Numerical investigation of air–water flow properties over steep flat and pooled stepped spillways

ABSTRACT

This study numerically investigated eight configurations of stepped spillways with 45° slopes. The rounded and sharped configurations exhibited the highest and second highest air concentrations, respectively. The baffled-shifted rounded configuration had the lowest air concentration and the highest turbulent dissipation rate and water head dissipation rate. The largest interfacial velocities and the smallest frictional drag were observed for the rounded configuration. The turbulent dissipation rate of the rounded configuration was higher than that of the sharped configuration. The silled-shifted sharped configuration had the lowest turbulent dissipation rate. Intense turbulent dissipation rates occurred in the mixing layer and the interfacial region with air concentrations of 90%. The residual energy of the baffled-shifted rounded configuration was approximately 8% and 13% lower than that of the rounded and sharped configurations, respectively. The highest residual energy under the baffled-shifted sharped configuration appeared to be associated with the lowest turbulent dissipation rate.

Keywords:

• Air concentration
• air–water flows
• flow resistance
• stepped spillway
• turbulent dissipation rate
• velocity distribution
• water head dissipation ratio

Acknowledgements

Thanks to the Editor, Associate Editor and anonymous reviewers for constructive suggestions which improved clarity of the presentation. The authors are also grateful to the associate Professor Jian-gang Chen and Yong Peng for their valuable comments which significantly improved the quality of the manuscript.

Additional information

Funding

This work was partly supported by the CAS “Light of West China” Program [grant no. Y6R2220220], the Young Scientists Research Fund of the Institute of Mountain Hazards and Environment CAS [grant no. Y6K2080080]. The Natural Science Foundations [grant nos. 51579165 and 51279118] were supported by the National Natural Science Foundation of China. The National Key Basic Research Program [grant no. 2013CB035905] was supported by the Ministry of Science and Technology of China.