Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-19T06:57:53.119Z Has data issue: false hasContentIssue false
  • English
  • Français

Laminar secondary flows in curved rectangular ducts

Published online by Cambridge University Press:  26 April 2006

S. Thangam  and
N. Hur
S. Thangam
Affiliation:
Department of Mechanical Engineering, Stevens Institute of Technology, Hoboken, NJ 07030, USA
N. Hur
Affiliation:
Department of Mechanical Engineering, Stevens Institute of Technology, Hoboken, NJ 07030, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The occurrence of secondary flow in curved ducts due to the centrifugal forces can often significantly influence the flow rate. In the present work, the secondary flow of an incompressible viscous fluid in a curved duct is studied by using a finite-volume method. It is shown that as the Dean number is increased the secondary flow structure evolves into a double vortex pair for low-aspect-ratio ducts and roll cells for ducts of high aspect ratio. A stability diagram is obtained in the domain of curvature ratio and Reynolds number. It is found that for ducts of high curvature the onset of transition from single vortex pair to double vortex pair or roll cells depends on the Dean number and the curvature ratio, while for ducts of small curvature the onset can be characterized by the Dean number alone. A comparison with the available theoretical and experimental results indicates good agreement. A correlation for the friction factor as a function of the Dean number and aspect ratio is developed and is found to be in good agreement with the available experimental and computational results for a wide range of parameters.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 217 , August 1990 , pp. 421 - 440
Copyright
© 1990 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Baylis, J. A. 1971 Experiments on laminar flow in curved channels of square sections. J. Fluid Mech. 48, 417–422.Google Scholar
Cheng, K. C. & Akiyama, M. 1970 Laminar forced convection heat transfer in curved rectangular channels. Intl J. Heat Mass Transfer 13, 471–490.Google Scholar
Cheng, K. C., Lin, R. C. & Ou, J. W. 1976 Fully developed laminar flow in curved rectangular channels. Trans. ASME I: J. Fluids Engng 98, 41–48.Google Scholar
Dean, W. R. 1927 Note on the motion of fluid in a curved pipe. Phil. Mag. 4, 208–223.Google Scholar
Dean, W. R. 1928 The streamline motion of fluid in a curved pipe. Phil. Mag. 5, 673–695.Google Scholar
Ghia, K. N. & Sokhey, J. S. 1977 Laminar incompressible viscous flow in curved ducts of regular cross-sections. Trans. ASME I: J. Fluids Engng 99, 640–648.Google Scholar
Hart, J. E. 1971 Instability and secondary motion in a rotating channel flow. J. Fluid Mech. 45, 341–351.Google Scholar
Hille, P., Vehrenkamp, R. & Schulz-Dubois, E. O. 1985 The development and structure of primary and secondary flow in a curved square duct. J. Fluid Mech. 151, 219–241.Google Scholar
Humphrey, J. A. C., Taylor, A. M. K. & Whitelaw, J. H. 1977 Laminar flow in a square duct of strong curvature. J. Fluid Mech. 83, 509–527.Google Scholar
Hur, N. 1988 Numerical study of secondary flows in curved ducts. Ph.D. thesis, Stevens Institute of Technology.
Joseph, B., Smith, E. P. & Adler, R. J. 1975 Numerical treatment of laminar flow in helically coiled tubes of square cross section, Part I. Stationary helically coiled tubes. AIChE J. 21, 965–974.Google Scholar
Kao, H. C. 1987 Torsion effect on fully developed flow in a helical pipe. J. Fluid Mech. 184, 335–356.Google Scholar
Kelleher, M. D., Flentie, D. L. & McKee, R. J. 1980 An experimental study of the secondary flow in a curved rectangular channel. Trans. ASME I: J. Fluids Engng 102, 92–96.Google Scholar
Kheshgi, H. S. & Scriven, L. E. 1985 Viscous flow through a rotating square channel. Phys. Fluids 28, 2968–2979.Google Scholar
Lezius, D. K. & Johnston, J. P. 1976 Roll-cell instabilities in rotating laminar and turbulent channel flows. J. Fluid Mech. 77, 153–175.Google Scholar
Manlapaz, 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
Mori, Y., Uchida, Y. & Ukon, T. 1971 Forced convective heat transfer in a curved channel with a square cross section. Intl J. Heat Mass Transfer 4, 1787–1805.Google Scholar
Patankar, S. V. 1980 Numerical Heat Transfer and Fluid Flow. McGraw-Hill.
Ravi Sankar, S., Nandakumar, K. & Masliyah, J. H. 1988 Oscillatory flows in coiled square ducts. Phys. Fluids 31, 1348–1359.Google Scholar
Roache, P. J. 1972 Computational Fluid Dynamics. Hermosa.
Speziale, C. G. 1982 Numerical study of viscous flow in rotating rectangular ducts. J. Fluid Mech. 122, 251–271.Google Scholar
Speziale, C. G. & Thangam, S. 1983 Numerical study of secondary flows and roll-cell instabilities in rotating channel flow. J. Fluid Mech. 130, 377–395.Google Scholar
Winters, K. H. 1987 A bifurcation study of laminar flow in a curved tube of rectangular cross-section. J. Fluid Mech. 180, 343–369.Google Scholar