Velocity Distribution in Open Channel Flows: Analytical Approach for the Outer Region
Publication: Journal of Hydraulic Engineering
Volume 139, Issue 1
Abstract
This paper presents an integration procedure for the Reynolds-averaged Navier-Stokes equations for the determination of the distribution of the streamwise velocity using the vertical component. This procedure is dedicated to the outer region and central part of channels. The proposed model is applicable to both rough and smooth flow regimes, provided the velocity at the inner-outer boundary has been properly defined. To generate a simplified expansion, a number of hypotheses are proposed, focusing in particular on the analytical modeling of the vertical component by adopting a negligible viscosity. The proposed hypotheses are validated by the experimental data existing in the literature. The proposed simplified expansion is studied through a sensitivity analysis and proved consistent in regards to model experimental data. The proposed model seems capable of demonstrating different kinds of flows, including dip phenomenon flow patterns.
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Acknowledgments
This text was proofread by Robert Sachs, a certified French-to-English translator.
References
Absi, R. (2008). “Comments on ‘turbulent velocity profile in fully-developed open channels flows’.” Environ. Fluid Mech., 8, 389–394.
AFNOR. (2009). “Hydrométrie—Mesurage du débit des liquides dans les.” NF EN 748, Paris.
Bonakdari, H., Larrarte, F., Lassabatere, L., and Joannis, C. (2008). “Turbulent velocity profile in fully-developed open channel flows.” Environ. Fluid Mech., 8, 1–17.
Cardoso, A. H., Graf, W. H., and Gust, G. (1989). “Uniform flow in a smooth open channel.” J. Hydraul. Res., 27(5), 603–616.
Castro-Orgas, O., and Dey, S. (2011). “Power-law velocity profile in turbulent boundary layers: An integral Reynolds-number dependent solution.” Acta Geophys., 59(5), 993–1012.
Cheng, N. S. (2007). “Power-law index for velocity profiles in open channel flows.” Adv. Water Resour., 30, 1775–1784.
Coleman, N. L. (1986). “Effects of suspended sediment on the open-channel velocity distribution.” Water Resour. Res., 22(10), 1377–1384.
Coles, D. (1956). “The law of the wake in the turbulent boundary layer.” J. Fluid Mech., 1, 191–226.
Dey, S., and Raikar, R. V. (2007) “Characteristics of loose rough boundary streams at near-threshold.” J. Hydraul. Eng., 133(3), 288–304.
Franca, M. J., Ferreira, R. M. L., and Lemmin, U. (2008). “Parameterization of the logarithmic layer of double-averaged streamwise velocity profiles in gravel-bed river flows.” Adv. Water Resour., 31, 915–925.
Guo, J., and Julien, P. Y. (2003). “Modified log-wake law for turbulent flow in smooth pipes.” J. Hydraul. Res., 41(5), 493–501.
Hurther, D., and Lemmin, U. (2001). “Discussion of ‘Equilibrium near-bed concentration of suspended sediment’.” J. Hydraul. Eng., 127(5), 430–433.
Ikeda, S. (1981). “Self-formed straight channels in sandy beds.” J. Hydraul. Div., 107(4), 389–406.
Keulegan, G. H. (1938). “Laws of turbulent flow in open channels.” J. Res. Nat. Bur. Stand., 21(6), 707–741.
Kironoto, B. A., and Graf, W. H. (1994). “Turbulence characteristics in rough uniform open channel flow.” Proc. Inst. Civ. Eng. Water Marit. Energy, 106, 333–344.
Larrarte, F. (2006). “Velocity fields within sewers: An experimental study.” Flow Meas. Instrum., 17, 282–290.
Montes, S. (1998). Hydraulics of open channel flow, ASCE Press, Reston, VA.
Nezu, I., and Nakagawa, H. (1993). Turbulent open-channel flows, IAHR Monograph, CRC Press, Taylor and Francis Group, Balkema, Rotterdam.
Nikuradse, J. (1950). Laws of flow in rough pipes, Tech. Memorandum 1292, National Advisory Committee for Aeronautics, Washington, DC.
Pu, J. H. (2008). “Efficient finite volume numerical modelling and experimental study of 2D shallow water free surface turbulent flows.” Ph.D. dissertation, Univ. of Bradford, Bradford, UK.
Pu, J. H., Bonakdari, H., Lassabatère, L., Joannis, C., and Larrarte, F. (2010). “Profil de vitesses turbulent: une nouvelle loi pour les canaux étroits.” La Houille Blanche (Int. Water J.), 3, 65–70.
Sarma, K. V. N., Lakshminarayana, P., and Rao, N. S. L. (1983). “Velocity distribution in smooth rectangular open channels.” J. Hydraul. Eng., 109(2), 270–289.
Wang, X., Wang, Z. Y., Yu, M., and Li, D. (2001). “Velocity profile of sediment suspensions and comparison of log law and wake law.” J. Hydraul. Res., 39(2), 211–217.
Yang, S. Q., Lim, S. Y., and McCorquodale, J. A. (2005). “Investigation of near wall velocity in 3-D smooth channel flows.” J. Hydraul. Res., 43(2), 149–157.
Yang, S. Q., and McCorquodale, J. A. (2004). “Determination of boundary shear stress and Reynolds shear stress in smooth rectangular channel flows.” J. Hydraul. Eng., 130(5), 458–462.
Yang, S. Q., Tan, S. K., and Lim, S. Y. (2004). “Velocity distribution and dip-phenomenon in smooth uniform open channel flows.” J. Hydraul. Eng., 130(12), 1179–1186.
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Information
Published In
Journal of Hydraulic Engineering
Volume 139 • Issue 1 • January 2013
Pages: 37 - 43
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Sep 30, 2011
Accepted: Apr 9, 2012
Published online: Apr 12, 2012
Published in print: Jan 1, 2013
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