Abstract

The smoothed particle hydrodynamics (SPH) method was used to simulate the flow over smooth and stepped spillways in the nonaerated, skimming flow regime. Two-dimensional numerical simulations were carried out using the DualSPHysics software and compared with experimental data on a 2H:1V sloping spillway for smooth and stepped inverts. Continuous inflow fluid layers with constant height and uniform velocity were used to establish the flow rate on the broad crested weir. The ability of the SPH to reproduce the main flow characteristics was analyzed by comparing the numerical flow depths and velocity profiles with their experimental counterparts. Firstly, a convergence analysis was carried out for various initial particle spacing. The flow characteristics along the stepped spillway were more sensitive to the particle spacing compared to the smooth chute one. In general, the numerical flow depths compared well with the corresponding experimental data and with empirical formulas available in the literature. The velocity profiles, and the free-stream velocity in particular, were also well reproduced by the SPH method; however, larger differences were obtained near the solid boundary.

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Data Availability Statement

Some or all data, models, or code generated or used during the study are available in a repository online in accordance with funder data retention policies (www.dual.sphysics.org).
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request (experimental and numerical flow depths and velocities).

Acknowledgments

The authors acknowledge the support of the Portuguese Foundation for Science and Technology (FCT), through the RECI/ECM-HID/0371/2012 Project, and Prof. Rui Ferreira in particular, for providing the computational server to run the simulations. Thanks also are extended to Luís Palma Mendes for his assistance. The first author acknowledges the scholarships from the Capes, CNPq and Erasmus Mundus-Smart2 Project. The third author acknowledges CNPq Project 307105/2015-6.

