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Velocity redistribution in curved rectangular channels

Published online by Cambridge University Press:  20 April 2006

H. J. De Vriend
Affiliation:
Department of Civil Engineering, Delft University of Technology, The Netherlands

Abstract

The main velocity redistribution in steady flow through curved conduits of shallow rectangular cross-section is considered. Its mechanism is analysed using a mathematical model of steady incompressible laminar flow in coiled rectangular pipes. The transverse transport of main-flow momentum by the secondary circulation is shown to be the principal cause of this velocity redistribution. The importance of the side-wall regions, even in shallow channels, is assessed and the neglect of the influence of the side walls in the commonly applied simplified models of flow through shallow curved channels is shown to be strongly limiting in case of long bends with a rectangular cross-section.

Type
Research Article
Copyright
© 1981 Cambridge University Press

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References

Adler, M. 1934 Strömung in gekrümmten Rohren. Z. angew. Math. Mech. 257275.Google Scholar
Bathurst, J. C., Thorne, C. R. & Hey, R. D. 1979 Secondary flow and shear stress at river bends. Proc. A.S.C.E., J. Hydraulic Div. 105 (HY10), 12771293.Google Scholar
Böss, P. 1938 In Wasser- und Geschiebebewegung in gekrümmten Flusstrecken (ed. H. Wittman & P. Böss). Springer.
Boussinesq, J. 1868 Mémoire sur l'influence de frottement dans les mouvements réguliers des fluïdes. J. Math. pures et appl. (2ème série) 13, 413000.Google Scholar
Cheng, K. C. & Akiyama, M. 1970 Laminar forced convection heat transfer in curved rectangular channels. Int. J. Heat Mass Transfer 13, 471490.Google Scholar
Cheng, K. C., Lin, R.-C. & Ou, J.-W. 1976 Fully developed laminar flow in curved rectangular channels. Trans. A.S.M.E. I, J. Fluids Engng 98, 4148.Google Scholar
Choudhary, U. K. & Narasimhan, D. 1977 Flow in 180$ open channel rigid boundary bends. Proc. A.S.C.E., J. Hydraulic Div. 103 (HY6), 651657.Google Scholar
Collins, W. M. & Dennis, S. C. R. 1975 The steady motion of a viscous fluid in a curved tube. Quart. J. Mech. Appl. Math. 28, 133156.Google Scholar
Collins, W. M. & Dennis, S. C. R. 1976 Steady flow in a curved tube of triangular cross-section. Proc. Roy. Soc. A 352, 189211.Google Scholar
Cuming, H. G. 1952 The secondary flow in curved pipes. Aero. Res. Center R. & M. 2880.Google Scholar
Dean, W. R. 1928a The stream-line motion of fluid in a curved pipe. Phil. Mag. S7, 5, 673695.Google Scholar
Dean, W. R. 1928b Fluid motion in a curved channel. Proc. Roy. Soc. A 121, 402420.Google Scholar
De Vriend, H. J. 1973 Theory of viscous flow in curved shallow channels. Comm. on Hydraulics, Delft Univ. of Techn., Rep. 711. (Also: Proc. Int. Symp. River Mech., Bankok, 1973, paper A17.)
De Vriend, H. J. 1976 A mathematical model of steady flow in curved shallow channels. Comm. on Hydraulics, Delft Univ. of Techn., Rep. 761. (Also: J. Hydraulic Res. 15, 1917, 37–54.)
De Vriend, H. J. 1978 Fully developed laminar flow in curved ducts. Lab. Fluid Mech., Delft Univ. Tech., Int. rep. 278.
De Vriend, H. J. 1979 Flow measurements in a curved rectangular channel. Lab. Fluid Mech., Delft Univ. Tech., Int. rep. 979.
De Vriend, H. J. & Koch, F. G. 1977 Flow of water in a curved open channel with a fixed plane bed. Delft Hydr. Lab., Delft Univ. of Tech., TOW-rep. R657-VI/M1415-I.
