Skip to main content
SpringerLink
Log in

Inception point of air entrainment over stepped spillways

  • Published:
Journal of Hydrodynamics Aims and scope Submit manuscript

Abstract

The location of the inception point of the air entrainment directly affects the energy dissipation ratio, the cavitation damage control, and the training wall height designs for a stepped spillway and a stilling basin. In this paper, the boundary layer theory of plates is used to predict the location of the inception point of the air entrainment over the stepped spillways by assuming the steps on the spillways as a kind of roughness. An empirical formula is presented based on the physical model experiments, with the maximum error less than 1% except at one point where the error is 1.6%, as compared to the experimental data. Meanwhile, it is shown that the location of the inception point of the air entrainment for the stepped spillway is much nearer to the top of the spillway than that for a smooth spillways, which explains why the high ratio of the energy dissipation is provided for the stepped spillway.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. STEPHENSON D. Energy dissipation down stepped spillways[J]. International Water Power and Dam Construction, 1991, 43(9): 27–30.

    Google Scholar 

  2. ZHANG Zhi-chang, ZENG Dong-yang and ZHENG Aman et al. Experimental investigation on the pressure characteristics of skimming flow on stepped spill-ways[J]. Chinese Journal of Hydrodynamics, 2003, 18(5): 652–659(in Chinese).

    Google Scholar 

  3. CHANSON H. Hydraulics of stepped spillways: Current status[J]. Journal of Hydraulic Engineering, Asce, 2000, 126(9): 636–637.

    Article  Google Scholar 

  4. CHENG Xiang-ju, CHEN Yong-cai and LUO Lin. Numerical simulation of air-water two-phase flow over stepped spillways[J]. Science in China, Ser. E: Technological Sciences, 2006, 49(6): 674–684.

    Article  Google Scholar 

  5. CHINNARASRI C., WONGWISES S. Flow patterns and energy dissipation over various stepped chutes[J]. Journal of Irrigation and Drainage Engineering, 2006, 132(1): 70–76.

    Article  Google Scholar 

  6. QIAN Zhong-dong, HU Xiao-qing and HUAI Wen-xin. Numerical simulation and analysis of water flow over stepped spillways[J]. Science in China, Ser. E: Technological Sciences, 2009, 52(7): 1958–1965.

    Article  Google Scholar 

  7. FELDER S., CHANSON H. Energy dissipation down a stepped spillway with nonuniform step heights[J]. Journal of Hydraulic Engineering, Asce, 2011, 137(11): 1543–1548.

    Article  Google Scholar 

  8. PFISTER M., HAGER W. H. Self-entrainment of air on stepped spillways[J]. International Journal of Multiphase Flow, 2011, 37(2): 99–107.

    Article  Google Scholar 

  9. PFISTER M., HAGER W. H. and MINOR H.-E. Stepped chutes: Pre-aeration and spray reduction[J]. Inter-national Journal of Multiphase Flow, 2006, 32(2): 269–284.

    Article  Google Scholar 

  10. CHEN Jian-gang, ZHANG Jian-min and XU Wei-lin. Practical engineering application and hydraulic characteristics of the flow in stepped spillway with pre-aerator slot[J]. Journal of Sichuan University (Enginee-ring Science Edition), 2010, 42(6): 6–11(in Chinese).

    Google Scholar 

  11. MICHAELS V., LOVELY M. Some prototype observa-tions of air entrained flows[C]. Proceedings of Minnesota Conference, IAHR. Minnesota, USA, 1953, 403–414.

    Google Scholar 

  12. WOOD I. R., ACKERS P. and LOVELESS J. General method for critical point on spillways[J]. Journal of Hydraulic Engineering, Asce, 1983, 109(2): 308–312.

    Article  Google Scholar 

  13. CHANSON H. Hydraulics of skimming flows over stepped channels and spillways[J]. Journal of Hydraulic Research, IAHR, 1994, 32(3): 445–460.

    Article  Google Scholar 

  14. HUNT S. L., KADAVY K. C. Inception point relationship for flat-sloped stepped spillways[J]. Journal of Hydraulic Engineering, ASCE, 2011, 137(2): 262–266.

    Article  Google Scholar 

  15. BOES R. M., HAGER W. H. Two-phase flow characteristics of stepped spillways[J]. Journal of Hydraulic Engineering, Asce, 2003, 129(9): 661–670.

    Article  Google Scholar 

  16. RU Shu-xun, TANG Chao-yang and LIANG Chuan. Inception point location of air entrainment on curve-type spillways with steps[J]. Journal of Yangtze River Scientific Research Institute, 1996, 13(2): 7–16(in Chinese).

    Google Scholar 

  17. ZHANG Zhi-chang, ZENG Dong-yang and LIU Ya-fei. Experimental investigations of air entrainment for ste-pped spillway[J]. Chinese Journal of Applied Mechanics, 2003, 20(4): 97–100(in Chinese).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing, 210098, China

    Jian-hua Wu, Bin Zhang & Fei Ma

Authors
  1. Jian-hua Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fei Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jian-hua Wu.

Additional information

Project supported by the National Natural Science Foun- dation of China (Grant No. 51179114).

Biography: WU Jian-hua (1958-), Male, Ph. D., Professor

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, Jh., Zhang, B. & Ma, F. Inception point of air entrainment over stepped spillways. J Hydrodyn 25, 91–96 (2013). https://doi.org/10.1016/S1001-6058(13)60342-X

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1016/S1001-6058(13)60342-X

Key words

Search

Navigation