References

Amador, A., M. Sánchez-Juny, and J. Dolz. 2006. “Characterization of the nonaerated flow region in a stepped spillway by PIV.” J. Fluids Eng.-Trans. ASME 128 (6): 1266–1273. https://doi.org/10.1115/1.2354529.
Amador, A., M. Sánchez-Juny, and J. Dolz. 2009. “Developing flow region and pressure fluctuations on steeply sloping stepped spillways.” J. Hydraul. Eng. 135 (12): 1092–1100. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000118.
Amador, A. T. 2005. “Comportamiento hidráulico de los aliviaderos escalonados en presas de hormigón compactado.” [In Spanish.] Ph.D. thesis, Dept. de Ingeniería Hidráulica, Marítima y Ambiental, Universitat Politècnica de Catalunya.
André, M., and P. Ramos. 2003. Hidráulica de descarregadores de cheia em degraus: Aplicação a descarregadores com paredes convergentes. [In Portuguese.] Lisbon, Portugal: Instituto Superior Técnico, Universidade de Lisboa.
André, S. 2004. “High velocity aerated flows on stepped chutes with macro-roughness elements.” Ph.D. thesis, École Polytechnique Fédérale de Lausanne.
Boes, R. M., and W. H. Hager. 2003. “Two-phase flow characteristics of stepped spillways.” J. Hydraul. Eng. 129 (9): 661–670. https://doi.org/10.1061/(ASCE)0733-9429(2003)129:9(661).
Bombardelli, F. A., I. Meireles, and J. Matos. 2011. “Laboratory measurements and multi-block numerical simulations of the mean flow and turbulence in the non-aerated skimming flow region of steep stepped spillways.” Environ. Fluid Mech. 11 (3): 263–288. https://doi.org/10.1007/s10652-010-9188-6.
Bung, D. B. 2011. “Developing flow in skimming flow regime on embankment stepped spillways.” J. Hydraul. Res. 49 (5): 639–648. https://doi.org/10.1080/00221686.2011.584372.
Cabrita, J. 2007. “Caracterização do escoamento deslizante sobre turbilhões em descarregadores de cheias em degraus com paredes convergentes.” [In Portuguese.] M.Sc. thesis, Instituto Superior Técnico, Universidade de Lisboa.
Chamani, M. R., and N. Rajaratnam. 1999. “Characteristics of skimming flow over stepped spillways.” J. Hydraul. Eng. 125 (4): 361–368. https://doi.org/10.1061/(ASCE)0733-9429(1999)125:4(361).
Chanson, H. 2002. The hydraulics of stepped chutes and spillways. Lisse, Netherlands: A.A. Balkema.
Chanson, H., D. B. Bung, and J. Matos. 2015. “Stepped spillways and cascades.” In Energy dissipation in hydraulic structures, IAHR Monograph, edited by H. Chanson, 45–64. Leiden, Netherlands: CRC Press, Taylor & Francis Group.
Chanson, H., and L. Toombes. 2002a. “Air-water flows down stepped chutes: Turbulence and flow structure observations.” Int. J. Multiphase Flow 28 (11): 1737–1761. https://doi.org/10.1016/S0301-9322(02)00089-7.
Chanson, H., and L. Toombes. 2002b. “Energy dissipation and air entrainment in stepped storm waterway: Experimental study.” J. Irrig. Drain. Eng. 128 (5): 305–315. https://doi.org/10.1061/(ASCE)0733-9437(2002)128:5(305).
Chen, Q., G. Dai, and H. Liu. 2002. “Volume of fluid model for turbulence numerical simulation of stepped spillway overflow.” J. Hydraul. Eng. 128 (7): 683–688. https://doi.org/10.1061/(ASCE)0733-9429(2002)128:7(683).
Chinnarasri, C., D. Kositgittiwong, and P. Y. Julien. 2014. “Model of flow over spillways by computational fluid dynamics.” Proc. Inst. Civ. Eng.-Water Manage. 167 (3): 164–175. https://doi.org/10.1680/wama.12.00034.
Crespo, A. J. C., J. M. Domínguez, B. D. Rogers, M. Gómez-Gesteira, S. Longshaw, R. Canelas, R. Vacondio, A. Barreiro, and O. García-Feal. 2015. “DualSPHysics: Open-source parallel CFD solver based on Smoothed Particle Hydrodynamics (SPH).” Comput. Phys. Commun. 187 (Feb): 204–216. https://doi.org/10.1016/j.cpc.2014.10.004.
Essery, I. T. S., and M. W. Horner. 1978. The hydraulic design of stepped spillways. London: Construction Industry Research and Information Association.
Felder, S., and H. Chanson. 2008. Turbulence and turbulent length and time scales in skimming flows on a stepped spillway. Dynamics similarity, physical modelling and scale effects: Hydraulic model report CH series. Brisbane, Australia: Div. of Civil Engineering, Univ. of Queensland.
Felder, S., and H. Chanson. 2012. “Free-surface profiles, velocity and pressure distributions on a broad-crested weir: A physical study.” J. Irrig. Drain. Eng. 138 (12): 1068–1074. https://doi.org/10.1061/(ASCE)IR.1943-4774.0000515.
Felder, S., and H. Chanson. 2013. “Aeration, flow instabilities, and residual energy on pooled stepped spillways of embankment dams.” J. Irrig. Drain. Eng. 139 (10): 880–887. https://doi.org/10.1061/(ASCE)IR.1943-4774.0000627.
Frizell, K. H. 1992. “Hydraulics of stepped spillways for RCC dams and dam rehabilitations.” In Proc., 3rd Specialty Conf. on Roller Compacted Concrete, 423–439. New York: ASCE.