Einstein, H. A. & Harder, J. A. 1954 Velocity distribution and boundary layer at channel bends. Trans. Am. Geophys. Un. 35, 114120.Google Scholar
Engelund, F. 1974 Flow and bed topography in channel bends. Proc. A.S.C.E., J. Hydraulic Div. 100 (HY11). 16311648.Google Scholar
Falcón, M. A. 1979 Analysis of flow in alluvial channel bends. Ph.D. thesis, Univ. of Iowa.
Görtler, H. 1940 Über eine dreidimensionale Instabilität laminarer Grenzschichten an konkaven Wänden. Nachr. Wiss. Ges. Göttingen, Math. Phys. Klasse, Neue Folge 2, no. 1.
Gottlieb, L. 1976 Three-dimensional flow pattern and bed topography in meandering channels. I.S.V.A., Techn. Univ. of Denmark, Series Paper no. 11.Google Scholar
It, H. 1951 Theory on laminar flow through curved pipes of elliptic and rectangular cross-section. Rep. Inst. High Speed Mech. Tohoku Univ. 1, 116.Google Scholar
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. A.I.Ch.E.J. 21, 965974.Google Scholar
Kalkwijk, J. P. Th. & de Vriend, H. J. 1980 Computation of the flow in shallow river bends. J. Hydraulic Res. 18, no. 4.Google Scholar
Kamiyama, S. 1966 Two dimensional potential theory on flow through bend of arbitrary profile (Report 2). Rep. Inst. High Speed Mech. Tohoku Univ. 18, no. 172, 2542.Google Scholar
Leopold, L. B., Wolman, M. G. & Miller, J. P. 1964 Fluvial Processes in Geomorphology. San Francisco.
Leschziner, M. & Rodi, W. 1978 Calculation of three-dimensional turbulent flow in strongly curved open channels. Univ. Karlsruhe, Rep. SFB80/T/126. (Also: Proc. A.S.C.E., J. Hydraulic Div. 105 (HY10), 1297–1315, 1979.)Google Scholar
Mori, Y., Uchida, U. & Ukon, T. 1971 Forced convective heat transfer in a curved channel with a square cross-section. Int. J. Heat Mass Transfer 14, 17871804.Google Scholar
Muramoto, Y. 1965 Flow through curved open channels, Part I — On characteristics of upper layer in fully developed region. Bull. Dis. Prev. Res. Inst. 14, pt. 2, 114.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, 539551.Google Scholar
Patankar, S. V., Pratap, V. S. & Spalding, D. B. 1975 Prediction of turbulent flow in curved pipes. J. Fluid Mech. 67, 583595.Google Scholar
Perkins, H. J. 1970 The formation of streamwise vorticity in turbulent flow. J. Fluid Mech. 44, 721740.Google Scholar
Prandtl, L. 1952 Essentials of Fluid Dynamics. London: Blackie.
Pratap, V. S. & Spalding, D. B. 1975 Numerical computations of the flow in curved ducts. Aero. Quart. 26, 219228.Google Scholar
Rao, K. V. 1975 Secondary flow in a curved channel as revealed by a laser doppler anemometer. Proc. LDA-Symp. Copenhagen, pp. 710718.Google Scholar
Reynolds, A. J. 1974 Turbulent Flows in Engineering. Wiley.
Rozovskii, I. L. 1961 Flow of water in bends of open channels. Israel Program for Scientific Translation, Jerusalem (in Russian, 1957).
Schlichting, H. 1951 Boundary Layer Theory. Karlsruhe: Braun. (English edition; McGraw-Hill, 1968.
Taylor, G. I. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. Roy. Soc. A 223, 289343.Google Scholar
Van Bendegom, L. 1947 Some considerations on river morphology and river improvement. De Ingenieur 59, no. 4, B1-11 (in Dutch). Transl. 1963 National Res. Council Canada, Techn. Transl. no. 1054).Google Scholar
Yen, B. C. 1965 Characteristics of subcritical flow in a meandering channel. Inst. Hydr. Res., Univ. of Iowa.