Multilayer Velocity Model Predicting Flow Resistance of Aerated Flows Down Grass-Lined Spillway
Publication: Journal of Hydraulic Engineering
Volume 148, Issue 10
Abstract
Grass-lined spillways are flow conveyance structures with environmental benefits. The stability of such spillways has been typically assessed considering soil erosion, but the design of grass-lined spillways based on hydraulic considerations has rarely been conducted. While subcritical flows in channels with grass have been studied extensively, studies of velocities and flow resistance in supercritical flows in spillways are limited. Herein, this experimental study investigated the application of a multilayer velocity model for supercritical self-aerated flows on a spillway with submerged artificial grass. Velocities were measured with a pitot tube and dual-tip air–water flow conductivity probe, providing the most systematic assessment of velocities and flow resistance in supercritical vegetated flows to date. The velocity distributions were well described with a multilayer velocity model previously developed for subcritical flow conditions, and a constant interfacial velocity supplemented the observed supercritical aerated free-surface layer. Based on this velocity model, explicit expressions for the mean flow velocity and the friction factor were developed for grass-lined spillways, which were also applicable for subcritical flow conditions with comparable vegetation cover. The flow resistance model provides a theoretically developed design option for grass-lined spillways that is solely based on vegetation properties and hydraulic boundary conditions.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request. For practical applications, a MATLAB version R2020b code for the simultaneous solution of mean velocity and clear water flow depth is available at https://github.com/MatthiasKramer/Flow-resistance-on-vegetated-chutes.
Acknowledgments
The authors thank Rob Jenkins and Larry Paice (WRL, UNSW Sydney) for their technical assistance.
References
Brocchini, M., and D. H. Peregrine. 2001. “The dynamics of strong turbulence at free surfaces. Part 1. Description.” J. Fluid Mech. 449 (Dec): 225–254. https://doi.org/10.1017/S0022112001006012.
Carollo, F. G., V. Ferro, and D. Termini. 2002. “Flow velocity measurements in vegetated channels.” J. Hydraul. Eng. 128 (7): 664–673. https://doi.org/10.1061/(ASCE)0733-9429(2002)128:7(664).
Chanson, H., and T. Brattberg. 2000. “Experimental study of the air–water shear flow in a hydraulic jump.” Int. J. Multiphase Flow 26 (4): 583–607. https://doi.org/10.1016/S0301-9322(99)00016-6.
Chanson, H., and L. Toombes. 2002. “Experimental investigations of air entrainment in transition and skimming flows down a stepped chute.” Can. J. Civ. Eng. 29 (1): 145–156.
Chow, V. T. 1959. Open-channel hydraulics. New York: McGraw-Hill.
Ciraolo, G., and G. B. Ferreri. 2007. “Log velocity profile and bottom displacement for a flow over a very flexible submerged canopy.” In Proc., 32nd IAHR World Congress. Venice, Italy: International Association for Hydro-Environment Engineering and Research.
Coles, D. 1956. “The law of the wake in the turbulent boundary layer.” J. Fluid Mech. 1 (2): 191–226. https://doi.org/10.1017/S0022112056000135.
Cox, M. B. 1942. Tests on vegetated waterways. Washington, DC: USDA.
Cui, H., M. Kramer, and S. Felder. 2020. “Velocity profiles on a grass-lined spillway in supercritical flow.” In Proc., 1st IAHR Young Professionals Congress. Madrid, Spain: International Association for Hydro-Environment Engineering and Research.
Dey, S. 2014. Fluvial hydrodynamics: Hydrodynamic and sediment transport phenomena. Berlin: Springer.
Erpicum, S., B. M. Crookston, F. Bombardelli, D. B. Bung, S. Felder, S. Mulligan, M. Oertel, and M. Palermo. 2020. “Hydraulic structures engineering: An evolving science in a changing world.” WIREs Water 8 (2): e1505. https://doi.org/10.1002/wat2.1505.
Felder, S., B. Hohermuth, and R. Boes. 2019. “High-velocity air-water flows downstream of sluice gates including selection of optimum phase-detection probe.” Int. J. Multiphase Flow 116 (Jul): 203–220. https://doi.org/10.1016/j.ijmultiphaseflow.2019.04.015.
Fiener, P., and K. Auerswald. 2003. “Effectiveness of grassed waterways in reducing runoff and sediment delivery from agricultural watershed.” J. Environ. Qual. 32 (3): 927–936. https://doi.org/10.2134/jeq2003.9270.
Ghisalberti, M., and H. Nepf. 2002. “Mixing layers and coherent structures in vegetated aquatic flows.” J. Geophys. Res. 107 (C2): 3. https://doi.org/10.1029/2001JC000871.
Hager, W. H. 1991. “Uniform aerated chute flow.” J. Hydraul. Eng. 117 (4): 528–533. https://doi.org/10.1061/(ASCE)0733-9429(1991)117:4(528).
Hewlett, H., L. Boorman, and M. Bramley. 1987. Design of reinforced grass waterways. London: Construction Industry Research and Information Association.