Frizell, K. W., and K. H. Frizell. 2015. Guidelines for hydraulic design of stepped spillways.. Denver: Bureau of Reclamation.
Gonzalez, C., and H. Chanson. 2007. “Hydraulic design of stepped spillways and downstream energy dissipators for embankment dams.” Dam Eng. 17 (4): 223–244.
González-Cao, J., O. García-Feal, J. M. Domínguez, A. J. C. Crespo, and M. Gómez-Gesteira. 2018. “Analysis of the hydrological safety of dams combining two numerical tools: Iber and DualSPHysics.” J. Hydrodyn. 30 (1): 87–94. https://doi.org/10.1007/s42241-018-0009-6.
González-Cao, J., O. García-Feal, J. M. Domínguez, A. J. C. Crespo, and M. Gómez-Gesteira. 2019. “Numerical analysis of ski jumps using DualSPHysics.” In Proc., 14th Int. SPHERIC Workshop, 308–312. Exeter, England: Univ. of Exeter.
Gotoh, H., S. Shao, and T. Memita. 2004. “SPH-LES model for numerical investigation of wave interaction with partially immersed breakwater.” Coastal Eng. J. 46 (1): 39–63. https://doi.org/10.1142/S0578563404000872.
Gu, S., L. Ren, X. Wang, H. Xie, Y. Huang, J. Wei, and S. Shao. 2017. “SPHysics simulation of experimental spillway hydraulics.” Water 9 (12): 973. https://doi.org/10.3390/w9120973.
Hunt, S. L., and K. C. Kadavy. 2010. “Energy dissipation on flat-sloped stepped spillways: Part 1. Upstream of the inception point.” Trans. ASABE 53 (1): 103–109. https://doi.org/10.13031/2013.29506.
Hunt, S. L., and K. C. Kadavy. 2011. “Inception point relationship for flat-sloped stepped spillways.” J. Hydraul. Eng. 137 (2): 262–266. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000297.
Hunt, S. L., K. C. Kadavy, and G. J. Hanson. 2014. “Simplistic design methods for moderate-sloped stepped chutes.” J. Hydraul. Eng. 140 (12): 04014062. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000938.
Hunt, S. L., D. Reep, and K. C. Kadavy. 2008. “RCC stepped spillways for Renwick Dam—A partnership in research and design.” Dam Saf. J. 6 (2): 32–40.
Husain, S. M., J. R. Muhammed, H. U. Karunarathna, and D. E. Reeve. 2014. “Investigation of pressure variations over stepped spillways using smooth particle hydrodynamics.” Adv. Water Resour. 66 (Apr): 52–69. https://doi.org/10.1016/j.advwatres.2013.11.013.
Liu, G. R., and M. B. Liu. 2003. Smoothed particle hydrodynamics: A meshfree particle method. Singapore: World Scientific Publishing.
Liu, M. B., and G. R. Liu. 2010. “Smoothed particle hydrodynamics (SPH): An overview and recent developments.” Arch. Comput. Methods Eng. 17 (1): 25–76. https://doi.org/10.1007/s11831-010-9040-7.
Lopes, P., J. Leandro, R. F. Carvalho, and D. B. Bung. 2017. “Alternating skimming flow over a stepped spillway.” Environ. Fluid Mech. 17 (2): 303–322. https://doi.org/10.1007/s10652-016-9484-x.
López, D., M. de Blas, R. Marivela, J. J. Rebollo, R. Díaz, M. Sánchez-Juny, and S. Strella. 2011. “Estudio hidrodinámico de vertederos y rápidas escalonadas con modelo numérico tridimensional SPH: Proyecto ALIVESCA.” [In Spanish.] In Proc., II Jornadas de Ingeniería del Agua: Modelos Numéricos en Dinámica Fluvial, 1–10. Barcelona: FLUMEN.
Lúcio, I. 2015. “Modelação numérica do escoamento deslizante sobre turbilhões em descarregadores de cheias em degraus: Aplicação a pequenas barragens de aterro.” [In Portuguese.] M.Sc. thesis, Instituto Superior Técnico, Universidade de Lisboa.
Matos, J. 1999. “Emulsionamento de ar e dissipação de energia do escoamento em descarregadores em degraus.” [In Portuguese.] Ph.D. thesis, Instituto Superior Técnico, Universidade de Lisboa.
Matos, J. 2000. “Hydraulic design of stepped spillways over RCC dams.” In Proc., 1st Int. Workshop on Hydraulics of Stepped Spillways, edited by H.-E. Minor and W. H. Hager, 187–194. Rotterdam, Netherlands: A.A. Balkema.
Matos, J. 2001. “Discussion of ‘Onset of skimming flow on stepped spillways’ by M. R. Chamani and N. Rajaratnam.” J. Hydraul. Eng. 127 (6): 519–525. https://doi.org/10.1061/(ASCE)0733-9429(2001)127:6(519).
Matos, J., and I. Meireles. 2014. “Hydraulics of stepped weirs and dam spillways: Engineering challenges, labyrinths of research.” In Proc., 5th IAHR Int. Symp. on Hydraulic Structures, edited by H. Chanson and L. Toombes, 1–30. Brisbane: Univ. of Queensland.
McDonald, J. E., and N. F. Curtis. 1997. Applications of roller-compacted concrete in rehabilitation and replacement of hydraulic structures.. Washington, DC: USACE.
McLean, F. G., and K. D. Hansen. 1993. “Roller compacted concrete for embankment overtopping protection.” In Proc., Specialty Conf., Geotechnical Practice in Dam Rehabilitation. New York: ASCE.
Meireles, I., F. A. Bombardelli, and J. Matos. 2014. “Air entrainment onset in skimming flows on steep stepped spillways: An analysis.” J. Hydraul. Res. 52 (3): 375–385. https://doi.org/10.1080/00221686.2013.878401.
