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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
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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

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