Hostname: page-component-77c89778f8-gvh9x Total loading time: 0 Render date: 2024-07-17T17:53:54.028Z Has data issue: false hasContentIssue false
  • English
  • Français

Developing fluid flow in a curved duct of square cross-section and its fully developed dual solutions

Published online by Cambridge University Press:  21 April 2006

W. Y. Soh
W. Y. Soh
Affiliation:
Sverdrup Technology Inc., NASA Lewis Research Center, 21000 Brookpark Road, Cleveland, OH 44135, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Developing fluid flow in a curved duct of square cross-section is studied numerically by a factored ADI finite-difference method on a staggered grid. A central-difference scheme with primitive variables is used inside the computational domain to reduce numerical diffusion. Two Reynolds numbers, 574 and 790, based upon a bulk velocity and hydraulic diameter are chosen for curvature ratios of 1/6.45 and 1/2.3, respectively. It is found that the secondary flow is far more complicated than expected, with the appearance of at least two pairs of vortices. Main-flow separation is also observed for the higher curvature ratio. Furthermore, it is observed that the flow develops into two quite different states downstream, depending upon the inlet conditions.

Solution of the fully developed Navier-Stokes equations is shown to be not unique beyond a certain critical Reynolds number. Developing flow seems to evolve into the fully developed state along a particular branch, into which the fully developed solution bifurcates.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 188 , March 1988 , pp. 337 - 361
Copyright
© 1988 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

Agrawal, Y., Talbot, L. & Gong, K. 1978 Laser anemometer study of flow development in curved circular pipes. J. Fluid Mech. 85, 497.Google Scholar
Benjamin, T. B. 1978 Bifurcation phenomena in steady flows of a viscous fluid II. Experiments. Proc. R. Soc. Lond. A 359, 27.Google Scholar
Briley, W. R. & McDonald, H. 1980 On the structure and use of linearized block implicit schemes. J. Comp. Phys. 34, 54.Google Scholar
Chorin, A. J. 1967 A numerical method for solving incompressible viscous flow problems. J. Comp. Phys. 2, 12.Google Scholar
Cliffe, K. A. & Mullin, T. 1985 A numerical and experimental study of anomalous modes in the Taylor experiment. J. Fluid Mech. 153, 243.Google Scholar
Dean, W. R. 1927 Note on the motion of fluid in a curved pipe. Phil. Mag. 20, 208.Google Scholar
Dean, W. R. 1928 The stream-line motion of fluid in a curved pipe. Phil. Mag. 30, 673.Google Scholar
Dennis, S. C. R. & Ng, M. 1982 Dual solution for steady laminar flow through a curved tube. Q. J. Mech. Appl. Maths 35, 305.Google Scholar
Eustice, J. 1910 Flow of water in curved pipes. Proc. R. Soc. Lond. A 84, 107.Google Scholar
Eustice, J. 1911 Experiments on stream-line motion in curved pipes. Proc. R. Soc. Lond. A 85, 119.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.Google Scholar
Humphrey, J. A. C. 1977 Flow in ducts with curvature and roughness. Ph.D. thesis, Imperial College of Science and Technology.
Humphrey, J. A. C., Chang, S. M. & Modavi, A. 1982 Developing turbulent flow in a 180° bend and downstream tangent of square cross-section. LBL Rep. 14844. Berkeley.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.Google Scholar
Kao, H. C., Burstadt, P. L. & Johns, A. L. 1983 Flow visualization and interpretation of visualization data for deflected thrust V/STOL nozzle. NASA TM-83554.Google Scholar
Masliyah, J. H. 1980 On laminar flow in curved semicircular ducts. J. Fluid Mech. 99, 469.Google Scholar
Nandakumar, K. & Masliyah, J. H. 1982 Bifurcation in steady laminar flow through curved tubes. J. Fluid Mech. 119, 475.Google Scholar
Patankar, S. V., Pratap, V. S. & Spalding, D. B. 1974 Prediction of laminar flow and heat transfer in helically coiled pipes. J. Fluid Mech. 62, 539.Google Scholar
Soh, W. Y. 1987 Time-marching solution of incompressible Navier-Stokes equations for internal flow. J. Comp. Phys. 70, 232.Google Scholar
Soh, W. Y. & Berger, S. A. 1984 Laminar entrance flow in a curved pipe. J. Fluid Mech. 148, 109.Google Scholar
Soh, W. Y. & Berger, S. A. 1987 Fully developed flow in a curved pipe of arbitrary curvature ratio. Intl J. Numer. Meth. in Fluids 7, 733.Google Scholar
Winters, K. H. 1984 A bifurcation study of laminar flow in a curved tube of rectangular cross section. AERE-TP. 1104. AERE Harwell.