Meireles, I., and J. Matos. 2009. “Skimming flow in the nonaerated region of stepped spillways over embankment dams.” J. Hydraul. Eng. 135 (8): 685–689. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000047.
Meireles, I., F. Renna, J. Matos, and F. Bombardelli. 2012. “Skimming, nonaerated flow on stepped spillways over roller compacted concrete dams.” J. Hydraul. Eng. 138 (10): 870–877. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000591.
Molteni, D., and A. Colagrossi. 2009. “A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH.” Comput. Phys. Commun. 180 (6): 861–872. https://doi.org/10.1016/j.cpc.2008.12.004.
Monaghan, J. J. 1994. “Simulating free surface flows with SPH.” J. Comput. Phys. 110 (2): 399–406. https://doi.org/10.1006/jcph.1994.1034.
Moreira, A., A. Leroy, D. Violeau, and F. Taveira-Pinto. 2019. “Dam spillways and the SPH method: Two case studies in Portugal.” J. Appl. Water Eng. Res. 7 (3): 228–245. https://doi.org/10.1080/23249676.2019.1611496.
Moreira, A. B., A. Leroy, D. Violeau, and F. A. Taveira-Pinto. 2020. “Overview of large-scale smoothed particle hydrodynamics modeling of dam hydraulics.” J. Hydraul. Eng. 146 (2): 03119001. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001658.
Ohtsu, I., Y. Yasuda, and M. Takahashi. 2004. “Flow characteristics of skimming flows in stepped channels.” J. Hydraul. Eng. 130 (9): 860–869. https://doi.org/10.1061/(ASCE)0733-9429(2004)130:9(860).
Rebollo, J. J., M. de Blas, D. López, R. Díaz, and R. Marivela. 2010. “Hydrodynamic verification with SPH of under gate flow in the Alarcón spillway (Spain).” In Proc., 1st European IAHR Congress, 1–9. Edinburgh, UK: School of the Built Environment, Heriot-Watt Univ.
Rice, C. E., and K. C. Kadavy. 1996. “Model study of a roller compacted concrete stepped spillway.” J. Hydraul. Eng. 122 (6): 292–297. https://doi.org/10.1061/(ASCE)0733-9429(1996)122:6(292).
Saunders, K., M. Prakash, P. W. Cleary, and M. Cordell. 2014. “Application of smoothed particle hydrodynamics for modelling gated spillway flows.” Appl. Math. Modell. 38 (17-18): 4308–4322. https://doi.org/10.1016/j.apm.2014.05.008.
Sorensen, R. M. 1985. “Stepped spillway hydraulic model investigation.” J. Hydraul. Eng. 111 (12): 1461–1472. https://doi.org/10.1061/(ASCE)0733-9429(1985)111:12(1461).
Tafuni, A., J. M. Domínguez, R. Vacondio, and A. J. C. Crespo. 2018. “A versatile algorithm for the treatment of open boundary conditions in smoothed particle hydrodynamics GPU models.” Comput. Methods Appl. Mech. Eng. 342 (Dec): 604–624. https://doi.org/10.1016/j.cma.2018.08.004.
Takahashi, M., and I. Ohtsu. 2012. “Aerated flow characteristics of skimming flow over stepped chutes.” J. Hydraul. Res. 50 (4): 427–434. https://doi.org/10.1080/00221686.2012.702859.
Toro, J. P., F. A. Bombardelli, and J. Paik. 2017. “Detached eddy simulation of the nonaerated skimming flow over a stepped spillway.” J. Hydraul. Eng. 143 (9): 04017032. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001322.
Toro, J. P., F. A. Bombardelli, J. Paik, I. Meireles, and A. Amador. 2016. “Characterization of turbulence statistics on the non-aerated skimming flow over stepped spillways: A numerical study.” Environ. Fluid Mech. 16 (6): 1195–1221. https://doi.org/10.1007/s10652-016-9472-1.
Violeau, D., and B. D. Rogers. 2016. “Smoothed particle hydrodynamics (SPH) for free-surface flows: Past, present and future.” J. Hydraul. Res. 54 (1): 1–26. https://doi.org/10.1080/00221686.2015.1119209.
Wan, H., R. Li, C. Gualtieri, H. Yang, and J. Feng. 2017a. “Numerical simulation of hydrodynamics and reaeration over a stepped spillway by the SPH method.” Water 9 (8): 565. https://doi.org/10.3390/w9080565.
Wan, H., R. Li, X. Pu, H. Zhang, and J. Feng. 2017b. “Numerical simulation for the air entrainment of aerated flow with an improved multiphase SPH model.” Int. J. Comput. Fluid Dyn. 31 (10): 435–449. https://doi.org/10.1080/10618562.2017.1420175.
Ward, J. 2002. “Hydraulic design of stepped spillways.” Ph.D. thesis, Dept. of Civil Engineering, Colorado State Univ.
Wendland, H. 1995. “Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree.” Adv. Comput. Math. 4 (1): 389–396. https://doi.org/10.1007/BF02123482.
Zhang, G., and H. Chanson. 2016. “Hydraulics of the developing flow region of stepped spillways. II: Pressure and velocity fields.” J. Hydraul. Eng. 142 (7): 04016016. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001136.
Zhang, G., and H. Chanson. 2018. “Application of local optical flow methods to high-velocity free-surface flows: Validation and application to stepped chutes.” Exp. Therm Fluid Sci. 90 (Jan): 186–199. https://doi.org/10.1016/j.expthermflusci.2017.09.010.