Huthoff, F. 2007. “Modeling hydraulic resistance of floodplain vegetation.” Ph.D. thesis, Faculty of Engineering Technology, Univ. of Twente.
Jarvela, J. 2005. “Effect of submerged flexible vegetation on flow structure and resistance.” J. Hydrol. 307 (1–4): 233–241. https://doi.org/10.1016/j.jhydrol.2004.10.013.
Kirby, J. T., S. R. Durrans, R. Pitt, and P. D. Johnson. 2005. “Hydraulic resistance in grass swales designed for small flow conveyance.” J. Hydraul. Eng. 131 (1): 65–68. https://doi.org/10.1061/(ASCE)0733-9429(2005)131:1(65).
Kirkgöz, M. S., and M. Ardiçlioğlu. 1997. “Velocity profiles of developing and developed open channel flow.” J. Hydraul. Eng. 123 (12): 1099–1105. https://doi.org/10.1061/(ASCE)0733-9429(1997)123:12(1099).
Klopstra, D., H. J. Barneveld, J. M. Van Noortwijk, and E. H. Van Velzen. 1997. “Analytical model for hydraulic roughness of submerged vegetation.” In Proc., 27th IAHR Congress, 775–780. Madrid, Spain: International Association for Hydro-Environment Engineering and Research.
Kramer, M., S. Felder, B. Hohermuth, and D. Valero. 2021a. “Drag reduction in aerated chute flow: The role of bottom air concentration.” J. Hydraul. Eng. 147 (11): 04021041. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001925.
Kramer, M., B. Hohermuth, B. Valero, and S. Felder. 2020. “Best practices for velocity estimations in highly aerated flows with dual-tip phase-detection probes.” Int. J. Multiphase Flow 126 (May): 103228. https://doi.org/10.1016/j.ijmultiphaseflow.2020.103228.
Kramer, M., B. Hohermuth, D. Valero, and S. Felder. 2021b. “On velocity estimations in highly aerated flows with dual-tip phase-detection probes—Closure.” Int. J. Multiphase Flow 134 (Jan): 103475. https://doi.org/10.1016/j.ijmultiphaseflow.2020.103475.
Kramer, M., D. Valero, H. Chanson, and D. B. Bung. 2019. “Towards reliable turbulence estimations with phase-detection probes: An adaptive window cross-correlation technique.” Exp. Fluids 60 (1): 6. https://doi.org/10.1007/s00348-018-2650-9.
Luhar, M., and H. Nepf. 2011. “Flow-induced reconfiguration of buoyant and flexible aquatic vegetation.” Limnol. Oceanogr. 56 (6): 2003–2017. https://doi.org/10.4319/lo.2011.56.6.2003.
Monin, A. S., and A. M. Yaglom. 1975. Vol. 1 of Statistical fluid mechanics: Mechanics of turbulence. Boston: MIT Press.
Nepf, H. 2012. “Flow and transport in regions with aquatic vegetation.” Ann. Rev. Fluid Mech. 44 (1): 123–142. https://doi.org/10.1146/annurev-fluid-120710-101048.
Nepf, H., and M. Ghisalberti. 2008. “Flow and transport in channels with submerged vegetation.” Acta Geophys. 56 (3): 753–777. https://doi.org/10.2478/s11600-008-0017-y.
Nepf, H. M., and E. Vivoni. 2000. “Flow structure in depth-limited, vegetated flow.” J. Geophys. Res. Oceans 105 (C12): 28547–28558. https://doi.org/10.1029/2000JC900145.
Nezu, I., and H. Nakagawa. 1993. Turbulence in open-channel flows. IAHR Monograph. Rotterdam, Netherlands: A.A. Balkema.
Nezu, I., and W. Rodi. 1986. “Open-channel flow measurements with a laser Doppler anemometer.” J. Hydraul. Eng. 112 (5): 335–355. https://doi.org/10.1061/(ASCE)0733-9429(1986)112:5(335).
Nezu, I., and M. Sanjou. 2008. “Turburence structure and coherent motion in vegetated canopy open-channel flows.” J. Hydro-environ. Res. 2 (2): 62–90. https://doi.org/10.1016/j.jher.2008.05.003.
Nikora, N., and V. Nikora. 2010. “Flow penetration into the canopy of the submerged vegetation: Definitions and quantitative estimates.” In Proc., River Flow 2010, 437–444. Karlsruhe, Germany: Bundesanstalt für Wasserbau.
Nikora, N., V. Nikora, and T. O’Donoghue. 2013. “Velocity profiles in vegetated open-channel flows: Combined effects of multiple mechanisms.” J. Hydraul. Eng. 139 (10): 1021–1032. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000779.
Nikora, V., D. Goring, I. McEwan, and G. Griffiths. 2001. “Spatially averaged open-channel flow over rough bed.” J. Hydraul. Eng. 127 (2): 123–133. https://doi.org/10.1061/(ASCE)0733-9429(2001)127:2(123).
