Abstract
ABSTRACT The traditional approach for the hydrodynamic characterization of the flow down stepped spillways is through physical modeling, which is susceptible to scale effects and has limitations related to experimental apparatus, laboratory space and the spatial discretization of data collection. Computational fluid dynamics (CFD) is an important tool for hydrodynamic analysis because, if used properly, it presents great potential for application in hydraulics. In this work, CFD was used to model the skimming flow down a stepped spillway to investigate the effects of possible pressure measurement errors due to uncertainties in the position of the sensors within the steps. The numerical model was validated through literature velocity profiles and pressure experimental data. The results showed that the best values of water fraction (α) to define free surface are α = 0.30 in the nonaerated region and α = 0.10 in the aerated region. Statistical parameters were calculated using experimental data to estimate extreme pressures. These parameters and the simulation results were used to determine that the extreme maximum and minimum pressures occur, respectively, in the region of 0.81 < x/l < 0.98, in the horizontal faces, and in the region of 0.93 < y/h < 0.98, in the vertical faces.
Highlights
The approach of hydrodynamic characterization of flow down stepped spillways is done through physical modeling (Amador et al, 2009; 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
To answer the two questions, the methodology presented in this paper aims to validate the numerical model, to analyze the behavior of the mean pressures on horizontal and vertical faces of steps and to estimate how far these values distance themselves from the average maximum pressures and minimum that would be measured if, experimentally, the measurement of pressures were continuous along the steps
By analyzing the relative positions of the pressure points of the cited studies, it can be seen that the positions of the points closest to the outer corners of the horizontal faces vary from x/l = 86% (Amador et al, 2009) to x/l = 94% (Sánchez‐Juny et al, 2007)
Summary
When spillways are constructed in steps, part of the energy of the flow dissipates along the spillway itself, allowing to reduce the dimensions of the energy dissipation structures constructed downstream of the dams (Chen et al, 2002; Frizell & Frizell, 2015; Sanagiotto & Marques, 2008; Simões et al, 2010; Tabari & Tavakoli, 2016), generating significant financial savings.There are two approaches to estimate the characteristics of air-water two-phase flows down stepped structures: physical modeling and numerical simulation, and both approaches have uncertainties (Pfister & Hager, 2014). The approach of hydrodynamic characterization of flow down stepped spillways is done through physical modeling (Amador et al, 2009; 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
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