Skip to main content
SpringerLink
Log in

Discharge coefficient and energy dissipation over stepped spillway under skimming flow regime

  • Water Engineering
  • Published:
KSCE Journal of Civil Engineering Aims and scope

Abstract

Stepped spillways have a wide range of applicability as a hydraulic structure in large dams to dissipate energy of high-velocity flows at a downstream area of dams as well as release overflows into the downstream. In this study, the numerical simulation of the flow over the stepped spillway was investigated by using Flow3D software as an analytic flow field. The RNG k-ε model was applied as the turbulence model, and Volume of Fluid (VOF) model was used to determine the free surface flow profiles. At the first stage, the model was verified by reliable experimental data. Then, in order to investigate the various features of skimming flow regime, 112 numerical spillway models was designed, which 96 models were stepped spillway models and 16 models were smooth spillway models (i.e., WES profile). In these numerical experiment, two step sizes, six configuration, four passing discharge and four profile slopes (15, 30, 45 and 60 degrees) with various relative discharges were considered to investigate the energy dissipation and discharge coefficient rates. The results indicated that discharge coefficient rate and energy dissipation rate have inverse relationship. Also it was observed that when relative discharges increased, energy dissipation rate decreased and discharge coefficient rate increased.

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

  • Akbari, G. H. and Barati, R. (2012). “Comprehensive analysis of flooding in unmanaged catchments.” Proceedings of the ICE-Water Management, Vol. 165, No. 4, pp. 229–238, DOI: 10.1680/wama.10.00036.

    Article  Google Scholar 

  • Amador, A., Sánchez-Juny, M., and Dolz, J. (2009). “Developing flow region and pressure fluctuations on steeply sloping stepped spillways.” Journal of Hydraulic Engineering, Vol. 135, No. 12, pp. 1092–1100, DOI: 10.1061/(ASCE)HY.1943-7900.0000118.

    Article  Google Scholar 

  • Arndt, R. E. and Ippen, A. T. (1968). “Rough surface effects on cavitation inception.” Journal of Basic Engineering, Vol. 90, No. 2, pp. 249–261.

    Article  Google Scholar 

  • Azhdary Moghaddam, M. (1997). The hydraulics of ogee-stepped spillway profile, PhD Thesis, Ottawa, Canada.

    Google Scholar 

  • Barati, R. (2011). “Parameter estimation of nonlinear Muskingum models using Nelder-Mead simplex algorithm.” Journal of Hydrologic Engineering, Vol. 16, No. 11, pp. 946–954, DOI: 10.1061/(ASCE)HE.1943-5584.0000379.

    Article  Google Scholar 

  • Barati, R. (2013). “Application of excel solver for parameter estimation of the nonlinear Muskingum models.” KSCE Journal of Civil Engineering, KSCE, Vol. 17, No. 5, pp. 1139–1148, DOI: 10.1007/s12205-013-0037-2.

    Article  Google Scholar 

  • Barati, R., Akbari, G., and Rahimi, S. (2013). “Flood routing of an unmanaged river basin using Muskingum-Cunge model; Field application and numerical experiments.” Caspian Journal of Applied Sciences Research, Vol. 2, No. 6, pp. 08–20.

    Google Scholar 

  • Barati, R., Rahimi, S., and Akbari, G. H. (2012). “Analysis of dynamic wave model for flood routing in natural rivers.” Water Science and Engineering, Vol. 5, No. 3, pp. 243–258.

    Google Scholar 

  • Baylar, A., Bagatur, T., and Emiroglu, M. E. (2007). “Aeration efficiency with nappe flow over stepped cascades.” Proceedings of the ICEWater Management, Vol. 160, No. 1, pp. 43–50, DOI: 10.1680/wama.2007.160.1.43.

    Article  Google Scholar 

  • Baylar, A., Unsal, M., and Ozkan, F. (2010). “Hydraulic structures in water aeration processes.” Water, Air, & Soil Pollution, Vol. 210, No. 1–4, 87–100, DOI: 10.1007/s11270-009-0226-2.

    Article  Google Scholar 

  • Baylar, A., Unsal, M., and Ozkan, F. (2011a). “The effect of flow patterns and energy dissipation over stepped chutes on aeration efficiency.” KSCE Journal of Civil Engineering, KSCE, Vol. 15, No. 8, pp. 1329–1334, DOI: 10.1007/s12205-011-1360-0.