Nikora, V., K. Koll, I. McEwan, S. McLean, and A. Dittrich. 2004. “Velocity distribution in the roughness layer of rough-bed flows.” J. Hydraul. Eng. 130 (10): 1036–1042. https://doi.org/10.1061/(ASCE)0733-9429(2004)130:10(1036).
Nikuradse, J. 1933. Laws of flow in rough pipes. Washington, DC: National Advisory Committee for Aeronautics.
Palmer, V. J. 1946. “Retardance coefficients for low flow in channels lined with vegetation.” Trans. Am. Geophys. Union 27 (2): 187–191. https://doi.org/10.1029/TR027i002p00187.
Pan, C., L. Ma, J. Wainwright, and Z. Shangguan. 2016. “Overland flow resistances on varying slope gradients and partitioning on grassed slopes under simulated rainfall.” Water Resour. Res. 52 (4): 2490–2512. https://doi.org/10.1002/2015WR018035.
Poggi, D., C. Krug, and G. Katul. 2009. “Hydraulic resistance of submerged rigid vegetation derived from first-order closure models.” Water Resour. Res. 45 (10): W10442. https://doi.org/10.1029/2008WR007373.
Ralston, D. C., and J. A. Brevard. 1988. “Design and performance of earth spillways.” In Proc., ASCE Hydraulics Division, Special Conf., 871–876. Reston, VA: ASCE.
Raupach, M., J. Finnigan, and Y. Brunei. 1996. “Coherent eddies and turbulence in vegetation canopies: The mixing-layer analogy.” In Boundary-layer meteorology, 351–382. New York: Springer.
Samani, J. M. V., and N. Kouwen. 2002. “Stability and erosion in grassed channels.” J. Hydraul. Eng. 128 (1): 40–45. https://doi.org/10.1061/(ASCE)0733-9429(2002)128:1(40).
Scheres, B., H. Schüttrumpf, and S. Felder. 2020. “Flow resistance and energy dissipation in supercritical air-water flows down vegetated chutes.” Water Resour. Res. 56 (2): 1–18. https://doi.org/10.1029/2019WR026686.
Severi, A. 2018. “Aeration performance and flow resistance in high-velocity flows over moderately sloped spillways with micro-rough bed.” Ph.D. thesis, School of Civil and Environmental Engineering, Univ. of New South Wales.
Singh, H., and A. Thompson. 2016. “Effect of antecedent soil moisture content on soil critical shear stress in agricultural watersheds.” Geoderma 262 (Jan): 165–173. https://doi.org/10.1016/j.geoderma.2015.08.011.
Temple, D. M. 1980. “Tractive force design of vegetated channels.” Trans. Am. Soc. Agric. Eng. 23 (4): 884–890. https://doi.org/10.13031/2013.34681.
Tinoco, R., J. San Juan, and J. Mullarney. 2020. “Simplification bias: Lessons from laboratory and field experiments on flow through aquatic vegetation.” Earth Surf. Processes Landforms 45 (1): 121–143. https://doi.org/10.1002/esp.4743.
USDA. 1954. Handbook design water of channel for soil and water conservation. Washington, DC: USDA.
Valero, D., and D. B. Bung. 2018. “Reformulating self-aeration in hydraulic structures: Turbulent growth of free surface perturbations leading to air entrainment.” Int. J. Multiphase Flow 100 (Mar): 127–142. https://doi.org/10.1016/j.ijmultiphaseflow.2017.12.011.
Van Hemert, H., M. Igigabel, R. Pohl, M. Sharp, J. Simm, R. Tourment, and M. Wallis. 2013. The international levee handbook. London: CIRIA.
Wilcock, R., P. Champion, J. Nagels, and G. Croker. 1999. “The influence of aquatic macrophytes on the hydraulic and physico-chemical properties of a New Zealand lowland stream.” Hydrobiologia 416 (Dec): 203–214. https://doi.org/10.1023/A:1003837231848.
Wilson, C. 2007. “Flow resistance models for flexible submerged vegetation.” J. Hydrol. 342 (3–4): 213–222. https://doi.org/10.1016/j.jhydrol.2007.04.022.
Yang, W., and S. U. Choi. 2010. “A two-layer approach for depth-limited open-channel flows with submerged vegetation.” J. Hydraul. Res. 48 (4): 466–475. https://doi.org/10.1080/00221686.2010.491649.
Yong, K. C. 1968. Scour resistance of farm dam spillways with grass dormant. Manly Vale, Australia: Univ. of New South Wales Water Research Laboratory.
Zhang, X., and H. Nepf. 2020. “Flow-induced reconfiguration of aquatic plants, including the impact of leaf sheltering.” Limnol. Oceanogr. 65 (11): 2697–2712. https://doi.org/10.1002/lno.11542.
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Received: Sep 27, 2021
Accepted: May 5, 2022
Published online: Jul 28, 2022
Published in print: Oct 1, 2022
Discussion open until: Dec 28, 2022
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