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Laboratory measurements and multi-block numerical simulations of the mean flow and turbulence in the non-aerated skimming flow region of steep stepped spillways

Abstract

We present and discuss the results of a comprehensive study addressing the non-aerated region of the skimming flow in steep stepped spillways. Although flows in stepped spillways are usually characterized by high air concentrations concomitant with high rates of energy dissipation, the non-aerated region becomes important in small dams and/or spillways with high specific discharges. A relatively large physical model of such spillway was used to acquire data on flow velocities and water levels and, then, well-resolved numerical simulations were performed with a commercial code to reproduce those experimental conditions. The numerical runs benefited from the ability of using multi-block grids in a Cartesian coordinate system, from capturing the free surface with the TruVOF method embedded in the code, and from the use of two turbulence models: the \({k{-}\varepsilon}\) and the RNG\({k{-}\varepsilon}\) models. Numerical results are in good agreement with the experimental data corresponding to three volumetric flow rates in terms of the time-averaged velocities measured at diverse steps in the spillway, and they are in very satisfactory agreement for water levels along the spillway. In addition, the numerical results provide information on the turbulence statistics of the flow. This work also discusses important aspects of the flow, such as the values of the exponents of the power-law velocity profiles, and the characteristics of the development of the boundary layer in the spillway.

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Acknowledgments

Fabián Bombardelli gratefully acknowledges the support of the California Department of Water Resources (DWR), through Award 4600007984 TO BD01, and the California Water Resources Control Board (CAWRCB), through Award 06-447-300 TO 5. Inês Meireles was a Visiting Scholar at the University of California, Davis, during the months of September 2007–March 2008, and was financially supported by a Fulbright/FLAD Research Grant. This support is gratefully acknowledged. The financial support granted by INAG, Portuguese Water Institution (Project 2003/2029/INAG), and by the Portuguese Foundation for Science and Technology (FCT), through Project PTDC/ECM/108128/2008, is also gratefully acknowledged. Currently, Inês Meireles is supported by FCT, Grant No. SFRH/BD/38003/2007.

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Bombardelli, F.A., Meireles, I. & Matos, J. 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, 263–288 (2011). https://doi.org/10.1007/s10652-010-9188-6

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Keywords

  • Stepped spillway
  • Non-aerated flow
  • Multi-phase flows
  • Two-phase flows
  • Experimental data
  • Back-flushing Pitot tube
  • Conductivity probe
  • Numerical simulations
  • Computational fluid dynamics (CFD)
  • Turbulence modeling
  • \({k{-}\varepsilon}\) model
  • RNG \({k{-}\varepsilon}\) model