    Article  Google Scholar 

  • Baylar, A., Unsal, M., and Ozkan, F. (2011b). “GEP modeling of oxygen transfer efficiency prediction in aeration cascades.” KSCE Journal of Civil Engineering, KSCE, Vol. 15, No. 5, pp. 799–804, DOI: 10.1007/s12205-011-1282-x.

    Article  Google Scholar 

  • Bindo, M., Gautier, J., and Lacroix, F. (1993). “The stepped spillway of M’Bali Dam.” Int. Water Power & Dam Construction, Vol. 45, No. 1, pp. 35–36.

    Google Scholar 

  • Boes, R. and Hager, W. (2003). “Hydraulic design of stepped spillways.” Journal of Hydraulic Engineering, Vol. 129, No. 9, pp. 671–679, DOI: 10.1061/(ASCE)0733-9429(2003)129:9(661).

    Article  Google Scholar 

  • Chanson, H. (1994). “Hydraulics of skimming flows over stepped channels and spillways.” Journal of Hydraulic Research, Vol. 32, No. 3, pp. 445–460.

    Article  Google Scholar 

  • Chanson, H. (1998). “Review of studies on stepped channel flows.” Workshop on Flow Characteristics Around Hydraulic Structures and River Environment, Nihon University, Tokyo, Japan (November).

    Google Scholar 

  • Chanson, H. (2002). The hydraulics of stepped chutes and spillways, Balkema.

    Google Scholar 

  • Chanson, H. and Toombes, L. (2002). Air-water flows down stepped chutes: Turbulence and flow structure observations, Department of Civil Engineering, University of Queensland, Brisbane, Australia.

    Google Scholar 

  • Chen, J. G., Zhang, J. M., Xu, W. L., and Wang, Y. R. (2010). “Numerical simulation of the energy dissipation characteristics in stilling basin of multi-horizontal submerged jets.” Journal of Hydrodynamics, Ser. B, Vol. 22, No. 5, pp. 732–741, DOI: 10.1016/S1001-6058(09)60110-4.

    Article  Google Scholar 

  • Chen, J. G., Zhang, J. M., Xu, W. L., Li, S., and He, X. L. (2013). “Particle image velocimetry measurements of vortex structures in stilling basin of multi-horizontal submerged jets.” Journal of Hydrodynamics, Ser. B, Vol. 25, No. 4, pp. 556–563, DOI: 10.1016/S1001-6058(11)60396-0.

    Article  Google Scholar 

  • Chen, J., Zhang, J., Xu, W., and Peng, Y. (2014). “Characteristics of the velocity distribution in a hydraulic jump stilling basin with five parallel offset jets in a twin-layer configuration.” Journal of Hydraulic Engineering, Vol. 140, No. 2, pp. 208–217, DOI: 10.1061/(ASCE)HY.1943-7900.0000-17.

    Article  Google Scholar 

  • Christodoulou, G. C. (1993). “Energy dissipation on stepped spillway.” Journal of Hydraulic Engineering, Vol. 119, No. 5, pp. 473–482, DOI: 10.1061/(ASCE)0733-9429(1993)119:5(644).

    Article  MathSciNet  Google Scholar 

  • Dolatshah, A. and Vosoughifar, H. (2012). “Determination of aerated steps number over broad-crest stepped spillways under jet flow regime by using artificial neural network.” Journal of Water Sciences Research, Vol. 4, No. 1, pp. 11–18.

    Google Scholar 

  • Emiroglu, M. E. and Tuna, M.C. (2011). “The effect of tailwater depth on the local scour downstream of stepped-chutes.” KSCE Journal of Civil Engineering, KSCE, Vol. 15, No. 5, pp. 907–915, DOI: 10.1007/s12205-011-0921-6.

    Article  Google Scholar 

  • Essery, I. T. S. and Horner, M. W. (1978). The hydraulic design of stepped spillways, Report 33 Constr. Industry Res. and Information Assoc., London, England.

    Google Scholar 

  • Felder, S. and Chanson, H. (2014a). “Triple decomposition technique in air-water flows: Application to instationary flows on a stepped spillway.” International Journal of Multiphase Flow, Vol. 58, January 2014, pp. 139–153, DOI: 10.1016/j.ijmultiphaseflow.2013.09.006.

    Article  Google Scholar 

  • Felder, S. and Chanson, H. (2014b). “Effects of step pool porosity upon flow aeration and energy dissipation on pooled stepped spillways.” Journal of Hydraulic Engineering, Vol. 140, No. 4, pp. 04014002–1–04014002–11, DOI: 10.1061/(ASCE)HY.1943-7900.0000-58.

