Hydraulics of the Developing Flow Region of Stepped Spillways. I: Physical Modeling and Boundary Layer Development

Combination of experimental and numerical approaches to determine the main characteristics of skimming flow in stepped spillways

“…The value found for the exponent, N = 3.9, is closer to the exponent found in other studies performed for the nonaerated region with experimental approaches, where Zhang & Chanson (2016a) obtained the exponent N = 4.5 in a model with slope of 1.0V:1.0H, Meireles et al (2012) obtained N = 3.4 for a stepped spillway with a slope of 1.0V:0.75H and Amador et al (2009) obtained N = 3.0 for a similar structure with a slope of 1.0V:0.8H. From a numerical approach, similar to what is presented in the present work, Bombardelli et al (2011) calculated an exponent N = 5.4 for the nonaerated region of the skimming flow down a stepped spillway with a slope of 1.0V:0.75H.…”

“…The velocities obtained numerically were used to adjust a power-law velocity profile expressed by Equation 9 for the boundary layer development in the nonaerated region. The adjustment coefficient (1/N) serves as a parameter of validation of the numerical model through comparison with values presented in the literature Bombardelli et al, 2011;Meireles et al, 2012;Zhang & Chanson, 2016a). For the aerated region of the flow, the power law to be adjusted is expressed by Equation 10 (Boes & Hager, 2003;Chanson, 1994), where the dimensionless variable of the x-axis is related to the flow depth ( 90 h ), and not to the thickness of the boundary layer (δ ).…”

“…A widely used methodology for the validation of numerical models is the visual comparison between physical and numerical model data of depths (Chen et al, 2002;Tabbara et al, 2005), velocities (Arantes, 2007;Bombardelli et al, 2011;Chen et al, 2002) and pressures (Arantes, 2007;Chen et al, 2002) or even in visual comparison on a prototype scale of these variables (Araújo Filho & Ota, 2016). In the present work, this validation was carried out from data of mean pressure (Conterato et al, 2015) and velocity data found in the literature Boes & Hager, 2003;Meireles et al, 2012;Tozzi, 1992;Zhang & Chanson, 2016a).…”

“…Traditionally, the approach of hydrodynamic characterization of flow down stepped spillways is done through physical modeling Chanson, 1993;Gomes, 2006;Sanagiotto & Marques, 2008;Tozzi, 1992;Zhang & Chanson, 2016a, 2016b), from which it was possible to characterize the flow on different configurations of stepped spillways by analyzing average and instantaneous pressures, energy dissipation and aeration in structures with chutes of different slopes, such as: 1.0V:0.75H (e.g., Meireles et al, 2012;Sanagiotto & Marques, 2008), 1.0V:0.8H (e.g., Amador et al, 2009;Sánchez-Juny et al, 2007), 1.0V:1. 0H (e.g., Dai Prá et al, 2012;Simões et al, 2013;Zhang & Chanson, 2016a), 1.0V:2.0H (e.g., Bung, 2011), among others.…”

Effects of Step and Cavity Shapes on Aeration and Energy Dissipation Performances of Stepped Chutes

“…The discharge was obtained by integrating the velocity profiles measured at the centreline. Further details on the inflow conditions and broad-crested weir calibration can be found in Zhang and Chanson (2016b). Air-entrainment and energy dissipation measurements were performed in a 45° chute downstream of the broad-crested weir.…”