(1999). “Flow in helical pipes.” Acta Mech. Sin., 15(4), 299–312.
Zhang, J., Shen, X., and Zhang, B.(2000a). “Fluid flow in a curved rotating pipe.” J. Hydrodynam., 12, 108–116.
Zhang, J., Zhang, B., and Chen, H.(2000b). “Flow in helical annular pipes.” J. Eng. Mech., 126, 1040–1047.
Zhang, J., Zhang, B., and Ju, J.(2001b). “Flow in a rotating helical pipe.” J. Hydraul. Eng., 5, 32–37 (In Chinese).
Zhang, J., and Zhang, B.(2000). “Laminar fluid flow in helical elliptical pipe.” J. Hydrodynam., 12(2), 62–71.
Zhang, J., Zhang, B., and Ju, J.(2001a). “Flow in rotating rectangular ducts.” Int. J. Heat Fluid, 22, 593–602.
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Copyright © 2003 American Society of Civil Engineers.
History
Received: Jan 31, 2002
Accepted: Dec 17, 2002
Published online: Jun 13, 2003
Published in print: Jul 2003
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