    Article  Google Scholar 

  • Flow Science Inc. (2005). FLOW-3D user’s manual (version 9.0), Flow Science Inc., Santa Fe, NM.

    Google Scholar 

  • Frizell, K. and Melford, B. (1991). “Designing spillways to prevent cavitation damage.” Concrete International, Vol. 13, No. 5, pp. 58–64.

    Google Scholar 

  • Frizell, K. H. (1991). “Stepped spillway design for flow over embankment.” Proc. Nat. Conf. Hydraulic Engineering, ASCE, Vol. 2, Nashville, Tennessee, pp. 118–123.

    Google Scholar 

  • Frizell, K. W., Renna, F. M., and Matos, J. (2013). “Cavitation potential of flow on stepped spillways.” Journal of Hydraulic Engineering, Vol. 139, No. 6, pp. 630–636, DOI: 10.1061/(ASCE)HY.1943-7900.0000-15.

    Article  Google Scholar 

  • Gang, L., Jian-min, Z., Jian-Gang, C., Fei, Y., and Lu, L. (2011). “3-D Numerical simulation research of flow in a vortex drop shaft which have two volute chambers with aeration.” Proceedings of the 34th World Congress of the International Association for Hydro-Environment Research and Engineering: 33rd Hydrology and Water Resources Symposium and 10th Conference on Hydraulics in Water Engineering (p. 1779), Engineers Australia.

    Google Scholar 

  • Gomes, J., Marques, M., and Matos, J. (2007). “Predicting cavitation inception on steeply sloping stepped spillways.” Proc., 32nd IAHR Congress, International Assoc. for Hydraulic Research, Venice, Italy.

    Google Scholar 

  • Khatsuria, R. M. (2004). Hydraulics of spillways and energy dissipators, CRC Press.

    Book  Google Scholar 

  • Khdhiri, H., Potier, O., and Leclerc, J. P. (2014). “Aeration efficiency over stepped cascades: Better predictions from flow regimes.” Water Research, pp. 194–202.

    Google Scholar 

  • H. E. Schulz, and A. L. A. Simñes. (2011). “Analysis of two phase flows on stepped spillways.” Hydrodynamics- Optimizing Methods and Tools.

    Chapter  Google Scholar 

  • Meireles, I., Renna, F., Matos, J., and Bombardelli, F. (2012). “Skimming, nonaerated flow on stepped spillways over roller compacted concrete dams.” Journal of Hydraulic Engineering, Vol. 138, No. 10, pp. 870–877, DOI: 10.1061/(ASCE)HY.1943-7900.0000591.

    Article  Google Scholar 

  • Ohtsu, I., Yasuda, Y. (1997). “Characteristics of flow conditions of stepped channels.” Proc. 27th IAHR Congress, San Francisco, USA, 583–588.

    Google Scholar 

  • Peterka, A. J. (1953). “The effect of entrained air on cavitation pitting.” Proceedings Minnesota International Hydraulic Convention, ASCE, 507–518.

    Google Scholar 

  • Peterka, A. J. (1958). Hydraulic design of stilling basins and energy dissipaters. engineering monograph, No. 25, USBR, Denver, CO.

    Google Scholar 

  • Peyras, L., Royet, P., and Degoutte, G. (1991). “Flows and dissipation of energy on gabion weirs.” J. Houille Blanche, No. 1, pp. 37–47.

    Article  Google Scholar 

  • Pfister, M., Hager, W. H., and Minor, H. E. (2006). “Bottom aeration of stepped spillways.” Journal of Hydraulic Engineering, Vol. 132, No. 8, pp. 850–853, DOI: 10.1061/(ASCE)0733-9429(2006)132:8(850).

    Article  Google Scholar 

  • Rajaratnam, N. (1990). “Skimming flow in stepped spillways.” Journal of Hydraulic Engineering, Vol. 116, No. 4, pp. 587–591.

    Article  Google Scholar 

  • Rice, C. E. and Kadavy, K. C. (1996). “Model study of a roller compacted concrete stepped spillway.” Journal of Hydraulic Engineering, Vol. 122, No. 6, pp. 292–297, DOI: 10.1061/(ASCE)0733-9429(1996)122:6(292).

