Numerical Investigation into Secondary Currents and Wall Shear in Trapezoidal Channels
Publication: Journal of Hydraulic Engineering
Volume 137, Issue 4
Abstract
This paper presents the use of computational fluid dynamics (CFD) to determine the distribution of the bed and sidewall shear stresses in trapezoidal channels. The impact of the variation of the slant angle of the side walls, aspect ratio, and composite roughness on the shear stress distribution is analyzed. The shear stress data can be directly output from the CFD models at the boundaries, but they can also be derived using the Guo and Julien equations for the average bed and side wall shear stresses. These equations compute the shear stress as a function of three components; gravitational, secondary flows, and interfacial shear stress, and are hence used to gauge the respective merits of the different components of wall shear. The results show a significant contribution from the secondary currents and internal shear stresses on the overall shear stress at the boundaries. This work also extends previous work of the authors on rectangular channels.
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References
ANSYS, Inc. (2008). ANSYS-CFX, version 11.0, Ansys, Canonsburg, PA.
Cacqueray, N. D., Hargreaves, D. M., and Morvan, H. P. (2009). “A computational study of shear stress in smooth rectangular channels.” J. Hydraul. Res., 47(1), 50–57.
Chiu, C. L., and Chiou, J. D. (1986). “Structure of 3-D flow in rectangular open channels.” J. Hydraul. Eng., 112(11), 1050–1068.
Cokljat, D. (1993). “Turbulence models for non-circular ducts and channels.” Ph.D. thesis, Dept. of Civil Engineering, City University, London.
Cruff, R. W. (1965). “Cross-channel transfer of linear momentum in smooth rectangular channels.” Paper 1592-B, U.S. Geological Survey, B1–B26.
Einstein, H. A. (1942). “Formulas for the transportation of bed load.” Trans. Am. Soc. Civ. Eng., 107, 561–597.
Flintham, T. P., and Carling, P. A. (1988). “The prediction of mean bed and wall boundary shear in uniform and compositely rough channels.” Int. Conf. on River Regime, Hydraulics Research Ltd., Wiley, Wallingford, UK, 267–287.
Ghosh, S. N., and Roy, N. (1970). “Boundary shear distribution in open channel flow.” J. Hydraul. Div., 96(4), 967–994.
Guo, J., and Julien, P. Y. (2005). “Shear stress in smooth rectangular open-channel flows.” J. Hydraul. Eng., 131(1), 30–37.
Haywood, O. G. (1942). “Discussion on ‘Formulas for the transportation of bed load’ by H. A. Einstein.” Trans. Am. Soc. Civ. Eng., 107, 583–590.
Kartha, V. C., and Leutheusser, H. J. (1970). “Distribution of tractive force in open channels.” J. Hydraul. Div., 96(7), 1469–1483.
Keulegan, G. H. (1938). “Laws of turbulent flow in open channels.” J. Res. Natl. Bur. Stand., 21, 708–741.
Knight, D. W. (1981). “Boundary shear in smooth and rough channels.” J. Hydraul. Div., 107(7), 839–851.
Knight, D. W., Demetriou, J. D., and Hamed, M. E. (1984). “Boundary shear in smooth rectangular channels.” J. Hydraul. Eng., 110(4), 405–422.
Knight, D. W., and Sterling, M. (2000). “Boundary shear in circular pipes running partially full.” J. Hydraul. Eng., 126(4), 263–275.
Launder, B. E., Reece, G. J., and Rodi, W. (1975). “Progress in the developments of a Reynolds-stress turbulence closure.” J. Fluid Mech., 68, 537–566.
Leighly, J. (1932). “Toward a theory of the morphologic significance of turbulence in the flow of water in streams.” Prog. Phys. Geo., 6(1), 1–22.
Mathworks. (2006). Matlab, version 7.3, Mathworks Natick, MA.
Mohammadi, M., and Knight, D. W. (2004). “Boundary shear stress distribution in a V-Shaped channel.” Hydraulics of Dams and River Structures, F. Yazdandoost and J. Attari, eds., Taylor and Francis, London, 401–410.
Morvan, H. P., and Hargreaves, D. M. (2009). “A computational study of secondary currents and wall shear stress in prismatic channels.” Proc. of the 33rd IAHR Congress, IAHR, Vancouver, Canada.
Morvan, H. P., Pender, G., Wright, N. G., and Ervine, D. A. (2002). “Three-dimensional hydrodynamics of meandering compound channels.” J. Hydraul. Eng., 128(7), 674–682.
Myers, W. R. C. (1978). “Momentum transfer in a compound channel.” J. Hydraul. Res., 16(2), 139–150.
Noutsopoulos, G. C., and Hadjipanos, P. A. (1982). “Discussion on boundary shear in smooth and rough channels by D. W. Knight.” J. Hydraul. Div., 108(6), 809–812.
Patel, H. S. (1984). “Boundary shear in rectangular and compound ducts.” Ph.D. thesis, Univ. of Birmingham, Birmingham, UK.
Rhodes, D. G. (1991). “An experimental investigation of the mean flow structure in wide ducts of simple rectangular and trapezoidal compound cross section, examining in particular zones of higher lateral shear.” Ph.D. thesis, Univ. of Birmingham, Birmingham, UK.
Speziale, C. G., Sarkar, S., and Gatski, T. B. (1991). “Modelling the pressure-strain correlation of turbulence: An invariant dynamical systems approach.” J. Fluid Mech., 227, 245–272.
Yang, S. Q., and Lim, S. Y. (1997). “Mechanism of energy transportation and turbulent flow in a 3D channel.” J. Hydraul. Eng., 123(8), 684–692.
Yang, S. Q., and Lim, S. Y. (1998). “Boundary shear stress distribution in smooth rectangular open channel flows.” Proc. ICE Water Marit. Eng., 130(3), 163–173.
Yuen, K. W. H. (1989). “A study of boundary shear stress, flow resistance and momentum transfer in open channels with simple and compound trapezoidal cross sections.” Ph.D. thesis, Univ. of Birmingham, Birmingham, UK.
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Information
Published In
Journal of Hydraulic Engineering
Volume 137 • Issue 4 • April 2011
Pages: 432 - 440
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Dec 7, 2009
Accepted: Sep 1, 2010
Published online: Mar 15, 2011
Published in print: Apr 1, 2011
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