Hostname: page-component-76dd75c94c-ccc76 Total loading time: 0 Render date: 2024-04-30T08:43:25.226Z Has data issue: false hasContentIssue false
  • English
  • Français

Laminar flow in a square duct of strong curvature

Published online by Cambridge University Press:  12 April 2006

J. A. C. Humphrey ,
A. M. K. Taylor  and
J. H. Whitelaw
J. A. C. Humphrey
Affiliation:
Department of Mechanical Engineering, Imperial College, London
A. M. K. Taylor
Affiliation:
Department of Mechanical Engineering, Imperial College, London
J. H. Whitelaw
Affiliation:
Department of Mechanical Engineering, Imperial College, London
Get access Rights & Permissions [Opens in a new window]

Abstract

Calculated values of the three velocity components and measured values of the longitudinal component are reported for the flow of water in a 90° bend of 40 x 40mm cross-section; the bend had a mean radius of 92mm and was located downstream of a 1[sdot ]8m and upstream of a 1[sdot ]2m straight section. The experiments were carried out at a Reynolds number, based on the hydraulic diameter and bulk velocity, of 790 (corresponding to a Dean number of 368). Flow visualization was used to identify qualitatively the characteristics of the flow and laser-Doppler anemometry to quantify the velocity field. The results confirm and quantify that the location of maximum velocity moves from the centre of the duct towards the outer wall and, in the 90° plane, is located around 85% of the duct width from the inner wall. Secondary velocities up to 65% of the bulk longitudinal velocity were calculated and small regions of recirculation, close to the outer corners of the duct and in the upstream region, were also observed.

The calculated results were obtained by solving the Navier–Stokes equations in cylindrical co-ordinates. They are shown to exhibit the same trends as the experiments and to be in reasonable quantitative agreement even though the number of node points used to discretize the flow for the finite-difference solution of the differential equations was limited by available computer time and storage. The region of recirculation observed experimentally is confirmed by the calculations. The magnitude of the various terms in the equations is examined to determine the extent to which the details of the flow can be represented by reduced forms of the Navier–Stokes equations. The implications of the use of so-called ‘partially parabolic’ equations and of potential- and rotational-flow analysis of an ideal fluid are quantified.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 83 , Issue 3 , 5 December 1977 , pp. 509 - 527
Copyright
© 1977 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

Ahmed, S. & Brundrett, E. 1971a Turbulent flow in non-circular ducts. Part I. Mean flow properties in the developing region of a square duct. Int. J. Heat Mass Transfer 14, 365.Google Scholar
Ahmed, S. & Brundrett, E. 1971b Characteristic lengths for non-circular ducts. Int. J. Heat Mass Transfer 14, 157.Google Scholar
Amsden, A. A. & Harlow, F. H. 1970 The SMAC method. Los Alamos Sci. Lab. Rep. LA-4370.Google Scholar
Austin, L. R. & Seader, J. D. 1973 Fully developed viscous flow in coiled circular pipes. A.I.Ch.E. J. 19, 85.Google Scholar
Bergeles, G. 1976 Three-dimensional discrete-hole cooling processes. An experimental and numerical study. Ph.D. thesis, University of London.
Brundrett, E. & Baines, W. D. 1964 The production and diffusion of vorticity in duct flow. J. Fluid Mech. 19, 375.Google Scholar
Cheng, K. G., Lin, R. C. & Ou, J. W. 1976 Fully developed laminar flow in curved rectangular channels. A.S.M.E. J. Fluids Engng 198, 41.Google Scholar
Chorin, A. J. 1968 Numerical solution of the Navier — Stokes equations. Math. Comp. 22, 745.Google Scholar
Durst, F. & Whitelaw, J. H. 1971 Integrated optical units for laser anemometry. J. Phys. E 4, 804.Google Scholar
Durst, F., Melling, A. & Whitelaw, J. H. 1976 Principles and Practices of Laser-Doppler Anemometry. Academic Press.
Gessner, F. B. 1964 Turbulence and mean flow characteristics of fully-developed flow in rectangular channels. Ph.D. thesis, Purdue University.
Gessner, F. B. & Jones, J. B. 1965 On some aspects of fully developed turbulent flow in rectangular channels. J. Fluid Mech. 23, 689.Google Scholar
Gosman, A. D. & Pun, W. M. 1973 Calculation of recirculating flows. Imperial College Mech. Engng Dept. Rep.Google Scholar
Harlow, F. H. & Welch, J. E. 1965 Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8, 2182.Google Scholar
Hawthorne, W. R. 1951 Secondary circulation in fluid flow. Proc. Roy. Soc. A 206, 374.Google Scholar
Huang, W. H., Robertson, J. M. & McPherson, M. B. 1967 Some analytical results for plane 90 degree bend flow. J. Hydraul. Div., Proc. A.S.C.E. HY6, 169.
Humphrey, J. A. C. 1977 Flow in ducts with curvature and roughness. Ph.D. thesis, University of London.
Humphrey, J. A. C. & Whitelaw, J. H. 1976 Measurements in curved flows. Proc. SQUID Conf. Internal Flows, Airlie House.
Ito, H. 1960 Pressure losses in smooth pipe bends. Trans. A.S.M.E. D 82, 131.Google Scholar
Joseph, B., Smith, E. P. & Allen, R. J. 1975 Numerical treatment of laminar flow in helically coiled tubes of square cross section 1. Stationary helically coiled tubes A.I.Ch.E. J. 21, 965.Google Scholar
Launder, B. E. & Ying, W. M. 1972 Secondary flows in ducts of square cross-section. J. Fluid Mech. 54, 289.Google Scholar
Launder, B. E. & Ying, W. M. 1973 Prediction of flow and heat transfer in ducts of square cross section. Heat Fluid Flow 3, 115.Google Scholar
Melling, A. & Whitelaw, J. H. 1976 Turbulent flow in a rectangular duct. J. Fluid Mech. 78, 289.Google Scholar
Patankar, S. V., Pratap, V. S. & Spalding, D. B. 1975 Prediction of turbulent flow in curved pipes. J. Fluid Mech. 67, 583.Google Scholar
Patankar, S. V. & Spalding, D. B. 1971 A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. Int. J. Heat Mass Transfer 15, 1787.Google Scholar
Pratap, V. S. & Spalding, D. B. 1975 Numerical computations of the flow in curved ducts. Aero. Quart. 26, 219.Google Scholar
Squire, H. B. & Winter, K. G. 1951 The secondary flow in a cascade of airfoils in a nonuniform stream. J. Aero. Sci. 18, 271.Google Scholar
Tatchell, D. G. 1975 Convection processes in confined three dimensional boundary layers. Ph.D. thesis, University of London.
Ward-Smith, A. J. 1971 Pressure Losses in Ducted Flows. Butterworths.