    Article  Google Scholar 

  • Roushangar, K., Akhgar, S., Salmasi, F., and Shiri J. (2014). “Modeling energy dissipation over stepped spillways using machine learning approaches.” Journal of Hydrology, Vol. 508, pp. 254–265, DOI: 10.1016/j.jhydrol.2013.10.053.

    Article  Google Scholar 

  • Rudman, M. (1997). “Volume-tracking methods for interfacial flow calculations.” International journal for numerical methods in fluids, Vol. 24, No. 7, pp. 671–691, DOI: 10.1002/(SICI)1097-0363(19970415)24:7671::AID-FLD5083.0.CO;2-9.

    Article  MATH  MathSciNet  Google Scholar 

  • Savage, B. M. and Johnson, M. C. (2001). “Flow over ogee spillway: Physical and numerical model case study.” Journal of Hydraulic Engineering, Vol. 127, No. 8, pp. 640–649, DOI: 10.1061/(ASCE)0733-9429(2001)127:8(640).

    Article  Google Scholar 

  • Shahheydari, H. (2010). Investigating on stepped spillway geometry to achieve maximum energy dissipation, MSc Thesis, University of Sistan and Baluchestan, Zahedan, Iran.

    Google Scholar 

  • Sorensen, R. M. (1985). “Stepped spillway hydraulic investigation.” Journal of Hydraulic Engineering, Vol. 111, No. 12, pp. 1461–1472, DOI: 10.1061/(ASCE)0733-9429(1985)111:12(1461).

    Article  Google Scholar 

  • USBR (1977). Design of small dams, Bureau of Reclamation, Washington, D.C.

    Google Scholar 

  • Vischer, D. L. and Hager, W. H. (1998). Dam hydraulics, Wiley & Sons, Chichester.

    Google Scholar 

  • Wu, J. H., Zhang, B., and Ma, F. (2013). “Inception point of air entrainment over stepped spillways.” Journal of Hydrodynamics, Ser. B, Vol. 25, No. 1, pp. 91–96, DOI: 10.1016/S1001-6058(13)60342-X.

    Article  Google Scholar 

  • Yakhot, V. and Smith, L. M. (1992). “The renormalization group, the- expansion and derivation of turbulence models.” Journal of Scientific Computing, Vol. 7, No. 1, pp. 35–61.

    Article  MATH  MathSciNet  Google Scholar 

  • Yakhot, V., Orszag, S. A., Thangam, S., Gatski, T. B. and Speziale, C. G. (1992), “Development of turbulence models for shear flows by a double expansion technique.” Physics of Fluids A: Fluid Dynamics (1989–1993), Vol. 4, No. 7, pp. 1510–1520.

    Article  MATH  MathSciNet  Google Scholar 

  • Zhang, J. M., Chen, J. G., Xu, W. L., and Peng, Y. (2013). “Characteristics of vortex structure in multi-horizontal submerged jets stilling basin.” Proceedings of the ICE- Water Management (in press), DOI: 10.1680/wama.12.00071.

    Google Scholar 

  • Zhang, J., Chen, J., and Wang, Y. (2012). “Experimental study on timeaveraged pressures in stepped spillway.” Journal of Hydraulic Research, Vol. 50, No. 2, pp. 236–240, DOI: 10.1080/00221686.2012.666879.

    Article  Google Scholar 

  • Zhao, C. H., Zhu, D. Z., Sun, S. K., and Liu, Z. P. (2006). “Experimental study of flow in a vortex drop shaft.” Journal of Hydraulic Engineering, Vol. 132, No. 1, pp. 61–68, DOI: 10.1061/(ASCE)0733-9429(2006)132:1(61).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Sistan and Baluchestan, Zahedan, 98155-987, Iran

    Hossein Shahheydari

  2. Semnan University, Semnan, 19111-35131, Iran

    Ehsan Jafari Nodoshan

  3. Tarbiat Modares University, Tehran, 14115-143, Iran

    Reza Barati

  4. University of Sistan and Baluchestan, Zahedan, 98155-987, Iran

    Mehdi Azhdary Moghadam

Authors
  1. Hossein Shahheydari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ehsan Jafari Nodoshan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Reza Barati
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mehdi Azhdary Moghadam
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Reza Barati.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shahheydari, H., Nodoshan, E.J., Barati, R. et al. Discharge coefficient and energy dissipation over stepped spillway under skimming flow regime. KSCE J Civ Eng 19, 1174–1182 (2015). https://doi.org/10.1007/s12205-013-0749-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12205-013-0749-3

Keywords

Search

Navigation