Exact Solution for Asymmetric Turbulent Channel Flow with Applications in Ice-Covered Rivers
Publication: Journal of Hydraulic Engineering
Volume 143, Issue 10
Abstract
Asymmetric turbulent channel flow, such as ice-covered river flow, is a century-old problem but still unsolved in hydraulics and fluid mechanics. This study finds exact solutions for its eddy (or turbulent) viscosity and mean velocity distributions, which are independent of any assumption without any fit parameter. Specifically, it first applies Guo’s quartic eddy viscosity and complete log-law from high-Reynolds-number pipe flow to symmetric turbulent channel flow. It then formulates a functional equation, involving both bottom and top plane shear velocities, to govern the eddy viscosity distribution in asymmetric channel flow. The analytic solution for the eddy viscosity then leads to a velocity distribution solution that includes four components: bottom shear velocity effect, top plane shear velocity effect, symmetric interaction between both about a critical point, and antisymmetric interaction between both. The velocity distribution solution agrees well with field data and so is applicable in ice-covered rivers. Laboratory data also confirm the velocity distribution structure, but a turbulent mixing intensity parameter depends on the Reynolds number. Therefore, future laboratory tests should focus on high-Reynolds-number flow.
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Acknowledgments
This research was supported by the U.S. Federal Highway Administration Hydraulics R&D Program (Contract DTFH61-349 11-D-00010) through the Genex System to the University of Nebraska-Lincoln, the China Open Fund research programs at the State Key Lab of Hydraulic Engineering Simulation and Safety (Contract HESS-1604), Tianjin University, and at the State Key Lab of Hydraulics and Mountain River Engineering (Contract SKHL1511), Sichuan University. The authors also thank Prof. M. P. Schultz at the U.S. Naval Academy for providing the data in Figs. 2 and 3 for symmetric channel flow.
References
Barrows, H. K., and Horton, R. E. (1907). Determination of stream flow during the frozen season, USGS, Washington, DC.
Engmann, E. O. (1977). “Turbulent diffusion in channels with a surface cover.” J. Hydraul. Res., 15(4), 327–335.
Faruque, M. A. A. (2009). “Smooth and rough wall open channel flow including effects of seepage and ice cover.” Ph.D. thesis, Univ. of Windsor, Windsor, ON, Canada.
Guo, J. (2017). “Eddy viscosity and complete log-law for turbulent pipe flow at high Reynolds numbers.” J. Hydraul. Res., 55(1), 27–39.
Hanjalic, K., and Launder, B. E. (1972). “Fully developed asymmetric flow in a plane channel.” J. Fluid Mech., 51(2), 301–335.
Healy, D., and Hicks, F. E. (2004). “ Index velocity methods for winter discharge measurement.” Can. J. Civ. Eng., 31(3), 407–419.
Hultmark, M. (2011). “Reynolds number effects on turbulent pipe flow.” Ph.D. thesis, Princeton Univ., Princeton, NJ.
Krishnappan, B. G. (1984). “Laboratory verification of turbulent flow model.” J. Hydraul. Eng., 500–514.
Lau, Y. L., and Krishnappan, B. G. (1981). “Ice cover effects on stream flows and mixing.” J. Hydraul. Div., 107(10), 1225–1242.
Launder, B. E., and Spalding, D. B. (1974). “The numerical calculation of turbulent flows.” Comput. Methods Appl. Mech. Eng., 3(2), 269–289.
Marusic, I., Monty, J. P., Hultmark, M., and Smits, A. J. (2013). “On the logarithmic region in wall turbulence.” J. Fluid Mech., 716(R3), 1–11.
MATLAB [Computer software]. MathWorks, Natick, MA.
Monty, J. P. (2005). “Developments in smooth wall turbulent duct flows.” Ph.D. thesis, Univ. of Melbourne, Melbourne, Australia.
Papadakis, J. E. (1988). The two-power law for analysis of velocity profiles in ice-covered river, Report of Institute of Ocean Science, Sidney, BC, Canada.
Parthasarathy, R. N., and Muste, M. (1994). “Velocity measurements in asymmetric turbulent channel flows.” J. Hydraul. Eng., 1000–1020.
Perry, A. E., Hadez, S., and Chong, M. S. (2001). “A possible reinterpretation of the Princeton superpipe data.” J. Fluid Mech., 439, 395–401.
Schultz, M. P., and Flack, K. A. (2013). “Reynolds-number scaling of turbulent channel flow.” Phys. Fluids, 25(2), 025104.
Scientific WorkPlace 5.5 [Computer software]. Mackichan Software, Poulsbo, WA.
Tatinclaux, J.-C., and Gogus, M. (1983). “Asymmetric plane flow with application to ice jams.” J. Hydraul. Eng., 1540–1554.
Teal, M. J., Ettema, R., and Walker, J. F. (1994). “ Estimation of mean flow velocity in ice-covered channels.” J. Hydraul. Eng., 1385–1400.
Tsai, W.-F, and Ettema, R. (1994). “Modified eddy viscosity model in fully developed asymmetric channel flows.” J. Eng. Mech., 720–732.
Tsai, W.-F., and Ettema, R. (1996). “A study of ice-covered flow in an alluvial bend.”, Univ. of Iowa, Iowa City, IA.
Urroz, G. E., and Ettema, R. (1994). “Application of two-layer hypothesis to fully developed flow in ice-covered curved channels.” Can. J. Civ. Eng., 21(1), 101–110.
Wang, D., McCurry, P., and Bourdages, R. (2000). “Application of flow velocity distribution models to channel discharge measurements.” Proc., ASCE Joint Conf. on Water Resources Engineering and Water Resources Planning and Management (CD-ROM), ASCE, Reston, VA.
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Published In
Journal of Hydraulic Engineering
Volume 143 • Issue 10 • October 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Nov 29, 2016
Accepted: Apr 21, 2017
Published online: Jul 21, 2017
Published in print: Oct 1, 2017
Discussion open until: Dec 21, 2017
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