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Journal of Hydraulic Engineering
Volume 146Issue 8August 2020

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Received: Mar 7, 2019
Accepted: Feb 5, 2020
Published online: May 26, 2020
Published in print: Aug 1, 2020
Discussion open until: Oct 26, 2020

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Juliana D. Nóbrega [email protected]
Research Fellow, Dept. of Hydraulics and Sanitation, São Carlos School of Engineering, Univ. of São Paulo, São Carlos, SP 13566590, Brazil (corresponding author). Email: [email protected]
Jorge Matos [email protected]
Professor, Civil Engineering Research and Innovation for Sustainability, Instituto Superior Técnico, Universidade de Lisboa, Lisbon 1049-001, Portugal. Email: [email protected]
Harry E. Schulz [email protected]
Professor, Dept. of Hydraulics and Sanitation, São Carlos School of Engineering, Univ. of São Paulo, São Carlos, SP 13566590, Brazil; Visiting Professor, Dept. of Hydraulic and Environmental Engineering, Federal Univ. of Ceará, Fortaleza, CE 60451-970, Brazil. Email: [email protected]
Researcher, Marine, Environment and Technology Center, Instituto Superior Técnico, Universidade de Lisboa, Lisbon 1049-001, Portugal. ORCID: https://orcid.org/0000-0003-1780-6273. Email: [email protected]

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