Inception Point for Stepped Chute Designs with Multiple Sections of Different Step Heights
Publication: Journal of Hydraulic Engineering
Volume 147, Issue 4
Abstract
In the literature, a classical free-surface inception point empirical relationship for smooth chutes serves as a basis for the development of a free-surface inception point relationship for stepped chute applications. This study expands research on the free-surface inception point for stepped chutes with multiple sections with different step heights along the chute bottom surface. Data show that existing free-surface inception point relationships for stepped chutes do not always accurately predict where the free-surface inception point will occur when assuming a single step height in stepped chutes designed with multiple sections with different step heights. Accounting for the different step height sections and assuming a constant rate of boundary layer development for each step height allows the error for predicting the free-surface inception point location to be reduced to for stepped chutes with two different step height sections. The research results contribute to improving knowledge on the developing free-surface inception point in stepped chutes, and it provides additional validation data for modeling these flows in computational fluid dynamics models.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
Disclaimer
USDA is an equal opportunity provider and employer.
References
Bauer, W. J. 1954. “Turbulent boundary layer on steep slopes.” Trans. Am. Soc. Civ. Eng. 119 (1): 1212–1233.
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).
Bung, D. B., and A. Schlenkhoff. 2010. “Self-aerated flow on embankment stepped spillways—The effect of additional micro-roughness on energy dissipation and oxygen transfer.” In Proc., 1st IAHR European Congress, 6. Beijing. International Association for Hydro-Environment Engineering and Research.
Cain, P. 1978. Measurements within self-aerated flow on a large spillway. Christchurch, NZ: Univ. of Canterbury.
Chanson, H. 1994. “Hydraulics of skimming flows over stepped channels and spillways.” IAHR, J. Hydraul. Res. 32 (3): 445–460. https://doi.org/10.1080/00221689409498745.
Chanson, H. 2002. The hydraulics of stepped chutes and spillways. Steenwijk, Netherlands: A.A. Balkema.
Cheng, X., J. S. Gulliver, and D. Zhu. 2014. “Application of displacement height and surface roughness length to determination boundary layer development length over stepped spillway.” Water 6 (12): 3888–3912. https://doi.org/10.3390/w6123888.
Chow, V. T. 1959. Open-channel hydraulics. Boston: McGraw-Hill.
Felder, S., and H. Chanson. 2011. “Energy dissipation down a stepped spillway with nonuniform step heights.” J. Hydraul. Eng. 137 (11): 1543–1548. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000455.
Felder, S., and H. Chanson. 2014a. “Air-water flows and free-surface profiles on a non-uniform stepped chute.” J. Hydraul. Res. 52 (2): 253–263. https://doi.org/10.1080/00221686.2013.841780.
Felder, S., and H. Chanson. 2014b. “Effects of step pool porosity upon flow aeration and energy dissipation on pooled stepped spillways.” J. Hydraul. Eng. 140 (4): 04014002. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000858.
Felder, S., and H. Chanson. 2015. “Simple design criterion for residual energy on embankment dam stepped spillways.” J. Hydraul. Eng. 142 (4): 04015062. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001107.
Gonzalez, C. 2005. “An experimental study of free-surface aeration on embankment stepped chutes.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of Queensland.
Gonzalez, C. A., and H. Chanson. 2007. “Hydraulic design of stepped spillways and downstream energy dissipators for embankment dams.” Dam Eng. 17 (4): 223–243.
Gonzalez, C. A., M. Takahashi, and H. Chanson. 2008. “An experimental study of effects of step roughness in skimming flows on stepped chutes.” Supplement, J. Hydraul. Res. 46 (S1): 24–35. https://doi.org/10.1080/00221686.2008.9521937.
Halbronn, G. 1952. “Etude de la mise en régime des écoulements sur les ouvrages à forte pente.” Houille Blanche 3: 347–371. https://doi.org/10.1051/lhb/1952032.
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., and K. C. Kadavy. 2013. “Inception point for embankment dam stepped spillways.” J. Hydraul. Eng. 139 (1): 60–64. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000644.
Hunt, S. L., and K. C. Kadavy. 2017. “Estimated splash and training wall height requirements for stepped chutes applied to embankment dams.” J. Hydraul. Eng. 143 (11): 06017018. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001373.
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.
Lane, E. 1939. “Entrainment of air in swiftly flowing water.” Civ. Eng. 9 (2): 88–91.
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.
Pfister, M., and W. H. Hager. 2011. “Self-entrainment of air on stepped spillways.” Inter. J. Multiphase Flow 37 (2): 99–107. https://doi.org/10.1016/j.ijmultiphaseflow.2010.10.007.
Relvas, A. T., and A. N. Pinheiro. 2008. “Inception point and air concentration in flows on stepped chutes lined with wedge-shaped concrete blocks.” J. Hydraul. Eng. 134 (8): 1042–1051. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:8(1042).
Valero, D., and D. Bung. 2016. “Development of the interfacial air layer in the non-aerated region of high-velocity spillway flows. Instabilities growth, entrapped air, and influence of the self-aeration onset.” Inter. J. Multiphase Flow 84 (2016): 66–74. https://doi.org/10.1016/j.ijmultiphaseflow.2016.04.012.
Valero, D., and D. Bung. 2017. “Reformulating self-aeration in hydraulic structures: Turbulent growth of free surface perturbations leading to air entrainment.” Inter. J. Multiphase Flow 100 (2018): 127–142. https://doi.org/10.1016/j.ijmultiphaseflow.2017.12.011.
Wood, I. R., P. Ackers, and J. Loveless. 1983. “General method for critical point on spillways.” J. Hydraul. Eng. 109 (2): 308–312. https://doi.org/10.1061/(ASCE)0733-9429(1983)109:2(308).
Zare, H. K., and J. C. Doering. 2012. “Inception point of air entrainment and training wall characteristics of baffles and sills on stepped spillways.” J. Hydraul. Eng. 138 (12): 1119–1124. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000630.
Zhang, G., and H. Chanson. 2016. “Hydraulics of the developing flow region of stepped spillways. I: Physical modeling and boundary layer development.” J. Hydraul. Eng. 142 (7): 04016015. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001138.
Zhang, G., and H. Chanson. 2018. “Effects of step and cavity shapes and aeration and energy dissipation performances of stepped chutes.” J. Hydraul. Eng. 144 (9): 04018060. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001505.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 147 • Issue 4 • April 2021
Copyright
© 2021 Published by American Society of Civil Engineers.
History
Received: Sep 25, 2019
Accepted: Sep 10, 2020
Published online: Jan 19, 2021
Published in print: Apr 1, 2021
Discussion open until: Jun 19, 2021
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.